Identification of Damage Using Lamb Waves: From Fundamentals to Applications

Lecture Notes in Applied and Computational Mechanics Volume 48 Series Editors Prof. Dr.-Ing. Friedrich Pfeiffer Prof. Dr.-Ing. Peter Wriggers

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Identification of Damage Using Lamb Waves From Fundamentals to Applications Zhongqing Su and Lin Ye

123

Dr. Zhongqing Su The Hong Kong Polytechnic University Department of Mechanical Engineering Hung Hom, Kowloon Hong Kong E-mail: [email protected] Prof. Lin Ye The University of Sydney School of Aerospace, Mechanical & Mechatronic Engineering Centre for Advanced Materials Technology NSW 2006 Australia E-mail: [email protected]

ISBN: 978-1-84882-783-7

e-ISBN: 978-1-84882-784-4

DOI 10.1007/ 978-1-84882-784-4 Lecture Notes in Applied and Computational Mechanics

ISSN 1613-7736 e-ISSN 1860-0816

Library of Congress Control Number: Applied for © Springer-Verlag Berlin Heidelberg 2009 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other ways, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

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Preface

Lamb waves are guided waves that propagate in thin plate or shell structures. There has been a clear increase of interest in using Lamb waves for identifying structural damage, entailing intensive research and development in this field over the past two decades. Now on the verge of maturity for diverse engineering applications, this emerging technique serves as an encouraging candidate for facilitating continuous and automated surveillance of the integrity of engineering structures in a cost-effective manner. In comparison with conventional nondestructive evaluation techniques such as ultrasonic scanning and radiography which have been well developed over half a century, damage identification using Lamb waves is in a stage of burgeoning development, presenting a number of technical challenges in application that need to be addressed and circumvented. It is these two aspects that have encouraged us to write this book, with the intention of consolidating the knowledge and know-how in the field of Lamb-wave-based damage identification, and of promoting widespread attention to mature application of this technique in the practical engineering sphere. This book provides a comprehensive description of key facets of damage identification technique using Lamb waves, based on the authors’ knowledge, comprehension and experience, ranging from fundamental theory through case studies to engineering applications. It is noteworthy that although it has a goal of delineating the state of the art of Lamb-wave-based damage identification technique by addressing all key aspects, this book does not attempt to be a complete compendium or all-encompassing review covering all known achievements and results over the full scope of this technique. Given the large amount of excellent literature in the area, it was incumbent on us to focus on topics of most substantial interest to scholars and engineers without overemphasising those that are already widely accessible. Therefore, our apologies go to the researchers and scholars whose contributions to this field were not included in the book. The majority of the research work from which this book arises was accomplished at the Centre for Advanced Materials Technology (CAMT) in the School of Mechanical and Mechatronic Engineering (AMME), the University of Sydney, Australia, from 2001 to 2008.

VI

Preface

No work can be done in isolation, and the writing of such a book is no exception. First and foremost, this book has greatly benefited from discussions with Dr. Ye Lu at AMME, Dr. Xiaoming Wang at the Commonwealth Scientific and Industrial Research Organisation, Australia, Prof. Li Cheng at the Hong Kong Polytechnic University (HKPU) and Prof. Xiongzhu Bu at the Nanjing University of Science and Technology. We sincerely thank all our colleagues and friends who have given us their invaluable support and encouragement, from CAMT in Sydney, HKPU in Hong Kong and other institutions. Special thanks are addressed to Prof. Yiu-Wing Mai, Prof. Limin Zhou, Prof. Guang Meng, Dr. Fucai Li, Dr. Chunhui Yang, Mr. Dong Wang, Mr. Nao Huang and Mr. Nan Pan for their indispensable support. In addition, we wish to thank a number of outstanding individuals whose administrative skills made this book possible. Without the support and encouragement from Mr. Oliver Jackson and Ms. Aislinn Bunning at Springer, this book might never have been finished. We appreciate Ms. Joan Rosenthal for her excellent work in improving the readability of the book. We also appreciate our students and in particular Mr. Jiangang Chen and Mr. Chao Zhou for acquiring copyright permission for us to cite a deal of the work done by many other researchers in the area. Last but not the least, our utmost gratitude is reserved for our individual families. Zhongqing owes his wife Wei a lot for her formidable patience and understanding, while Lin is indebted to his family, especially his wife Pei, for their love and self-giving support over many years. Hong Kong Sydney May 2009

Zhongqing Su Lin Ye

Contents

1 Introduction..................................................................................................... 1 1.1 Background .............................................................................................. 1 1.2 Lamb-wave-based Damage Identification ............................................... 3 1.3 About this Book ..................................................................................... 11 References.............................................................................................. 12 2 Fundamentals and Analysis of Lamb Waves.............................................. 15 2.1 Retrospect .............................................................................................. 15 2.2 Fundamentals and Theory ...................................................................... 15 2.2.1 Theory of Lamb Waves .............................................................. 16 2.2.2 Lamb Waves in Plate of Multiple Layers ................................... 22 2.2.3 Shear Horizontal Waves and Love Waves.................................. 22 2.2.4 Cylindrical Lamb Waves ............................................................ 24 2.2.5 Propagation Velocity – Phase vs. Group Velocities.................... 25 2.2.6 Slowness ..................................................................................... 26 2.2.7 Dispersion ................................................................................... 27 2.3 Numerical and Semi-analytical Study.................................................... 31 2.3.1 Transfer Matrix Method.............................................................. 33 2.3.2 Global Matrix Method ................................................................ 34 2.4 Finite Element Modelling and Simulation ............................................. 35 2.4.1 Modelling Lamb Waves.............................................................. 35 2.4.2 Modelling Structural Damage..................................................... 36 2.5 Attenuation of Lamb Waves .................................................................. 42 2.6 Influence of Temperature....................................................................... 47 2.7 Influence of Damage Orientation and Size ............................................ 48 2.8 Summary ................................................................................................ 51 References.............................................................................................. 53 3 Activating and Receiving Lamb Waves ...................................................... 59 3.1 Introduction............................................................................................ 59 3.2 Transducers of Lamb Waves.................................................................. 59

VIII

3.3

3.4

3.5

3.6

Contents

3.2.1 Ultrasonic Probes........................................................................ 59 3.2.2 Piezoelectric Wafers and Piezocomposite Transducers .............. 61 3.2.3 Laser-based Ultrasonics .............................................................. 62 3.2.4 Interdigital Transducers .............................................................. 62 3.2.5 Fibre-optic Sensors – Reception Only ........................................ 64 Activation of Desired Diagnostic Lamb Waves..................................... 64 3.3.1 Selection of Appropriate Wave Mode ........................................ 64 3.3.2 Optimal Design of Waveform..................................................... 69 Mechanistic Models of Piezoelectric Transducers ................................. 72 3.4.1 Various Models........................................................................... 72 3.4.2 Influence of Transducer Shape ................................................... 73 Case Study: Activating and Receiving Lamb Waves (Both the S0 and A0 Modes) in Delaminated Composite Laminates with Surface-bonded PZT Wafers ............................................................................................ 76 3.5.1 Modelling Coupled PZT Actuator .............................................. 76 3.5.2 Modelling Coupled PZT Sensor ................................................. 84 3.5.3 Validation in FEM Simulation.................................................... 85 Summary ................................................................................................ 88 References.............................................................................................. 88

4 Sensors and Sensor Networks ...................................................................... 99 4.1 Introduction............................................................................................ 99 4.2 Piezoelectric Transducer ...................................................................... 101 4.2.1 Design of Piezoelectric Actuator and Sensor............................ 102 4.2.2 Surface-mounting vs. Embedding ............................................. 106 4.3 Fibre-optic Sensor ................................................................................ 109 4.3.1 Optical Fibre and Fibre-optic Sensor ........................................ 109 4.3.2 Fibre Bragg Grating Sensor ...................................................... 110 4.3.3 FBG Sensor for Lamb Wave Collection ................................... 112 4.3.4 Surface-mounting vs. Embedding ............................................. 116 4.3.5 Directivity ................................................................................. 117 4.4 Hybrid Piezoelectric Actuator-optic Sensor Unit................................. 119 4.5 Sensor Network.................................................................................... 121 4.5.1 Arrangement and Optimisation of Sensor Network.................. 123 4.5.2 Standardised Sensor Network ................................................... 126 4.5.3 Commercial Sensor Network Techniques................................. 128 4.6 Recent Developments .......................................................................... 130 4.6.1 Large-scale Sensor Network ..................................................... 130 4.6.2 Wireless Sensor ........................................................................ 131 4.7 Summary .............................................................................................. 133 References............................................................................................ 134 5 Processing of Lamb Wave Signals ............................................................. 143 5.1 Introduction.......................................................................................... 143 5.2 Digital Signal Processing ..................................................................... 144 5.2.1 Time Domain Analysis ............................................................. 144

Contents

5.3

5.4

5.5 5.6

IX

5.2.2 Frequency Domain Analysis..................................................... 152 5.2.3 Joint Time-frequency Domain Analysis ................................... 155 Wavelet Transform .............................................................................. 158 5.3.1 Continuous Wavelet Transform................................................ 159 5.3.2 Discrete Wavelet Transform ..................................................... 161 5.3.3 Selection of Wavelet Function.................................................. 164 5.3.4 Extracting Signal Features Using Wavelet Transform.............. 164 Processing of Lamb Wave Signals....................................................... 168 5.4.1 Averaging and Normalisation ................................................... 168 5.4.2 De-nosing.................................................................................. 170 5.4.3 Feature Extraction and Damage Index...................................... 171 5.4.4 Compression ............................................................................. 178 A Signal Processing Approach for Lamb Waves: Digital Damage Fingerprints .......................................................................................... 181 Summary .............................................................................................. 184 References............................................................................................ 186

6 Algorithms for Damage Identification – Fusion of Signal Features ....... 195 6.1 Introduction.......................................................................................... 195 6.2 Data Fusion and Damage Identification Algorithms............................ 196 6.2.1 Damage Index ........................................................................... 199 6.2.2 Time-of-flight ........................................................................... 199 6.2.3 Time Reversal – for Identifying Damage ................................. 209 6.2.4 Migration Technique................................................................. 209 6.2.5 Lamb Wave Tomography ......................................................... 213 6.2.6 Probability-based Diagnostic Imaging...................................... 219 6.2.7 Phased-array Beamforming ...................................................... 228 6.2.8 Artificial Intelligence................................................................ 234 6.3 Architecture and Scheme of Data Fusion............................................. 241 6.3.1 Fusion Architecture................................................................... 241 6.3.2 Fusion Scheme.......................................................................... 243 6.4 Summary .............................................................................................. 246 References............................................................................................ 248 7 Application of Algorithms for Identifying Structural Damage – Case Studies .......................................................................................................... 255 7.1 Identifying a Notch in a Structural Alloy Beam Using Damage Index .................................................................................................... 255 7.1.1 Establishment of DI .................................................................. 256 7.1.2 Assessing Changes in Notch Size Using DI ............................. 258 7.2 Locating Delamination in a Composite Panel Using Time-of-flight ... 261 7.3 Hierarchically Locating Multiple Delamination in a Composite Panel Using Time-of-flight ............................................................................ 263 7.3.1 Rationale ................................................................................... 264 7.3.2 Experimental Validation ........................................................... 265

X

Contents

7.4

7.5

7.6

7.7 7.8

Evaluating Multiple Delamination in a Composite Panel Using Probability-based Diagnostic Imaging ................................................. 268 7.4.1 Establishment of Prior Perceptions from a Sensing Path in Terms of ToF ............................................................................ 268 7.4.2 Establishment of Probability of Presence of Damage............... 268 7.4.3 Fusion of Probabilities for Diagnostic Imaging ........................ 271 Quantitatively Predicting Delamination in Composite Beams Using an Artificial Neural Network ............................................................... 273 7.5.1 Training Data Preparation......................................................... 273 7.5.2 ANN Training and Experimental Validation ............................ 276 7.5.3 Discussion................................................................................. 276 Quantitatively Estimating Through-thickness Hole and Delamination in Composite Panels Using an Artificial Neural Network.................... 277 7.6.1 Training Data Preparation......................................................... 277 7.6.2 Parameterised Modelling .......................................................... 280 7.6.3 ANN Training and Experimental Validation ............................ 281 7.6.4 Discussion: Influential Issues ................................................... 283 Identifying Structural Damage in a Composite Laminate Using Bayesian Inference............................................................................... 292 Summary .............................................................................................. 293 References............................................................................................ 293

8 Systems and Engineering Applications ..................................................... 299 8.1 Introduction.......................................................................................... 299 8.2 System for Implementation .................................................................. 299 8.2.1 Signal Generation Subsystem ................................................... 301 8.2.2 Data Acquisition Subsystem ..................................................... 301 8.2.3 Central Control/Analysis Unit .................................................. 302 8.2.4 Calibration of System ............................................................... 302 8.3 Application in Engineering Structures ................................................. 305 8.3.1 Detection of Corrosion in Pipelines .......................................... 305 8.3.2 Identification of Damage in Aerospace Structures ................... 313 8.3.3 Evaluation of Integrity of Civil Infrastructure .......................... 320 8.4 Summary .............................................................................................. 324 References............................................................................................ 325 9 Looking Forward ........................................................................................ 329 9.1 State of the Art ..................................................................................... 329 9.2 Prospects .............................................................................................. 331 References............................................................................................ 339 Index .................................................................................................................. 341

1 Introduction

1.1 Background Engineered assets – land, water, air and space vehicles, infrastructure, heavy equipment and domestic appliances, for example – have become ubiquitous. Yet the presence of damage in these engineered assets, in whatever form it is manifested, can significantly jeopardise their operation and safety without timely awareness. Structural damage has the potential to cause immense monetary loss and even loss of life. This concern is particularly accentuated for transportation vehicles, in which failure often leads to irretrievable and catastrophic consequences. For example, between 1990-2007 there were 1502 commuter aircraft crashes in the U.S. of which 386 (26%) were fatal, resulting in 1104 deaths [1]. Many of these failures were the result of the presence of structural damage or progressive accumulation of material defects upon reaching a critical level. As vehicles age or undergo fatigue loads, the possibility of failure increases. The German Eschede train crash in 1998, the world’s most serious high-speed train disaster, was caused by fatigue cracks in the wheel rims under repetitive load (500,000 cycle per day) [2]. When such engineering assets disintegrate into debris, they claim not only loss of life but sorriness of today’s science and technology capabilities. The recognition of safety, integrity and durability as the principal priorities for engineered structures and assets has entailed intensive research and development of nondestructive evaluation (NDE) techniques. With efficient, continuous and automated NDE techniques it is possible to identify structural damage at a very early stage so as to prevent further failure occurring, producing huge economic and human benefit. This evaluation procedure for structural damage is often referred to as damage identification, damage diagnostics or state awareness. Modern NDE techniques are typified by radioscopy, ultrasonic scanning, shearography, dye penetrant testing, magnetic resonance imagery, laser interferometry, acoustic holography, infrared thermography and eddy-current [3-8], leading to vast achievements in the areas. Over half a century, these NDE techniques have attained maturity in engineering practice, playing a significant role in evaluating the integrity and durability of engineered structures and assets. Z. Su and L. Ye: Identification of Damage Using Lamb Waves, LNACM 48, pp. 1–14. springerlink.com © Springer-Verlag Berlin Heidelberg 2009

2

Identification of Damage Using Lamb Waves

It is well understood that damage can induce changes in the local and global properties of a structure (e.g., local effective stiffness, density, mass, thermal properties, electric/magnetic conductivity, electro-mechanical impedance and strain energy). These changes are included in dynamic response signals captured from the structure. The challenge in this aspect is to figure out, with the assistance of appropriate mechanisms and tools, what these changes in signals mean physically about the structures. Most NDE approaches have been developed by scrutinising the structural dynamic response signals captured by various transducers. Then, by referencing baseline signals (collected from a benchmark structure supposed to be damage-free), the damage can be pinpointed. That is the premise of these approaches [9]. However, today’s NDE, usually conducted at regular scheduled intervals during the lifetime of engineered structures and assets, is clearly too unwieldy to achieve automatic damage identification when the structures and assets are in service. That is because the NDE equipment used cannot provide efficient access to appropriate sections of the structures in a real-time manner. Therefore most current NDE approaches provide limited information about structural integrity. For instance, the fall of the vertical stabiliser off Flight TS961 (Airbus A310®1) in 2005 took place just five days after its A-Check (a routine check) and the next major C-Check inspection was scheduled for 2006 [10]. Driven by recent advances and technical breakthroughs in sensor technology, manufacturing, electronic packaging, signal processing, informatics, diagnostics, applied mechanics and material sciences, conventional NDE techniques are now being retrofitted, with the aim of continuous/real-time and automated surveillance of the overall integrity of structures through consideration of working condition updates and structural ageing. This technology is termed online damage identification or structural health monitoring (SHM). More strictly, SHM is defined as ‘the nondestructive and continuous monitoring characteristics using an array of sensors related to the fitness of an engineered component as it operates, so as to diagnose the onset of anomalous structural behaviour. It involves measuring and evaluating the state properties and relating these to defined performance parameters’ [11]. SHM provides comprehensive information concerning (i) operational and environmental loads, (ii) damage caused by loads, (iii) growth of damage, and (iv) performance of the structure as damage accumulates, in aspects such as residual strength and life. Objectives (i)-(iii) are associated with damage diagnosis (qualitative or quantitative identification and assessment of damage), and (iv) falls into the category of damage prognosis (estimate of a system’s remaining useful life [12]). It has been demonstrated that an effective SHM technique can reduce the total maintenance cost compared to traditional NDE approaches by more than 30% for an aircraft fleet [13], with substantial improvements in fleet reliability. Such tremendous potential for life safety and economic benefits has significantly motivated the intensive research and development of SHM techniques in recent years. Table 1.1 highlights some tools that can be employed for developing SHM techniques. Theoretically, changes in either global or local properties of a structure under inspection can be associated with damage parameters [7, 14-19]. However, approaches capitalising on changes in global dynamic properties including 1

Airbus A310® is a registered trademark of Airbus. http://www.airbus.com

Introduction

3

eigen-frequency, mode shape and curvature, strain energy, and damping properties are less sensitive to damage before it reaches a noticeable extent (e.g., 10% of the characteristic dimension/area of the structure), since damage is a local event which would not significantly change structural global responses. Electro-mechanical impedance and static parameters such as displacement or strain are features that can be used to calibrate local changes in the presence of damage [20], but they are relatively insensitive to damage that is distant from sensors. Acoustic emission (AE) is an effective means to triangulate damage and predict damage growth, but such a passive detection technique is unable to further evaluate damage severity. Last but not least, wave-based approaches canvass damage-induced abnormalities in captured wave signals when propagating across an area containing damage (wave propagation being a localised phenomenon). A wave-based approach can quantitatively evaluate damage that is greater than half the size of its wavelength [21]. The elastic waves can be actively activated, giving the detection high tolerance to environmental noise [22-25].

1.2 Lamb-wave-based Damage Identification With advantages including capability of propagation over a significant distance and high sensitivity to abnormalities and inhomogeneity near the wave propagation path, elastic waves can be energised to disseminate in a structure, and any changes in material properties or structural geometry created by a discontinuity, boundary or structural damage can be identified by examining the scattered wave signals. In general, key questions to be answered by an elastic-wave-based damage identification approach, in terms of difficulty in implementation, are: (i) is there damage? (qualitative awareness of presence of damage); (ii) where is the damage? (quantitative localisation of damage); and (iii) what is its size or severity? (quantitative assessment of damage). Two basic configurations are usually used in elastic-wave-based damage identification, ‘pitch-catch’ and ‘pulse-echo’, in a manner similar to the human procedure of locating an object in terms of acoustic waves, as shown schematically in Figure 1.1. In a pitch-catch configuration, elastic waves activated by a source (e.g., wave actuator) travel across an object and are then captured by a sensor at the other end of the wave path. In a pulse-echo configuration, both source and sensor are located at the same side of the object, and the sensor receives the echoed wave signals from the object. Differences in the position and geometry of the object can modulate the activated wave signals to different extents, causing deferral of wave arrival, reduction of signal magnitude, dispersion of wave signal, dissipation of signal energy, etc. Thus elastic waves can provide ample information accumulated along their propagation paths for depicting the object.

4

Table 1.1. Major approaches for developing SHM techniques technique

Modal-data-based (eigen-frequency, mode shape and curvature, strain energy, flexibility, sensitivity, damping properties, etc.)

Electro-mechanicalimpedance-based

Static-parameter-based (displacement, strain, etc.)

Mechanism

Merits and applications

Demerits and limitations

Based on the fact that presence of structural damage reduces structural stiffness, shifts eigen-frequencies, and changes frequency response function and mode shapes.

Simple and low cost; particularly effective for detecting large damage in large infrastructure or rotating machinery.

Insensitive to small damage or damage growth; difficult to excite high frequencies; need for a large number of measurement points; hypersensitive to boundary and environmental changes.

Based on the fact that the composition of a system contributes a certain amount to its total electricalmechanical impedance of the system, and presence of damage modifies the impedance in a high frequency range, normally higher than 30 kHz.

Low cost and simple for implementation; particularly effective for detecting defects in planar structures.

Unable to detect damage distant from sensors; not highly accurate; accurate for large damage only.

Based on the observation that presence of damage causes changes in displacement and strain distribution in comparison with benchmark.

Locally sensitive to defects; simple and cost-effective.

Relatively insensitive to undersized damage or the evolution of deterioration.

Identification of Damage Using Lamb Waves

Approach

Table 1.1. (continued)

Approach

Acoustic emission

Elastic-wave-based (Lamb wave tomography, etc.)

Merits and applications

Demerits and limitations

Based on the fact that rapid release of strain energy generates transient waves, whereby presence or growth of damage can be evaluated by capturing damage-emitted acoustic waves.

Able to triangulate damage in different modalities including matrix crack, fibre fracture, delamination, microscopic deformation, welding flaw and corrosion; able to predict damage growth; surface mountable and good coverage.

Prone to contamination by environmental noise; complex signal; for locating damage only; passive method; high damping ratio of the wave, and therefore suitable for small structures only.

Based on the fact that structural damage causes unique wave scattering phenomena and mode conversion, whereby quantitative evaluation of damage can be achieved by scrutinising the wave signals scattered by damage.

Cost-effective, fast and repeatable; able to inspect a large structure in a short time; sensitive to small damage; no need for motion of transducers; low energy consumption; able to detect both surface and internal damage.

Need for sophisticated signal processing due to complex appearance of wave signals, multiple wave modes available simultaneously; difficult to simulate wave propagation in complex structures; strong dependence on prior models or benchmark signals.

Introduction

Mechanism

5

6

Identification of Damage Using Lamb Waves

Object

Ear

Sound source

a

Object

Ear

Sound source

b Fig. 1.1. Mechanisms of human procedure of locating an object by hearing the objectscattered sound waves in a. pitch-catch; and b. pulse-echo configurations

The earliest exploration of elastic waves for the purpose of damage identification can be dated back to the distance measurement (a prototype of the sonar technique) and blemish detection used for ships and submarine hulls in the 19th century. The sinking of Titanic in 1912 and the desire to develop navigation techniques for submarines in World War I led to the famous experiment in 1915 by French physicist Paul Langévin, which was probably the inaugural of elasticwave-based damage identification in the ultrasonic range (the wave at a frequency of 150 kHz was used in the experiment). In the experiment, a transducer called a ‘hydrophone’ was invented, comprised of a mosaic of thin quartz crystals glued

Introduction

7

between two steel plates, several of which were placed in conformity to a pulseecho configuration to generate and collect ultrasound signals. Hydrophones formed the basis of naval pulse-echo sonar in the following years. The introduction of quartz transducers and the clinical application of ultrasound in the middle of last century further propelled this technique. In recent years, researchers have increasingly become interested in taking advantage of elastic waves to develop novel damage identification techniques for various engineered structures and assets, based on mature understanding of elastic waves [8, 26, 27] and awareness of the potential of elastic waves for identifying damage in a cost-effective manner. In particular, Lamb waves – elastic waves in thin plate/shell structures – have been at the core of intensive efforts since the late 1980s. Lamb waves can propagate over a relatively long distance, even in materials with high attenuation ratios, such as polymer composites, and thus allow a broad area to be covered with only a few transducers. Lamb waves have offered an intriguing avenue to develop novel damage identification and SHM techniques, in recognition of the observations that (i) interaction of Lamb waves with structural damage can significantly influence their propagation properties, accompanying wave scattering and mode conversion. Rich information about damage is encoded in the Lamb waves scattered by that damage; and (ii) different locations and severity of damage cause unique scattering phenomena. As witnessed over the past two decades, there have been a number of pilot studies for developing damage identification techniques using Lamb waves [28-35], highlighted in some review articles in the literature [22-25, 36]. Through intensive researches in this area, Lamb waves have identified their superb niche for costeffective damage identification and SHM. Actually, Lamb waves are now the most widely used acousto-ultrasonic guided waves for damage identification [37]. At a rudimentary level, successful damage identification using Lamb waves includes some essential steps: (i) activating the desired diagnostic Lamb wave signal using an appropriate transmitter and capturing the damage-scattered wave signals using a sensor or a sensor network in accordance with either the pitch-catch or the pulseecho configuration; (ii) extracting and evaluating the characteristics of the captured wave signals with appropriate signal processing tools; (iii) establishing quantitative or qualitative connections between the extracted signal characteristics and the damage parameters (presence, location, geometric identity, severity, etc.) through some sort of physical or mechanistic model; and (iv) figuring out the damage parameters of interest in terms of captured signals, based on the quantitative connections established in step (iii). Note that in practice different approaches may not be strictly in line with this sequence. Though it appears straightforward, damage identification using Lamb waves is actually an inverse problem, in which the outcome (e.g., a damage-scattered wave signal) is known beforehand but the reason leading to such outcome (e.g., the

8

Identification of Damage Using Lamb Waves

damage) is unknown. An inverse problem is often highly ill-posed and very difficult to solve. In comparison with other NDE approaches, those capitalising on Lamb waves can offer faster and more cost-effective evaluation of various types of damage. For example, rather than using a single ultrasonic probe to inspect a long insulated pipe point by point, one can employ a wave transmitter and receiver pair at one location on the pipe, using the pulse-echo configuration to check the entire pipe instantaneously by examining the reflected wave signals without removing the insulating layer. Types of damage to which ultrasonic Lamb waves are particularly sensitive include voids, porosity, debonding, corrosion, cracking, hole, delamination, resin variation, broken fibre, fibre misalignment, resin crack, cure variation, inclusions and moisture, as summarised in details elsewhere [38]. Smaller instances of damage down to a few millimetres can be accurately detected using Lamb waves in the frequency range from 1 to 10 MHz, as seen in Figure 1.2, than using other well established NDE techniques. Furthermore, less power is required by a Lamb wave transmitter for identifying damage than by other methods, Figure 1.3. However, because it is comprised of multiple wave modes which exist synchronously and overlap each other, a captured Lamb wave signal is often complex in appearance. Propagating at fast velocities (e.g., over 5000 m/s in an aluminium plate for example), wave packets reflected from structural boundaries can easily mask damage-scattered wave packets in the signal. Lamb waves are prone to contamination from a variety of interference sources including high-frequency ambient noise, low-frequency structural vibration, temperature fluctuation, inhomogeneity and anisotropy of materials. All these factors make damage identification using Lamb waves a multidisciplinary challenge for the community of researchers and engineers. In conclusion, damage identification techniques using Lamb waves are envisioned to be a promising method in lieu of traditional NDE approaches because Lamb waves feature: (i) the capacity to inspect a large area using few transducers in a sparse configuration (it has been demonstrated that the ratio of the planar area of the plate that can be inspected to the area of a circular wave transducer can be about 3000:1 [23]); (ii) the ability to examine the entire cross-sectional area of the structure in terms of multiple wave modes, thereby detecting internal damage as well as surface defects; (iii) the capability of classifying various types of damage using different wave modes; (iv) high sensitivity to damage and therefore high identification precision; (v) the possibility of inspecting coated or insulated structures such as pipeline under water/ground; (vi) the potential for integration with engineered structures and assets for developing online automated damage detection and SHM techniques; and (vii) low energy consumption with great cost-effectiveness; but (viii) complexity of signal appearance, requiring well-calibrated signal processing and interpretation techniques.

Introduction

9

Fig. 1.2. Comparison of Lamb-wave-based damage identification with other methods: minimum size of detectable damage vs. size of sensor [39]

10

Identification of Damage Using Lamb Waves

Fig. 1.3. Comparison of Lamb-wave-based damage identification with other methods: minimum size of detectable damage vs. power required by sensor (exclusive of power required for data acquisition) [39]

Introduction

11

1.3 About this Book From the early 1990s onwards there has been a clear increase of interest in using Lamb waves for developing practical and cost-effective damage identification and SHM techniques. Intensive endeavours in this burgeoning research area have led to an impressive number of achievements, with significant advances in knowledge and technology. This book is dedicated to a comprehensive coverage of key aspects of damage identification using Lamb waves based on the authors’ knowledge, comprehension and experience. It aims to provide the essential knowledge and know-how for developing the Lamb-wave-based damage identification techniques. It brings together fundamentals and mechanisms of wave activation, propagation and acquisition, selection of transducers and design of active sensor networks, signal processing for de-noising, compression, and feature extraction in time, frequency, and time-frequency domains. It also provides some detailed description of various algorithms for fusion of signal features for quantitative determination of damage parameters such as location, size, and severity. The book sequentially addresses key knowledge aspects of this technique from the theory to engineering applications. Chapter 2 introduces the fundamentals, theory and propagation characteristics of Lamb waves in various engineering structures (including metallic materials, composite laminates and cylindrical tubes), in terms of analytical derivation, numerical simulation, finite element method (FEM) and experimental characterisation. Some practical concerns, including Lamb wave attenuation, susceptibility to environmental temperature, effect of damage size and orientation, are discussed in this chapter. Chapter 3 serves as a compendium to review a diversity of transducers for activating and receiving Lamb waves. The selection of the appropriate Lamb mode and optimal design of a diagnostic wave signal, particularly explored in this chapter, are two cardinal issues for practical applications. Apart from various models for activating and receiving Lamb waves, a modelling technique is elaborated for evaluating Lamb waves generated by piezoelectric wafers surface-mounted on composite laminates. Piezoelectric transducers and fibre optic sensors, two of the most commonly adopted Lamb waves actuator and sensor types, are introduced in Chapter 4. Sensor network technology (active and standardised sensor network, wireless sensor, optimisation of sensor network, etc.), which has undergone remarkable advances in recent years, is accentuated in this chapter. The last decade has seen ever-accelerating development of digital signal processing and information fusion techniques for all spheres of engineering applications, and Lamb-wave-based damage identification is no exception. Chapters 5 and 6 embrace these two thriving areas: processing of Lamb wave signals and algorithms for damage identification, respectively. Signal processing is introduced in Chapter 5 in terms of the domain where it is conducted, including time, frequency, and joint time-frequency analyses. All these signal processing tools have been specially customised for Lamb wave signals for de-noising, feature extraction, compression and establishment of damage indices. A novel signal processing

12

Identification of Damage Using Lamb Waves

approach, ‘digital damage fingerprints’, developed for Lamb-wave-based damage identification, is in particular presented in Chapter 5. Chapter 6 explores primary fusion algorithms commonly used for Lamb-wavebased identification, exemplified by time-of-flight-based damage triangulation, Lamb wave tomography, probability-based diagnostic imaging, phased-array beamforming, and artificial-intelligence-based pattern recognition. Peripheral issues concerning the development of fusion algorithms, including selection of fusion architecture and fusion scheme, are discussed. Chapter 7 expands on the key issues discussed in the preceding chapters, presenting several representative case studies using Lamb waves. The effectiveness of these schemes is then demonstrated by quantitative identification of a crack in an aluminium beam, through-thickness hole and delamination in fibre-reinforced composite beams or panels, and multiple delamination in composite laminates. As a significant step towards engineering application, the development of systems comprised of software and hardware has been the subject of intense efforts, as particularly emphasised in Chapter 8. Some laudable and representative engineering applications, such as detection of damage in long range pipelines and SHM of aircraft structures, are briefly presented there. Problematic issues behind the success of the approach, suggestions for further development and discussion of prospects of this technique conclude Chapter 9.

References 1. National Institute for Occupational Safety and Health, http://www.cdc.gov/NIOSH/ 2. The National Aeronautics and Space Administration (NASA): Derailed. System Failure Case Studies 1(5), 1-4 (2007) 3. Balageas, D.L.: Structural health monitoring R&D at the European Research Establishments in Aeronautics (EREA). Aerospace Science and Technology 6, 159– 170 (2002) 4. Gray, J., Tillack, G.-R.: X-ray imaging methods over the last 25 years - new advances and capabilities. In: Thompson, D.O., Chimenti, D.E. (eds.) Review of Progress in Quantitative Nondestructive Evaluation, vol. 20, pp. 16–32. American Institute of Physics, New York (2001) 5. Boller, C.: Ways and options for aircraft structural health management. Smart Materials and Structures 10, 432–440 (2001) 6. Sohn, H., Farrar, C.R., Hemez, F.M., Shunk, D.D., Stinemates, D.W., Nadler, B.R.: A Review of Structural Health Monitoring Literature: 1996-2001. Los Alamos National Laboratory Report, LA-13976-MS (2003) 7. Achenbach, J.D.: Quantitative nondestructive evaluation. International Journal of Solids and Structures 37, 13–27 (2000) 8. Cheeke, J.D.N.: Fundamentals and Applications of Ultrasonic Waves. CRC Press, Boca Raton (2002) 9. Montalvão, D., Maia, N.M.M., Ribeiro, A.M.R.: A review of vibration-based structural health monitoring with special emphasis on composite materials. The Shock and Vibration Digest 38(4), 295–324 (2006)

Introduction

13

10. Pascoe, D.: Composite Troubles in Aircraft, http://www.yachtsurvey.com/index.html 11. Moyo, P., Brownjohn, J.M.W.: Detection of anomalous structural behaviour using wavelet analysis. Mechanical Systems and Signal Processing 16, 429–445 (2002) 12. Farrar, C.R., Lieven, N.A.J., Bement, M.T.: An introduction to damage prognosis. In: Inman, D.J., Farrar, C.R., Lopes Jr., V., Steffen Jr., V. (eds.) Damage Prognosis: for Aerospace, Civil and Mechanical Systems, ch. 1, pp. 1–12. John Wiley & Sons, Chichester (2005) 13. Chang, F.-K.: Introduction to health monitoring: context, problems, solutions. Presentation at the 1st European Pre-workshop on Structural Health Monitoring, Paris, France, July 9 (2002) 14. Salawu, O.S.: Detection of structural damage through changes in frequency: a review. Engineering Structures 19(9), 718–723 (1997) 15. Zou, Y., Tong, L., Steven, G.P.: Vibration-based model-dependent damage (delamination) identification and health monitoring for composite structures - a review. Journal of Sound and Vibration 230(2), 357–378 (2000) 16. Farrar, C.R., Doebling, S.W., Nix, D.A.: Vibration-based structural damage identification. Philosophical Transactions of the Royal Society, A: Mathematical, Physical and Engineering Sciences 359(1778), 131–149 (2001) 17. Tandon, N., Choudhury, A.: A review of vibration and acoustic measurement methods for the detection of defects in rolling element bearings. Tribology International 32, 469–480 (1999) 18. Doebling, S.W., Farrar, C.R., Prime, M.B., Shevitz, D.W.: Damage Identification and Health Monitoring of Structural and Mechanical Systems from Changes in Their Vibration Characteristics: A Literature Review. Los Alamos National Laboratory Report, LA-13070-MS (1996) 19. Shen, J.Y., Sharpe Jr., L.: An overview of vibration-based nondestructive evaluation techniques. In: Proceedings of the SPIE, vol. 3397, pp. 117–128 (1998) 20. Giurgiutiu, V., Rogers, C.A.: Recent advancements in the Electro-Mechanical (E/M) impedance method for structural health monitoring and NDE. In: Proceedings of the SPIE, vol. 3329, pp. 536–547 (1998) 21. Lee, B.C., Staszewski, W.J.: Modelling of Lamb waves for damage detection in metallic structures: part II - wave interactions with damage. Smart Materials and Structures 12, 815–824 (2003) 22. Su, Z., Ye, L., Lu, Y.: Guided Lamb waves for identification of damage in composite structures: a review. Journal of Sound and Vibration 295, 753–780 (2006) 23. Raghavan, A., Cesnik, C.E.S.: Review of guided-wave structural health monitoring. The Shock and Vibration Digest 39(2), 91–114 (2007) 24. Rose, J.L.: A baseline and vision of ultrasonic guided wave inspection potential. Journal of Pressure Vessel Technology 124, 273–282 (2002) 25. Chimenti, D.E.: Guided waves in plates and their use in materials characterization. Applied Mechanics Review 50(5), 247–284 (1997) 26. Rose, J.L.: Ultrasonic Waves in Solid Media. Cambridge University Press, New York (1999) 27. Achenbach, J.D.: Wave Propagation in Elastic Solids. North-Holland Pub. Co./American Elsevier Pub. Co, New York (1973)

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Identification of Damage Using Lamb Waves

28. Wang, C.S., Chang, F.-K.: Built-in diagnostics for impact damage identification of composite structures. In: Chang, F.-K. (ed.) Proceedings of the 2nd International Workshop on Structural Health Monitoring, Stanford, CA, USA, September 8-10, 1999, pp. 612–621. Technomic Publishing Co (1999) 29. Tang, B., Henneke, E.G.: Lamb-wave monitoring of axial stiffness reduction of laminated composite plates. Materials Evaluation 47, 928–934 (1991) 30. Tan, K.S., Guo, N., Wong, B.S., Tui, C.G.: Experimental evaluation of delaminations in composite plates by the use of Lamb waves. Composites Science and Technology 53, 77–84 (1995) 31. Alleyne, D.N., Cawley, P.: The interaction of Lamb waves with defects. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 39(3), 381–397 (1992) 32. Guo, N., Cawley, P.: Lamb waves for the NDE of composite laminates. In: Thompson, D.O., Chimenti, D.E. (eds.) Review of Progress in Quantitative Nondestructive Evaluation, vol. 11, pp. 1443–1450. Plenum Press, New York (1992) 33. Cawley, P., Alleyne, D.: The use of Lamb waves for the long range inspection of large structures. Ultrasonics 34, 287–290 (1996) 34. Alleyne, D.N., Cawley, P.: Optimisation of Lamb wave inspection techniques. NDT&E International 25(1), 11–22 (1992) 35. Roh, Y.-S., Chang, F.-K.: Effect of impact damage on Lamb wave propagation in laminated composites. In: Sun, C. (ed.) Proceedings of the ASME International Mechanical Engineering Congress and Exposition (Dynamic Responses and Behavior of Composites), San Francisco, CA, USA, November 12-17, 1995, pp. 127–138 (1995) 36. Rose, J.L.: Guided wave nuances for ultrasonic nondestructive evaluation. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 47(3), 575–583 (2000) 37. Lee, B.C., Staszewski, W.J.: Modelling of Lamb waves for damage detection in metallic structures: part I - wave propagation. Smart Materials and Structures 12, 804– 814 (2003) 38. Wong, B.S., Williams, R.: Non-destructive testing methodologies of advanced composite materials. In: Proceedings of the New Challenges in Aircraft Maintenance and Engineering Conference, Singapore, February 21-22 (2000) 39. Kessler, S.S.: Piezoelectric-Based In-Situ Damage Detection of Composite Materials for Structural Health Monitoring Systems, Ph.D. Dissertation, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA, USA (2002)

2 Fundamentals and Analysis of Lamb Waves

2.1 Retrospect The antecedent work on Lamb waves is not hard to identify. It was Lord Rayleigh in 1889 who first explained wave propagation along a guided surface [1], and the waves are known as Rayleigh waves today. Following Rayleigh's work, Horace Lamb, a British applied mathematician, reported the waves discovered in plates in one of his historic publications, On Waves in an Elastic Plate, in 1917 [2], and the waves were named after him as Lamb waves. Horace Lamb also established the theoretical rudiments of such waves. Lamb waves did not attract great attention because of the extremely complex equations needed to describe them, until Osborne and Hart revisited this topic in 1945 to examine Lamb waves activated in structures in underwater explosions [3]. Their study unveiled much potential for applications of Lamb waves. A comprehensive solution to Lamb waves was completed by Mindlin in 1950, followed by considerable detail provided by Gazis in 1958 [4] and Viktorov in 1967 [5] who also first evaluated the dispersive properties of Lamb waves. Firestone and Ling inaugurated Lamb-wave-based damage detection in the 1940-1950s [6, 7], after which Lamb waves found niche applications in seismology and nondestructive evaluation (NDE). In parallel with theoretical development, intensive experimental investigation, for the purpose of understanding fundamentals of Lamb waves, was contributed by Worlton in 1961 [8] and Frederick and Worlton in 1962 [9]. With advances in computing devices, the period from the 1980s until the present day has witnessed unprecedented prosperity of Lamb-wave-based engineering applications, in particular Lambwave-based damage identification techniques in recent years [10-22].

2.2 Fundamentals and Theory Although considerable literature exists addressing Lamb waves, it is incumbent on us to recapitulate the fundamentals and basic theory of Lamb waves here before we proceed to their applications in damage identification. Z. Su and L. Ye: Identification of Damage Using Lamb Waves, LNACM 48, pp. 15–58. springerlink.com © Springer-Verlag Berlin Heidelberg 2009

16

Identification of Damage Using Lamb Waves

Elastic waves in a solid medium can be one of the modalities described in Table 2.1, distinguished by the motion of particles. Amongst such wave modalities, Lamb waves refer to those in thin plates (with planar dimensions being far greater than that of the thickness and with the wavelength being of the order of the thickness) that provide upper and lower boundaries to guide continuous propagation of the waves [23]. 2.2.1 Theory of Lamb Waves In a thin isotropic and homogeneous plate as shown in Figure 2.1, the waves, regardless of the mode, can generally be described in a form of Cartesian tensor notation as [23]

µ ⋅ ui , jj + (λ + µ ) ⋅ u j , ji + ρ ⋅ f i = ρ ⋅ u$$i

( i, j = 1, 2, 3 ),

(2.1)

where ui and f i are the displacement and body force in the xi direction, respectively, ρ and µ are the density and shear modulus of the plate, respectively, and λ =

2µ ⋅ν ( λ is the Lamé constant; v is the Poisson’s ratio). 1 − 2ν

x3

x1

2h

x2 Fig. 2.1. A thin plate of 2h in thickness

The displacement potentials method based on Helmholtz decomposition [23, 24] is an efficient approach to decompose Equation 2.1 into two uncoupled parts under the plane strain condition

∂ 2φ ∂ 2φ 1 ∂ 2φ + = ∂x12 ∂x32 c L 2 ∂t 2

governing longitudinal wave modes,

(2.2a)

∂ 2ψ ∂ 2ψ 1 ∂ 2ψ + = ∂x12 ∂x32 cT 2 ∂t 2

governing transverse wave modes,

(2.2b)

Table 2.1. Elastic waves in solid media

Wave type

Definition and characteristics

Shear wave

Also termed a transverse wave, a shear wave is generated under vibration of particles perpendicular to the direction of wave propagation.

Rayleigh wave

Also defined as a surface wave, a Rayleigh wave exists along the free surface of a semi-infinite (or very thick) solid, decaying exponentially in displacement magnitude with distance from the surface.

Fundamentals and Analysis of Lamb Waves

Longitudinal wave

Travelling in a medium as a series of alternate compressions and rarefactions, a longitudinal wave vibrates particles back and forth in the direction of wave propagation.

Graphic description

17

18

Table 2.1. (continued)

Definition and characteristics

Lamb wave

Also known as a plate wave, a Lamb wave exists in a thin plate-like medium, guided by the free upper and lower surfaces. Infinite wave modes are available in a finite body, and their propagation characteristics vary with entry angle, frequency and structural geometry.

Stonely wave

A Stonely wave is a kind of wave existing at the interface between two media or in the neighbourhood of a free surface.

Creep wave

Also called a head wave, a creep wave is generated by refraction of a longitudinal wave from a boundary with the same propagation velocity. It has similar behaviour to a longitudinal wave.

Graphic description

Identification of Damage Using Lamb Waves

Wave type

Fundamentals and Analysis of Lamb Waves

19

where

φ = [ A1 sin( px3 ) + A2 cos( px3 )] ⋅ exp[i (kx1 − ωt )] ,

(2.3a)

ψ = [ B1 sin( qx3 ) + B2 cos(qx3 )] ⋅ exp[i (kx1 − ωt )] ,

(2.3b)

p2 =

ω2 cL

− k 2 , q2 =

2

ω2 cT

2

− k2 , k =

2π

λwave

.

(2.3c)

A1 , A2 , B1 and B2 are four constants determined by the boundary conditions. k , ω and λwave are the wavenumber, circular frequency and wavelength of the wave, respectively. cL and cT are the velocities of longitudinal and transverse/shear modes ( L stands for the longitudinal modes and T the transverse/shear modes hereafter), respectively, defined by

cL =

E (1 − ν ) = ρ (1 + ν )(1 − 2ν )

2µ (1 − ν ) , cT = ρ (1 − 2ν )

E = 2 ρ (1 + ν )

µ , ρ

(2.4)

where E denotes the Young’s modulus of the medium ( E = 2µ (1 + ν ) ). It can be seen that Lamb waves are actually the superposition of longitudinal and transverse/shear modes. An infinite number of modes exist simultaneously, superimposing on each other between the upper and lower surfaces of the plate, finally leading to well-behaved guided waves. As a result of plane strain, the displacements in the wave propagation direction ( x1 ) and normal direction ( x3 ) (Figure 2.1) can be described as

u1 =

∂φ ∂ψ ∂φ ∂ψ + − , u 2 = 0 , and u3 = , ∂x3 ∂x1 ∂x1 ∂x3

(2.5a)

∂ 2ψ ∂ 2ψ ∂ 2φ ∂ u 3 ∂ u1 ) = µ( ), + − + ∂x1∂x3 ∂x12 ∂x1 ∂ x3 ∂x32

(2.5b)

and therefore

σ 31 = µ (

σ 33 = λ (

∂u ∂ u1 ∂ u 3 ) + 2µ 3 + ∂x3 ∂x1 ∂x3

= λ(

∂ 2ψ ∂ 2φ ∂ 2φ ∂ 2φ ). + 2 ) + 2µ ( 2 − 2 ∂x3 ∂x1∂ x3 ∂x3 ∂x1

(2.5c)

For a plate with free upper and lower surfaces, by applying boundary conditions at both surfaces as follows

20

Identification of Damage Using Lamb Waves

u ( x, t ) = u 0 ( x, t )

(displacement),

(2.6a)

ti = σ ji n j

(traction),

(2.6b)

σ 31 = σ 33 = 0 at x3 = ± d 2 = ± h ,

(2.6c)

to Equation 2.5, where d is the plate thickness and h is the half thickness, we can obtain the general description of Lamb waves in an isotropic and homogeneous plate: tan(qh) 4k 2 qpµ . = 2 2 tan( ph) (λk + λp + 2µp 2 )(k 2 − q 2 )

(2.7)

Substituting Equations 2.3c and 2.4 into the above equation and considering that the trigonometric function tangent is defined with sine and cosine which have symmetric and anti-symmetric properties, respectively, Equation 2.7 can be split into two parts with solely symmetric and anti-symmetric properties, respectively, implying that Lamb waves in a plate consist of symmetric and anti-symmetric modes [23], tan( qh) 4k 2 qp =− 2 tan( ph) (k − q 2 ) 2 tan( qh) (k 2 − q 2 ) 2 =− tan( ph) 4k 2 qp

for symmetric modes, for anti-symmetric modes.

(2.8a) (2.8b)

For brevity, it is stipulated that the symbols Si and Ai ( i = 0, 1, A ) stand for the symmetric and anti-symmetric Lamb modes throughout this book, respectively, with the subscript being the order and in particular S0 and A0 being the lowest-order symmetric and anti-symmetric Lamb modes, respectively. Equations 2.8a and 2.8b are known as the Rayleigh-Lamb equations. Though simple in appearance, they can be solved analytically only in a few cases. The schematics of particle motion in the symmetric and anti-symmetric Lamb wave modes are plotted in Figure 2.2, indicating the displacement direction of particles and the resulting motion. Si modes predominantly have radial in-plane displacement of particles, Figure 2.2(a), while Ai modes mostly have out-of-plane displacement, Figure 2.2(b). Therefore, a symmetric wave mode is often described as ‘compressional’, showing thickness bulging and contracting; and an antisymmetric mode is known as ‘flexual’, presenting constant-thickness flexing, though higher-order anti-symmetric modes have increasingly complex throughthickness displacements. Under the same excitation condition, the magnitude of Si modes (in-plane motion) is normally smaller than that of Ai modes.

Fundamentals and Analysis of Lamb Waves

21

Radial in-plane motion

a

Out-of-plane motion

b Fig. 2.2. a. Symmetric; and b. anti-symmetric Lamb wave modes

The above discussion which applies to a plate with free surfaces can be extended to the condition of non-free surfaces, such as a plate immersed in a liquid or buried underground, which produces transverse confinements to the plate. For example,

22

Identification of Damage Using Lamb Waves

when a plate is immersed in water, Si modes will mostly be retained in the plate since it is difficult for in-plane particle motion to cross the plate-liquid interface, and as a result there is no pronounced energy leakage from the plate to the surrounding water for Si modes. However, partial energy of the out-of-plane Ai modes will leak into the water. This is known as leaky Lamb waves in a plate with surrounding liquid. Furthermore, replacing the liquid in the above discussion with soil, such as in the case when an oil pipeline is buried underground that supports both the in-plane and out-of-plane particle motion, the leaky Lamb waves include contributions from both Si and Ai modes. By applying corresponding boundary conditions at the interfaces where the plate comes into contact with the liquid or solid, leaky Lamb waves can be described, with more detail provided elsewhere [23]. 2.2.2 Lamb Waves in Plate of Multiple Layers

Elastic waves in multi-layered media such as polymer composite laminates are of a great interest, and this particular subject has been intensively studied in recent years along with the exponentially increased applications of advanced composites in various industrial sectors. The anisotropic nature of multi-layered structures introduces many unique phenomena (to be detailed in subsequent sections) such as directional dependence of wave speed, differences in phase and group velocities, wave skewing and slowness, and many somewhat more subtle features. Considering a plate comprised of macroscopically homogeneous layers, the propagation of Lamb waves inside the plate includes not only scattering on the upper and lower surfaces but reflection and refraction between layers. Expanding Equation 2.1 to an N-layered laminate, the displacement field, u , within each layer must satisfy the Navier’s displacement equations [23], and for the n th layer,

µ n ∇ 2u n + (λn + µ n )∇(∇ ⋅ u n ) = ρ n

∂ 2u n ∂t 2

( n = 1, 2, A , N ),

(2.9)

∂ ∂ ∂ ∂2 ∂2 ∂2 + + . Variables in the above , and ∇ 2 = + + 2 2 2 ∂x1 ∂x2 ∂x3 ∂x3 ∂x2 ∂x1 equation are distinguished by the superscript for each individual layer. Again, the Helmholtz decomposition previously mentioned is the most efficient way to decompose displacement fields, and further to obtain the displacement, strain and stress in each individual layer, as detailed elsewhere [23, 25]. where ∇ =

2.2.3 Shear Horizontal Waves and Love Waves

Alongside the two basic Lamb modes, Si and Ai , which dominate the radial inplane and out-of-plane (vertical) motion of particles in the plate, respectively, there is another kind of possible motion of particles, namely in-plane but in a direction perpendicular to the direction of wave propagation, as shown in Figure 2.3, where

Fundamentals and Analysis of Lamb Waves

23

the wave propagates along the x1 direction, while the particles vibrate in the x2 direction only and are confined in the x1 − x2 plane. This wave is referred to as the shear horizontal (SH) wave mode, contrasting with the out-of-plane (vertical) antisymmetric motion (i.e., Ai mode) which is sometimes termed the shear vertical (SV) mode. SH waves may occur along free surfaces. Like Lamb waves, wave modes in the SH family are either symmetric or anti-symmetric, denoted by SH i ( i = 0, 1, A ) hereafter. This wave form was first captured by Love in 1927 [25], and subsequent seismologic observations affirmed its existence in earthquakes. More recently, three-dimensional finite element method (FEM) simulations [26] demonstrated SH i modes by using models allowing particle motion in all directions, as did experimental studies [27, 28].

x3 Wave propagation

SH

x1

2h

x2 Fig. 2.3. SH wave mode in a thin plate of 2h in thickness

In terms of the definition ( u1 = u3 = 0 ), SH i waves are governed by the following equation [24], referring to Figure 2.3 for the definition of coordinate system, 1 ∂ 2u 2 ∂ 2u 2 ∂ 2u2 = ⋅ + . cT2 ∂t 2 ∂x32 ∂x12

(2.10)

Applying the boundary condition (

∂u2 = 0 at the surface, x3 = 0 ), the solution to ∂x3

Equation 2.10 has the form

u2 ( x1 , x3 , t ) = Ae −bx exp[i (kx1 − ω ⋅ t )] , 3

(2.11)

24

Identification of Damage Using Lamb Waves

where b = k[1 − (

1

ω k ⋅ cT

) 2 ] 2 and A is a constant. The displacement, stress and

strain of SH i waves can be obtained using the aforementioned Helmholtz decomposition [23]. As a typical SH wave mode, Love waves travel in a medium that is covered by a layer of a different material, as in polymer composite laminates. By way of illustration, considering a layer ( ρ1 , µ1 ) coupled on a half-space ( ρ 2 , µ 2 ), the SH wave, i.e., Love wave, in this coupled media consisting of two different materials can be described by expanding Equation 2.11 u2 ( x1 , x3 , t ) = ( Ae −b x + Be −b x ) exp[i (kx1 − ω ⋅ t )] , 1 3

where b1 = k[1 − (

ω k ⋅ cT 1

(2.12)

2 3

1

) 2 ] 2 , b1 = k[1 − (

transverse mode in the layer) and cT 2 =

ω k ⋅ cT 2

1

) 2 ] 2 , cT 1 =

µ1 ρ1

(velocity of

µ2 (velocity of transverse mode in the ρ2

half-space). 2.2.4 Cylindrical Lamb Waves

Lamb waves can also be identified in curved panels or tubular structures such as a pipe, provided the tangential dimensions of the structures are much greater than the thickness. The propagation characteristics of Lamb waves in a cylindrical pipe are similar to those in flat plates, except that some additional complexities arise. Strictly speaking, the waves in a cylindrical pipe of thin wall are called cylindrical Lamb waves [29] or helical waves [30], shown schematically in Figure 2.4, and are different from Lamb waves in flat plates in some aspects. Unlike Lamb waves of the symmetric ( S i ) or anti-symmetric ( Ai ) modes in a flat plate, cylindrical Lamb waves are distinguished and labelled with L , T and F in a tubular structure, corresponding to the longitudinal (similar to Lamb modes in a flat plate), torsional (similar to SH i modes in a flat plate) and flexural modes, respectively. At low frequencies, longitudinal, torsional and flexural modes dominate in wave signals, but at high frequencies the waves in the pipe behave more and more like the normal Lamb modes in a plate or shell. To further distinguish the wave modes in tubular structures of different geometries, all cylindrical Lamb modes are defined as L(n, m) , T (n, m) , and F (n, m) , where n and m ( n, m = 0, 1, A ) are two integers, the former being associated with the geometric properties of tubular structures and the latter denoting the order of the wave modes. In particular, n = 0 indicates that the pipe is axially symmetric, as is the case in most engineering applications. As a result, L(0, m) , T (0, m) and F (0, m) are the wave modes that attract most interest. Three cylindrical Lamb modes exist synchronously in tubular

Fundamentals and Analysis of Lamb Waves

25

structures and are intermingled with each other. In an axisymmetric tubular structure, L(0, m) modes are characterised by axisymmetric longitudinal and radial particle displacement; T (0, m) modes have axisymmetric but circumferential particle displacement only; F (0, m) modes are non-symmetric and have displacement components in all directions. In particular, L(0,1) propagates similarly to the A0 mode in flat plates, and L(0,2) has properties similar to the S0 mode in flat plates, in terms of the vibration of particles [31]. Both L(0,1) and L(0,2) are preferable to other modes for damage identification since their axisymmetric properties facilitate easy inspection of 360° along the circumference of pipes [30].

Fig. 2.4. Cylindrical Lamb waves in a pipe section, activated by an actuator at A and received by a sensor at B, showing six helical propagation paths [32]

Note that, in what follows, we focus on Lamb waves in plate-like structures unless specified. 2.2.5 Propagation Velocity – Phase vs. Group Velocities

The propagation of Lamb waves can be characterised by the phase ( c p ) and group ( c g ) velocities. The former is referred to as the propagation speed of the wave phase of a particular frequency contained in the overall wave signals, which can be linked with the wavelength, λwave , as c p = (ω 2π ) ⋅ λwave .

(2.13)

The group velocity is referred to as the velocity with which the overall shape of the amplitudes of the wave (known as the modulation or envelope of the wave) propagates through space, which is the actual velocity captured in experiments (the velocity of wave energy transportation). The group velocity is dependent on frequency and plate thickness, formulated by [23]

26

Identification of Damage Using Lamb Waves

⎛ω c g ( f ⋅ d ) = dω[d ⎜ ⎜ cp ⎝

⎞ −1 dc ⎟] = dω[ dω − ω p ]−1 2 ⎟ cp cp ⎠ dc p −1 dc p −1 2 2 ] = c p [c p − ( f ⋅ d ) ] , = c p [c p − ω dω d( f ⋅ d)

(2.14)

ω . Note that, when the 2π derivative of c p with respect to f ⋅ d becomes zero, c p = c g .

where f is the central frequency of the wave and f =

For SH i modes, these two types of velocity are respectively defined as c p ( f ⋅ d ) = 2cT (

f ⋅d 4( f ⋅ d ) 2 − n 2 cT2

c g ( f ⋅ d ) = cT 1 −

(n / 2) 2 , ( f ⋅ d / cT ) 2

),

(2.15a)

(2.15b)

where n ∈ [0, 2, 4, A] for symmetric and n ∈ [1, 3, 5, A] for antisymmetric SH modes. 2.2.6 Slowness

Propagating in isotropic plates, Lamb waves travel with the same velocity omnidirectionally and the wavefront forms a circle. However, that is not the case in non-isotropic materials such as fibre-reinforced composites, where the wave velocity is subject to the direction of propagation. As an example, Table 2.2 summarises the theoretically calculated and experimentally measured velocities of the S0 and A0 modes in carbon fibre-reinforced epoxy (CF/EP) composite laminates, where two Lamb wave modes travel at distinct velocities in different directions. To visually highlight the discrepancy in the propagation of Lamb waves in different directions, a slowness profile can be introduced, which is a function of the reciprocal of direction-dependent propagation velocity, 1 c g (θ ) ( θ is the wave propagation direction with regard to the 0°). The slowness profiles for the S0 , A0 and SH 0 modes in CF/EP composite laminates of two typical configurations are shown in Figure 2.5, indicating that these lowest-order modes behave quite distinctly in different propagation directions with regard to the 0° fibre, but all of them become almost independent of the direction in the laminate of a quasi-isotropic configuration (e.g., [±45/0/90]s). Such a mechanism is very important for studying Lamb waves in composite structures.

Fundamentals and Analysis of Lamb Waves

27

Table 2.2. Measured (meas.) and calculated (cal.) velocities of S 0 and A0 modes in CF/EP composite laminates of different configurations [28] Laminate layout

[0]8 (8-ply)

[0/90]2s (8-ply)

[±45/0/90]s (8-ply)

[0/90]4s (16-ply)

[±45/0/90]2s (16-ply)

Phase velocity [km/s] (at 1 MHz)

Group velocity [km/s] (at 0.8 MHz)

Cal. S0

Cal. A0

Cal. S0

Meas. S0

Meas. A0

0

10.3

1.9

10.25

9.9≤0.7

1.7≤0.1

±45

7.4

1.6

90

2.2

1.3

2.9≤0.2

1.4≤0.1

0

7.1

1.6

6.8≤0.3

1.6≤0.1

±45

5.5

1.5

5.3≤0.2

1.6≤0.1

90

7.3

1.5

6.9≤0.3

1.5≤0.1

0

6.5

1.5

6.1≤0.2

1.6≤0.1

±45

6.5

1.5

5.9≤0.2

1.6≤0.1

90

6.3

1.5

6.0≤0.2

1.5≤0.1

0

2.1

1.6

6.8≤0.3 *

1.6≤0.1

±45

1.9

1.6

5.1≤0.2 *

1.7≤0.1

90

1.9

1.6

6.9≤0.3 *

1.6≤0.1

0

1.9

1.6

6.0≤0.2 *

1.6≤0.1

±45

2.0

1.6

6.0≤0.2 *

1.6≤0.1

90

1.9

1.6

6.1≤0.2 *

1.6≤0.1

Prop. Direc.

6.77

6.27

6.67

6.07

* Measured at 0.5 MHz to avoid wave dispersion at high frequency (wave dispersion is defined in Section 2.2.7).

2.2.7 Dispersion

As with most guided waves, Lamb waves are dispersive, and their velocities are dependent on wave frequency and plate thickness. This phenomenon is referred to as dispersion. The spectral features (spectral analysis is detailed in Chapter 5) of Lamb waves after propagating a certain distance, excited at a central frequency of 300 kHz, are displayed in Figure 2.6. The S0 mode peaks at 293 kHz and the A0 mode at 332 kHz in the captured signal, deviating from the original central frequency of 300 kHz. Such a shift in the central frequency from the original excitation frequency is a key manifestation of wave dispersion.

28

Identification of Damage Using Lamb Waves 90°

90°

A0

SH0 S0

180°

0°

A1

180°

270°

270°

a

b

90°

90°

S0

180°

SH0

SH1

0°

A0 0°

0°

180°

270°

270°

c

d

Fig. 2.5. Slowness profiles of a. symmetric; and b. anti-symmetric Lamb modes in a [+456/456]s CF/EP composite laminate; c. symmetric; and d. anti-symmetric Lamb modes in a quasi-isotropic [+45/-45/0/90]s CF/EP laminate (the angle refers to the inclination between the wave propagation direction and 0° carbon fibre) [33]

In terms of Equations 2.3c, 2.13 and 2.14, the phase velocity, c p , and the group velocity, cg , of various Lamb wave modes can be related to frequency, ω , and plate thickness, d (or 2h ); meanwhile c p and cg can be related to wavenumber, k . Thus, for a plate made of isotropic materials, Equation 2.8 can be rearranged as tan( qh) 4k 2 p tan( ph) + =0 q (k 2 − q 2 ) 2 q tan(qh) +

(k 2 − q 2 ) 2 tan( ph) =0 4k 2 p

for symmetric modes,

(2.16a)

for anti-symmetric modes.

(2.16b)

Fundamentals and Analysis of Lamb Waves

29

-80

Power spectral density [dB/Hz]

S0

-100

-120 A0

-140

100

300

500

700

900

Frequency [kHz]

Fig. 2.6. Spectral features of the S 0 and A0 modes after propagating a certain distance (original excitation frequency: 300 kHz) [34]

The equations above are the dispersion equations of Lamb waves [23], and the graphic depiction of solutions of the dispersion equations is called the dispersion curves. Dispersion curves are used to describe and predict the relationship among frequency, phase/group velocity and thickness. The dispersion equations can be satisfied by an infinite number of real roots of wavenumbers at a given frequency. The dispersion curves of Si , Ai and SH i modes in an aluminium plate, as a paradigm, are displayed in Figure 2.7. This figure illustrates that: (i) both the phase and group velocities of any wave mode are a function of the algebraic product of the excitation frequency and plate thickness; (ii) all Si , Ai and SH i ( i = 0, 1, A ) modes are synchronously available in structures at any given frequency, and higher-order modes appear as an increase in frequency, with obvious dispersive behaviour, although the SH 0 mode propagates at a constant speed; and (iii) a less-dispersive region exists in the low frequency range (frequencies being below than the cut-off frequencies of higher-order modes) where the S0 and A0 modes travel at almost constant velocities, frequently referred to as the non-dispersion region, as highlighted with a dotted rectangle in Figure 2.7. For an N-layered laminate with free upper and lower surfaces, the general solution to Equation 2.9 for each layer has four unknown constants, C1n , C2n , C3n and C4n ( n = 1, 2, A, N ). Upon applying boundary and continuity conditions of normal/transverse traction and displacement at individual N − 1 interfaces and two free surfaces, there are in total 4N equations for the entire laminate:

30

Identification of Damage Using Lamb Waves

Dimensionless velocity c/cT

3.0 S2

S1

S4

S3

2.0 S0

1.0

2000

0.0

10000

6000

Thickness × frequency [Hz·m]

a Dimensionless velocity c/cT

3.0 A2

A1

A4

A3

2.0

A0

1.0

2000

0.0

10000

6000

Thickness × frequency [Hz·m]

Dimensionless velocity c/cT

b

1.8 SHA1

SHA3 SHA2

SH1

SH3 SH2

SHA0

1.0 SH0 2

6

4

8

(Thickness × frequency) / cT

c Fig. 2.7. Dispersion curves of a. S i ; b. Ai ; and c. SH i modes ( i = 0, 1, A ) in an aluminium plate ( SH i : symmetric SH mode; SHAi : anti-symmetric SH modes; cT : velocity of shear wave defined by Equation 2.4; cT =3170 m/s in aluminium alloy) [17]

Fundamentals and Analysis of Lamb Waves

⎡ A11 ⎢ A ⎢ 21 ⎢ B ⎢ ⎢⎣ A( 4 N )1

A12 A22

B A( 4 N ) 2

31

A

A1( 4 N ) ⎤ ⎡ C11 ⎤ ⎡0⎤ ⎢ ⎥ A A2( 4 N ) ⎥⎥ ⎢ C21 ⎥ ⎢0⎥ =⎢ ⎥. ⎥⎢ B ⎥ ⎢B ⎥ D B ⎥⎢ ⎥ ⎢ ⎥ A A( 4 N )( 4 N ) ⎥⎦ ⎣⎢C4N ⎦⎥ ⎣0⎦

(2.17)

[A] stands for the coefficient matrix. To make the above equation generally tenable, the determinant [A] must be zero, i.e.,

(

)

A ω , k , λn , µ n , d n = 0 .

(2.18)

Equation 2.18 is an implicit equation relating frequency ω to wavenumber k , depending on the effective material properties ( λn , µ n ) and the thickness ( d n ) of individual layers ( λn is the Lamé constant for the nth layer as defined in Equation 2.1), viz., the dispersion equations of Lamb waves in multi-layered structures. Similarly, at any given frequency, there are an infinite number of real roots of wavenumbers to satisfy the equation. In addition, the dispersion properties of Lamb waves in multi-layered structures are subject to the propagation direction when materials are anisotropic (i.e., slowness as introduced in Section 2.2.6), as seen in Figure 2.8, where the wave modes exhibit distinct dispersion properties in different propagation directions in laminates of different configurations. Incidentally, the SH 0 mode does not propagate at a constant speed any more in composite laminates, unlike its propagation in isotropic materials. Because of their dispersive nature, captured Lamb wave signals often present much complexity. Various efforts have been made to reveal the intrinsic properties of Lamb waves, including theoretical analysis, FEM and experimental studies.

2.3 Numerical and Semi-analytical Study Mathematically, at a given frequency there are infinite wavenumbers either real or purely imaginary satisfying the dispersion equations of Lamb waves, Equation 2.16. However, in the form of a high-order transcendental equation, the dispersion equations of Lamb waves do not generally have analytical solutions, and in most cases can only be solved using graphic or numerical methods. To numerically solve Equation 2.16 so as to obtain the dispersion curves of Lamb waves, one can use following key steps [23]: (i) choose an initial frequency-thickness product (ω ⋅ h) 0 or ( f ⋅ h) 0 ; (ii) make an initial estimate of the velocity (c p )0 or (cg ) 0 ; (iii) evaluate the signs of each of the left-hand sides of Equation 2.16 by assuming they are not equal to zero; (iv) choose another velocity (c p )1 > (c p )0 or (c g )1 > (c g ) 0 and re-evaluate the signs of Equation 2.16;

32

Identification of Damage Using Lamb Waves

(v) repeat steps (iii) and (iv) until the sign changes. Because the functions involved are continuous, a change in sign must be accompanied by a crossing through zero. Therefore, a root exists in the interval where a sign change occurs. Assume that this occurs between velocities (c p ) n and (c p ) n+1 or (cg ) n and (c g ) n+1 ; (vi) use some sort of iterative root-finding algorithm such as Newton-Raphson and bisection, to locate precisely the velocity in the interval (c p ) n < (c p ) < (c p ) n+1 or (c g ) n < (cg ) < (c g ) n+1 ; (vii) after finding the root, continue searching at the current (ω ⋅ h) or ( f ⋅ h) for other roots according to steps (ii) through (vi); and (viii) choose another (ω ⋅ h) or ( f ⋅ h) and repeats steps (ii) through (vii). As an example, the dispersion curves of various Lamb wave modes in a titanium plate in accordance with above steps are shown in Figure 2.9. 8.0

8.0 S0

S2

Cg [km/s]

Cg [km/s]

4.0

SH2

SH0

4.0

2.0

2.0

A0 SH1

S1 0.0

SH3

A1 6.0

6.0

2.0

4.0

6.0

8.0

10.0

0.0

12.0

2.0

4.0

6.0

A2 A3 8.0 10.0

12.0

Dimensionless frequency h/cT

Dimensionless frequency h/cT

a

b 6.0

6.0

S0

A1 A3

4.0

4.0 Cg [km/s]

Cg [km/s]

SH2 SH0 S2

2.0

SH3

A0

2.0

SH1 A2

S1 0.0

2.0

4.0 6.0 8.0 10.0 Dimensionless frequency h/cT

12.0

c

0.0

2.0

4.0

6.0

8.0

10.0

12.0

Dimensionless frequency h/cT

d

Fig. 2.8. Dispersion curves of a. symmetric; and b. anti-symmetric Lamb modes along 30° with regard to the 0° axis in a [+456/-456]s CF/EP composite laminate; c. symmetric; and d. anti-symmetric Lamb modes along 45° with regard to 0° fibre in a quasi-isotropic [+45/45/0/90]s CF/EP composite laminate ( cT = G12 ρ ≈ 2000m / s ; G12 / ρ : effective shear modulus/density of the laminate) [33]

Fundamentals and Analysis of Lamb Waves

33

14

Phase velocity [km/s]

12 Frequency sweep

Roots of

at fixed velocity

10

characteristic function

8

Roots of characteristic function

6 4 2

Velocity sweep at fixed frequency

0 0

2

4

6

Frequency [MHz]

Fig. 2.9. Dispersion curves of Lamb waves in a titanium plate of 1.0 mm in thickness

For multi-layered structures, the anisotropic nature of individual layers further hinders any attempt to seek analytical solutions to the dispersion equations. The matrix technique is one efficient approach to semi-analytically obtain the dispersion curves, typified by the transfer matrix method (also called the Thomson-Haskell method) and the global matrix method. 2.3.1 Transfer Matrix Method

Considering an N-layered laminate, it suffices to assume four waves at each individual layer: longitudinal and shear waves coming from the ‘upper’ interface and leaving the ‘lower’ interface (L+, S+, respectively), and similarly, longitudinal and shear waves coming from the ‘lower’ interface and leaving the ‘upper’ interface (L-, S-, respectively) [35], as illustrated in Figure 2.10. Snell’s law [35] requires that all these waves must share the same frequency and spatial properties along the propagation direction at all interfaces, imposing the restriction that all the displacements and stresses have the same frequency and wavenumber. Based on this, the transfer matrix method works by condensing the dispersion equations of individual layers in the laminate into a set of only four equations relating the boundary conditions at the first interface to those at the last interface. In this process, all the dispersion equations for intermediate interfaces are eliminated, so that the fields in all the layers of the laminate are described solely in terms of the external boundary conditions. A relation linking wave frequency ( ω ) with wavenumber ( k ) is therefore established for the entire laminate, referred to as the characteristic function. The loci of roots of the function are the dispersion curves of Lamb waves in such an N-layered laminate, which can be obtained using the numerical root-finding approaches previously mentioned.

34

Identification of Damage Using Lamb Waves Layer I

L+

S+

Interface I

L-

SLayer II

L+

S+

Interface II

L-

SLayer III

x3

L+

S+

L-

S-

x1 Fig. 2.10. Elastic waves in a multi-layered structure

2.3.2 Global Matrix Method

The transfer matrix method may become ill-conditioned and numerically unstable when the laminate-thickness, d , is large or the frequency, f , is high, presenting the so-called ‘large f ⋅ d problem’ [35], because of the poor capacity of a single matrix formed by eliminating equations at all interfaces to describe various wave modes in multi-layered structures. This problem can be circumvented by using the global matrix method, developed by Knopoff [35]. The principle of such an approach is based on a procedure for obtaining the characteristic functions which is similar to that used in the transfer matrix method, but it directly assembles a single matrix consisting of 4( N − 1) equations to represent the entire laminate, where N is the total number of layers. This approach can deliver numerically robust and stable solutions (dispersion curves) even in the case of large f ⋅ d , albeit with a relatively slow computational convergence. Other representative numerical and analytical techniques for studying Lamb waves in isotropic and multi-layered structures include the effective elastic constant technique based on the homogenisation theory [36] where the composite laminate is deemed to behave as a homogeneous orthotropic plate, the normal mode expansion technique [37] which is specialised for the three-dimensional problem of Lamb wave excitation in an isotropic plate, the stiffness method [38] and some other more specific endeavours [39-46]. Disperse1 is a computing code, initiated and refined by the NDE group at Imperial College, London, over a period of 10 years, based on intensive study of the propagation characteristics of Lamb waves [47, 48]. It has the capacity to calculate the dispersion curves of Lamb waves in various materials (such as Teflon®2, titanium, motor car oil, fibre composites with arbitrary number of layers 1

Disperse is licensed commercially by Imperial College Consultants Ltd and supported technically by Professor Michael J S Lowe and Doctor Brian Pavlakovic of the NDE Group, Imperial College London, South Kensington Campus, London SW7 2AZ, UK. ([email protected]). http://www3.imperial.ac.uk/nde 2 Teflon® is a registered trademark of E.I. du Pont de Nemours and Company. http://www.dupont.com

Fundamentals and Analysis of Lamb Waves

35

and configurations) and structures (flat or cylindrical, in vacuum, liquid or solid, etc.). The software can present the results in diverse ways, including plots of phase/group velocity, wavenumber, mode shapes, displacements and energy density. A robust root-finding algorithm and a mode tracing approach are employed to overcome some technical difficulties that are often confronted, including numerical instability and the ‘large f ⋅ d problem’.

2.4 Finite Element Modelling and Simulation Analytical studies are complex but often have a somewhat limited application capacity, and in particular they may become computationally expensive and unsuitable for studying Lamb waves in actual engineering structures featuring various boundaries or discontinuities such as structural damage. The FEM has therefore been introduced to evaluate the propagation characteristics of Lamb waves in more general cases. 2.4.1 Modelling Lamb Waves

Lee and Staszewski [49] summarised the major achievements of modelling Lamb waves for the purpose of damage identification. The approaches include FEM, finite difference method, boundary element method (BEM), finite strip element method (FSM), spectral element method, mass spring lattice method and local interaction simulation approach. Among the different approaches, FEM-based modelling and simulation is the most cost-effective, with commercial software available such as ABAQUS®3, ANSYS®4 and Patran®5 [11, 26, 28, 50-55]. Basically, the use of FEM to simulate the propagation of Lamb waves in a solid medium has two components: activation of Lamb waves, and acquisition of Lamb waves upon travelling a certain distance. For the activation, in accordance with particle motion, S0 , A0 and SH 0 wave modes can be activated by imposing radial in-plane, out-of-plane and tangential in-plane constraints (e.g., displacement, force or stress), respectively, on the FEM nodes of the actuator, in line with their definitions (Section 2.2.1). The mechanisms of such approaches to activating Lamb and SH waves are elaborated schematically in Figures 2.2 and 2.3, respectively. For the acquisition, S0 , A0 and SH 0 wave modes can be captured by calculating the radial in-plane, out-of-plane and tangential in-plane dynamic responses (e.g., displacement or strain), respectively, at the FEM nodes or in FEM elements of the sensor. By way of illustration, Figure 2.11 shows a three-dimensional wave actuator model, where radial uniform displacements in the x1 − x2 plane are applied on circumferential FEM nodes to activate the S0 mode. 3 4

5

ABAQUS® is a registered trademark of ABAQUS, Inc., in the United States and other countries. http://www.abaqus.com ANSYS® is a registered trademark of SAS IP, Inc., a wholly owned subsidiary of ANSYS, Inc. http://www.ansys.com Patran® is a registered trademark of MSC.Software Corporation in the United States and/or other countries. http://www.mscsoftware.com

36

Identification of Damage Using Lamb Waves Imposed displacement

x3

x2

x1

Fig. 2.11. FEM model for Lamb wave actuator with uniform displacement applied on circumferential FEM nodes

Dispersion curves and interlaminar displacement/stress distributions are of great interest for Lamb-wave-based damage identification, which help the most sensitive Lamb modes be selected. Using the aforementioned methods for activation and acquisition of Lamb waves, dispersion curves of Lamb waves in an aluminium plate and carbon-fibre T800/924 composite laminates of several typical configurations are compared in Figure 2.12. Also shown in these diagrams are the results obtained using the analytical approach (effective elastic constant method mentioned previously). Particle displacement u , v , and w (in the x1 ( x) , x2 ( y ) , and x3 ( z ) directions, respectively, in Figure 2.1), and normal stress σ zz , shear stresses σ zx and σ zy throughout the laminate thickness for different layouts are collated in Figures 2.13 and 2.14 (for the S0 mode as example), respectively. Based on these results, the Lamb wave modes that are most sensitive to changes in displacement or stress fields with regard to interlaminar location in laminate thickness can be selected for identification of damage. Note that damage in composite laminates, such as delamination that is located at interfaces where the shear stress for a particular wave mode falls to zero, may not be detected by this particular wave mode [53], though this concern is not conspicuous in practice since most damage in multi-layered composite structures such as delamination spans a number of layers. 2.4.2 Modelling Structural Damage

Modelling structural damage is crucial for the development of Lamb-wave-based damage identification. This subject has attracted intensive research efforts over a long period, associated with the development of fracture, fatigue and damage mechanics for life prediction and integrity analysis of engineering materials and structures, as reviewed elsewhere [56]. Damage in an engineered structure can manifest itself as a crack, notch, void, corrosion, exfoliation or inclusion in metallic structures; and as fibre breakage, matrix cracking, through-thickness hole, local delamination, and interfacial debonding or a combination of these, in composite structures. Some basic principles adopted over the years for describing the interaction of Lamb waves with damage are briefly reviewed in this section.

Fundamentals and Analysis of Lamb Waves

37

8000

10000

S1

S0

Phase velocity [m/s]

Phase velocity [m/s]

A1 6000

S0

4000

A0

2000

L3

8000

6000

L2 L1

4000 L0 2000

Plate thickness: 1.3mm 0 0.0

500.0k

1.0M

1.5M

2.0M

2.5M

A0 0 0.0

3.0M

500.0k

Frequency [Hz] Frequency [Hz]

1.0M

1.5M

a

2.5M

3.0M

b 8000

8000

S0 6000

L2

L1

4000

L0 2000

6000

4000

500.0k

A1

L0

2000 A0

A0 0 0.0

S1

A1

S1

Phase velocity [m/s]

S0

Phase velocity [m/s]

2.0M

Frequency [Hz] Frequency [Hz]

1.0M

1.5M

2.0M

Frequency [Hz] Frequency [Hz]

c

2.5M

3.0M

0 0.0

500.0k

1.0M

1.5M

2.0M

2.5M

3.0M

Frequency [Hz] Frequency [Hz]

d

Fig. 2.12. Dispersion curves of Lamb waves in a. an aluminium plate; b. 8-ply unidirectional; c. 8-ply [0/90]2s cross-ply; and d. 8-ply quasi-isotropic [45/-45/0/90]s laminates ( S i : symmetric mode; Ai : anti-symmetric mode; Li : Love mode;

i = 0, 1, A ; solid lines: from effective elastic constant model; dotted lines: from FEM model) [28]

Cracks and notches in metallic structures typically run perpendicular to the surface. A fully developed crack or notch can extend through the whole thickness. In line with this, a crack or notch can be modelled either by removing some fine FEM elements at the place of damage while keeping both created surfaces apart (an opening scenario), or by duplicating FEM nodes along the damage while keeping both created surfaces in contact (a closing scenario), though prevailing approaches use the former method.

38

Identification of Damage Using Lamb Waves

0.4

1.0

p Normalised amplitude

p Normalised amplitude

0

-0.4 u v w

-0.8

0

0

0

0

0

0

0

0

0 -1.2 0

0

0

0

0

0

0

0

-0.5mm

0

0

0

+45 0.5mm

0.5

u v w

-0.5mm

0

0

-45

a

p Normalised amplitude

p Normalised amplitude

u v w

0

-0.5mm

0

0

0

0

90

-0.5

0

90

0

0

0

90

Laminate thickness [mm] Through Thickness Position [mm]

c

0

+45

0.5mm

1.0

0.5

90

0

-45

b

1.0

0

0

90

Laminate thickness [mm] Through Thickness Position [mm]

Laminate thickness Through Thickness Position[mm] [mm]

0

0

0

90

0

0

0.5mm

u v w

0.5

-0.5

0

0

0

0

0

0 900 00 90 0 90 0

0

0

0

0

0

0

0 -1.0 0 90 0 90 0 90 0

-1.0mm

1.0mm

Laminate thickness Through Thickness Position[mm] [mm]

d

Fig. 2.13. Nodal displacement (at 1.0 MHz) for the S 0 mode throughout thickness of a. 8ply unidirectional; b. 8-ply quasi-isotropic [45/-45/0/90]s; c. 8-ply [0/90]2s cross-ply; and d. 16-ply [0/90]4s cross-ply laminates (at 0.75 MHz to avoid wave dispersion at high frequencies) [28]

Delamination, appearing as debonding between adjoining plies in composite laminates, is the most common but hazardous damage in fibre-reinforced composite structures under out-of-plane stresses or subjected to transverse impact. Through-width delamination in a one-dimensional structural beam, parallel to the beam surfaces along the span, can be modelled as shown in Figure 2.15 [53, 57]. In this FEM model, nodes at the interface between layers where the delamination is located are moved apart by a small distance to form the delamination. This ‘zero volume’ does not remove any mass of the composites. This FEM modelling technique can be extended to three-dimensional delamination in composite

Fundamentals and Analysis of Lamb Waves

39

laminates, as an example shown in Figure 2.16. Reflecting the fact that actual delamination is often elliptical in shape, a volume-split is enveloped by two isolated surfaces sharing the same boundary in this three-dimensional model, in which FEM nodes are symmetrically allocated in accordance with an elliptic spherical function. A surface contact algorithm provided by ABAQUS®/EXPLICIT can be applied to handle the contact issue of two delamination surfaces. This contact algorithm permits a small relative sliding displacement and arbitrary rotation between nodes but no mutual penetration of the two surfaces. 1.0 1.0

p Normalised amplitude

p Normalised amplitude

ZX Shear Stress ZY Shear Stress ZZ Normal Stress

0.8 0.6 0.4 0.2

0

0

-0.5mm

0

0

0

0

0 0 0 -0.2 0

0

0

0

0

0.5mm

Laminate thickness [mm] Through Thickness Position

-0.5

ZX Shear Stress ZY Shear Stress ZZ Normal Stress

+45

0

0

0

0.5

0

0

0

-45

0

90 -1.0 900

1.0

p Normalised amplitude

p Normalised amplitude -0.5mm

0

90

0

0

-0.5

0

0

90 -1.0 90

0

0

0

90

0

0

0.5mm

Laminate thickness [mm] Through Thickness Position

c

0.5mm

b

0.5

0

0

+45

Laminate thickness Through Thickness Position[mm] [mm]

1.0

0

0

-45

-0.5mm

a

ZX Shear Stress ZY Shear Stress ZZ Normal Stress

0

0

0.5 ZX Shear Stress ZY Shear Stress ZZ Normal Stress

-0.4

0

0

0

0

0

0

0

0 0 0 0 0 0 0 0 90 0 90 0 90 0 -0.5 0 90 0 90 0 90 0

-1.0mm

Laminate thickness Through Thickness Position[mm] [mm]

1.0mm

d

Fig. 2.14. Stress distribution (at 1.0 MHz) for the S 0 mode throughout thickness of a. 8-ply unidirectional; b. 8-ply quasi-isotropic [45/-45/0/90]s; c. 8-ply [0/90]2s cross-ply; and d. 16-ply [0/90]4s cross-ply laminates (at 0.75 MHz to avoid wave dispersion at high frequencies) [28]

40

Identification of Damage Using Lamb Waves

FEM nodes

Delamination

Fig. 2.15. FEM model for delamination in a one-dimensional laminate beam

To correctly characterise the scattering phenomena of Lamb waves upon encountering structural damage, some key points should be taken into account when developing an FEM model: (i) a fine FEM mesh, featuring at least 8-12 [28, 58-60] or even 50 nodes [61] per Lamb wavelength, is a prerequisite to deliver good spatial precision; (ii) a laminate may have to be divided into sub-laminates in thickness, to characterise individual laminae; and (iii) the time step for dynamic calculation must be less than the ratio of the minimum distance of any two adjoining nodes to the maximum wave velocity (often the velocity of the S0 mode). The above three basic requirements can sometimes become highly demanding in terms of computational cost, particularly for large structures. To balance the need for precision and computational capacity, transition elements can be used to connect parts of different types of elements and different degrees of freedom (DoF) [62, 63], whereby the areas of interest can be especially fine-meshed while the other parts of less interest can be coarsely meshed, making it possible to simulate Lamb waves in large-scale structures without sacrificing precision.

Fundamentals and Analysis of Lamb Waves

41

α (ξ ,

ζ)

θ β

Volume split

h Delamination surfaces

Single lamina

Fig. 2.16. FEM model for delamination in a three-dimensional composite laminate (five damage parameters: position ( ξ , ζ ), semi-major/minor axis ( α , β ), and orientation θ (the angle between the major axis of delamination and 0º axis)) [64]

Hybrid modelling techniques which combine analytical tools with FEM simulation have been developed, so as to avoid the problems encountered in the sole use of FEM. For example, Liu [65] examined the Lamb wave scattered by a crack and an inclusion in composite laminates using a combined FEM-FSM approach. Moulin et al. [66] established a hybrid approach based on FEM coupled with a normal mode expansion technique, to determine the magnitude of Lamb wave modes in a composite plate activated by surface-bonded or embedded piezoelectric actuators. Cortes et al. [67] combined a semi-analytical approach with FEM to compute the dispersion curves of Lamb waves in multi-layered composite laminates. Cho and Rose [68] integrated a BEM method coupled with the normal mode expansion to study the edge reflection of Lamb waves and mode conversion with variation of plate thickness. Galan and Abascal [43] evaluated the Lamb wave propagation characteristics in sandwich plates in terms of an absorbing boundary condition derived from a truncated normal mode expansion technique. Also using the normal mode expansion technique, Grondel et al. [69] created an hybrid FEM model for surface-bonded piezoelectric elements, to optimally generate anti-symmetric Lamb modes.

42

Identification of Damage Using Lamb Waves

2.5 Attenuation of Lamb Waves It is common knowledge that the energy of Lamb waves dissipates with distance, a phenomenon known as attenuation, manifesting as the gradual reduction in magnitude of wave signals. With the existence of damage or inhomogeneity such as stiffeners or fasteners, the dissipation increases. For example, it has been observed that 52% of the total energy dissipates when Lamb waves pass through a damage area of 7 mm in diameter in a composite laminate (100 mm × 100 mm) [70]. Note that ‘attenuation’ is different from ‘dispersion’ addressed in Section 2.2.7; the latter refers to changes in propagation velocity and signal bandwidth subject to wave frequency. Table 2.3 enumerates the experimentally measured attenuation coefficients of Lamb waves (defined as loss of power per unit distance) in some typical composite materials, including carbon fibre-reinforced polymer (CFRP) and glass fibre-reinforced polymer (GFRP). Also tabulated is the distance that the waves can propagate before decaying to 10% of their original magnitude. It can be seen that: Lamb waves propagate relatively farther in carbon fibre composites than in (i) glass fibre counterparts; and the S0 mode tends to travel farther than the A0 mode. (ii) The relatively high attenuation of the A0 mode can be attributed to the dominant out-of-plane displacements of particles, which leak partial energy to the surrounding environment, compared with symmetric modes which mostly have inplane displacements and whose energy is therefore confined within the plate [71, 72]. The relatively high attenuation property of the A0 mode becomes more pronounced when this mode is used to detect damage in structures immersed in water or buried in soil, due to the leakage phenomenon highlighted in Section 2.2.1 [73]. The presence of liquid loading on one or both surfaces of the plate may cause slight attenuation in the S0 mode but significant attenuation in the A0 mode. For example, at 150 kHz in a 5 mm thick steel plate with water on one surface, attenuation of the S0 mode is approximately 1 dB/m, whereas it is approximately 57 dB/m for the A0 mode. As observed, the magnitude of Lamb waves in a plate decays at a rate that is proportional to the inverse square root of the propagation distance. Thus, when measuring the wave magnitude at two points along the propagation path, we have

A(d1 ) = A(d 2 )

d2 d1

,

(2.19)

where A(d1 ) and A(d 2 ) are the magnitudes of Lamb waves at distances of d1 and

d 2 away from the actuator, respectively.

Fundamentals and Analysis of Lamb Waves

43

Table 2.3. Attenuation coefficients of Lamb waves in composite materials [74] Lamb mode

Excitation frequency [kHz]

Attenuation coefficient [mm-1]

Distance until decay to 10% [mm]

CFRP woven (8-ply)

S0

250

0.0014

1700

CFRP woven (10-ply)

A0

285

0.027

85

S0 (ll)

250

0.00078

3000

S0 ( )

250

0.0016

1500

GFRP random

S0

220

0.0035

660

CFRP/GFRP hybrid sandwich foam core

S0

250

0.013

182

S0

250

0.0036

640

S0

150

0.0015

1600

S0

250

0.015

150

S0

150

0.011

210

Composite layouts

CFRP woven 10-ply with T-stringers *

CFRP/GFRP hybrid sandwich honeycomb core

GFRP filament wound pipe

* ll: parallel to stringers; : perpendicular to stringers.

As suggested by Equation 2.19, the attenuation of Lamb waves can appropriately be compensated for by multiplying the measured signal magnitude with the square root of the time elapsed, t , as

f ′(t ) = f (t ) ⋅ t .

(2.20)

where f ′(t ) and f (t ) are the compensated and originally measured signals. This is so-called ‘amplitude correction due to beam spreading’ used in NDE [72, 75]. To experimentally quantify the attenuation of Lamb waves, five piezoelectric discs are allocated at an interval of 200 mm in a straight line and surface-mounted on an aluminium plate of 1.6 mm in thickness. With the first piezoelectric disc being the actuator, the captured signals by the other discs are combined in Figure 2.17, revealing that the S0 mode at a frequency of 0.3 MHz attenuates at a rate of 10.5 dB/m; and that Lamb waves have the capacity to maintain the original waveform for up to 1.0 m [76].

44

Identification of Damage Using Lamb Waves

1.00

Sensor IV

Normalised amplitude

0.75 0.50 0.25 0.00 -0.25 -0.50 -0.75

Sensor II

Sensor I

Sensor III

-1.00 50

100

150

200

250

Time [ s]

Fig. 2.17. Integrated Lamb wave signals in an aluminium plate of 1.6 mm in thickness (sensor I/II/III/IV: 200/400/600/900 mm away from the actuator, respectively; after being normalised by the magnitude extremum of the signal captured by sensor I)

To further interrogate the influence of structural inhomogeneity on wave attenuation, a quasi-isotropic CF/EP laminate (500 mm × 500 mm × 3.6 mm) is bonded with a stiffener made of the same material, which is further fastened to the laminate using a set of screws (Hi-lok bolts) at a spacing of 30 mm. Lamb waves are activated in the laminate and then captured after propagating across the stiffener using piezoelectric discs embedded in the laminate. A representative signal is displayed in Figure 2.18(a), compared with its counterpart signals captured in the same laminate before the stiffener is attached, Figure 2.18(b). It is evident from the signal magnitudes that the stiffener greatly increases the attenuation of the Lamb waves, by approximately 60%. Upon removing the screws and repeating the measurement, it is observed that the screws in the stiffener further dissipate the wave energy [77]. Lamb wave attenuation has been evaluated in composite structures with multiple stiffeners in aircraft [78]. The structure under investigation is a slightly curved panel (length: 1500 mm; width: 500 mm), which was stiffened with six evenly distributed stringers on its inner surface, as shown in Figure 2.19(a). The measured magnitude of the S0 mode after passing through different numbers of stiffeners is presented in Figure 2.19(b). It is clearly seen that the S0 mode can propagate across all six stringers, with the most significant energy loss occurring upon passing through the first stringer but with relatively insignificant loss for the succeeding ones.

Fundamentals and Analysis of Lamb Waves

1.00

Benchmark Plate

S0

0.75

Normalised amplitude

45

0.50 0.25 0.00 -0.25 -0.50 -0.75 -1.00 0.0

5.0x10

-5

1.0x10

-4

1.5x10

-4

-4

2.0x10

2.5x10

-4

Time [s]

a 1.00

Stiffener-reinforced Plate

Normalised amplitude

0.75 0.50

S0

0.25 0.00 -0.25 -0.50 -0.75 -1.00 0.0

-5

5.0x10

1.0x10

-4

-4

1.5x10

-4

2.0x10

2.5x10

-4

Time [s]

b Fig. 2.18. Lamb wave signals (at 250 kHz) in a. benchmark; and b. stiffener-reinforced laminates (after being normalised by the magnitude extremum of the signal in benchmark laminate)

Propagation of Lamb waves in the wing panel of an airplane decommissioned from the US Navy has been examined [79]. The wing section was made of aluminium alloys and coated with paint. Figure 2.20(a) shows a schematic of this wing panel and the distribution of rivets used to fasten stiffeners onto the wing panel. Figure 2.20(b) presents the S0 mode of 1.8 MHz captured by a series of sensors 20-200 mm away from the wave actuator (Case 1 in the figure), illustrating that Lamb waves attenuate with propagation distance and the average attenuation rate of the S0 mode in the direction parallel to the stiffeners is 0.044 dB/mm. However,

46

Identification of Damage Using Lamb Waves

Energy of transmitted signal

for the wave attenuation across stiffeners (Case 2 in the figure), the riveted stiffeners introduce considerable wave scattering and energy dissipation; the S0 mode propagates across the stiffeners with an average attenuation rate of 15 dB per rivet row, of which about 9 dB is due to rivets and stiffeners, with the rest due to the propagation distance. In all the tests, it was noticed that paint and coating play a substantial role in wave attenuation, although the waveform maintains over the distance.

12

Stiffener

10 8 6 4 2 0 0.0

Stiffener

0.1

0.3

0.2

0.4

Panel width dimension

a

b

Fig. 2.19. a. An aircraft panel for evaluating Lamb wave attenuation; and b. energy of the transmitted S 0 mode in the panel [78]

Case 1

Case 2

Normalised amplitude

0.5

0.0

-0.5 0

20

40

60

80

100

Time [µs]

a

b

Fig. 2.20. a. Sketch of distribution of rivets and transducers in wing section (rivet rows 6.5 cm apart, rivets 9 mm apart; ‘T’: actuator; ‘X’: sensor in Case 1; ‘ ’: sensor in Case 2); and b. integrated Lamb wave signals captured by a series of sensors in a straight line (Case 1) [79]

Fundamentals and Analysis of Lamb Waves

47

2.6 Influence of Temperature Studies [80, 81] of the effect of ambient temperature on Lamb wave propagation have shown that when temperature increases from -90°C to 25°C, the magnitude of Lamb wave signals in a sandwich laminate increases linearly by a significant level of 50% (Figure 2.21(a)); the propagation velocity decreases also to a pronounced degree, reflected by the increased time used to travel the same distance (Figure 2.21(b)). Relative change in travelling time

Relative change in amplitude

1.2

0.8

0.4

0 -100

-80

-60

-40

-20

Temperature [°C]

a

0

20

40

1.2

0.8

0.4

0 -100

-80

-60

-40

-20

0

20

40

Temperature [°C]

b

Fig. 2.21. Effect of temperature on Lamb waves: a. relative change in magnitude of signal amplitude; and b. relative change in time consumed for travelling the same distance [80]

Other studies [72, 75, 82] of the long-term stability of Lamb-wave-based damage identification systems under varying ambient temperature also highlight a slight shift in the central frequency of captured wave signals with regard to the original excitation frequency, if the variation of ambient temperature is not too acute. Changes in the piezoelectric properties of piezoelectric transducers used for activating and capturing Lamb wave signals under variation in working temperature may be the major reason for this phenomenon. In addition, alterations in properties of the adhesive bonding between transducers and the host structure, difference in the thermal expansion coefficients of the piezoelectric transducer and the host structure, slight changes in structural dimensions (causing a change in the distance between actuator and sensor) and elastic properties including density and Young’s modulus of the medium (producing a change in the wave velocity) also contribute to such an effect, though probably not significant in most cases. For example, it has been observed by the authors that the density and Young’s modulus of an aluminium alloy decrease by 0.22% and 2.8%, respectively, when the ambient temperature increases from 25°C to 50°C, and the group velocities of the S0 , A0 and SH 0 modes accordingly decrease by 1.27%, 1.27% and 1.68% only, respectively. Therefore, there is no need to apply special corrections to compensate for a small change in ambient temperature in normal applications [83-86]. However, the influence of temperature may not be ignored if the damage to be detected is small,

48

Identification of Damage Using Lamb Waves

where modulation of the signal by the damage may be overwhelmed by influences associated with changes in ambient temperature [87], or if sensors work in an environment of elevated temperature [88]. To increase the accuracy of damage identification in an environment with temperature variation, the following two compensation measures can be employed: (i) use a simple linear interpolation or extrapolation, depending on the case, which is defined as [89]

f T (t ) =

T − T1 ( f T 2 (t ) − fT 1 (t )) + f T 1 (t ) , T − T2

(2.21)

where fT (t ) is the compensated signal at temperature T . fT 1 (t ) and fT 2 (t ) are signals captured using the same actuator and sensor but at another two temperatures, T1 and T2 , respectively. This approach may offset the influence of temperature change; or (ii) collect a series of baseline signals from the intact structure under conditions of varying ambient temperature ( T1 , T2 , A, Ti , A, TN ) for a certain period of time such as 24 hours, and calculate the square errors, E (i ) , [90, 91] M

E (i ) = ∑ [ f (m) − Fi (m)]2 m =1

( i = 1, 2, A , N ; m = 1, 2, A , M ),

(2.22)

where f (m) is the discretised signal, having M sampling points and captured from the structure under inspection in a condition of unknown ambient temperature, and Fi (m) ( i = 1, 2, A, N ) are the discretised baseline signals having M sampling points at temperature Ti . When E (i ) reaches the minimum, the corresponding baseline signal is selected as the benchmark signal for damage identification.

2.7 Influence of Damage Orientation and Size As introduced in Chapter 1, interaction of Lamb waves with structural damage can significantly influence their propagation, accompanied by wave scattering effects such as reflection, transmission and mode conversion; and different locations and severity of damage cause unique scattering phenomena. The above is the premise of the Lamb-wave-based damage identification. When the damage is delamination or a through-thickness hole in composite laminates, upon interaction with the damage, Lamb waves are scattered omnidirectionally, ‘creeping’ around the damage. In such cases, the location of sensors with regard to the damage location is not a crucial concern. However, a crack/notch or some other types of damage of

Fundamentals and Analysis of Lamb Waves

49

significant length in a particular dimension may exert strong directionality on wave propagation, and scattered waves may not be captured efficiently by sensors at certain locations. Under such a circumstance, the orientation, size and relative position of damage with regard to sensors become important factors, which must be taken into account in the development of Lamb-wave-based damage identification approaches [59, 92, 93]. To scrutinise the influence of the orientation and size of damage on Lamb wave propagation, an aluminium panel (550 mm × 550 mm × 1.6 mm) was evaluated [76], bearing a through-thickness notch 0.6 mm in width, varying from 5 to 100 mm in length with an increment of 2 mm. Twenty-one piezoelectric discs, symbolised by Pi ( i = 1, 2, A , 21 ), were surface-bonded on the panel at different locations to serve as wave actuators and sensors, as shown in Figure 2.22. 550 mm

P1

P4 P7

P19

θi X P8 P11 P14 P17 P20

Crack

P5 P2 50 mm

P16

Y

50 mm

550 mm

P13

200 mm

P10

P3 P6

P21 P18 P15 P12 P9

Fig. 2.22. Distribution of piezoelectric elements surface-bonded on an aluminium plate with supported edges for canvassing the influence of notch orientation on wave propagation [76]

Using these distributed piezoelectric discs, the notch-scattered (reflected and transmitted) Lamb waves were captured by sensors at different angles ( θ i , ( i = 1, 2, A , 21 )) with regard to the notch. Reflection coefficients (ratio of the largest magnitude of damage-reflected first wave component captured by the sensor to that of incident wave) and transmission coefficients (ratio of the largest magnitude of first wave component after wave propagating across the damage, captured by the sensor, to that of incident wave) are presented in Figure 2.23, subject to different incident angles ( θ i ), when the notch length is 20 and 40 mm, respectively. It is apparent that the reflection coefficient decreases while the

50

Identification of Damage Using Lamb Waves

transmission coefficient increases substantially as θ i increases, showing strong angular dependence of the scattered Lamb waves.

1.2

Crack=20mm (FEM) Crack=20mm (Experiment) Crack=40mm (FEM) Crack=40mm (Experiment)

0.5

Transmission coefficient

Reflection coefficient

0.6

0.4

0.3

0.2

0.1

Crack=20mm (FEM) Crack=20mm (Experiment) Crack=40mm (FEM) Crack=40mm (Experiment)

1.0

0.8

0.6

0.4

0.2

0

15

30

45

60

Incident angle [degree]

a

75

90

0

15

30

45

60

75

90

Incident angle [degree]

b

Fig. 2.23. a. Reflection; and b. transmission coefficients of Lamb wave signals scattered by a notch versus the angle of incident wave

On the other hand, at the same θi , the transmission coefficient decreases with notch length while the reflection coefficient increases monotonically with notch length in a range of 5-60 mm, but it oscillates after 70 mm, as observed in the reflection and transmission coefficients shown in Figure 2.24 when θ i = 00 . This suggests that the notch length may not be defined solely by the reflection coefficient, since that may refer to two different notch lengths. For normal wave incidence ( θ i = 00 ), the reflection and transmission coefficients measured by sensors at different locations are presented in a polar coordinate chart, Figure 2.25, indicating that two coefficients vary with measurement angle θ r (reflected) and θ t (transmitted), sharing the same trend. In particular, the reflection coefficient for a notch of 20 mm in length under normal incidence ( θ i = 00 ) is close to that when the notch is 40 mm in length but

θ i = 300 . As a result, using only the measured reflection coefficient from one actuator-sensor pair, it is unlikely that notch parameters can be assessed definitively. In addition to notch length, the notch width can also affect the reflection and transmission of Lamb waves, showing a similar trend [94].

Fundamentals and Analysis of Lamb Waves 0.6

1.2

Transmission coefficient

FEM Experiment

Reflection coefficient

51

0.4

0.2

0

20

40

60

Crack length [mm]

80

100

FEM Experiment

1.0

0.8

0.6

0.4

0.2

0

20

40

60

80

100

Crack length [mm]

a

b

Fig. 2.24. a. Reflection; and b. transmission coefficients of Lamb wave signals scattered by a notch versus the notch length at frequency of 0.3 MHz ( θ i = 0 0 )

2.8 Summary Lamb waves are elastic waves in thin plate-like structures, including symmetric ( Si ) and anti-symmetric ( Ai ) modes. The propagation characteristics of Lamb waves have been the subject of intensive study for nearly a century, in terms of theoretical analysis, FEM simulation and experiments. Lamb waves feature some unique and complex properties, including dispersion, mode conversion, slowness, directional dependence of wave speed, difference in the phase and group velocities. These mechanisms give Lamb waves two distinct characteristics – they are sensitive to damage in structures, and they are difficult to interrogate when used for damage identification. The transfer matrix method and its enhanced form, the global matrix method, are two means to analytically interrogate Lamb waves in multilayered laminate structures, but applications are restricted due to their complexity. In most cases there is no explicit analytical solution to dispersion equations of Lamb waves. On the other hand, FEM approaches can provide great cost-effectiveness when evaluating the propagation characteristics of Lamb waves in various media. With the purpose of damage identification, FEM modelling techniques have been particularly specialised for analysing Lamb waves and simulating structural damage. With FEM simulation and experimental validation, conclusions have been drawn that:

Identification of Damage Using Lamb Waves

Transmission Coefficient Reflection Coefficient

52

15

1.4

30

30

1.2

Crack=20mm (FEM) Crack=20mm (Experiment)

θr [Degree] 0 15

45

1.0 0.8

45

Incident Wave

60

60

0.6 0.4

75

75

0.2 0.0

90

90

0.2 0.4

75

75

Crack

0.6 0.8

60

1.0

60 45

45

1.2

30

30

1.4

15

15 0 θt [Degree]

Transmission Coefficient Reflection Coefficient

a

15

1.4

30

30

1.2

Crack=40mm (FEM) Crack=40mm (Experiment)

θr [Degree] 0 15

45

1.0 0.8

45

Incident Wave

60

60

0.6 0.4

75

75

0.2 0.0

90

90

0.2 0.4

75

75

Crack

0.6 0.8 1.0

60

60 45

45

1.2 1.4

30

30 15

0

15

θt [Degree]

b Fig. 2.25. Reflection and transmission coefficients of Lamb wave signals under normal incidence ( θi =0°) scattered by a notch of a. 20 mm; and b. 40 mm in length (notch being horizontally located at the centre of the polar charts; θ r and θ t are the measurement angles of the sensor with regard to the notch to receive the reflected and transmitted signals, respectively)

Fundamentals and Analysis of Lamb Waves

53

(i)

Lamb waves can propagate a relatively long distance in metallic plates and fibre-reinforced composite laminates; (ii) a less-dispersive region exists in the low frequency band where both the S0

(iii)

(iv) (v)

(vi)

and A0 modes travel at almost constant velocities, frequently referred to as the ‘non-dispersion region’; Lamb wave modes in this region can be employed for damage identification; the symmetric modes tend to travel farther than their anti-symmetric counterparts with less attenuation, and the former also travel faster than the latter at the same frequency; structural inhomogeneity (e.g., stiffener, bolt and rivet) can impose marked attenuation on Lamb waves, introducing considerable energy dissipation; an increase in ambient temperature can increase the amplitude while decrease the velocity of Lamb waves. In normal applications with temperature varying between 20°C and 40°C there is no need to apply special compensation, but some corrections can be introduced if the damage to be detected is small in size; and crack/notch-like damage of significant length in a specific dimension exerts strong directionality on Lamb wave propagation, and as a result it is unlikely that damage parameters of a crack or notch can be ascertained definitively using one actuator-sensor pair only.

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Identification of Damage Using Lamb Waves

11. Guo, N., Cawley, P.: Lamb waves for the NDE of composite laminates. In: Thompson, D.O., Chimenti, D.E. (eds.) Review of Progress in Quantitative Nondestructive Evaluation, vol. 11, pp. 1443–1450. Plenum Press, New York (1992) 12. Chimenti, D.E.: Guided waves in plates and their use in materials characterization. Applied Mechanics Review 50(5), 247–284 (1997) 13. Rose, J.L.: Guided wave nuances for ultrasonic nondestructive evaluation. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 47(3), 575–583 (2000) 14. Raghavan, A., Cesnik, C.E.S.: Review of guided-wave structural health monitoring. The Shock and Vibration Digest 39(2), 91–114 (2007) 15. Achenbach, J.D.: Quantitative nondestructive evaluation. International Journal of Solids and Structures 37, 13–27 (2000) 16. Rose, J.L.: A baseline and vision of ultrasonic guided wave inspection potential. Journal of Pressure Vessel Technology 124, 273–282 (2002) 17. Giurgiutiu, V., Cuc, A.: Embedded non-destructive evaluation for structural health monitoring, damage detection, and failure prevention. The Shock and Vibration Digest 37(2), 83–105 (2005) 18. Montalvão, D., Maia, N.M.M., Ribeiro, A.M.R.: A review of vibration-based structural health monitoring with special emphasis on composite materials. The Shock and Vibration Digest 38(4), 295–324 (2006) 19. Balageas, D.L.: Structural health monitoring R&D at the European Research Establishments in Aeronautics (EREA). Aerospace Science and Technology 6, 159– 170 (2002) 20. Boller, C.: Ways and options for aircraft structural health management. Smart Materials and Structures 10, 432–440 (2001) 21. Wilcox, P.D., Konstantinidis, G., Croxford, A.J., Drinkwater, B.W.: Strategies for guided wave structural health monitoring. In: Thompson, D.O., Chimenti, D.E. (eds.) Review of Progress in Quantitative Nondestructive Evaluation, vol. 26, pp. 1469– 1476. American Institute of Physics, New York (2007) 22. Su, Z., Ye, L., Lu, Y.: Guided Lamb waves for identification of damage in composite structures: a review. Journal of Sound and Vibration 295, 753–780 (2006) 23. Rose, J.L.: Ultrasonic Waves in Solid Media. Cambridge University Press, New York (1999) 24. Achenbach, J.D.: Wave Propagation in Elastic Solids. North-Holland Pub. Co./American Elsevier Pub. Co., New York (1973) 25. Cheeke, J.D.N.: Fundamentals and Applications of Ultrasonic Waves. CRC Press, Boca Raton (2002) 26. Birt, E.A.: Damage detection in carbon-fibre composites using ultrasonic Lamb waves. Insight 40(5), 335–339 (1998) 27. Badcock, R.A., Birt, E.A.: The use of 0-3 piezocomposite embedded Lamb wave sensors for detection of damage in advanced fibre composites. Smart Materials and Structures 9, 291–297 (2000) 28. Percival, W.J., Birt, E.A.: A study of Lamb wave propagation in carbon-fibre composites. Insight 39, 728–735 (1997) 29. Alleyne, D.N., Cawley, P.: The excitation of Lamb waves in pipes using dry-coupled piezoelectric transducers. Journal of Nondestructive Evaluation 15(1), 11–20 (1996) 30. Hinders, M.: Guided wave helical ultrasound tomography of pipes and tubes, http://www.as.wm.edu/Faculty/Hinders/HUT-W&M.pdf

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31. Tua, P.S., Quek, S.T., Wang, Q.: Detection of cracks in cylindrical pipes and plates using piezo-actuated Lamb waves. Smart Materials and Structures 14, 1325–1342 (2005) 32. Leonard, K.R., Hinders, M.K.: Guided wave helical ultrasonic tomography of pipes. Journal of the Acoustical Society of America 114(2), 767–774 (2003) 33. Wang, L., Yuan, F.G.: Group velocity and characteristic wave curves of Lamb waves in composites: modeling and experiments. Composites Science and Technology 67, 1370–1384 (2007) 34. Kim, Y.-H., Kim, D.-H., Han, J.-H., Kim, C.-G.: Damage assessment in layered composites using spectral analysis and Lamb wave. Composites: Part B 38, 800–809 (2007) 35. Lowe, M.J.S.: Matrix techniques for modelling ultrasonic waves in multilayered media. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 42(4), 525–541 (1995) 36. Habeger, C.C., Mann, R.W., Baum, G.A.: Ultrasonic plate waves in paper. Ultrasonics 17, 57–62 (1979) 37. Santosa, F., Pao, Y.-H.: Transient axially asymmetric response of an elastic plate. Wave Motion 11, 271–295 (1989) 38. Karunasena, W., Shah, A.H., Datta, S.K.: Wave propagation in a multilayered laminated cross-ply composite plate. Journal of Applied Mechanics 58, 1028–1033 (1991) 39. Ghoshal, A., Martin, W.N., Schulz, M.J.: Simulation of asymmetric Lamb wave propagation for health monitoring. In: Balageas, D. (ed.) Proceedings of the 1st European Workshop on Structural Health Monitoring, Paris, France, July 10-12, 2002, pp. 365–373. DEStech Publications, Inc. (2002) 40. Nayfeh, A.H., Chimenti, D.E.: Free wave propagation in plates of general anisotropic media. Journal of Applied Mechanics 56, 881–887 (1989) 41. Wilcox, P.: Modeling the excitation of Lamb and SH waves by point and line sources. In: Thompson, D.O., Chimenti, D.E. (eds.) Review of Progress in Quantitative Nondestructive Evaluation, vol. 23, pp. 206–213. Springer, Heidelberg (2004) 42. Aberg, M., Gudmundson, P.: Micromechanical modeling of transient waves from matrix cracking and fibre fracture in laminated beams. International Journal of Solids and Structures 37, 4083–4102 (2000) 43. Galan, J.M., Abascal, R.: Numerical simulation of Lamb wave scattering in semiinfinite plates. International Journal for Numerical Methods in Engineering 53, 1145– 1173 (2002) 44. Adamou, A.T.I., Craster, R.V.: Spectral methods for modeling guided waves in elastic media. Journal of the Acoustical Society of America 116, 1524–1535 (2004) 45. Mal, A.K.: Wave propagation in layered composite laminates under periodic surface loads. Wave Motion 10, 257–266 (1998) 46. Lih, S.-S., Mal, A.K.: On the accuracy of approximate plate theories for wave field calculations in composite laminates. Wave Motion 21, 17–34 (1995) 47. Xu, X., Goossens, J., Shkerdin, G., Glorieux, C.: Effect of loading a plate with different liquids on the propagation of Lamb-like waves studied by laser ultrasonics. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 55, 675–685 (2008) 48. http://www.imperial.ac.uk/ndt/public/productservice/ disperse.htm

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49. Lee, B.C., Staszewski, W.J.: Modelling of Lamb waves for damage detection in metallic structures: part I - wave propagation. Smart Materials and Structures 12, 804– 814 (2003) 50. Olson, S.E., DeSimio, M.P., Derriso, M.M.: Beam forming of Lamb waves for structural health monitoring. Journal of Vibration and Acoustics 129, 730–738 (2007) 51. Diamanti, K., Soutis, C., Hodgkinson, J.M.: Piezoelectric transducer arrangement for the inspection of large composite structures. Composites: Part A 38, 1121–1130 (2007) 52. Alleyne, D.N., Cawley, P.: The interaction of Lamb waves with defects. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 39(3), 381–397 (1992) 53. Guo, N., Cawley, P.: The interaction of Lamb waves with delamination in composite laminates. Journal of the Acoustical Society of America 94(4), 2240–2246 (1993) 54. Chang, F.-K., Markmiller, F.C., Ihn, J.-B., Cheng, K.Y.: A potential link from damage diagnostics to health prognostics of composites through built-in sensors. Journal of Vibration and Acoustics 129, 718–729 (2007) 55. Luo, R.K.: The evaluation of impact damage in a composite plate with a hole. Composites Science and Technology 60, 49–58 (2000) 56. Ostachowicz, W.M.: Damage detection of structures using spectral finite element method. Computers and Structures 86, 454–462 (2008) 57. Guo, N., Cawley, P.: Lamb wave propagation in composite laminates and its relationship with acousto-ultrasonics. NDT&E International 26(2), 75–84 (1993) 58. Wong, C.K.W., Chiu, W.K., Rajic, N., Galea, S.C.: Can stress waves be used for monitoring sub-surface defects in repaired structures? Composite Structures 76, 199– 208 (2006) 59. Diligent, O., Lowe, M.J.S.: Reflection of the S0 Lamb mode from a flat bottom circular hole. Journal of the Acoustical Society of America 118(5), 2869–2879 (2005) 60. Alleyne, D., Cawley, P.: A 2-dimensional Fourier transform method for the quantitative measurement of Lamb modes. In: Thompson, D.O., Chimenti, D.E. (eds.) Review of Progress in Quantitative Nondestructive Evaluation, vol. 10, pp. 201–208. Plenum Press, New York (1991) 61. Lowe, M.J.S., Diligent, O.: Low-frequency reflection characteristics of the S0 Lamb wave from a rectangular notch in a plate. Journal of the Acoustical Society of America 111(1), 64–74 (2002) 62. Kim, J., Ko, B., Lee, J.-K., Cheong, C.-C.: Finite element modeling of a piezoelectric smart structure for the cabin noise problem. Smart Materials and Structures 8, 380–389 (1999) 63. Huang, N., Ye, L., Su, Z.: Parameterised modelling technique and its application to artificial neural network-based structural health monitoring. In: Ye, L., Mai, Y.-W., Su, Z. (eds.) Proceedings of the 4th Asian-Australasian Conference on Composite Materials (ACCM 2004), Sydney, Australia, July 6-9, 2004, pp. 999–1004. Woodhead Publishing Ltd. (2004) 64. Su, Z., Ye, L.: Lamb wave propagation-based damage identification for quasi-isotropic CF/EP composite laminates using artificial neural algorithm, part I: methodology and database development. Journal of Intelligent Material Systems and Structures 16, 97– 111 (2005) 65. Liu, G.R.: A combined finite element-strip element method for analyzing elastic wave scattering by cracks and inclusions in laminates. Computational Mechanics 28, 76–81 (2002)

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66. Moulin, E., Assaad, J., Delebarre, C., Grondel, S., Balageas, D.: Modeling of integrated Lamb waves generation systems using a coupled finite element-normal modes expansion method. Ultrasonics 38, 522–526 (2000) 67. Cortes, D.H., Datta, S.K., Mukdadi, O.M.: Dispersion of elastic guided waves in piezoelectric infinite plates with inversion layers. International Journal of Solids and Structures 45, 5088–5102 (2008) 68. Cho, Y., Rose, J.L.: A boundary element solution for a mode conversion study on the edge reflection of Lamb waves. Journal of the Acoustical Society of America 99, 2097–2109 (1996) 69. Grondel, S., Paget, C., Delebarre, C., Assaad, J., Levin, K.: Design of optimal configuration for generating A0 Lamb mode in a composite plate using piezoceramic transducers. Journal of the Acoustical Society of America 112(1), 84–90 (2002) 70. Prasad, S.M., Balasubramaniam, K., Krishnamurthy, C.V.: Structural health monitoring of composite structures using Lamb wave tomography. Smart Materials and Structures 13, N73–N79 (2004) 71. Kim, S.B., Sohn, H.: Instantaneous reference-free crack detection based on polarization characteristics of piezoelectric materials. Smart Materials and Structures 16, 2375–2387 (2007) 72. Konstantinidis, G., Drinkwater, B.W., Wilcox, P.D.: The temperature stability of guided wave structural health monitoring systems. Smart Materials and Structures 15, 967–976 (2006) 73. Wilcox, P., Lowe, M., Cawley, P.: Omnidirectional guided wave inspection of large metallic plate structures using an EMAT array. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 52(4), 653–665 (2005) 74. Pierce, S.G., Culshaw, B., Manson, G., Worden, K., Staszewski, W.J.: The application of ultrasonic Lamb wave techniques to the evaluation of advanced composite structures. In: Claus, R.O., Spillman Jr., W.B. (eds.) Proceedings of the SPIE, vol. 3986, pp. 93–103 (2000) 75. Konstantinidis, G., Drinkwater, B.W., Wilcox, P.D.: The long term stability of guided waves structural health monitoring systems. In: Proceedings of the AIP Conference on Quantitative Nondestructive Evaluation, March 6, 2006, vol. 820, pp. 1702–1709 (2006) 76. Lu, Y., Ye, L., Su, Z., Huang, N.: Quantitative evaluation of crack orientation in aluminium plates based on Lamb waves. Smart Materials and Structures 16, 1907– 1914 (2007) 77. Su, Z., Wang, X., Chen, Z., Ye, L., Wang, D.: A built-in active sensor network for health monitoring of composite structures. Smart Materials and Structures 15, 1939– 1949 (2006) 78. Monnier, T.: Lamb waves-based impact damage monitoring of a stiffened aircraft panel using piezoelectric transducers. Journal of Intelligent Material Systems and Structures 17, 411–421 (2006) 79. Zhao, X., Gao, H., Zhang, G., Ayhan, B., Yan, F., Kwan, C., Rose, J.L.: Active health monitoring of an aircraft wing with embedded piezoelectric sensor/actuator network: I. defect detection, localization and growth monitoring. Smart Materials and Structures 16, 1208–1217 (2007) 80. Blaise, E., Chang, F.-K.: Built-in diagnostic for debonding in sandwich structures under extreme temperature. In: Chang, F.-K. (ed.) Proceedings of the 3rd International Workshop on Structural Health Monitoring, Stanford, CA, USA, September 12-14, 2001, pp. 154–163. CRC Press, Boca Raton (2001)

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81. Blaise, E., Chang, F.-K.: Built-in damage detection system for sandwich structures under cryogenic temperatures. In: Proceedings of the SPIE, vol. 4701, pp. 97–107 (2002) 82. Konstantinidis, G., Wilcox, P.D., Drinkwater, B.W.: An investigation into the temperature stability of a guided wave structural health monitoring system using permanently attached sensors. IEEE Sensors Journal 7(5), 905–912 (2007) 83. Nguyen, C.-H., Pietrzko, S., Buetikofer, R.: The influence of temperature and bonding thickness on the actuation of a cantilever beam by PZT patches. Smart Materials and Structures 13, 851–860 (2004) 84. Sirohi, J., Chopra, I.: Fundamental understanding of piezoelectric strain sensors. Journal of Intelligent Material Systems and Structures 11, 246–257 (2000) 85. Andrews, J.P., Palazotto, A.N., DeSimio, M.P., Olson, S.E.: Lamb wave propagation in varying isothermal environments. Structural Health Monitoring: An International Journal 7(3), 265–270 (2008) 86. Qing, X.P., Beard, S.J., Kumar, A., Sullivan, K., Aguilar, R., Merchant, M., Taniguchi, M.: The performance of a piezoelectric-sensor-based SHM system under a combined cryogenic temperature and vibration environment. Smart Materials and Structures (in press) 87. Lee, B.C., Manson, B., Staszewski, W.J.: Environmental effects on Lamb wave responses from piezoceramic sensors. In: Proceedings of the 5th International Conference on Modern Practice in Stress and Vibration Analysis, Glasgow, Scotland, September 9-11, 2003, vol. 440-441, pp. 195–202 (2003) 88. Raghavan, A., Cesnik, C.E.S.: Effects of elevated temperature on guided-wave structural health monitoring. Journal of Intelligent Material Systems and Structures 19, 1383–1398 (2008) 89. Inman, D.J., Farrar, C.R., Lopes Jr., V., Steffen Jr., V.: Damage Prognosis: for Aerospace, Civil and Mechanical Systems. John Wiley & Sons, Inc, Chichester (2005) 90. Michaels, J.E.: Detection, localization and characterization of damage in plates with an in situ array of spatially distributed ultrasonic sensors. Smart Materials and Structures (in press) 91. Michaels, J.E., Michaels, T.E.: An integrated strategy for detection and imaging of damage using a spatially distributed array of piezoelectric sensors. In: Proceedings of the SPIE (Conference on Health Monitoring of Structural and Biological Systems), vol. 6532 (2007) Paper No.: 653203 92. Jin, J., Quek, S.T., Wang, Q.: Design of interdigital transducers for crack detection in plates. Ultrasonics 43, 481–493 (2005) 93. Tua, P.S., Quek, S.T., Wang, Q.: Detection of cracks in plates using piezo-actuated Lamb waves. Smart Materials and Structures 13, 643–660 (2004) 94. Lee, B.C., Staszewski, W.J.: Lamb wave propagation modelling for damage detection: II. damage monitoring strategy. Smart Materials and Structures 16, 260–274 (2007)

3 Activating and Receiving Lamb Waves

3.1 Introduction Over the past few decades there have been substantial advances in the design and development of functional materials. Many of the products, piezoelectric materials for example, have been widely used to build a variety of transducers for activating and receiving Lamb waves. Integrating these transducers with host structures under monitoring is an essential step towards automated damage identification and structural health monitoring (SHM) techniques.

3.2 Transducers of Lamb Waves In practice, Lamb waves can be activated and received by a variety of means roughly grouped into five major categories in terms of the transducers adopted. 3.2.1 Ultrasonic Probes Preferred for their high precision and good controllability, perspex wedgecoupled angle-adjustable ultrasonic probes [1-12], Figure 3.1(a), comb ultrasonic probes [12], Figure 3.1(b) and Hertzian contact probes [13], Figure 3.1(c), are the most popular transducers for activating and capturing Lamb waves. These transducers can be actively tuned to selectively produce a specific Lamb wave mode in accordance with Snell’s law which describes the relationship between the angles of incidence and refraction [14]. Without the complexity caused by multiple wave modes, captured signals are easy to interpret. But, with ultrasonic probes operated in a contact manner, the efficiency of wave activation and reception may be diminished due to certain technical factors associated with using couplant. Innovative ultrasonic probes have therefore been introduced to activate and receive Lamb waves in a non-contact manner, as typified by air/gascoupled [15, 16] or fluid-coupled [17] transducers and electro-magnetic acoustic transducers (EMATs) [18-20]. In particular, EMAT can excite SH i modes very efficiently [20]. Z. Su and L. Ye: Identification of Damage Using Lamb Waves, LNACM 48, pp. 59–98. springerlink.com © Springer-Verlag Berlin Heidelberg 2009

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a Transducer

Extensional waves Buffer rod

b

Activated Lamb waves Sample

c Fig. 3.1. Ultrasonic probes for activating Lamb waves: a. perspex wedge-coupled angleadjustable ultrasonic probe; b. comb ultrasonic probe [12]; and c. Hertzian contact probe [13]

However, low precision can result from large acoustical mismatches between the air/fluid and the objects under inspection. EMATs are normally used for metallic structures only, since electrical conductivity of the object is a prerequisite. The narrowband pulse is extensively used for these transducers to activate Lamb waves since it can provide sufficient and centralised incident energy. But narrowband pulse-activated Lamb waves are likely to disperse considerably as they propagate, complicating signal interpretation [21]. Further, downtime of the object or even disassembly of it from main structures is sometimes required so as to insure that probes can access the object. Moreover, the weight and size of these probes are normally non-negligible. All these factors may limit the applications of such ultrasonic probes in SHM techniques.

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3.2.2 Piezoelectric Wafers and Piezocomposite Transducers The weak coupling capacity of wedge ultrasonic transducers with a structure under inspection and difficulties in integrating them with the structure have promoted techniques with which small transducers packaged in various modalities can be directly inserted into or mounted on a host structure, as represented by piezoelectric lead zirconate titanate (PZT) wafer/elements [22-32]. In fact, a conventional ultrasonic probe excites and senses Lamb waves indirectly through the interaction between activated guided waves and structural surface, whereas a PZT wafer/element excites and senses Lamb waves directly through in-plane strain coupling. A PZT wafer can deliver wide frequency responses with low power consumption/acoustic impedance/cost. Small and light, like the examples shown in Figure 3.2, PZT wafers/elements are particularly suitable for integration into host structures with good coupling capacity but without significant intrusion, serving as good candidates for built-in wave actuators and sensors. Further, a PZT sensor network can be configured using a number of distributed PZT elements, to achieve multi-point measurements. A PZT wafer has negligible decline in performance even when damage occurs near it.

Fig. 3.2. PZT wafers in various sizes [33]

However PZT wafer-generated Lamb waves unavoidably contain multiple wave modes, unlike those produced by wedge-coupled or comb probes, and sophisticated signal processing is therefore of vital importance for signal interpretation. A PZT wafer may exhibit non-linear behaviour and hysteresis under large strains/voltages or at high temperatures; meanwhile, weak driving force/displacement and brittleness may also narrow its application domain. To circumvent the brittleness of PZT and to achieve improved surface conformability in curved shell structures, piezoelectric powder and piezoceramic fibre have been incorporated into an epoxy resin to form poled film sheets, for activating and receiving Lamb waves in an effort to couple the electromechanical efficiency of a PZT with the flexibility of polymer films, called piezocomposite transducers [34]. These include the macro fibre composites (MFCs) [35-38] and active fibre composites developed at NASA’s Langley Research Centre [35]. The former have been primarily utilised for structural control, vibration suppression and guided wave activation [37, 39, 40]; the latter are used for guided wave activation and reception in the low hundreds of kilohertz range [41-43]. Both transducers are made of very thin piezoceramic fibres that are unidirectionally aligned and

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sandwiched between two sets of inter-digitated electrodes symmetrically allocated on the upper and lower surfaces of the epoxy matrix film [36, 44]. Piezocomposite transducers exhibit properties much superior to traditional PZTs of the same size, plus a notable reduction in manufacturing costs. An MFC transducer is shown in Figure 3.3. Since the activating motion of the MFC is along the piezoceramic fibre, rather than in the transverse direction along which a traditional PZT wafer oscillates, the driving force provided by the MFC can be three times as high as that provided by a piezoelectric wafer of the same size [38].

Fig. 3.3. An MFC transducer [38]

3.2.3 Laser-based Ultrasonics Activating waves using laser sources and collecting structural responses using laser interferometers has become an encouraging approach for contactless activation and acquisition of Lamb waves [11, 18, 45-58]. Fabry-Pérot and heterodyne interferometers are the devices often employed in this aspect. Flexibly controllable, a laser source can be designed to be broadband or narrowband depending on the application, so as to meet different spatial resolution requirements. This approach is particularly effective for irregular surfaces, complex geometry or stringent environments where direct access of transducers to the object is not feasible. By using a short laser pulse it is possible to excite a broad bandwidth signal with several Lamb modes, permitting selective generation of a desired wave mode. Nevertheless, laser-based ultrasonics (LBU) is subject to similar concerns as those encountered by wedge-coupled ultrasonic transducers, such as bulkiness and high cost of equipment, and therefore may not be easily adopted for practical application. 3.2.4 Interdigital Transducers Interdigital transducers (IDTs) using polyvinylidene fluoride (PVDF) piezoelectric polymer films have been introduced to cater for more versatile applications [5968]. Compared with a PZT element, a PVDF film features better flexibility and

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greater ease of handling. Like the example shown in Figure 3.4, PVDF film is soft and can be easily shaped to cope with curved structural surfaces. The basic configuration of a PVDF-based IDT consists of interdigital electrodes deposited on a piezoelectric substrate [65]. Through careful design of the electrodes and adjustment of the spacing between interdigital electrodes, a specific Lamb wave mode with the desired bandwidth, focused propagation direction and customised wavelength can be generated [64]. This capacity for activating Lamb waves with controllable wavelength and even dispersion properties has attracted great attention in recent research and development of SHM techniques. Most PVDFbased IDTs used for composite structures are surface-bonded, for the reason that processing of composites at elevated temperatures can destroy the piezoelectric properties of PVDF. In most studies, because of their low modulus of elasticity and viscoelastic behaviour, PVDF-based IDTs have been used as sensors only, though some studies [69, 70] have employed them as actuators within a low operating frequency range (up to 500 Hz).

Fig. 3.4. A PVDF piezoelectric polymer film [71]

Although PVDF-based IDTs bring advantages in durability and flexibility when compared to traditional PZT wafers, they work best in a high frequency range only (normally 0.5-4 MHz), which however comes with the cost of fast wave attenuation. In addition, PVDF is egregiously sensitive to certain environmental factors, particularly temperature (which is why a PVDF is often used as a thermometer). Traditional IDTs must be permanently fixed on the structure to maximise the efficiency of reception of wave signals. Recently, benefiting from some recent breakthroughs in material sciences and manufacturing techniques, a mobile IDT technique has been developed [72, 73] where the IDT can be moved as well as rotated to interrogate the object very efficiently. A study of the performance of PZT elements and IDTs for damage detection [64] has revealed that both the PZT elements and IDTs can successfully detect and locate cracks in aluminium plates. In particular, IDTs are more accurate, procedurally simpler, and are an efficient alternative to PZT elements.

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3.2.5 Fibre-optic Sensors – Reception Only With features including wide bandwidth, good compatibility, immunity to electromagnetic interference, long service life, low power consumption, and in particular light weight and tiny volume, optical fibres have been increasingly adopted for fabricating various sensing devices [53, 74-93]. They are exceptionally good at capturing a static or quasi-dynamic strain. However, applications as a Lamb wave sensor in the ultrasonic range are rare [1, 48, 74, 76, 78, 81, 82, 84, 87, 88, 91, 92, 94], because of the low sampling rate of the optical spectrum analyser, the equipment used for capturing optical signal. This difficulty has recently been circumvented by using a fibre Bragg grating (FBG) filter connected with a photodetector (Section 4.3.3 for detail). The major drawback in receiving Lamb waves using fibre-optic sensors is that careful analysis of the output is necessary to correctly extract the axial composition of the measurands since the response captured by a fibre-optic sensor is of a three-dimensional nature. In addition, the accuracy of measurement can be affected by environmental conditions and the alignment of sensors (for example, a Lamb wave signal captured by an fibre-optic sensor perpendicular to the wave propagation can be 100 times less in magnitude than that collected by a sensor parallel to the wave propagation direction). Other recent innovations in transducer development for activating and acquiring Lamb waves include magnetostrictive sensors [95] and micro-electro-mechanical system (MEMS)-sensor-based micro-IDTs [96, 97].

3.3 Activation of Desired Diagnostic Lamb Waves Activation of a diagnostic Lamb wave signal with an appropriate mode in an appropriate waveform and of an appropriate frequency is vital for Lamb-wavebased damage identification. At a rudimentary level, a diagnostic Lamb wave should, if possible, feature (i) non-dispersion, (ii) low attenuation, (iii) high sensitivity to damage, (iv) easy excitability, and (v) good detectability. 3.3.1 Selection of Appropriate Wave Mode 3.3.1.1 Various Lamb Modes Studies [98-100] based on the calculated stress and displacement fields of different Lamb modes in a plate reveal that if the magnitude of changes in stress or displacement of a certain Lamb wave mode at the preferred sensor location due to the existence of damage is higher than the other modes, this mode is most effective in identifying this particular type of damage. This observation becomes more pronounced when the damage is a void or delamination. On the other hand, it has been demonstrated that the mode which produces large shear stress at the interface is most sensitive to interface damage such as delamination [98].

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In the majority of studies [21, 26, 27, 82, 101-106], the S0 mode is selected for damage identification, due to, in contrast to the A0 mode, its: (i)

lower attenuation (as addressed in Section 2.5, the A0 mode usually presents higher attenuation during propagation because of the dominant out-of-plane movement of particles in the mode shape, which leaks partial energy to the surrounding medium; whereas the S0 mode has mostly in-plane displacement and its energy is confined within the plate); (ii) faster propagation velocity, which means that complex wave reflection from the boundary can sometimes be avoided; and (iii) lower dispersion in the low frequency range, benefiting signal interpretation.

On the other hand, there has been increasing awareness of using the A0 mode for damage identification [23, 25, 61, 64, 104, 107-122]. Its merits, in comparison with the S0 mode, include: (i) shorter wavelength at a given excitation frequency (in recognition of the fact that the half wavelength of a selected wave mode must be shorter than or equal to the damage size to allow the wave to interact with the damage); (ii) larger signal magnitude (the A0 mode in a wave signal is usually much stronger than the S0 mode if two modes are activated simultaneously, giving a signal with high signal-to-noise ratio (SNR), though as mentioned earlier it attenuates more quickly); and (iii) easier means of activation (the out-of-plane motion of particles in a plate can more easily be activated). Generally speaking, both the S 0 and A0 modes are sensitive to structural damage, and both can be used for identifying damage, though the S0 mode exhibits higher sensitivity to damage in the structural thickness and delamination in particular [30, 123], whereas the A0 mode outperforms the S0 mode with higher sensitivity to surface damage such as surface cracks [17, 124, 125], corrosion [107], or surface crack growth [126]. For the same damage, the S0 mode may provide a stronger reflection than the A0 mode [124], implying that if the S0 mode is selected for damage identification, the sensor should preferably be located in such a position that the reflection rather than the transmission signal is captured for identifying damage. In addition, exploration of higher-order wave modes has indicated that higher-order modes such as the S1 mode can be more suitable for finding minute structural damage [127], although it is difficult to activate and interpret higherorder wave modes in practice. Besides, the SH 0 mode has the same sensitivity level as the S0 mode [101]. 3.3.1.2 Implementation of Mode Selection Preferences for utilisation of different Lamb modes have mandated wave mode selection (or called wave mode tuning) techniques. Activation of a pure and desired Lamb mode can easily be realised using an ultrasonic probe coupled with

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a perspex wedge (Section 3.2.1), but it becomes awkward when using a PZT wafer/element. A PZT wafer affixed to a host structure generates both symmetric and anti-symmetric modes simultaneously, which superimpose and influence each other. As a result, interpretation of PZT-generated wave signals has been a troublesome task. At present, most mode selection approaches are developed based on the rationale that a desired wave mode can be enhanced while other undesired modes can be cancelled or minimised in a resultant signal, after mutual interaction of various Lamb wave modes generated by a series of appropriately placed PZT wafers. This mode selection technique is often termed a ‘multi-sensor mode tuning technique’. A mode selection technique of using one pair of PZT wafers controlled by a circuit is shown schematically in Figure 3.5. Two PZT wafers (6.9 mm in diameter and 0.5 mm in thickness) are symmetrically mounted on the upper and lower surfaces of a plate, sharing the same planar coordinates. (i) When dual wafers are energised in-phase (Terminals B, Figure 3.5, are simultaneously activated in both switches), symmetric electric fields will be applied on both wafers, to activate the S0 mode with the dominant signal energy, and the weak A0 mode. (ii) When dual wafers are energised out-of-phase (Terminals C are simultaneously activated in both switches), anti-symmetric electric fields will be applied on both wafers, to activate the A0 mode accounting for the majority of signal energy. (iii) When either of the two wafers is energised, both the S0 and A0 modes will be activated simultaneously. Accordingly, a desired Lamb wave mode can be selectively activated via one of the above three approaches. This mode selection technique has been applied to activating pure Lamb wave modes in a quasi-isotropic composite laminate [128] and an aluminium plate [129].

Amplified excitation signal

Fig. 3.5. A control circuit for selective activation of symmetric and anti-symmetric Lamb modes [128]

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Likewise, by exploiting the mutual interaction between two wave modes generated by a pair of PZT elements bonded a certain distance apart on the same side of a plate, a mode tuning approach has been developed to activate the A0 mode dominantly [107]. In this approach, a theoretical relationship between the distance of the two PZT elements (termed inter-element distance in what follows) and the induced Lamb wave (described by the normal and tangential displacement) was established, in Figure 3.6. With in-phase excitation applied on both PZT elements, the inter-element distance of 17 mm (twice the wavelength of the generated A0 mode at 180 kHz) gives the maximum normal displacement of the A0 mode but the minimum displacement of the S 0 mode, and the latter is negligible because of its small magnitude. This approach offers a practical way to produce a desired Lamb wave mode along the projection of connection between two PZT elements on the same side of a plate, via the superposition of waves generated by them with an appropriately selected distance. Tangential displacement [nm]

Normal displacement [nm]

1.0

A0 0.8 0.6 0.4

S0

0.2 0.0

10

30

20

Inter-element distance [mm]

a

40

1.0 0.8 0.6

S0

0.4

A0 0.2 0.0

10

30

20

40

Inter-element distance [mm]

b

Fig. 3.6. a. Normal; and b. tangential displacement of the S 0 and A0 modes activated by two PZT elements on the same side of a plate versus inter-element distance [107]

The ‘piezoelectric wafer active sensors’ (PWASs) is an array of square PZT wafers allocated in a straight line, surface-mounted on a host structure or inserted between layers of composite laminates, to realise mode tuning [32, 66, 130]. From a theoretical model developed to characterise the Lamb waves activated by PWASs, it has been observed that a particular wave mode can be activated by PWASs to dominate the signal energy, when the side length of the square PZT element in PWASs equals an odd multiple of one-half the wavelength ( λwave 2 ) of such a wave mode (provided that the inter-element distance of PWASs remains constant). For validation, the PWAS-based tuning approach was used to activate desired Lamb wave mode and detect cracking adjacent to rivet heads in an aircraft panel [32, 131], Figure 3.7. It was found that the PWASs (7 mm × 7 mm × 0.2 mm for each wafer in the array) could activate the S 0 and A0 modes of different energy intensities at different excitation frequencies, illustrated in Figure 3.8.

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Therefore, it is possible to select a specific Lamb mode by either changing the size of PZT wafers in PWAS array or adjusting the excitation frequency.

Fig. 3.7. PWASs mounted on an aircraft panel (7 mm × 7 mm × 0.2 mm for each PZT wafer) with an electric-discharge-machined crack [131]

Normalised strain

1.0

0.5

0.0 0

200

400

600

800

1000

Excitation frequency [kHz] Fig. 3.8. Lamb wave responses (normalised strain) in a 1.6-mm aluminium plate under excitation of PWAS array at different excitation frequencies ( S0 : continuous line; A0 : dotted line) [32, 130, 131]

Further to the above study, the concept of a ‘sweet spot’ has been established [32, 132], referring to the central frequency of the excitation signal, at which the maximum wave peak magnitude ratio of the S 0 to A0 modes is reached, so as to minimise the inherent interference between the two wave modes and thus benefit signal interpretation. It is noteworthy that such a PWAS-based tuning technique must be customised for plates of different thicknesses, since plate thickness influences the dispersive properties of wave modes, as does the size of PWASs. Figure 3.9 illustrates the peak energy shift of the S0 and A0 modes due to

Activating and Receiving Lamb Waves

69

different plate thicknesses. Other somewhat more specific mode tuning approaches include one based on a single wave actuator made of a thin PZT ceramic layer and inserted between two composite layers with different coefficients of thermal expansion. Under different thermal expansion forces, a bending moment is generated to enhance the A0 mode [133]. 10

10

A0 S0 Amplitude [mV]

Amplitude [mV]

S0 A0

5

0

A1 5

0 0

400

200

600

0

400

200

Excitation frequency [kHz]

Excitation frequency [kHz]

a

b

600

Fig. 3.9. Lamb wave responses in aluminium plates of different thicknesses under excitation of PWAS array at different excitation frequencies: a. 1.07 mm; and b. 3.15 mm (both from experiment) [130]

It is worth emphasising that all the aforementioned mode tuning approaches can more or less enhance a specific Lamb mode at a given frequency and meanwhile suppress the others modes, but they cannot cancel a wave mode in a signal completely. 3.3.2 Optimal Design of Waveform

Upon selecting a Lamb mode as the diagnostic wave, the bandwidth, cycle number, frequency and magnitude of this mode are some very important factors that can enhance or impair the capability of damage identification to a certain extent. By examining various Lamb modes at different frequencies in plates [134, 135], it has been concluded that a narrow bandwidth signal with a certain number of cycles can greatly prevent wave dispersion. For that reason, windowed tonebursts rather than a single pulse are used much more often for activating diagnostic wave signals in practice, although a pulse signal may offer higher and more concentrated incident energy. Window techniques are used to narrow the bandwidth of a selected Lamb mode. In particular, the Hanning function, h(n) , is the most widely adopted window function, defined as h( n) =

1 n [1 − cos(2π )] 2 N −1

( n = 1, 2, A, N ),

(3.1)

70

Identification of Damage Using Lamb Waves

where h(n) is discretised using N sampling points. Applying a five-cycle Hanning window on a Lamb wave signal with a waveform of continuous sinusoid tonebursts and at a central frequency of 0.5 MHz, the modulated signal and its energy spectrum obtained by Fourier transform (to be detailed in Chapter 5) are displayed in Figure 3.10, where the energy of the modulated wave signal is observed to be concentrated within a very narrow frequency range (centralised at 0.5 MHz), reducing wave dispersion considerably. 3.0

Signal power

Normalised amplitude

1.0

0

-1.0 0

5

10

15

20

2.0

1.0

0 0.0

Time [ s]

a

0.5

1.0

1.5

2.0

2.5

Frequency [MHz]

b

Fig. 3.10. Five-cycle Hanning window-modulated sinusoid tonebursts in: a. time domain; and b. frequency domain after Fourier transform

For Lamb wave signals, the relationships between (i) the excitation frequency bandwidth [ f min , f max ], (ii) the toneburst cycle number n , and (iii) the central excitation frequency f 0 can be formulated by [134] f min = f 0 ⋅ (1 − k / n) ,

(3.2a)

f max = f 0 ⋅ (1 + k / n) ,

(3.2b)

where k is a constant depending on the bandwidth. Equation 3.2 hints that, as the cycle number of tonebursts increases, the wave bandwidth is reduced, the signal energy is more concentrated near the central excitation frequency, the peak amplitude increases, and accordingly wave dispersion is minimised [132]. However, considering the fact that the received signal is the accumulation of input waves, scattered waves from the damage and the boundary, and others associated with wave dispersion, a large cycle number may result in a pronounced overlap among the different wave components. A compromise between the cycle number of the diagnostic wave signal and its duration must therefore be considered case by case. On the other hand, the most suitable cycle number and frequency of a diagnostic Lamb wave signal can be determined in terms of the minimum resolvable distance (MRD), which is defined as [114, 136]

Activating and Receiving Lamb Waves

MRD =

v0 1 1 − [l ⋅ ( ) + Tinitial ] , d vmin vmax min

71

(3.3)

where l and d are the wave propagation distance and plate thickness; v0 , vmin and vmax are the group velocity at the central frequency of the input wave-packet, and the minimum and maximum velocities of the wave-packet to travel the distance of l , respectively. Tinitial is the initial time duration of the wave-packet. It has been found that the lower a MRD value, the better the resolution, and the more suitable the current frequency and cycle number for damage identification. S0 and A0 have been found to possess very low MRD values and accordingly are often selected for damage identification. As for excitation frequency, since the wavelength of a wave mode is inversely proportional to frequency, a high frequency wave mode (i.e., small wavelength) is always preferred so as to have the capacity to detect small sized damage, since the wavelength of the wave must be less than one-half the size of damage, as addressed in Chapter 1. However, in the high frequency range, Lamb waves may exhibit more dispersive properties. A balance between the above two considerations must be met in practice. Power-spectral-density (PSD), which is the energy distribution of a wave in the frequency domain, is a good indicator in achieving such a balance [137]. The most suitable frequency can be ascertained by calculating the PSD of a series of Lamb wave signals among a range of candidate frequencies and finding the one with the maximum PSD value, since a higher value of PSD is a consequence of higher energy dedicated to the excitation frequency in diagnostic signals and therefore more accurate extraction of signal signatures [138]. With regard to the magnitude of the diagnostic signal, an increase in the excitation voltage proportionately increases the magnitude of the diagnostic Lamb wave signal and response signal. Usually, activation of a PZT element at 5-10 V can produce a response signal of 10-25 mV, with accompanying noise at the level of 1-5 mV [138]. Greater magnitude of the signal can increase the SNR, leading to an explicit response signal with less noise, though at the cost of higher energy consumption. However, excessive voltage can depolarise PZT elements. One should bear in mind that the maximum working electrical loading for a PZT element, without its being depolarised, is about 250-300 V/mm in the element thickness [139]. In fact, the electrical loading applied in practice to a PZT element is normally much lower than such a limit, accounting for the linear relationship between the electrical loading and mechanical response of the PZT element.

72

Identification of Damage Using Lamb Waves

3.4 Mechanistic Models of Piezoelectric Transducers 3.4.1 Various Models

There is a crucial difference in activating/sensing Lamb waves for SHM and nondestructive evaluation (NDE). Transducers such as piezoelectric elements for SHM are typically mounted permanently on structures, whereas movable transducers such as ultrasonic probes are widely employed in NDE applications. As explained in Section 3.2, a diagnostic Lamb wave signal can be activated and received very efficiently with a PZT element. The mechanics of activation and acquisition of Lamb waves using PZT elements has been a subject of intensive scrutiny [24, 30, 32, 66, 123, 132, 140-153] and is well reviewed elsewhere [143], addressing the coupling effects of PZT elements with host structures in the manner of surface-bonding or embedment. Most analytical approaches were developed using either two/three-dimensional elasticity theories or mechanistic theories. The model established using twodimensional elasticity theory by Viktorov [154] is one of the pioneering studies in analysing the activation of Lamb waves in an isotropic plate. In modelling coupling mechanisms between a PZT actuator and a host structure, different assumptions are applied. In accordance with the characteristics of particle motion, it is presumed that a PZT actuator, surface-bonded on a host structure, ‘taps’ the structural surface, i.e., imposing uniform normal traction over the contact area, to activate mainly anti-symmetric modes, such as the A0 mode; or ‘pinches’ the host structure, i.e., causing shear traction at the edge of the actuator, to activate mainly symmetric Lamb modes including the S0 mode [38, 131]. Ditri and Rose [155] mixed a plane-strain model with a normal mode expansion technique to describe PZT-generated Lamb waves in composite laminates. Shah et al. [156] developed a quasi-three-dimensional model for a piezoelectric layer inserted in a composite laminate containing delamination. Performed twodimensionally but allowing a degree of freedom in the third direction, this model can describe the responses of the embedded piezoelectric layer. Wilcox [157] presented a three-dimensional elasticity model describing harmonic Lamb waves generated by generic surface point sources in isotropic plates. With the same theoretical basis, the characteristics of Lamb waves in composites, activated and received by surface-mounted PZT actuators and sensors, respectively, were investigated by Wang and Yuan [123]. Using a local interaction simulation approach, Lee et al. [104] concluded that a coupling layer can distort Lamb waves activated by a PZT actuator because of the low impedance at the interface and low propagation speed of waves within the coupling layer. Karp [158] produced analytical solutions to symmetric Lamb waves under different non-uniform excitation conditions. The bi-orthogonality relation was employed in deriving the relative magnitude of each mode at given excitation, revealing that far-field responses are largely indifferent to whether the excitation is based on displacement or stress. In an analytical model developed by Giurgiutiu [159], shear forces were assumed to distribute along the edges of surface-bonded PZT transducers to produce harmonic Lamb waves in an isotropic plate. Moulin et al. [160] developed

Activating and Receiving Lamb Waves

73

a coupled finite-element-normal-mode expansion approach to deal with multiple transducers either surface-bonded or embedded in a composite laminate. The influences of the PZT transducer’s dimension, position and excitation delay on the propagation of Lamb waves were evaluated. In parallel with work based on elasticity theory, some analytical models were developed using the Mindlin theory by considering the coupling between a PZT element and a host structure [65, 142, 144, 161, 162]. Lin and Yuan [144] modelled an aluminium plate with one pair of PZT wafers symmetric with regard to the neutral plane of the plate. The Mindlin theory incorporates transverse shear and rotary inertia effects, whereby the models developed are able to simulate propagation of the A0 mode by applying out-of-phase bending moments along the edges of two wafers. Based on the same theory, Rose and Wang [142] derived Lamb wave responses activated by a point moment, point vertical force and various doublet combinations, respectively. In the study, Lamb wave displacement fields activated by PZT actuators of circular and narrow rectangular shapes were also obtained. Veidt et al. [65] used a hybrid theoretical-experimental approach for solving excitation fields generated by surface-bonded rectangular or circular actuators in terms of the Mindlin theory. One concern about using the Mindlin plate theory to model a Lamb wave actuator is that it can describe only the lowestorder anti-symmetric Lamb mode ( A0 ), and therefore the effectiveness of the model is guaranteed when the excitation frequency-plate thickness product is sufficiently low that higher-order anti-symmetric modes are not excited. 3.4.2 Influence of Transducer Shape

The shape of a PZT transducer plays an important role in activating and receiving Lamb waves [7, 24, 132, 143, 146, 149, 163-165]. Generally speaking, a rectangular PZT actuator produces Lamb waves with energy dominant in the direction perpendicular to its long length, showing strong directionality of wave generation. In contrast, a circular PZT actuator generates a uniform and omnidirectional Lamb wave field. A general review of this issue was published by Chee et al. [146]. In particular, the efficiency of wave activation using flat PZT wafers of rectangular, triangular, circular and elliptic shape in a surface-attached or an embedded manner was elaborated by Sonti et al. [164]. In terms of equivalent force and wavenumber spectra in a polar coordinate system, this study concluded: (i) a PZT actuator coupled with a host structure generates line moments along actuator edges regardless of its shape, which are generally constant along the circumference, exception in the case of an pie-shaped PZT actuator (i.e., a sector cut from a circle or an ellipse actuator); (ii) transverse point forces exist at the corners of a non-circular actuator if the corner is not a right angle or the aspect ratio of the actuator is not uniform; (iii) in addition to line moments, an actuator with curved edges generates a transverse line force along the edge; (iv) if the curvature of the edge varies with the polar angle, as in an elliptic actuator, line moments and line forces vary with angle; and

74

Identification of Damage Using Lamb Waves

(v) the wavenumber spectra of shaped PZT actuators are dominated by line moments except at low wavenumbers where the effect of the point and line forces becomes pronounced. Santoni et al. [130] experimentally and theoretically compared the capacity of PZT wafers of different shapes in activating Lamb waves in an aluminium alloy plate, including square, rectangular and round shape in a sweep frequency range from 10 kHz-700 kHz. The study highlighted that the energy distribution of the S0 and A0 modes is dependent on the shape of the PZT wafer. When activated by a square wafer (7 mm × 7 mm × 0.2 mm), the first maximum magnitude of the A0 mode occurs at around 60 kHz, at which the S0 mode is very weak, Figure 3.11(a); the S0 mode becomes dominant at around 210 kHz, at which point the A0 becomes zero almost in magnitude. On the other hand, both peak frequencies shift significantly when a rectangular wafer (25 mm × 5 mm × 0.15 mm) is used, Figure 3.11(b). 10

3

Amplitude [mV]

Amplitude [mV]

S0 S0 A0

5

0

1.5

A0

0 0

400

200

Excitation frequency [kHz]

a

600

0

125

250

Excitation frequency [kHz]

b

Fig. 3.11. Lamb waves captured experimentally in an aluminium plate (2024-T3, 1.07 mm in thickness) activated by a. square (7 mm × 7 mm × 0.2 mm); and b. rectangular (25 mm × 5 mm × 0.15 mm) PZT wafers [130]

In contrast to most analytical studies which have focused on activation of Lamb waves in infinite isotropic plates, Raghavan and Cesnik [143] presented an analytical model based on the three-dimensional elasticity theory, to obtain Lamb wave fields in finite isotropic plates activated by surface-bonded PZT actuators in arbitrary shapes. The PZT actuator produces in-plane traction of uniform magnitude along its perimeter, in the direction normal to the edge. The model was also used to deduce the optimal dimensions of the PZT actuator and sensor in circular and rectangular shape, in terms of the relationship between sensor response magnitude and excitation central frequency. For circular actuators, the magnitude of generated Lamb wave signals is an oscillating function with regard to the radius of actuator, Figure 3.12, suggesting that an increase in size of the actuator does not always enhance the wave signal. However, for a rectangular actuator (measuring 2a1 × 2a2 ), Figure 3.13, in order to maximise the harmonic response of the sensor

Activating and Receiving Lamb Waves

75

as shown in the figure, a2 should be as large as possible. For a1 , any of the lengths given by following relation are equally optimal values [143]: 2a1 =

1 1 vwave ⋅ (n + ) = λwave ⋅ (n + ) 2 2 f

( n = 0, 1, 2, A ),

(3.4)

where vwave , f and λwave are the velocity, frequency and wavelength of the desired Lamb wave, respectively. On the other hand, when a rectangular PZT element used as a sensor, the peak magnitudes of the A0 and S 0 modes increase with a decrease in PZT sensor size ( 2a1 × 2a2 ).

Normalised sensor response

1.00

0.75

0.50

0.25

0.0 0.0

0.5

1.0

1.5

2.0

2.5

Actuator radius (×10 mm)

Fig. 3.12. Amplitude variation of response ( S0 mode at 100 kHz) in a 1 mm-thick aluminium plate under excitation using surface-bonded PZT actuator of different radii

2a2

PZT actuator 2a1

PZT sensor

Fig. 3.13. Lamb wave generation using a rectangular PZT actuator

76

Identification of Damage Using Lamb Waves

The above discussion of the influence of the geometry of piezoelectric transducers on propagation of Lamb waves is relevant for (i) optimal activation and acquisition of diagnostic Lamb wave signals, (ii) optimal positions between sensors and actuators, (iii) directing diagnostic waves in a desired direction, and (iv) selection of a specific wave mode.

3.5 Case Study: Activating and Receiving Lamb Waves (Both the S0 and A0 Modes) in Delaminated Composite Laminates with Surface-bonded PZT Wafers In this section, an analytical model is described for studying the activation and acquisition of Lamb waves using surface-bonded piezoelectric wafers, including the S0 and A0 modes, in composite laminates. With the model, the interaction of activated Lamb waves with delamination in a fibre-reinforced composite laminate is simulated using finite element method (FEM) modelling approaches. 3.5.1 Modelling Coupled PZT Actuator

Two scenarios of activation of Lamb waves are considered, using surfacemounted single and dual PZT wafers, respectively. 3.5.1.1 Single Actuator The electro-mechanical constitutive equation of a piezoelectric wafer in free status, with regard to direct (applied mechanical stress inducing an electric charge) and converse (applied electric field producing mechanical strain) piezoelectric effects, is defined by [144]

⎧ Q1 ⎫ ⎡ p1 ⎪ ⎪ ⎢0 ⎪ Q2 ⎪ ⎢ ⎪ Q3 ⎪ ⎢ 0 ⎪ ⎪ ⎢ ⎪ε11 ⎪ ⎢ 0 ⎪ ⎪ ⎢ ⎨ε 22 ⎬ = 0 ⎪ε ⎪ ⎢ 0 ⎪ 33 ⎪ ⎢ ⎪ε 23 ⎪ ⎢ 0 ⎪ ⎪ ⎢ ⎪ε13 ⎪ ⎢d15 ⎪⎩ε12 ⎪⎭ ⎢⎣ 0

0 p1 0 0 0 0 d15 0 0

0 0 0 0 0 0 0 0 p3 d 31 d31 d 33 d 31 c11 c12 c13 d 31 c12 c11 c13 d33 c13 c13 c33 0 0 0 0 0 0 0 0 0 0 0 0

0 d15 0 0 0 0 c55 0 0

d15 0 0 0 0 0 0 c55 0

0 ⎤ ⎧ Κ1 ⎫ 0 ⎥⎥ ⎪⎪ Κ 2 ⎪⎪ 0 ⎥ ⎪Κ3 ⎪ ⎥ ⎪ ⎪ 0 ⎥ ⎪σ 11 ⎪ ⎪ ⎪ 0 ⎥ ⋅ ⎨σ 22 ⎬ , ⎥ ⎪ ⎪ 0 ⎥ σ 33 ⎪ ⎪ 0 ⎥ ⎪σ 23 ⎪ ⎥ ⎪ ⎪ 0 ⎥ ⎪σ 13 ⎪ ⎥ c66 ⎦ ⎪⎩σ 12 ⎪⎭

(3.5)

where orthogonal components Qi and Κ i ( i = 1, 2, 3 ) are the electric displacement (charge/PZT area) and electric field (voltage/PZT thickness), respectively. σ ij and ε ij are stresses and strains of the PZT wafer ( i, j = 1, 2, 3 ). d , p and c with subscripts denote the piezoelectric strain constants, dielectric

Activating and Receiving Lamb Waves

77

permittivity and compliance constants, respectively. Provided the polarising direction is perpendicular to the wafer surface, Equation 3.5, in the absence of inplane electric fields (i.e., Κ 1 = Κ 2 = 0 ), can be simplified in the wafer’s polar coordinate system ( r − θ − Z ), referring to Figure 3.14(a), as Q3 = p3Κ 3 + d 31 (σ r + σ θ ) ,

(3.6a)

σr =

E PZT [(ε r + ν PZT ε θ ) − (1 + ν PZT ) ⋅ d 31Κ 3 ] , 1 − ν 2 PZT

(3.6b)

σθ =

E PZT [(ε θ + ν PZT ε r ) − (1 + ν PZT ) ⋅ d 31Κ 3 ] , 1 − ν 2 PZT

(3.6c)

where σ r , ε r , σ θ , and ε θ are the radial stress, strain, tangential stress and strain, respectively. EPZT and ν PZT stand for the Young’s modulus and Poisson’s ratio of the PZT wafer, respectively. For a thin PZT wafer ( R in radius and hPZT in thickness), the in-plane radial strain, ε r − PZT and in-plane tangential strain ε θ − PZT , when an external voltage V is applied, are

ε r − PZT =$ ε θ − PZT = d 31Κ 3 =

d 31 ⋅V = Π . hPZT

(3.7)

Consider that the PZT wafer is surface-bonded on a panel of quasi-isotropic or isotropic properties, Figure 3.14(b). Without losing generality, it is assumed that the panel is a quasi-isotropic composite laminate in the following discussion ( hLMT in thickness). For this coupled system, introducing the strain continuity at the bonding interface ( ε ri − PZT = ε ri − LMT = ε ri and ε θi − PZT = ε θi − LMT = εθi , where superscript i denotes the interface; variables are distinguished by subscripts PZT for the PZT wafer and LMT for the laminate), Equation 3.6b can be rewritten as

σ ri − PZT =

EPZT [(ε ri +ν PZT ε θi ) − (1 +ν PZT ) ⋅ Π ] . 1 −ν 2 PZT

(3.8)

Since both the wafer and laminate are thin, the classic lamination theory is applicable and strain distribution can be assumed to be linear in the thickness direction, leading to

σ r − LMT =

σ r −PZT =

σ ri − LMT hneu

⋅ (hneu + z )

( − hLMT ≤ z ≤ 0 ),

E PZT 1 − ν LMT E PZT σ ri − LMT ⋅ ⋅ ⋅ (hneu + z ) − ⋅Π hneu 1 − ν PZT E LMT 1 − ν PZT

(3.9a)

( 0 ≤ z ≤ hPZT ), (3.9b)

78

Identification of Damage Using Lamb Waves

as depicted in Figure 3.14(c). In the above equation, hneu is the distance between the abscissa plane and neutral plane of the PZT-coupled laminate. Based on the fact that a PZT actuator operates by ‘pinching’ the structure, i.e., causing shear traction at the edge of the actuator, which is equivalent to uniform bending moments applied along the actuator edge (Section 3.4.1), the equilibrium of moments regarding the neutral plane and forces gives

Laminate

Z

r 3

hPZT

V

θ

R

PZT wafer

2

1

hLMT a

Z Interface of coupled system

PZT polarisation

R hPZT

X hneu

hLMT

b Fig. 3.14. Model for a PZT-wafer-coupled laminate system: a. a PZT wafer in its polar coordinate system; b. single PZT activation; c. stress/strain distribution throughout the thickness for single PZT activation case; dual-PZT activation with d. anti-symmetric; and e. symmetric electrical fields; stress/strain distribution throughout the thickness for f. antisymmetric dual-PZT activation case; and g. symmetric dual-PZT activation case

Activating and Receiving Lamb Waves

79

Z

σ r − PZT

ε r− PZT

σ r − LMT

ε r− LMT

hPZT

hLMT

X hneu

c

Z

Electrical field

PZT motion

+

hPZT

hLMT

-_ PZT polarisation

d Fig. 3.14. (continued)

X

80

Identification of Damage Using Lamb Waves

Z

Electrical field

PZT motion

+

hPZT

hLMT

X

+ PZT polarisation

e

Z

ε r− PZT

ε r− LMT

f Fig. 3.14. (continued)

σ r − PZT

hPZT

σ r − LMT

hLMT

X

Activating and Receiving Lamb Waves

81

Z

ε r− PZT

σ r − PZT

hPZT

σ r − LMT

ε r − LMT

hLMT

X

g Fig. 3.14. (continued) h PZT

0

∫

2π R ⋅ σ r − LMT ⋅ z ⋅ dz +

− h LMT

r − PZT

⋅ z ⋅ dz = 0 ,

(3.10a)

0

h PZT

0

∫

∫ 2π R ⋅ σ

2π R ⋅ σ r − LMT ⋅ dz +

− h LMT

∫ 2π R ⋅σ

r − PZT

⋅ dz = 0 ,

(3.10b)

0

and yields the stresses of the coupled system at the interface

~ E PZT ~ ~ E PZT D ⋅Π − ⋅Π = E ⋅Π , 1 − ν PZT E LMT ~ = D⋅Π ,

σ ri − PZT = A ⋅

(3.11a)

σ ri − LMT

(3.11b)

where ~ 1 − ν LMT , A= 1 − ν PZT ~ 3 2 3 + 3E LMT hLMT ~ E E h (4 E LMT hLMT hPZT + A E PZT hPZT ) , D = LMT PZT PZT ~ ~ B +C

82

Identification of Damage Using Lamb Waves

~ E E PZT ~ ~ E = ( A ⋅ PZT D − ), E LMT 1 − ν PZT ~ 2 2 ), B = 2 E LMT E PZT hLMT hPZT ⋅ (1 −ν LMT ) ⋅ (2hLMT + 3hLMT hPZT + 2hPZT 2 4 ~ E 2 h 4 (1 − ν PZT ) 2 + E PZT hPZT (1 − ν LMT ) 2 . C = LMT LMT (1 − ν PZT )

To substitute Equations 3.11 into 3.8, the strain of the PZT wafer at the interface can further be obtained. Since the wafer is small in size ( ε ri ≈ ε θi = ε i ), by integrating the interface strain ( ε ri ), equivalent radial deformation, d r , along its circumference, is R

d r = ∫ ε i dr = R ⋅ 0

~ d 31 E (1 −ν PZT ) + 1] ⋅V . [ hPZT EPZT

(3.12)

Equation 3.12 suggests that the equivalent radial displacement along the circumference of a PZT wafer actuator surface-mounted on a panel of quasiisotropic or isotropic properties is proportional to the applied voltage V with a ~ d E (1 −ν PZT ) scale factor of R ⋅ 31 [ + 1] . Note that under single PZT actuation both hPZT EPZT symmetric and anti-symmetric Lamb modes are activated synchronously. 3.5.1.2 Dual Actuators We now extend the above discussion to the case that a pair of PZT wafers are symmetrically mounted on the upper and lower surfaces of the same laminate. Due to the symmetry, hneu becomes zero in the above derivation and the stress distributes symmetrically with regard to the neutral plane, as [144]

σ r −LMT =

2σ ri − LMT ⋅z hLMT

(0 ≤ z ≤

~ E PZT 2σ ri − LMT E PZT ⋅ ⋅z− ⋅Π 1 − ν PZT E LMT hLMT

σ r − PZT = A ⋅

hLMT ), 2 (

(3.13a)

hLMT h ≤ z ≤ LMT + hPZT ). (3.13b) 2 2

Two types of electrical field can be applied on this PZT wafer pair: antisymmetric or symmetric with regard to the neutral plane, leading to opposite or coincident in-plane oscillation of the PZT wafers, respectively, as elucidated in Figures 3.14 (d) and (e). As a result, the anti-symmetric and symmetric Lamb modes are activated, respectively.

Activating and Receiving Lamb Waves

83

For the anti-symmetric case, Figure 3.14(d), the equilibrium of moment regarding the neutral plane is h LMT

h LMT

2

∫ 2π R ⋅σ

r − LMT

2

+ hPZT

∫ 2π R ⋅σ

⋅z ⋅ dz +

h LMT

0

r − PZT

⋅z ⋅ dz = 0 ,

(3.14)

2

which yields the stress of the wafer at the interface ~

σ ri − PZT = F ⋅ V , where

~ F= 3 (1 − ν PZT ) ⋅ [hLMT

(3.15)

6d 31hLMT E PZT ⋅ (hLMT + hPZT ) , ~ E 2 2 + 2 A ⋅ PZT ⋅ hPZT (3hLMT + 4hPZT + 6hLMT hPZT )] E LMT

as

portrayed in Figure 3.14(f). For the symmetric case, Figure 3.14(e), the equilibrium of shear force is h LMT

h LMT

2

∫ 2π R ⋅σ r − LMT ⋅dz + 0

2

+ h PZT

∫ 2π R ⋅ σ

hLMT

r − PZT

⋅dz = 0 ,

(3.16)

2

which gives the stress of the wafer at the interface ~

σ ri − PZT = G ⋅ V , ~ where G =

1 1 −ν PZT

⋅

(3.17)

d31 ⋅ EPZT , as depicted in Figure 3.14(g). ⎛ ~ EPZT ⎞⎛ hLMT ⎞ ⎜⎜ A ⋅ ⎟⎟⎜ + hPZT ⎟ − 1 ⎠ ⎝ ELMT ⎠⎝ 4

Substituting Equations 3.15 and 3.17 into Equation 3.8 produces the strain of the PZT actuator at the interface ( ε ri ). Since the wafer is small in size ( ε ri ≈ ε θi = ε i ), by integrating the interface strain, equivalent radial deformation, d r , along its circumference, can be obtained as ~ ⎡ F ⋅ (1 −ν PZT ) d 31 ⎤ + d r = ∫ ε dr =R ⋅ ⎢ ⎥ ⋅V EPZT hPZT ⎦⎥ ⎣⎢ 0 for the anti-symmetric mode, R

i

and

(3.18a)

84

Identification of Damage Using Lamb Waves

~ R ⎡G ⋅ (1 −ν PZT ) d31 + d r = ε i dr =R ⋅ ⎢ EPZT hPZT ⎢⎣ 0

∫

⎤ ⎥ ⋅V ⎥⎦ for the symmetric mode.

(3.18b)

In a fashion similar to Equation 3.12, Equation 3.18 determines the proportional scale factors of deformation of a pair of PZT wafers under anti-symmetric and symmetric electrical field excitation, for activating the anti-symmetric and symmetric Lamb modes, respectively. With the above developed models for PZT wafer actuator(s) surface-bonded on a host structure, which relate the radial displacement, d r , along the PZT wafer circumference to the applied voltage V (i.e., the electrical signal of the desired waveform), one can activate (i) the S0 and A0 modes simultaneously in terms of Equation 3.12, (ii) pure A0 mode in terms of Equation 3.18a, and (iii) pure S0 mode in terms of Equation 3.18b. 3.5.2 Modelling Coupled PZT Sensor

Considering planar deformation only, Equation 3.5 for a PZT wafer when used as a sensor ( R in radius and hPZT in thickness) can be simplified in its local polar coordinate system ( r − θ − Z ), in the absence of an external electric field, as [144] Q = d 31 (σ r + σ θ ) =

d 31 E PZT (ε r + ε θ ) . 1 −ν PZT

(3.19)

where Q is the electric displacement (charge/PZT area) defined previously. Under voltage, V , electric charges, Θ , accumulated on both surfaces of the wafer, are equal and can be calculated by, upon applying Gauss’ theorem [144], Θ=

d 31 E PZT 4π (1 −ν PZT )

∫∫ (ε

r

+ εθ ) ⋅ r ⋅ dr ⋅ dθ .

(3.20)

Regarded as a capacitor with a capacitance of C , the PZT wafer induces an output voltage, Votp , under the deformation that it senses Votp =

Θ Θ ⋅ hPZT = , C πξ 3 p0 R 2

(3.21)

where ξ 3 and p0 represent the relative dielectric constant and the dielectric permittivity of a free space, respectively. Combining Equations 3.20 and 3.21 results in

Activating and Receiving Lamb Waves

Votp =

d 31EPZT hPZT 4ξ3 p0 (π R) 2 (1 −ν PZT )

∫∫ (ε

r

+ ε θ ) ⋅ r ⋅ dr ⋅ dθ .

85

(3.22)

Compared with the host plate, the PZT wafer is geometrically small and it therefore has ε r ≈ ε θ ≈ ε cen , where ε cen is the strain at the centre of the wafer. Equation 3.22 then becomes ~ Votp = H ⋅ ε cen ,

(3.23)

d31E PZT hPZT . This indicates that, for a PZT wafer when used as a 4πξ 3ε 0 (1 −ν PZT ) sensor, the output signal in the form of voltage induced by the local deformation as a result of Lamb wave propagation is proportional to the central strain of the ~ wafer with a scale factor of H . With Equation 3.23, Lamb wave signals captured by a PZT wafer sensor can accordingly be defined. ~ where H =

3.5.3 Validation in FEM Simulation

Three Lamb wave activation schemes, defined by Equations 3.12, 3.18a and 3.18b, are now validated in FEM simulation. An electrical field described by fivecycle sinusoidal tonebursts modulated with a Hanning window at a central frequency of 300 kHz is applied to the single and dual-actuator models in accordance with the symmetric and anti-symmetric activation schemes, respectively. The FEM simulation is conducted using the ABAQUS®1/EXPLICIT FEM code. With the modelling techniques specified for Lamb waves introduced in Section 2.4.1, eleven FEM nodes are allocated per wavelength and the step of calculation time is controlled to be less than the ratio of the minimum distance of any two adjoining nodes to the maximum wave velocity, to ensure accurate simulation. The captured Lamb waves in an aluminium plate measuring 500 mm × 500 mm × 1.5 mm using the sensor model defined by Equation 3.23 (100 mm away from the actuator) are displayed in Figure 3.15. In Figure 3.15(a), when single actuator is energised, both the S0 and A0 modes, plus boundary-reflected S0 mode, S0−boundary , are observed successively; whereas in (b) when dual actuators are energised with symmetric electrical fields, only the S0 mode and its reflection from boundary, S0−boundary , are observed; and in (c) when dual actuators are energised with anti-symmetric electrical fields, only the A0 mode is observed. Furthermore, by repeating the above FEM simulation in a sweep frequency ranging from 0.05 MHz to 2.0 MHz, the dispersion curves of various Lamb modes in an eight-layer quasi-isotropic carbon fibre-reinforced epoxy (T650/F584) composite laminates (1.275 mm in thickness) are diagrammed in Figure 3.16. For comparison, the figure also includes the dispersion curves obtained by using an analytical approach already described (effective elastic constant method) and by using experimental measurement. 1

ABAQUS® is a registered trademark of ABAQUS, Inc., in the United States and other countries. http://www.abaqus.com

Identification of Damage Using Lamb Waves

1.0

1.0

S0

Normalised amplitude

S0

S00

0-boundary SS0-boundary

A0

A0

Normalised amplitude

86

0

-1.0 0

S0-boundary S0-boundary

0

-1.0 20

40

60

0

80

20

40

60

80

Time [ s]

Time [ s]

a

b

Normalised amplitude

1.0

A0

A0

0

-1.0 0

20

40

60

80

Time [ s]

c Fig. 3.15. Lamb wave signals excited by a. single PZT actuator; by dual PZT actuators under b. symmetric; and c. anti-symmetric electrical fields (from FEM simulation) [166]

With the validated PZT actuator and sensor models, the interaction of Lamb waves with delamination in the above composite laminate is examined [167]. The delamination is simulated using the modelling approach detailed in Section 2.4.2. Figure 3.17 shows the Lamb wave signals in the laminate without and with delamination captured by the sensor model. In the latter the delamination-induced lowest-order shear horizontal ( SH 0 ) mode can be clearly detected between S 0 and S 0−boundary (Section 2.2.3 for description of SH 0 mode). The observation from the simulation is consistent with the characteristics of Lamb waves introduced in Chapter 2 with regard to the mode conversion upon encountering structural damage. Signals captured experimentally in the laminate with the same configuration as in the FEM simulation [167], Figures 3.17(c) and (d), match well those from the FEM simulation in Figures 3.17(a) and (b), demonstrating the capacity of the developed PZT actuator/sensor models and modelling techniques.

Activating and Receiving Lamb Waves

87

9.0

Group velocity [km/s]

S0

S1

6.0

A1 SH0

3.0

A0

FEM model Effective elastic constant model Experiment

0.0

0

1.0

3.0

2.0

Frequency · plate thickness [MHz · mm]

Fig. 3.16. Dispersion curves of Lamb waves in a quasi-isotropic composite laminate [167] 1.0

Normalised amplitude

Normalised amplitude

1.0

0

-1.0

0

-1.0 5500

4500

6500

4500

Sampling point

a

6500

b 1.0

Normalised amplitude

1.0

Normalised amplitude

5500

Sampling point

0

0

-1.0

-1.0 5500

4500

Sampling point

c

6500

5500

4500

6500

Sampling point

d

Fig. 3.17. Lamb wave signals in a. benchmark laminate from FEM simulation; b. laminate with delamination from FEM simulation; c. benchmark laminate from experiment; and d. laminate with delamination from experiment [106]

88

Identification of Damage Using Lamb Waves

3.6 Summary Lamb waves can be activated and received with various transducers, exemplified by ultrasonic probe (e.g., Hertzian contact probe), EMAT, piezoelectric element/wafer, piezocomposite transducer, LBU, IDT (e.g., PVDF) and fibre-optic sensor (e.g., FBG sensor). In particular, small and light, piezoelectric elements/wafers are most suitable for integration into host structures to serve as built-in Lamb wave actuators and sensors. To activate a diagnostic Lamb wave signal for damage identification, the wave mode, waveform, excitation frequency, bandwidth, cycle number and magnitude need to be appropriately selected so as to reduce the dispersion and attenuation of wave signal, enhance its sensitivity to damage and facilitate subsequent signal processing and interpretation. Both the S 0 and A0 modes can be used for identifying damage, though the S 0 mode exhibits higher sensitivity to damage in the structural thickness (e.g., delamination), whereas A0 outperforms S0 in sensitivity to surface damage (e.g., cracks or corrosion). In addition, the S 0 mode features lower attenuation, a faster propagation speed and less dispersion, but the A0 mode has advantages that include a shorter wavelength (therefore greater sensitivity to damage of small size), larger magnitude and greater ease of activation. To activate a desired wave mode, a number of properly aligned actuators can be used by taking advantage of the mutual interaction of Lamb waves generated by them, although such an approach may not completely cancel one wave mode. A windowed signal helps to narrow the bandwidth of a selected Lamb mode and a large wave cycle reduces wave dispersion but at the cost of increased difficulty in signal processing due to overlap among different wave components. To understand the mechanisms of activation and acquisition of Lamb waves with piezoelectric transducers, a variety of theoretical models has been developed such as those based on the Mindlin plate theory. In particular, a modelling technique for the PZT actuator and sensor surface-bonded on a composite laminate was introduced and validated by simulating Lamb wave propagation in quasi-isotropic composite laminates containing delamination.

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91. Takeda, N., Okabe, Y., Kuwahara, J., Kojima, S., Ogisu, T.: Development of smart composite structures with small-diameter fiber Bragg grating sensors for damage detection: quantitative evaluation of delamination length in CFRP laminates using Lamb wave sensing. Composites Science and Technology 65, 2575–2587 (2005) 92. Betz, D.C., Thursby, G., Culshaw, B., Staszewski, W.J.: Structural damage location with fiber Bragg grating rosettes and Lamb waves. Structural Health Monitoring: An International Journal 6(4), 299–308 (2007) 93. Amano, M., Okabe, Y., Takeda, N., Ozaki, T.: Structural health monitoring of an advanced grid structure with embedded fiber Bragg grating sensors. Structural Health Monitoring: An International Journal 6(4), 309–324 (2007) 94. Jang, T.S., Lee, S.S., Kim, Y.G.: Surface-bonded fiber optic Sagnac sensors for ultrasound detection. Ultrasonics 42, 837–841 (2004) 95. Kwun, H., Light, G.M., Kim, S.-Y., Spinks, R.L.: Magnetostrictive sensor for active health monitoring in structures. In: Proceedings of the SPIE, vol. 4702, pp. 282–288 (2002) 96. Varadan, V.K.: Nanotechnology, MEMS and NEMS and their applications to smart systems and devices. In: Proceedings of the SPIE, vol. 5062, pp. 20–43 (2003) 97. Neumann, J.J., Greve, D.W., Oppenheim, I.J.: Comparison of piezoresistive and capacitive ultrasonic transducers. In: Proceedings of the SPIE, vol. 5391, pp. 230– 238 (2004) 98. Maslov, K., Kundu, T.: Selection of Lamb modes for detecting internal defects in composite laminates. Ultrasonics 35, 141–150 (1997) 99. Kundu, T., Maslov, K.: Material interface inspection by Lamb waves. International Journal of Solids and Structures 34, 3885–3901 (1996) 100. Kundu, T., Potel, C., de Belleval, J.F.: Importance of the near Lamb mode imaging of multilayered composite plates. Ultrasonics 39(3), 283–290 (2001) 101. Wilcox, P., Lowe, M., Cawley, P.: Omnidirectional guided wave inspection of large metallic plate structures using an EMAT array. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 52(4), 653–665 (2005) 102. Hu, N., Shimomukai, T., Yan, C., Fukunaga, H.: Identification of delamination position in cross-ply laminated composite beams using S0 Lamb mode. Composites Science and Technology 68(6), 1548–1554 (2008) 103. Betz, D.C., Staszewski, W.J., Thursby, G., Culshaw, B.: Structural damage identification using multifunctional Bragg grating sensors: II. damage detection results and analysis. Smart Materials and Structures 15, 1313–1322 (2006) 104. Lee, B.C., Staszewski, W.J.: Sensor location studies for damage detection with Lamb waves. Smart Materials and Structures 16, 399–408 (2007) 105. Michaels, J.E.: Detection, localization and characterization of damage in plates with an in situ array of spatially distributed ultrasonic sensors. Smart Materials and Structures (in press) 106. Su, Z., Ye, L.: Lamb wave propagation-based damage identification for quasiisotropic CF/EP composite laminates using artificial neural algorithm, part I: methodology and database development. Journal of Intelligent Material Systems and Structures 16, 97–111 (2005) 107. Grondel, S., Paget, C., Delebarre, C., Assaad, J., Levin, K.: Design of optimal configuration for generating A0 Lamb mode in a composite plate using piezoceramic transducers. Journal of the Acoustical Society of America 112(1), 84–90 (2002)

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108. Diamanti, K., Soutis, C., Hodgkinson, J.M.: Piezoelectric transducer arrangement for the inspection of large composite structures. Composites: Part A 38, 1121–1130 (2007) 109. Diaz Valdes, S.H., Soutis, C.: Real-time nondestructive evaluation of fiber composite laminates using low-frequency Lamb waves. Journal of the Acoustical Society of America 111(5), 2026–2033 (2002) 110. Ip, K.-H., Mai, Y.-W.: Delamination detection in smart composite beams using Lamb waves. Smart Materials and Structures 13, 544–551 (2004) 111. Park, S., Yun, C.-B., Roh, Y., Lee, J.-J.: PZT-based active damage detection techniques for steel bridge components. Smart Materials and Structures 15, 957–966 (2006) 112. Diamanti, K., Hodgkinson, J.M., Soutis, C.: Damage detection of composite laminates using PZT generated Lamb waves. In: Balageas, D. (ed.) Proceedings of the 1st European Workshop on Structural Health Monitoring, Paris, France, July 10-12, 2002, pp. 398–405. DEStech Publications, Inc (2002) 113. Petculescu, G., Krishnaswamy, S., Achenbach, J.D.: Group delay measurements using modally selective Lamb wave transducers for detection and sizing of delaminations in composites. Smart Materials and Structures (in press) 114. Kudela, P., Ostachowicz, W., Zak, A.: Damage detection in composite plates with embedded PZT transducers. Mechanical Systems and Signal Processing 22(6), 1327– 1335 (2008) 115. Park, S., Yun, C.-B., Roh, Y.: Damage diagnostics on a welded zone of a steel truss member using an active sensing network system. NDT&E International 40, 71–76 (2007) 116. Fromme, P.: Monitoring of plate structures using guided ultrasonic waves. In: Thompson, D.O., Chimenti, D.E. (eds.) Review of Progress in Quantitative Nondestructive Evaluation, vol. 27, pp. 78–85. American Institute of Physics, New York (2008) 117. Konstantinidis, G., Drinkwater, B.W., Wilcox, P.D.: The temperature stability of guided wave structural health monitoring systems. Smart Materials and Structures 15, 967–976 (2006) 118. Konstantinidis, G., Drinkwater, B.W., Wilcox, P.D.: The long term stability of guided waves structural health monitoring systems. In: Proceedings of the AIP Conference on Quantitative Nondestructive Evaluation, March 6, 2006, vol. 820, pp. 1702–1709 (2006) 119. Osmont, D., Barnoncel, D., Devillers, D., Dupont, M.: Health monitoring of sandwich plates based on the analysis of the interaction of Lamb waves with damages. In: Balageas, D. (ed.) Proceedings of the 1st European Workshop on Structural Health Monitoring, Paris, France, July 10-12, 2002, pp. 336–343. DEStech Publications, Inc (2002) 120. Malinowski, P., Wandowski, T., Trendafilova, I., Ostachowicz, W.: A phased arraybased method for damage detection and localization in thin plates. Structural Health Monitoring: An International Journal 8, 5–15 (2009) 121. Diaz Valdes, S.H., Soutis, C.: A structural health monitoring system for laminated composites. In: Chang, F.-K. (ed.) Proceedings of the 3rd International Workshop on Structural Health Monitoring, Stanford, CA, USA, September 12-14, 2001, pp. 1476–1485. CRC Press, Boca Raton (2001)

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122. Kessler, S.S., Spearing, S.M.: In-situ sensor-based damage detection of composite materials for structural health monitoring. In: Proceedings of the 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Denver, CO, USA, April 22-25, 2002, vol. AIAA-2002-1545 (2002) 123. Wang, L., Yuan, F.G.: Group velocity and characteristic wave curves of Lamb waves in composites: modeling and experiments. Composites Science and Technology 67, 1370–1384 (2007) 124. Giurgiutiu, V., Bao, J., Zhao, W.: Piezoelectric wafer active sensor embedded ultrasonics in Beams and plates. Experimental Mechanics 43(4), 428–449 (2003) 125. Giurgiutiu, V., Zagrai, A., Bao, J.: Damage identification in aging aircraft structures with piezoelectric wafer active sensors. Journal of Intelligent Material Systems and Structures 15, 673–687 (2004) 126. Qing, X.P., Chan, H.-L., Beard, S.J., Kumar, A.: An active diagnostic system for structural health monitoring of rocket engines. Journal of Intelligent Material Systems and Structures 17, 619–628 (2006) 127. Rose, J.L., Pilarski, A., Ditri, J.J.: An approach to guided wave mode selection for inspection of laminated plate. Journal of Reinforced Plastics and Composites 12, 536–544 (1993) 128. Su, Z., Ye, L.: Selective generation of Lamb wave modes and their propagation characteristics in defective composite laminates. Proceedings of the Institution of Mechanical Engineers Part L - Journal of Materials: Design and Applications 218, 95–110 (2004) 129. Kim, Y.-H., Kim, D.-H., Han, J.-H., Kim, C.-G.: Damage assessment in layered composites using spectral analysis and Lamb wave. Composites: Part B 38, 800–809 (2007) 130. Santoni, G.B., Yu, L., Xu, B., Giurgiutiu, V.: Lamb wave-mode tuning of piezoelectric wafer active sensors for structural health monitoring. Journal of Vibration and Acoustics 129, 752–762 (2007) 131. Giurgiutiu, V.: Lamb wave generation with piezoelectric wafer active sensors for structural health monitoring. In: Proceedings of the SPIE’s 10th Annual International Symposium on Smart Structures and Materials and 8th Annual International Symposium on NDE for Health Monitoring and Diagnostics, San Diego, CA, USA, March 2-6 (2002), Paper No.: 5056-17 132. Wang, X., Lu, Y., Tang, J.: Damage detection using piezoelectric transducers and the Lamb wave approach: I. system analysis. Smart Materials and Structures (in press) 133. Bechet, A., Berthelot, Y.H., Lynch, C.S.: A stress gradient-enhanced piezoelectric actuator composite (GEPAC) with integrated ultrasonic NDE capability for continuous health monitoring. Journal of Intelligent Material Systems and Structures 16, 85–93 (2005) 134. Wilcox, P.D., Dalton, R.P., Lowe, M.J.S., Cawley, P.: Mode and transducer selection for long range Lamb wave inspection. Key Engineering Materials 167-168, 152–161 (1999) 135. Wilcox, P.D., Dalton, R.P., Lowe, M.J.S., Cawley, P.: Mode selection and transduction for structural monitoring using Lamb wave. In: Chang, F.-K. (ed.) Proceedings of the 2nd International Workshop on Structural Health Monitoring, Stanford, CA, USA, September 8-10, 1999, pp. 703–712. Technomic Publishing Co (1999) 136. Wilcox, P.D., Lowe, M., Cawley, P.: The effect of dispersion on long-range inspection using ultrasonic guided waves. NDT&E International 34, 1–9 (2001)

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137. Ge, M., Zhang, G., Du, R., Xu, Y.: Feature extraction from energy distribution of stamping processes using wavelet transform. Journal of Vibration and Control 8, 1023–1032 (2002) 138. Kessler, S.S., Spearing, S.M., Soutis, C.: Optimization of Lamb wave methods for damage detection in composite materials. In: Chang, F.-K. (ed.) Proceedings of the 3rd International Workshop on Structural Health Monitoring, Stanford, CA, USA, September 12-14, 2001, pp. 870–879. CRC Press (2001) 139. Kessler, S.S., Spearing, S.M., Atalla, M.J.: In-situ damage detection of composites structures using Lamb wave methods. In: Balageas, D. (ed.) Proceedings of the 1st European Workshop on Structural Health Monitoring, Paris, France, July 10-12, 2002, pp. 374–381. DEStech Publications, Inc (2002) 140. Wang, X., Ehlers, C., Neitzel, M.: An analytical investigation of static models of piezoelectric patches attached to beams and plates. Smart Materials and Structures 6, 204–213 (1997) 141. Perel, V.Y., Palazotto, A.N.: Finite element formulation for dynamics of delaminated composite beams with piezoelectric actuators. International Journal of Solids and Structures 39, 4457–4483 (2002) 142. Rose, L.R.F., Wang, C.H.: Mindlin plate theory for damage detection: source solutions. Journal of the Acoustical Society of America 116(1), 154–171 (2004) 143. Raghavan, A., Cesnik, C.E.S.: Finite-dimensional piezoelectric transducer modeling for guided wave based structural health monitoring. Smart Materials and Structures 14, 1448–1461 (2005) 144. Lin, X., Yuan, F.G.: Diagnostic Lamb waves in an integrated piezoelectric sensor/actuator plate: analytical and experimental studies. Smart Materials and Structures 10, 907–913 (2001) 145. Chee, C.Y.K., Tong, L., Steven, G.P.: A mixed model for composite beams with piezoelectric actuators and sensors. Smart Materials and Structures 8, 417–432 (1999) 146. Chee, C.Y.K., Tong, L., Steven, G.P.: A review on the modelling of piezoelectric sensors and actuators incorporated in intelligent structures. Journal of Intelligent Material Systems and Structures 9, 3–19 (1998) 147. Chee, C.Y.K., Tong, L., Steven, G.P.: A mixed model for adaptive composite plates with piezoelectric for anisotropic actuation. Computers and Structures 77, 253–268 (1999) 148. Yan, Y.J., Yam, L.H.: Mechanical interaction issues in piezoelectric composite structures. Composite Structures 59, 61–65 (2003) 149. Fernandes, A., Pouget, J.: Analytical and numerical modelling of laminated composites with piezoelectric elements. Journal of Intelligent Material Systems and Structures 15, 753–761 (2004) 150. Chakraborty, A., Gopalakrishnan, S.: A spectrally formulated finite element for wave propagation analysis in layered composite media. International Journal of Solids and Structures 41, 5155–5183 (2004) 151. Mahapatra, D.R., Gopalakrishnan, S.: A spectral finite element model for analysis of axial-flexural-shear coupled wave propagation in laminated composite beams. Composite Structures 59, 67–88 (2003) 152. Yao, L.Q., Zhang, J.G., Lu, L., Lai, M.O.: Nonlinear extension and bending of piezoelectric laminated plate under large applied field actuation. Smart Materials and Structures 13, 404–414 (2004)

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153. di Scalea, F.L., Matt, H., Bartoli, I.: The response of rectangular piezoelectric sensors to Rayleigh and Lamb ultrasonic waves. Journal of the Acoustical Society of America 121(1), 175–187 (2007) 154. Viktorov, I.A.: Rayleigh and Lamb Waves. Plenum Press, New York (1967) 155. Ditri, J., Rose, J.L.: Excitation of guided waves in generally anisotropic layers using finite sources. Journal of Applied Mechanics 61, 330–338 (1994) 156. Shah, D.K., Chan, W.S., Joshi, S.P.: Delamination detection and suppression in a composite laminate using piezoceramic layers. Smart Materials and Structures 3, 293–301 (1994) 157. Wilcox, P.: Modeling the excitation of Lamb and SH waves by point and line sources. In: Thompson, D.O., Chimenti, D.E. (eds.) Review of Progress in Quantitative Nondestructive Evaluation, vol. 23, pp. 206–213. Springer, Heidelberg (2004) 158. Karp, B.: Generation of symmetric Lamb waves by non-uniform excitations. Journal of Sound and Vibration 312, 195–209 (2008) 159. Giurgiutiu, V.: Lamb wave generation with piezoelectric wafer active sensors for structural health monitoring. In: Proceedings of the SPIE, vol. 5056, pp. 111–122 (2003) 160. Moulin, E., Assaad, J., Delebarre, C., Grondel, S., Balageas, D.: Modeling of integrated Lamb waves generation systems using a coupled finite element-normal modes expansion method. Ultrasonics 38, 522–526 (2000) 161. Wang, L., Yuan, F.G.: Damage identification in a composite plate using prestack reverse-time migration technique. Journal of Intelligent Material Systems and Structures 12, 469–482 (2001) 162. Lin, X., Yuan, F.G.: Experimental study applying a migration technique in structural health monitoring. Structural Health Monitoring: An International Journal 4(4), 341– 353 (2005) 163. Wang, C.H., Chang, F.-K.: Scattering of plate waves by a cylindrical inhomogeneity. Journal of Sound and Vibration 282, 429–451 (2005) 164. Sonti, V.R., Kim, S.J., Jones, J.D.: Equivalent forces and wavenumber spectra of shaped piezoelectric actuators. Journal of Sound and Vibration 187(1), 111–131 (1995) 165. Ha, S.K., Keilers, C., Chang, F.-K.: Finite element analysis of composite structures containing distributed piezoceramic sensors and actuators. AIAA Journal 30(3), 772– 780 (1992) 166. Lu, Y., Ye, L., Su, Z., Huang, N.: Quantitative evaluation of crack orientation in aluminium plates based on Lamb waves. Smart Materials and Structures 16, 1907– 1914 (2007) 167. Su, Z., Ye, L.: Fundamental Lamb mode-based delamination detection for CF/EP composite laminates using distributed piezoelectrics. Structural Health Monitoring: An International Journal 3(1), 43–68 (2004)

4 Sensors and Sensor Networks

4.1 Introduction The majority of nondestructive evaluation (NDE) and structural health monitoring (SHM) techniques have been developed in recognition of the fact that the presence of damage alters structural properties (stiffness, density, damping ratio, energy dissipation, etc.), and hence alters the captured dynamic signatures of the structure such as Lamb wave signals. Therefore, authentic acquisition of the dynamic signatures of the structure under inspection using appropriate sensors becomes a prerequisite for accurate damage evaluation. Akin to the soma or nerve cell in a biological neural system, a sensor is a device for detecting variations in physical, chemical or biological properties, and transforming the measurands by appropriate transduction into electrical signals [1]. Sensor technology is a rudimentary but crucial ingredient in damage identification techniques, interdisciplinarily spanning areas of physics, chemistry, materials, electronics, manufacturing and informatics. Basically, for damage identification a sensor should have certain key capacities and features including (i) veridical acquisition of changes in the host structure under interrogation, but preferably low sensitivity to changes in environment; (ii) faithful conveyance of captured signals; (iii) minimal intrusion to the host structure; (iv) endurance for general working conditions with a service life no less than that of the host structure; and (v) ease of handling, attachment, integration and operation. For aerospace applications such as the SHM of airframes, sensors should additionally have small size, light mass, long-term reliability, low cost and power consumption, little deterioration with ageing, good tolerance and robustness to noise, reduced wire or even wireless arrangement, etc. Hitherto a variety of sensors has been invented, some of which have demonstrated effectiveness in NDE and SHM applications, as summarised in Table 4.1. The selection of a sensor for a specific application is a debatable matter and there is no aptotic criterion. Z. Su and L. Ye: Identification of Damage Using Lamb Waves, LNACM 48, pp. 99–142. springerlink.com © Springer-Verlag Berlin Heidelberg 2009

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Modality of attachment

Ultrasonic probe

Detecting general structural damage or measuring distance and structural thickness; exact and efficient

Surface attaching or air/fluidcoupled

Acoustic emission (AE) sensor

Detecting changes in mechanical properties and triangulating damage; passive sensor

Surface attaching or embedding

Detecting cracks or measuring large deformations with magnetic leakage; magnetic field required

Surface attaching

Eddy-current transducer

Detecting damage in metal and measuring electromagnetic impedance, but not applicable for polymer composites; complicated operation and expensive equipment, high energy consumption

Surface attaching

Accelerometer

Detecting acceleration and measuring structural dynamic responses; good for high-frequency response

Surface attaching

Strain gauge

Detecting relatively large deformations; good for low-frequency responses, relatively large damage, low cost

Surface attaching

Shape memory alloy

Detecting deformation and active control; active sensor, good for low-frequency responses, relatively large driving force

Surface attaching or embedding

Laser interferometer

Measuring derivation, displacement and dynamic responses; contactless measurement with high precision, expensive equipment

Contactless

Fibre-optic sensor

Detecting deformation, damage location and temperature change; high precision but expensive equipment

Surface attaching or embedding

Detecting general structural damage; normally for metallic materials

Surface attaching

Detecting general damage; active sensor, good for high-frequency responses, low driving force/cost/energy consumption

Surface attaching or embedding

Detecting general structural damage and measuring vibration or temperature change; suitable for non-flat shapes and low cost

Surface attaching or embedding

Sensor

Magnetic sensor

Electro-magnetic acoustic transducer Piezoelectric lead zirconate titanate (PZT) element PZT paint / polyvinylidene fluoride (PVDF) piezoelectric films

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Among the options in Table 4.1, in particular, AE sensors, which detect a transient acoustic pulse of energy released during failure (e.g., cracking), are efficient for triangulating structural damage or monitoring expansion of damage. Accelerometers are often used to acquire structural global information such as modal data (frequency, mode shape, etc.). They are however insensitive to small damage which is a local phenomenon and therefore does not significantly modulate the global structural features. Strain gauges provide localised measurement, but they are good at capturing static or dynamic measurands at a relatively low variation rate only. Fibre-optic sensors measure local strain as well, but directivity and embeddability are factors that can influence the measurement accuracy to some extent. The majority of these sensors are passive in nature, i.e., ‘listening to’ or ‘observing’ structural responses rather than ‘interacting’ with them. However, a piezoelectric (PZT) element can be used as an active actuator as well as being a passive sensor, in terms of dual piezoelectric effects. The major advantages of using a PZT element for NDE or SHM are that: (i) the diagnostic wave signal can be activated with desired amplitude, frequency and waveform, to accommodate different cases; and (ii) the number of actuators/sensors can be halved since each PZT element can function as both an active actuator and a passive sensor. As elaborated in Chapter 2, PZT elements and fibre-optic sensors are two major sensors used for Lamb-wave-based damage identification. This chapter addresses some key aspects concerning the design and development of PZT element sensors, fibre-optic sensors and sensor networks.

4.2 Piezoelectric Transducer The sensor and actuator constitute the generic term transducer, which is more strictly defined as the converter of one type of energy or physical attribute into another. A Lamb wave sensor converts mechanical motion induced by wave propagation into an electrical signal, while a Lamb wave actuator works in the opposite way to convert electrical excitation into the mechanical drive to activate waves. Discovered by the Curie brothers in 1880 and first used for NDE purposes by Langevin in 1917 [2], piezoelectricity describes a phenomenon whereby an electric charge can be generated under mechanical deformation (direct effect, used for developing Lamb wave sensors), and conversely, mechanical strain can be induced in response to an electric field (converse effect, used for developing Lamb wave actuators). A comprehensive introduction to piezoelectricity can be found elsewhere [3]. Piezoelectric ceramics and polymer films, as elaborated in Section 3.2, are the major materials for manufacturing piezoelectric actuators and sensors. The relationships between the applied forces and the resultant responses depend upon the properties and size of the piezoelectric element, and the direction of the electrical and mechanical excitation [4]. The polar axis is often taken as the direction of polarisation within the element, denoted by ‘axis 3’. Poling occurs when a high direct current voltage is applied between electrodes on opposite faces

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of the element. Piezoelectric coefficients with double subscripts connect electrical and mechanical quantities. The first subscript gives the direction of the electrical field associated with the voltage applied, while the second subscript gives the direction of the mechanical stress or strain. The piezoelectric constants relating the mechanical strain produced by an applied electric field are termed the strain constants, d ij . Large d ij means large mechanical deformation under given electrical field. The coefficient d31 applies when addressing the relationship between the applied voltage in the polarisation axis and the mechanical deformation normal to the axis. Therefore, a surface-mounted PZT element mainly activates and captures Lamb wave signals in terms of the ‘3-1’ mode (described by d31 ), i.e., the inplane motion mode (perpendicular to the polarised direction, ‘1’) when the PZT element is under an electric field in the polarised direction (‘3’). 4.2.1 Design of Piezoelectric Actuator and Sensor

4.2.1.1 Actuator A PZT element is normally made of an oriented piezoelectric crystal or ceramic. With modern techniques piezoelectric ceramics can be produced in various geometries such as fibre, plate, disk, ring and tube. As experimentally observed, a circular PZT element can generate Lamb waves propagating normal to the actuator circumference, and those of non-circular shapes such as a rectangle can present strong directivity of the generated waves. Therefore, the shape and configuration of a PZT element when used as a Lamb wave actuator should optimally be designed so as to minimise any geometric effect and consequently avoid uneven wave propagation. An optimal criterion for selecting the dimensions of a PZT element for wave actuator is [5, 6] Lactuator =

1 1 vwave ⋅ (n + ) = λwave ⋅ (n + ) 2 2 f

( n = 0, 1, 2, A ),

(4.1)

where Lactuator is either the main length of a rectangular PZT element actuator or the diameter of a circular one; v wave , f and λwave are the velocity, frequency and wavelength of the desired Lamb wave mode to be activated, respectively. Meanwhile, considering that the energy consumed to drive a PZT element is proportional to Lactuator [7], n = 0 in Equation 4.1 is often selected for reducing energy consumption. As a special case of rectangular PZT elements, a strip-like PZT element (length being much greater than width) produces Lamb waves with dominant energy parallel to the length and little energy parallel to the width, showing strong directionality as discussed in Section 3.4.2. In contrast, a circular PZT element generates a uniform Lamb wave field in all directions. As to thickness, a thicker PZT element permits a more intensive electrical field to be applied to it, accordingly enhancing the signal-to-noise ratio (SNR) of captured signals. However, the maximum electrical load for a PZT element without being depolarised is about 250-300 V/mm [8]. An alternative way to increase this

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limit is to use a PZT stack actuator which consists of a certain number of PZT elements in series, with these elements being polarised in their thickness direction. For a PVDF-based interdigital transducer (IDT) to excite an even Lamb wave field of a specific wavelength as a PZT element does, it theoretically requires an infinite number of fingers [9, 10], and so the actuator would be infinitely large. Practically, a PVDF has a limited number of fingers, as shown in Figure 4.1(a), and therefore the activated Lamb waves have a certain wavelength bandwidth. One novel design is shown in Figure 4.1(b), where two sets of fingers of varying width are interlaced and driven by identical electrical fields of 180° out-of-phase, with which the bandwidth of generated Lamb waves can be confined. 2.4 mm

PVDF finger Connection tabs

a

b

Fig. 4.1. PVDF-based IDT (finger space: 2.4 mm) in a. plain; and b. apodised pattern [9]

PVDF films are commercially available in thicknesses up to 110 m. If a film of such thickness is directly bonded to a rigid substrate, the peak response of the activated Lamb waves can be at a frequency of up to 3.7 MHz [11]. Such a high frequency is normally beyond the non-dispersion cut-off frequency of the S 0 and A0 modes (Section 2.2.7), causing significant difficulties in signal interpretation. To operate a PVDF-based IDT effectively at a reasonably low frequency range, the film can be backed with a relatively high-density substrate such as copper, using the standard manufacturing techniques for printed-circuit boards. The frequency responses of a PVDF-based IDT of 110 m in thickness when used as an actuator, backed with copper of different thicknesses and then bonded onto an aluminium plate, are displayed in Figure 4.2(a). It can be seen that as the thickness of the substrate increases, the frequency at which the magnitude of the activated Lamb wave signal reaches its maximum decreases, Figure 4.2(b). In this way, a PVDF-based IDT can activate Lamb waves of different peak frequencies by changing the thickness of the copper substrate.

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Normalised amplitude

1

0

0

1

2

3

4

Frequency [MHz]

a

b

Fig. 4.2. a. Schematic of incrassated PVDF-based IDT (as actuator) bonded to substrate (not to scale); and b. frequency responses of the actuator (bonded to an aluminium plate and backed with different thicknesses of copper (thickness shown in m)) [11]

4.2.1.2 Sensor ‘Perfect measurements are possible only where the sensor is not there’ [12]. This statement means that a sensor, regardless of the attachment manner to the host structure, distorts genuine structural responses to a greater or lesser degree, introducing measurement error into the signal. The measurement errors caused by use of a PZT element or PVDF sensor for capturing Lamb wave signals can be one or more of the following [1]: (i)

sensor misalignment causes errors in three orthogonal measurement directions, in particular when a rectangular PZT element is used as sensor; (ii) temperature and humidity fluctuations cause shifts in system setting/calibration and therefore lower measurement accuracy; (iii) ambient noise may interfere with Lamb waves to a significant degree and conceal damage-scattered wave components in captured signals; (iv) variations in electrical and magnetic fields (e.g., moving of cables) cause sensors to respond; and (v) attaching a sensor to the host structure induces changes in the local stiffness that subsequently affect Lamb wave propagation in the structure. Lamb wave propagation induces dynamic mechanical strains along the propagation path. A PZT element or PVDF sensor measures strain variations and transfers measurands into electrical signals. To achieve an accurate measurement and minimise the aforementioned measurement errors, a Lamb wave sensor must be carefully designed. Theoretically, a sensor should be as small as possible to detect local (point) strain accurately. Basically, a PZT element when used as a sensor should be smaller than the half-wavelength of the Lamb wave mode to be captured, λwave 2 [5]. In practice, a sensor has a characteristic in-plane dimension of up to a few millimetres, and as a result it actually measures the average strain over the entire occupied area. Generally, a PZT element sensor of rectangular shape exhibits

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strong directivity in receiving Lamb wave signals, and is more often used to capture waves in one-dimensional structural beams [13, 14], whereas a circular sensor receives signal evenly from all directions, providing advantages in two- or threedimensional cases. It has been observed that [7] 1 , Lsensor

V sensor∝

(4.2)

where Lsensor is either the major length of a rectangular PZT element sensor or the diameter of a circular one, and Vsensor is the output response of the sensor in the form of electrical voltage. It is clear that, to reach a relatively high magnitude of Vsensor so as to enhance the SNR of the signal, Lsensor should be kept small, and only under such a circumstance is the captured electrical signal proportional to the local strain. In addition, a sensor of relatively large size may introduce weight and volume penalty to the host structure. Figure 4.3 shows the normalised amplitude of the output signal of the S0 mode versus characteristic dimension of the sensor. It can be seen that, at a given frequency, the smaller the sensor length the higher the magnitude of the sensor output. However, when the PZT element sensor is too small, the captured signal presents high vulnerability to environmental noise.

1.0

Normalised amplitude

0.125 cm (Sensor size) 0.25 cm

0.5 1.0 cm 2.0 cm

0 0

0.2

0.4

0.6

0.8

1.0

1.2

Frequency [MHz]

Fig. 4.3. Normalised amplitude of the output signal associated with the S0 mode versus characteristic dimension of sensor [7]

Altogether, in terms of the criteria described by Equations 4.1 and 4.2 for actuators and sensors, respectively, having an actuator and sensor of the same dimensions is obviously not the best from a view of optimisation, though this is common in practical applications for convenience.

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To guarantee a homogeneous piezoelectric effect, the two surfaces of a PZT element, serving as the anode and cathode respectively, need to be electroded evenly over the entire area, whether the element is used as actuator or sensor. Several electrode types are available, including fired-on/vacuum-evaporated gold, platinum or palladium, electroless nickel or copper, and air-drying silver paint. Vacuum-evaporated gold is frequently used for its good capability of coating onto PZT and good electrical conductivity [15, 16]. The electrode may distort the captured Lamb wave signal to certain extent, but this can be ignored when the frequency of the wave is lower than 100 MHz where the thickness of the electrode is much less than the wavelength of the wave. In addition, shielded coaxial cables must be used for data transmission. The conductive part of the wire is often made of copper, silver or gold, in various forms such as plain or multi-strand. All the above factors impose high requirements of proper fabrication and packaging for PZT actuators and sensors. 4.2.2 Surface-mounting vs. Embedding

A PZT element actuator or sensor can be either surface-mounted on or embedded in a host structure. In practice, the former is preferred [13, 17-22] because of the convenience in attachment, maintenance and replacement, exemplified by the PZT patch technique developed for the detection of debonding of composite laminates [23-26]. Either conductive glue (or silver powder-added epoxy, etc.), Figure 4.4(a), or adhesive conductive/copper tape, Figure 4.4(b), can be used for surfacemounting a PZT element onto a structure, though both may effect the wave signal to a certain extent because of the viscoelastic behaviour of the polymer-based glue and adhesives. However, this issue has not yet been a concern in practice. Before applying adhesive, the surface of the host structure needs light sanding and thorough cleaning using acetone for getting rid of grease and dust.

a

b

Fig. 4.4. PZT element surface-mounted on a. a composite beam using conductive glue; and b. an aluminium plate using adhesive copper tape [27]

Increasing argument has arisen in recent years concerning the accuracy of signals captured using surface-mounted PZT element sensors exposed directly to the

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environment, since the measurement errors and inaccuracy can be exacerbated by ambient noise. Thanks to the latest advances in printed circuits and manufacturing, it is possible to embed miniaturised PZT elements into composite structures as built-in actuators and sensors [16, 27-37]. With reduced exposure of transducers and utilities such as cables, embedding is an important step towards the practical implementation of SHM techniques. Raw Lamb wave signals acquired via two surface-mounted PZT element actuator-sensor pairs, Path I and Path II, which have the same distance between the actuator and sensor but are perpendicular to each other, in a quasi-isotropic carbon fibre-reinforced epoxy (CF/EP) composite laminate [28] are shown in Figure 4.5(a). For comparison, the signals acquired via another two embedded PZT element actuator-sensor pairs, Path I´ and Path II´ (which are immediately beneath Paths I and II in the laminate, respectively), are displayed in Figure 4.5(b). 300

Path II Path I

Amplitude [mV]

200

100

0

-100

-200

-300 100

50

150

Time [µs] a 300

Path I'

Path II'

Amplitude [mV]

200

100

0

-100

-200

-300 50

100

150

Time [µs] b Fig. 4.5. Lamb wave signals captured via a. surface-mounted; and b. embedded PZT element actuator-sensor pairs

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It can be seen that: (i) the magnitudes of all the captured wave signals have the same level of voltage though the magnitude of signals received by the surface-mounted sensors is somewhat higher than that of their embedded counterparts; and (ii) the wave signals acquired using the embedded sensors display much better coincidence in the two different directions in the quasi-isotropic laminate, including magnitude, waveform and signal phase, than those captured by surface-mounted sensors. Isolated from the environment, embedded sensors possess excellent immunity to ambient noise, thereby offering enhanced SNR of signals and excellent stability, durability and repeatability in data acquisition, even in rugged working conditions, and high sensitivity to internal damage. However, to embed a PZT element into a composite structure, some technical challenges must be met. First of all, an embedded PZT element, subjected to temperatures up to 180°C and pressures up to circa 700 kPa in autoclaving during the manufacturing process, can become short-circuited. One solution to circumvent this problem is to wrap the PZT element and its wires with epoxy or antitemperature/pressure insulating films such as polyimide (Kapton®1), as schematically shown in Figure 4.6, to keep the PZT element apart from the conductive carbon fibres. After insulation the PZT element can be connected using interconnectors. Typical interconnectors include shielded wires, coaxial cables, conductive plies and strips [16]. Secondly, an embedded PZT element and its cable may cause disturbance in the microstructure of the host structure, influencing the inter-laminar stress distribution in its vicinity and lowering the load-carrying capability of the composite laminate. This consequently impairs integrity and causes premature failure of the composite

a

b

Fig. 4.6. Typical insulation techniques for embeddable PZT elements: a. encapsulated in polyimide film [38]; and b. wrapped with epoxy resin [29]

1

Kapton® is a registered trademark of E.I. du Pont de Nemours and Company. http://www.dupont.com

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structure. The ultimate tensile strength of a CF/EP composite laminate with embedded transducers can be reduced by 4-10% in a tensile loading test [39, 40]. A basic consideration to minimise any such negative effect is that the built-in PZT element must be small in size and light in weight, and its elastic constants and thermal coefficients of expansion need to be as similar as possible to those of the host structure. The wires and coaxial cables should also be thin, to reduce their potential negative influence on structural integrity. Lastly, embedding a PZT element into a composite structure may incur a decreased working temperature limit and therefore narrow the functional temperature range of the composites. In any case, the working temperature and curing temperature of the composites must be at least 100°C less than the Curie temperature of the PZT element, where the crystal structure changes from a nonsymmetrical (piezoelectric) to a symmetrical (non-piezoelectric) form [4]. Apart from the above technical challenges, other problems arising from sensor embedding in comparison with surface-mounting also include the need for precise placement and alignment of sensors in composites during manufacturing, skilled operation (since the performance of an embedded sensor is somewhat subject to the quality of embedding), and proper connection with the signal activation/data acquisition unit. In fact, the appropriate connection of an embedded PZT element in composites with the unit can be a great challenge in practical applications, as laminated composite structures normally need trimming along the edges after autoclaving. In addition, the relatively high cost and difficulty of accessibility for maintenance are two more issues in practical applications.

4.3 Fibre-optic Sensor 4.3.1 Optical Fibre and Fibre-optic Sensor

Emerging as a key medium for long distance data transportation in lieu of traditional means in the telecommunication industry in the 1970s, optical fibre soon found an application niche for optoelectronic sensing devices as a small spin-off. A typical optical fibre is a dielectric material that can be used to guide light along a specific path, consisting of a silica core and cladding with a protective coating. An optical fibre can further be used to fabricate fibre-optic sensors for sensing static and dynamic strains in materials and structures. Fibre-optic sensors with a core diameter of circa 10 m can carry one mode of light wave only (single mode fibre), whereas those with a diameter of 50 - 100 m can carry more modes (multimode fibre). A single mode fibre-optic sensor has been shown experimentally to be much more sensitive to Lamb waves than a multimode fibre-optic sensor. In general, fibre-optic sensors feature good immunity to electromagnetic interference/water/corrosion, flexible structural integration (surface-mountable or embeddable), super-light weight and small size (down to as fine as a few hundred micrometers in diameter), low power consumption, high sensitivity, wide bandwidth, long lifetime, etc. A fibre-optic sensor can measure strains with much higher sensitivity by two to three orders of magnitude than a conventional electrical resistance strain gauge [41]. Compared with a piezoelectric element sensor, a fibre-optic sensor has higher bandwidth capability for capturing a wave signal

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Identification of Damage Using Lamb Waves

(up to 25 MHz), due to the absence of mechanical resonances [42]. Since, unlike electrically driven devices including PZT elements, optic sensors are not a spark source, they are well suited for acquisition of Lamb wave signals in particular applications with a high risk of fire, such as damage identification in petroleum storage tanks. With a number of fibre-optic sensors or a multiplexed fibre-optic sensor, an optic sensor network/array can further be constructed to achieve a broader coverage of inspection. A comprehensive review of fibre-optic sensors for damage detection can be found elsewhere [43]. In spite of the aforementioned merits, application of fibre-optic sensors to Lamb-wave-based damage identification also raises problematic issues, mainly including: (i) the measured strains are of a three-dimensional nature, so careful analysis of the output signal is necessary to extract axial decomposition; (ii) the captured wave signals may be interfered with by ambient light unless an optical shielding or a special time synchronous gating is used; (iii) integration of a fibre-optic sensor into a composite structure may create problems of incompatibility unless a small amount of fibre is used; (iv) repair or replacement of the optic sensor, whether surface-mounted or embedded, is almost impossible; (v) measurement is substantially dependent on the alignment direction of the fibre-optic sensor, i.e., there is strong directivity in acquisition of Lamb wave signals (to be detailed in the following section); (vi) appropriate connection of an embedded fibre-optic sensor with a signal acquisition cable can be a challenge in practical applications, as most composite structures require trimming along the edges after autoclaving and the trimming process can break the optical fibre; and (vii) relatively high cost is often incurred for acquiring and maintaining the associated optical equipment for signal acquisition and processing. 4.3.2 Fibre Bragg Grating Sensor

Generally speaking, a fibre-optic sensor works in one of three sensing modalities: based on light intensity changes, based on interferometry (difference in wavelength of light waves), and based on fibre Bragg gratings (FBGs). In the above three modalities, the direct physical measurands to which the optical fibre is sensitive is axial displacement. The fibre is stretched or compressed in the axial direction such that some observable properties of the light propagating in the fibre are changed. In particular, sensors based on FBG (called FBG sensors in what follows) have been used widely for sensing static or dynamic strains in various applications, having the potential to offer enhanced sensing resolution when used as Lamb wave receivers compared with PZT sensors. In brief, an FBG sensor is an optical fibre multiplexed with N permanent and intermittent reflective Bragg gratings along the fibre with central wavelengths of λB−1 , λB − 2 , λB − 3 , … λB − i , …, λB − N (termed Bragg wavelength, i = 1, 2, A, N ), respectively. The gratings are introduced into the fibre by lateral exposure of the core of the fibre to intense optical interference such as ultraviolet light using either

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interferometric holography inscription or phase mask inscription technique [7]. The length of an FBG sensor is normally in the range of 2-20 mm. To illustrate the sensing mechanism of an FBG sensor, we focus on an FBG sensor in its simplest form: having only one grating with a central wavelength, λB , which is defined as

λB = 2 n Λ ,

(4.3)

where n and Λ are the mean effective refractive index of the fibre core and the grating period, respectively. When broadband light is illuminated to pass through the FBG sensor, partial light of a very narrow bandwidth centralised at λB will be reflected from the grating (since this partial light has the maximum reflectivity at λB ), and rest of the light will continue propagating. Similarly, if an FBG sensor has N gratings, λB−1 , λB − 2 , λB − 3 , … λB − i , …, λB − N , part of the input broadband light centralised at λB−i ( i = 1, 2, A, N ) will be reflected from the grating with a Bragg wavelength of λB−i , and light of other wavelengths is continuously transmitted onward through the fibre. Such a sensing mechanism is elucidated schematically in Figure 4.7. Spectrum of

Intensity

broadband light grating 1

i

grating N

grating 2

λB −1

λB − 2

……

λB− N

Wavelength

Transmission spectra

Intensity

Intensity

Wavelength

After passing grating 3 Intensity

After passing grating 2

After passing grating 1

Wavelength

Wavelength

Reflection spectra After passing grating 2

Wavelength

After passing grating 3 Intensity

Intensity

Intensity

After passing grating 1

Wavelength

Wavelength

Fig. 4.7. Sensing mechanism of an FBG sensor multiplexed with N Bragg gratings

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More recently, to improve the capacity of integration of FBG sensors into composite materials, a sort of FBG sensor with a diameter as small as 50 m has been invented [44, 45]. The NASA-Langley Center has developed a novel inscription technique for manufacturing FBG sensors of very short gratings (only few hundred microns), allowing miniaturisation of FBG sensors and improvement of sensitivity to changes in a host structure, especially in the proximity of the sensors [46]. The technology to multiplex hundreds or thousands of FBGs into a single optical fibre has also become available for practical applications [47]. 4.3.3 FBG Sensor for Lamb Wave Collection

Since the Bragg wavelength of an FBG grating, λB , is proportional to the grating period as seen in Equation 4.3, Lamb waves, which alter n and Λ during their propagation, can thus be captured by measuring the shift of wavelength peak. With the Lamb wave-induced strain along the optical fibre, ε , and ambient temperature change, ΔT , the relative shift of the Bragg wavelength peak, ΔλB , is [48]

ΔλB

λB

= Cε ⋅ ε + CT ⋅ ΔT ,

(4.4)

where Cε and CT are two inherent material constants related to strain and temperature, respectively. This shift is positive when the FBG elongates and vice versa. In terms of Equations 4.3 and 4.4, provided the free Bragg wavelength is 1550 nm and ambient temperature is constant, a strain change of 1% can lead to a shift of 12.2 nm in the Bragg wavelength of the FBG sensor. This amount is sufficient for quantitative recognition in practical measurement. Because of this high sensitivity, FBG sensors have been increasingly used as sensors to capture Lamb wave signals [49-54]. To receive a Lamb wave signal efficiently, the length of an FBG sensor should be shorter than one-seventh of the wavelength of the Lamb wave [49]. The major technical challenge of using FBG sensors to capture Lamb wave signals is instant measurement of local dynamic micro-strains generated during the propagation of Lamb waves, which are normally of a low magnitude but with a frequency in the ultrasonic range of kilohertz or even megahertz. It is almost impossible for an optical spectrum analyser (OSA) with a nominal sampling rate of only a few hertz at the maximum to capture the wavelength shift in such a high frequency range. To circumvent this problem, an FBG filter is often applied using a wavelength-intensity conversion technique [55, 56]. An FBG filter has a very sharp wavelength, and the intensity of the light transmitted through the filter is subject to the Bragg wavelength. With the filter, the change in light intensity induced by ultrasonic Lamb waves, rather than the induced strain itself, is captured by a photodetector, a device which converts a light signal to an electrical voltage signal, at a high sampling rate up to 10 MHz. The captured voltage signal is then recorded by an oscilloscope or other signal acquisition equipment.

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The theoretical basis of such an approach is described as follows (for illustration, we use an FBG sensor in its simplest form: having only one grating with a central wavelength, λB ) [48]: since Lamb wave is a series of longitudinal expansions and compressions along the fibre axis, it produces a time-dependent strain field, ε (t ) , which in turn shifts the peak in the reflection spectrum, R . R is a complex function of ε as:

R(ε (t )) = R0 +

dR dλB dR ε (t ) = R0 + ⋅ ⋅ ε (t ) , dλB dε dε

where R0 is the initial reflection. Both

(4.5)

dR dλB and can be calibrated experidλB dε

dR is a function of the grating reflectivity and the gratdλB ing’s bandwidth, both of which depend on the length and strength of the grating; dλB corresponds to Cε in Equation 4.4. During measurement, the optical energy dε is converted to an electrical voltage U (t ) through a photodetector as

mentally. In particular,

ε (t ) = [U (t )

R0 dR R dR dλB −1 − R0 ] ⋅ ( ) −1 = [U (t ) 0 − R0 ] ⋅ ( ⋅ ) . U0 dε U0 dλ B dε

(4.6)

Furthermore, the time-dependent voltage can be expressed as the sum of the direct current and alternating current components, U 0 and ΔU (t ) , respectively, as U (t ) = U 0 + ΔU (t ) .

(4.7)

Substituting Equations 4.5 and 4.7 into Equation 4.6 yields, assuming U (0) = U 0 and ε (0) = 0 ,

ε (t ) = [ΔU (t )

R R0 dR dλ B −1 dR ] ⋅ ( ) −1 = [ΔU (t ) 0 ] ⋅ ( ⋅ ) . U 0 dλ B dε U0 dε

(4.8)

Equation 4.8 links the electrical voltage with the dynamic strain induced during the propagation of Lamb waves. Driven by such a sensing mechanism, an experimental setup for collecting Lamb waves using an FBG sensor in a pristine configuration is shown in Figure 4.8, where the light source can be a coherent gas or semiconductor diode laser, broadband incandescent lamp, white light, narrow-band LED, etc.; the optical coupler is for directing the light from the light source into an FBG sensor. With this setup, a Lamb wave signal captured by an FBG sensor attached to a perspex

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Identification of Damage Using Lamb Waves

plate, activated by five-cycle tonebursts at a central frequency of 150 kHz, is displayed in Figure 4.9. Oscillograph

Programmable signal generator

Broadband Photodetector

light source

Power amplifier FBG filter Coupler

FBG sensor

Lamb wave source, e.g., PZT

a Incident light

Light transmitted through Compression

Broadband light source

Light

Tension

FBG grating

FBG Grating 1 Coupler

Specimen

2

3 Sensing region

Light OpticalOSA spectrum Analyser (OSA)

Compression

Tension

Light reflected from FBG (recorded by OSA)

b Fig. 4.8. a. Schematic setup for collecting Lamb waves using an FBG sensor; and b. magnified dotted area in a.

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0.1

Amplitude [V]

Excitation

0.0

-0.1 0.0

80.0

160.0

240.0

320.0

Time [ s]

a 0.06

Amplitude [V]

Response

0.0

-0.06 0.0

200.0

100.0

300.0

400.0

Time [ s]

b Fig. 4.9. a. Excitation signal (five-cycle tonebursts at a central frequency of 150 kHz); and b. Lamb wave signal captured by an FBG sensor [48]

By comparing the performance in capturing a Lamb wave signal between an FBG sensor and a PZT sensor surface-mounted on an aluminium plate, the conclusion can be drawn that the signals captured by the two kinds of sensors show good consistency with regard to the arrival time of different Lamb modes, but display a certain discrepancy in signal amplitude, as shown in Figure 4.10. This discrepancy can be attributed to facts that (i) a PZT element sensor captures the ‘integrated’ Lamb wave signals in the entire element-covered area where the waves propagate, whereas an FBG sensor has very strong directivity (detailed in a subsequent section), sensing the ‘integrated’ wave signals mainly over the grating length; (ii) a PZT element sensor responds to both the S 0 and A0 modes, but an FBG sensor is less sensitive to the A0 mode; and (iii) the magnitude of a captured Lamb wave signal is a linear function of the gauge length (grating length for an FBG sensor and in-plane area for a PZT element sensor).

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Identification of Damage Using Lamb Waves

Therefore, it is not logical to directly compare the magnitudes of Lamb wave signals captured by a PZT element sensor and an FBG sensor, as the measurements are made on the basis of different sensing mechanisms. 0.8

a

0.4

Amplitude [V]

0.0 -0.4 -0.8 0.6

b

0.4 0.2 0.0 -0.2 -0.4 40.0

60.0

80.0

100.0

120.0

140.0

160.0

Time [ s]

Fig. 4.10. Lamb wave signals at a central frequency of 460 kHz in an aluminium plate (1 mm in thickness) captured by a. a PZT element sensor; and b. an FBG sensor [57]

An FBG sensor is more susceptible than a PZT element sensor to the influence of changes in ambient temperature because of difference in the coefficients of thermal expansion (approximately 4 − 6 × 10−6 / K for a PZT element [58], 0.5 × 10−6 / K for glass in optical fibre but 60 × 10 −6 / K for its coating [59]). It has been observed that the influence of temperature on the measurement accuracy of an FBG sensor in determining the arrival time of a Lamb wave mode is marginal, but it is pronounced in calibrating magnitude if the sensor is under different ambient temperatures varying from -20° to 70° [60], unlike a PZT sensor which is basically insensitive to changes in ambient temperature, as elaborated in Section 2.6. 4.3.4 Surface-mounting vs. Embedding

Like a PZT element sensor, a fibre-optic sensor can be either surface-mounted on a host structure using adhesive [20, 50, 52, 53, 61] or embedded in a composite laminate during fabrication [44, 50-52, 59, 62-64]. Both means of attachment have been demonstrated experimentally to perform as well in capturing Lamb wave signals as other precise devices such as ultrasonic probes [52, 56]. By examining Lamb wave signals captured by fibre-optic sensors surface-mounted on and embedded in a CF/EP composite laminate, Figure 4.11, it has been found that an embedded fibre-optic sensor is 20 times more sensitive to the S0 mode than its surface counterpart, in terms of the magnitude of captured signals, referring to Table 4.2. The reliability of using a surface-mounted fibre-optic sensor to collect Lamb wave signal is therefore under challenge [51], although surface attachment

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is more convenient in practice and there is less influence on the microstructure of composites. 1.0

Normalised amplitude

a

0.0

-1.0 0.1

b

0.0

-0.1 0.0

50.0

100.0

150.0

Time [ s]

Fig. 4.11. The S 0 mode in a CF/EP composite laminate captured by a. an embedded; and b. a surface-mounted fibre-optic sensor [56] Table 4.2. Performance of surface-mounted and embedded fibre-optic sensors in capturing Lamb wave signals in glass fibre-reinforced epoxy (GF/EP) and CF/EP composites [50] Embedded

Surface-mounted

Optical throughput [dBm]

Signal amplitude [V]

Optical throughput [dBm]

Signal amplitude [V]

GF/EP

-10.5

5.5

-11.5

0.24

CF/EP

-11.0

2.1

-11.0

0.10

Composites

4.3.5 Directivity

Unlike a circular PZT element sensor that collects Lamb wave signals omnidirectionally, the wave signal captured by a fibre-optic sensor is highly orientationdependent, in particular with respect to magnitude. Two Lamb wave signals in a perspex plate, activated by a PZT actuator and then captured using two FBG sensors perpendicular to and parallel to the major direction of wave propagation, respectively, are compared in Figure 4.12. The graphs show that the magnitude of the Lamb waves including the S0 and A0 modes captured by the FBG sensor

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Identification of Damage Using Lamb Waves

perpendicular to the wave propagation direction is approximately 100 times less than that measured by the sensor parallel to the wave propagation. 0.004

a

FBG sensor perpendicular to wave propagation 0.002 0.0

Amplitude [V]

-0.002 -0.004 -0.006 0.06

FBG sensor parallel to wave propagation

0.04

b

0.02 0.0 -0.02 -0.04 -0.06 0.0

50.0

100.0

150.0

200.0

250.0

300.0

350.0

400.0

Time [ s]

Fig. 4.12. Lamb wave signals captured by FBG sensors a. perpendicular to; and b. parallel to the major direction of wave propagation [48]

This can be explained as follows. For an isotropic material, the equation to describe the variation in magnitude of a captured Lamb wave signal in regard to the measurement direction in a two-dimensional plane is [54]

ε = ε 1 cos 2 α + ε 2 sin 2 α ,

(4.9)

where α is the angle between the axial direction of FBG sensor and the wave propagation direction. ε1 and ε 2 are two principal strains along and perpendicular to the wave propagation path. The directivity of an FBG sensor significantly lowers its efficiency in capturing Lamb wave signals. Ideally, an FBG sensor should be placed parallel to the wave propagation direction so as to achieve the maximum responses, in particular for waves scattered by damage, for obtaining a high SNR of signals. However, without prior awareness of the location of damage it is of course impossible to estimate the direction of damage-scattered waves. The recently developed FBG rosette technique, analogous to the strain gauge rosette [54], in Figure 4.13(a), can provide a solution for this concern. The rosette configuration consists of three FBG gratings placed at 120° to each other, forming an equilateral triangle. The magnitude of the signal captured by each individual FBG sensor in this rosette configuration is dependent on the angle between the direction of the wave propagation and the grating axes of the three FBG sensors. On the basis of trigonometry, the direction or pathway of the wave propagation

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corresponding to that of the maximum principal strain can be defined with respect to that of the rosette. Note that the sum of the signal magnitudes (analogous to the normal strains) of individual FBG sensors in the rosette remains constant and can be used for normalisation. This 120° setup has the advantage that it allows normalised measurement of Lamb waves, regardless of the direction from which the waves emanate. In fact, the rosette technique can also be used to directly triangulate damage based on the directions of captured Lamb waves. If two rosettes are used, as shown in Figure 4.13(b), the intersection point of wave directions estimated by each rosette will be the location of the wave source, e.g., the position of the damage by which the Lamb waves are scattered.

Grating 1

Grating 2

Grating 3

a

b

Fig. 4.13. a. Layout of an FBG rosette; and b. locating structural damage using FBG rosette technique [54]

4.4 Hybrid Piezoelectric Actuator-optic Sensor Unit To fully exploit the advantages of PZT elements and fibre-optic transducers, it is axiomatic to combine the PZT actuator with the FBG sensor to configure a hybrid actuator-sensor unit for Lamb wave activation and reception [20, 49, 52, 55, 57, 60, 65-67], where the PZT actuator is used as the active excitation source to activate fully customised diagnostic waves while the FBG sensor functions as the receiver to capture Lamb wave signals with high sensitivity. A great benefit of such a hybrid system is the improved actuator-sensor decoupling (i.e., minimum interference between the actuation input signal and sensor output signal) because they use different mechanisms for signal transmission: the actuators use electrical channels while the sensors use optical channels. Recent advances in photonic and optic technologies have made it possible to multiplex a large number of gratings of various wavelengths along a continuous optical fibre for multi-point measurement, thereby significantly reducing the number of sensors in such a hybrid actuation-acquisition technique.

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Identification of Damage Using Lamb Waves

As one example, a hybrid piezoelectric-fibre-optic (HyPFO) monitoring system developed for aerospace structures is shown in Figure 4.14(a). The multiplexed FBG sensors are distributed in the structure along a continuous optical fibre to achieve multi-point Lamb wave acquisition. Allowing for the strong directivity of fibre-optic sensors mentioned previously, each PZT element, used as actuator, is surrounded by several FBG sensors in different directions to guarantee comprehensive data collection. Using the HyPFO monitoring system, Lamb wave signals captured before and after the presence of damage in an aluminium plate are compared in Figure 4.14(b), from which the discrepancy between the two states of the aluminium plate can clearly be observed. Kim and Lee [68] developed a hybrid coin-sized transducer, called a diagnostic network patch. The patch incorporates multilayer piezoelectric disks and fibre-optic sensors, instrumented with a portable-microprocessor-based data logger, for Lamb wave activation using the piezoelectric disks while acquisition using the fibre-optic sensors.

Multiplexed FBG sensors

To signal generator

Fibre-optic sensor

To optical

PZT

demodulation unit

a Fig. 4.14. a. Schematic of the Lamb wave activation and acquisition unit based on PZT actuators and fibre-optic sensors; and b. Lamb wave signals captured by the unit shown in a. before and after the presence of damage in an aluminium plate [20]

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Signal amplitude [mV]

1.0

Signal before damage 0.5

0

-0.5

Signal after damage -1.0

0

25

50

75

100

125

150

Time [µs]

b Fig. 4.14. (continued) [20]

4.5 Sensor Network A single sensor, whatever the type, performs local acquisition of signals, and it generally tends to provide inadequate information for evaluating structural damage, thereby eroding the confidence in identification results. Accordingly, a series of spatially distributed sensors is often networked to configure a sensor array or sensor network. By ‘communicating’ with each other, the sensors in the array or network certainly provide more information. With sensors acting cooperatively, a sensor array or network provides desirable redundancy and reliability of signal acquisition. Sensing devices in a sensor array or network should be small and inexpensive, e.g., PZT elements, so that they can be produced and deployed in a large number. In a piezoelectric sensor network, any two PZT elements form an actuator-sensor pair (or say, two sensing paths in terms of dual piezoelectric effects) to activate and capture Lamb wave signals, as elucidated schematically in Figure 4.15. Sensor networks for SHM can be found either surface-mounted on or embedded in structures under monitoring. As one example shown in Figure 4.16(a), 12 PZT wafers (PI®2-151, 10 mm in diameter), with properties detailed in Table 4.3, are circuited using a printed circuit on a polyimide film to enclose a square area of 330 mm × 330 mm. This sensor network can be embedded into composite structures. To minimise the impact of embedded sensors on the integrity of inspected structures, each wafer is only 0.2 mm in thickness, contributing little weight and volume penalty. Each wafer is thoroughly protected by a pre-coating layer of epoxy, preventing electrodes of the wafer from coming into contact with conductive fibres such as carbon fibres. Thin and flexible, the circuit on polyimide film

2

GmbH & Co. KG is the owner of the registered trademark PI®

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Identification of Damage Using Lamb Waves

can deform with the host composite structure without breakage. As an individual functional unit, such a sensor network can be pre-fabricated, stored, transported and finally integrated into a large composite structure, as in the case shown in Figure 4.16(b) where the sensor network is embedded into a CF/EP panel.

Fig. 4.15. Sensing paths rendered by an active sensor network consisting of multiple PZT elements (arrow lines in the magnified area standing for possible sensing paths)

P6

P5

P7

P8

330mm

P4

P9

500 mm

P3 110mm 110mm P2

P10

PZT wafer

Circuit strip P1

P12

P11

Terminal (to signal generation/acquisition unit)

a

b

Fig. 4.16. a. An embeddable piezoelectric sensor network consisting of 12 PZT wafers; and b. a CF/EP composite laminate with the embedded sensor network shown in a.

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Table 4.3. Material properties of PZT wafer used for developing sensor network Product name Geometry Density Poisson’s ratio

PI 151 Diameter: 10.0 mm, thickness: 0.2 mm 7.80 g/cm3 0.31

Charge constant d31

-170×10-12 m/V

Charge constant d33

450×10-12 m/V

Relative dielectric constant Dielectric permittivity p0 Young’s modulus E

1280 8.85×10-12 Fm-1 66 GPa

4.5.1 Arrangement and Optimisation of Sensor Network

Theoretically, to form a sensor network, one can employ a large number of sensors to configure a very dense network with spacing between two sensors similar to or smaller than the scale of the anticipated damage, which is consistent with biologically inspired nervous systems like those in the human body. However, such a dense sensor network is obviously impractical for engineering applications. The alternative is a sparse network using a relatively small number of sensors, with the sensor spacing far greater than the scale of the anticipated damage, which is the usual case in practice. The arrangement of sensors in a spare sensor network can be diverse, exemplified by several cases shown in Figure 4.17, with the purpose of damage identification. Ideally, sensors in a network should be placed in an optimal way, so as to achieve (i) the minimum number of sensors, but not at the cost of sacrificing adequate information to describe damage, meanwhile tolerating certain measurement uncertainties (i.e., the capacity of measurement redundancy); and (ii) sufficient sensitivity to damage-scattered waves. These two requirements have led to the substantial interest in design and optimisation of a sensor network, with the aim of reaching a compromise between converge and sensitivity. Design and optimisation of sensor networks includes identifying the number, location and types of sensors in order to detect damage effectively. Some basic considerations in this aspect include: (i) sensors and actuators should be positioned not too close to structural boundaries, so as to avoid mutual interference between damage-scattered and boundary-reflected waves; (ii) sensors should be positioned not too far away from the region where damage may exist, to be sensitive to damage-scattered waves; (iii) distances between actuators and sensors should be not too great, to ensure that waves do not attenuate excessively before being received;

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(iv) location and number of sensors should be not subject to the damage, i.e., they should be application-independent; and (v) the sensor network should possess a certain robustness, to maintain its stability and reliability if some sensors malfunction.

Actuator or sensor

Damage

Actuator or sensor

Damage

Actuator or sensor

Damage

Fig. 4.17. Possible actuator/sensor arrangement in a sensor network for Lamb-wave-based damage identification [69, 70]

However, optimisation of sensor location with respect to damage is in fact a problem of ‘the chicken or the egg’, as locating damage is the aim of a damage identification exercise. Although it is often very difficult to have prior knowledge of damage location in a structure introduced by an unpredictable event such as random impact of an object, it is well acknowledged that damage such as fatigue and corrosion cracking is likely to initiate and accumulate in certain areas/parts of structures where high energy concentration or high mechanical loads exist, combined possibly with hostile chemicals and elevated temperatures. In this way, a preliminary estimation of the possible damage locations may help in the design of a sensor network.

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Proposing a sensor network that accommodates all the aforementioned considerations is still a challenge. It is obvious that the more complex a structure is, the greater the number of sensors is and the more difficult it is to find appropriate locations for individual sensors. This complexity is related to the increased dimensionality of the optimisation problem. Most current research activity for optimal design of sensor networks is targeted at maximising the zone of coverage, minimising power consumption and minimising the number of sensors [71, 72]. To determine the best position of a sensor in a sensor network, classical optimisation algorithms (e.g., Newtonian methods, linear and nonlinear programming, heuristics), soft computing (e.g., genetic algorithms, simulated annealing) and information-based techniques (e.g., mutual information) have been widely adopted, comprehensively described elsewhere [73-77]. Most of these approaches are based on the assumption that a sensor network is an integral part of the structure under examination, and any damage to the structure consequently modulates the properties of the sensor network. Inversely, the positions at which sensors are most sensitive to damage can theoretically be determined in terms of the changes in properties of the sensor network. For example Guo et al. [77] developed an approach to optimise locations of individual sensors in a sensor network using a Fisher information matrix, which is based on a summation of the contribution of individual sensor locations to the determination of mode shapes of a structure. Tongpadungrod et al. [78] employed eigenvalues as performance indicators, to evaluate the suitability of a sensor location. Focusing more on wave-based damage identification, Staszewski et al. [79] demonstrated that three sensors are the minimum number required to triangulate a damage instance with acceptable accuracy. Kammer [80] proposed an effective independence algorithm to examine the contribution of a set of candidate sensor locations, whereby the minimum number and best position of individual sensors could be ascertained. Hemez and Farhat [81] extended Kammer’s method by introducing strain energy as an indicator for the level of optimisation. Miller [82] computed a Gaussian quadrature formula using a weight function, whose nodes suggested the optimal locations of sensors. Wouwer et al. [83] presented an optimality criterion for selecting sensor locations based on the digitised independence of sensor responses. Cobb and Liebst [84] and Shi et al. [85] reported an optimisation approach based on sensitivity analysis, which was then used to ascertain the minimum number of sensors required and the best positions of individual sensors. Azarbayejani et al. [86] established a probability distribution function to identify the optimal sensor locations such that damage could be efficiently detected. The function was based on a neural network trained by a priori knowledge database from finite element simulations containing various damage locations and damage severities. The validation results demonstrated that a sensor network designed in accordance with such a probability distribution function was more efficient than a sensor network with uniformly distributed sensors. Lee and Staszewski [76] simulated Lamb wave propagation in damaged structures with a series of possible sensor locations, concluding that when the first wave package in a signal (i.e., the transmission signal passing through the damage) is used for damage identification, the best strategy is to put the sensor close to the area that potentially contains the

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damage; however, when the second wave package in the signal (i.e., the signal reflected from the damage) is relied upon for identification, the best sensor positions are those in areas near the edge of the structure, so as to avoid wave reflection from boundaries. 4.5.2 Standardised Sensor Network

During optimisation of a sensor network using the aforementioned approaches, the sensor number and location must be prudently customised for individual applications. However, structures to be inspected are often geometrically diverse, and the locations of damage change from one to another. Motivated by methods adopted in the automotive industry for standardised accessories and parts, some standardised sensor network techniques have been developed, such as the standard sensor unit (SSU) [87]. In that approach, four PZT wafers are collocated to encircle a square area of 172.5 mm × 172.5 mm (changeable in different applications) and controlled by a signal excitation/acquisition circuit, Figure 4.18. With a two-way switch to enable each PZT wafer to serve as either actuator or sensor, a total of six actuator-sensor pairs, viz., 12 sensing paths, can be rendered by one SSU. Serving as a rudimentary unit in a sensor network, the SSU is collocable, and thus diverse sensor networks can be customised by appropriately assembling a certain number of SSUs to flexibly accommodate various geometrical identities and boundary conditions of structures. During assembly, the number of sensors can be minimised by retaining just one sensor at coalescent nodes of neighbouring SSUs. Two-way switche r Switch

172.5 mm

Control circuit PZT Sensor PZT element

To To Computer computer 172.5 mm

Valid area for damage identification

Fig. 4.18. Concept of SSU

As previously introduced (Section 3.3.1.2), to facilitate active selection of the desired Lamb mode in a specific propagation direction for damage identification, a sensor array technique, termed piezoelectric wafer active sensors (PWASs), has

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been developed [88-90]. In the array, a certain number of PZT wafers are strategically positioned in a straight line to form a standard sensor network. The Lamb wave generated by these phased PZT wafers is the superposition of the waves generated by each individual element in the array. Such a standard sensor array technique is advantageous in four aspects in particular: (i) since the side length of each square PZT wafer in a PWAS array equals the odd multiple of one-half the wavelength ( λwave 2 ) of a particular wave mode (provided that the distance between any two adjoining wafers remains constant), the resulting waves, i.e., superposition of the waves generated by individual elements in a PWAS array, have the dominant energy for this particular Lamb mode. This is an endeavour for optimal sensor location in a sensor network, so-called Lamb mode tuning, which was elaborated in Section 3.3.1.2; (ii) with sequential firing of individual elements in accordance with a certain time sequence, the Lamb wavefront can be focused or steered in a specific direction, with an improved SNR in this direction. This is called transmitter beamforming, and is further to be detailed in Section 6.2.7.1; (iii) in addition to serving as actuators, all the PZT wafers in a PWAS array can also function as sensors to capture signals scattered by damage. Similar to (ii), by setting a certain time delay in the signals captured by each wafer and then superimposing all the signals, the resulting signal scattered from the damage and then captured by the sensor array will be further enhanced in magnitude with a greater improvement in SNR. This is called receiver beamforming, and is further to be detailed in Section 6.2.7.2; and (iv) by progressively changing the direction of SNR-enhanced Lamb waves (i.e., a wave beam) in the half surface of the structure under inspection, sweeping of the beam is achieved electronically without physically manipulating the transducers, whereby the whole area of the structure can be scanned. This is called wave steering, and is further to be detailed in Section 6.2.7.3. A PZT wafer in PWASs weighs 0.068 g, is 0.2 mm thick, and costs around US$10. In contrast, a conventional ultrasonic transducer weighs 50 g, is 20 mm thick, and costs around US$300. A PWAS-based standard sensor network technique was applied to evaluation of a crack in a large aluminium plate measuring 1220 mm × 1220 mm, shown schematically in Figure 4.19. The sensor network consisting of nine square PZT wafers (7 mm × 7 mm each) was used to activate the tuned S 0 mode (aspect (i) above). The generated Lamb wave was then steered and swept the whole plate surface (aspects (ii-iv) above) to identify damage, if any, in the plate.

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Offside crack

A PWAS array of nine PZT elements

Aluminium plate (1200 mm× 1200 mm)

Fig. 4.19. Setup for evaluating crack of aluminium plate using a PWAS-based standard sensor network technique

4.5.3 Commercial Sensor Network Techniques

Following intensive laboratorial efforts, some sensor network techniques have been commercialised, represented here by the SMART Layer® and HELP Layer®3 techniques. The SMART Layer® (Stanford Multi-Actuator-Receiver Transduction Layer), Figure 4.20(a), marketed by Acellent® Technologies4, Inc., is based on research of active sensor networks at Stanford University [34, 91]. It integrates distributed PZT elements into a dielectric film to form an active sensor network which can be interfaced with a ‘SMART suitcase’ supported by the Acellent Software Suite (ACESS™) [34]. The SMART suitcase accommodates key components including a signal generator for activating customised diagnostic Lamb wave signals, a high-frequency data acquisition unit for capturing dynamic responses of structures, an amplifier and multi-channel processing software for field applications. ACESS™ provides a feature-filled graphic interface for creating and displaying sensor layouts, drives Lamb wave generation and signal acquisition, and manages data with plug-in application modules. As a thin (0.25 mm in thickness) and flexible layer, the SMART Layer® can be either embedded in a composite laminate or mounted on a structure, without noticeable deterioration to the integrity of the structure. The layer can be customised to different shapes to cater for various applications [20, 30, 76, 91-99].

3

HELP Layer® is a registered trademark owned by the French national aerospace research center, ONERA (Office National d’Etudes et Recherches Aérospatiales). http://www.onera.fr 4 Acellent® and SMART Layer® are registered trademarks and ACESS™ is a trademark of Acellent Technologies, Inc. 835 Stewart Dr. Sunnyvale, CA 94085, USA. http://www.acellent.com

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Dielectric film

Thin PZT element

SMART Layer®

a

b

To signal generator

Fibre-optic sensor

To optical device

PZT

c

d Fig. 4.20. Commercial sensor network techniques: a. SMART Layer® in various shapes for embedding in composites [100]; b. filament-wound composite fuel tank with embedded SMART Layer® [101]; c. hybrid sensor network with integrated PZT elements and fibreoptic sensors [20]; and d. HELP Layer® [102]

For instance, as shown in Figure 4.20(b), a filament-wound composite fuel tank was embedded with a SMART Layer®, whereby the integrity of the tank could be monitored during the filament winding process [101]. Partial sensors in the SMART Layer® can also be replaced with other types of sensor such as fibre-optic

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sensors, as shown in Figure 4.20(c), to form a hybrid piezoelectric actuator-optic sensor unit as introduced in Section 4.4. A number of applications have demonstrated that the SMART Layer® technique can detect a surface crack as small as 4 mm in length and a through-thickness crack as small as 2 mm in depth in a high pressure engine pipe [93], and the layer remains functional under the combined cryogenic temperature, vibration and shock loads [93]. Unlike the SMART Layer® which activates and captures Lamb waves, the rationale of the HELP Layer® (Hybrid Electromagnetic Performing Layer), in Figure 4.20(d), developed by the French Aeronautics and Space Research Centre (ONERA) [102-104], is based on the fact that structural abnormality, if any, alters the electromagnetic field near it. This layer consists of a circuit printed on a 100 m-thick dielectric substrate film, including a double network of crossed wires, one for generating a local magnetic field and the other for measuring the electric field. The layer allows the detection of variations in local electric conductivity and dielectric permittivity induced by mechanical or thermal damage.

4.6 Recent Developments The period from the 1980s to the present day has witnessed the rapid development of sensor network techniques. Some recent advances at the frontier of this emerging technology include the large-scale sensor network and wireless sensors. 4.6.1 Large-scale Sensor Network

The demand for NDE and SHM in modern large structures such as airframes or infrastructure has necessitated the development of large-scale sensing networks that may consist of hundreds or even thousands of sensors, like the nerve system in an organism. The approach termed a structural neural system (SNS) [105] is an example of large-scale sensor network techniques. SNS employs a large number of piezoelectric sensors and analog electronics, and mimics the synaptic parallel computation networks in the human biological neural system. The piezoelectric sensors in SNS capture wave signals scattered by structural damage, if any. Although a large number of sensors are involved, the network has the capacity to reduce data acquisition channels while maintaining the ability to extract substantial structural response information. The number of channels for data acquisition is reduced from N 2 in a conventional data acquisition system to 2 N via appropriate algorithms ( N standing for the number of sensor of the sensor network) [105]. Success in evaluating damage growth in an in-service composite structure has demonstrated that a network designed in accordance with SNS concept can greatly simplify the development of a sensor network and enhance its performance for the purpose of NDE and SHM.

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4.6.2 Wireless Sensor

Today’s sensors are, for the majority, dumb, stuck in place and requiring weighty wiring. Though coaxial wires provide a reliable communication link, the installation of these wires or cables in structures can be expensive and labour-intensive. In civil engineering, sensors installed in high-rise buildings for SHM have been reported to cost in excess of US$5000 per sensing channel on average [106]. For example, the total cost of installing over 350 sensing channels on the Tsing-Ma bridge in Hong Kong was over US$8 million [106]. In the aerospace industry, complex sensing systems require additional expenditures with respect to cabling and electronics. Sensor positions in remote locations of an aircraft would make cable connections difficult to install and maintain. Even so, these wires are susceptible to breakage and vandalism in service. Insights from rapid advances in wireless sensor technology have led to new solutions and opportunities for addressing the above concerns. In combination with local signal acquisition, conditioning, processing and wireless communication supported by various protocols, wireless sensors eliminate the cost of cable deployment and the degradation of reliability due to the ageing of cables in traditional SHM systems, significantly reducing the complexity of the system. With the capacity for liberal distribution, a wireless sensor can be placed where it would be impractical to arrange data and power wires using traditional sensor network techniques, with potential reduction in the cost and consumption of power (a wireless sensor can usually be driven by power at a level of mW only, which means that an AA battery can continuously supply the power required to maintain the functionality of a wireless sensor for about 10 years [107]). Wireless techniques have distinct advantages such as simple installation, costeffectiveness, flexibility and the capacities of being reconfigurable, scalable, and remotely accessible. As information can be processed locally and interpreted within a wireless sensor, communication traffic can be greatly streamlined, thus holding the promise of developing a real-time SHM system with a large-scale coverage [108]. A comprehensive review of SHM techniques in conjunction with use of wireless sensors can be found elsewhere [106]. A wireless sensor is not a sensor per se; it is actually a platform or interface, to which diverse traditional actuators or sensors (e.g., PZT elements, accelerometers, strain gauges, and piezoelectric macrofiber composite (MFC) introduced in Chapter 3) can be attached, to form a wireless sensor unit, based on the chip-on-board technology. In brief, a wireless sensor unit consists of a miniaturised wireless platform, an attached sensor, a data acquisition unit, a wireless data transmitter and integrated signal processing and computing algorithms. As an example, a wireless sensor unit is shown in Figure 4.21, in which the lowest section is a supporting module attached directly to a battery holder and wired to the batteries; the signal processing section is in the middle; the transduction section is topmost. A traditional transducer, such as a piezoelectric element in this example, is then connected to the platform with wires, to activate and capture Lamb wave signals. Lamb wave signals captured by wireless means such as in this example are in very good agreement with those collected by wired sensors [109].

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Wireless base PZT element

Fig. 4.21. A wireless sensor unit including wireless platform and attached PZT element for capturing wave signals [109]

To date, a few wireless sensor platforms have been developed [110-113]. The Berkeley MICA Mote and MICA2 Mote are two of the most popular platforms. Based on those platforms, various wireless sensor networks can be further developed [114]. The majority of wireless sensors proposed for use in SHM operate at unlicensed radio frequencies. In the United States, 900 MHz, 2.4 GHz, and 5.0 GHz have been designated by the Federal Communications Commission (FCC) as the unlicensed industrial, scientific and medical (ISM) frequency bands [106]. Although still in the infancy stage for use in Lamb-wave-based damage identification, the potential of wireless technology is mind-boggling. Lynch et al. developed a wireless-driven PZT element sensor unit to excite and receive low energy Lamb waves along a plate surface [115]. With the aim of lowering the power consumption for long-distance data transmission, Kim et al. [116] fabricated a wireless sensor on a piezoelectric substrate in virtue of a microelectromechanical system technique. Since it incorporates microelectronics and conformal antennas with chip-sized transducers, this sensor can activate Lamb waves using little energy. Ihler et al. [117] examined various wireless piezoelectric sensor networks and compared different strategies of wireless sensing (passive without on-board energy supply, active with on-board power supply and active without on-board power supply) in terms of the power consumption, frequency selection, signal modulation and basic prerequisites for embedding the sensors into a CF/EP composite structures. They concluded that the passive strategy (all power has to be transmitted from remote sites), featuring small electrical circuits and simple electronics and therefore needing less space, was most suitable for the embedment of sensors in composite structures, but its applications were limited to cases using low frequency waves and with short distance of energy or signal transmission. Ihler et al. further concluded that the active strategy with on-board power supply provided energy for continuous measurement, storage of the data in memory and processing of data, and could capture high-quality signals. But the lifetime of the on-board power supply constrains its applicability to periodical activation of signals only, and the requirement of space for integrating the complex electronics and on-board power supply further limits its application to cases where embedding sensors is not required. Finally, it was found that the active strategy without

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on-board power supply was most flexible with respect to network configuration, continuous measurement and transmission demand. But such a strategy needs the most energy, the greatest volume and the most complex electronics, leading to a large system with relatively high power consumption, and therefore is not appropriate for most SHM. Liu and Yuan [118] proposed an approach, called direct memory access, for signal acquisition using a wireless sensor unit, with the aim of significantly improving sampling speed up to 900 kHz and power efficiency. Varadan and Varadan [119] developed a Lamb-wave-based damage identification approach in conjunction with a wireless PZT sensor network. Lamb waves at a central frequency of 350 kHz were activated and captured using PZT actuators and sensors attached on wireless platforms. Based on the wireless sensing technique, a small local diagnostic device was further developed and embedded into an aircraft wing panel to monitor the integrity of the wing panel [114]. It should be pointed out that the major obstacle to applying the wireless sensor technique to practical Lamb-wave-based damage identification lies in the fact that wireless sensors work well for capturing signals with a relatively low acquisition rate up to several hundred Hz or low kilohertz, limited by the capacity of the current chip-on-board system. That capacity is not adequate to accommodate the acquisition of signals with frequencies up to middle or high kilohertz or even megahertz, at which Lamb waves are often activated. This challenging issue may have recently been circumvented by a new wireless platform developed on a novel-dual-controller-based centralised architecture [109]. Such a wireless platform can support a sampling rate up to 20 MHz, sufficient to fulfill the requirements of Lamb wave acquisition. On the other hand, to save energy, as well as taking steps to lower power consumption [108], one can apply dynamic power management, whereby wireless sensors are programmed to automatically turn on or power down. With low duty cycles, a wireless sensor spends most of its time in hibernation mode and only resumes in the active mode for a small fraction of its lifetime. Performing data interrogation locally so as to reduce communication traffic has also been envisioned as a promising method to reduce power consumption [120]. In addition, improving the power efficiency of wireless communication by means such as communication protocols [121] and routing strategies [122] is another feature attracting increasing attention from researchers.

4.7 Summary The past two decades have witnessed an explosion of sensor technology for application in various sectors of industry, and the NDE community is no exception. A wide range of actuators/sensors have been developed particularly for activating and receiving Lamb waves, exemplified by piezoelectric elements and fibre-optic sensors (e.g., FBG sensors). Both are widely used in Lamb-wave-based damage identification, delivering great cost-effectiveness in activation and acquisition of Lamb wave signals. Surface-bonding and embedding are two ways of integrating a PZT element or fibre-optic sensor into a host structure. The former provides great convenience in attachment, maintenance and replacement, whereas the latter has

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advantages of less exposure of sensors to the environment and consequently higher SNR of captured signals. Unlike PZT elements receiving signals omnidirectionally, FBG sensors present strong directivity in capturing a wave signal, and a basic consideration is that the sensor should be placed parallel to the major direction of wave propagation. All the above observations imply that the shape, size, planar and thickness-wise position, orientation of a sensor and its attachment manner to the host structure, whatever the sensor type, are essential factors to take into account during selection of sensors and design of a sensor network. A hybrid PZT-FBG sensor unit is a solution that fully exploits the particular merits of two sorts of sensors. In order to bring Lamb-wave-based damage identification techniques closer to real field deployment, several packaged versions of piezoelectric transducers are now available commercially, typified by the SMART Layer®. Sensor network techniques have been introduced to diminish the strong dependence of signal acquisition on a particular single sensor. With a sensor network, ample information can be obtained for damage identification. The wireless sensor network, which integrates transducers with on-board power sources, computing chips and wireless telemetry, is an emerging development in recent years, though its mature application to Lamb-wave-based damage identification is still under investigation.

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5 Processing of Lamb Wave Signals

5.1 Introduction Substantially dependent on signals captured by a sensor or sensor network, the accuracy and precision of a Lamb-wave-based damage identification approach is largely subject to the processing and interpretation of signals. Captured Lamb wave signals carry comprehensive information as to interference existing in the path of wave propagation, such as damage in the medium. All the transducers described in Chapters 3 and 4 would be able to capture Lamb wave signals, although their efficiency and precision varies. Theoretically, some changes, more or less, always occur in the captured signals when damage exists. The key is to correctly tease out these changes and then associate them with particular variations in damage parameters (e.g., presence, location, size and severity). It sounds straightforward, but many challenging problems complicate this process, because of the existence of multiple wave modes, dispersion, mode conversion, superposition of scattered waves from structural boundaries or irregularities (e.g., joints, stiffeners and openings), broadband noise and other features. It is axiomatic that appropriate signal processing is of vital necessity and importance for correct damage identification. Efficient signal processing is expected to extract essential yet concise characteristics (e.g., magnitude, frequency, energy, wave speed and travelling time) from raw signals, to assist in assessment of damage parameters in conjunction with appropriate data fusion algorithms (to be addressed in Chapter 6). Approaches to signal processing for Lamb-wave-based nondestructive evaluation (NDE) and structural health monitoring (SHM) are legion, forming the main subject of this chapter. There is no clear demarcation between signal processing approaches for NDE and for SHM, but extra demands are normally imposed by the latter: the processing should be automated and capable of running in a nearreal time manner or at frequent intervals, preferably during the operation of the structural frames [1]. Z. Su and L. Ye: Identification of Damage Using Lamb Waves, LNACM 48, pp. 143–193. springerlink.com © Springer-Verlag Berlin Heidelberg 2009

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5.2 Digital Signal Processing In what follows, we limit our discussion to the processing of Lamb wave signals in a digital scope, i.e., digital signal processing (DSP). DSP is the study of any signals in digital representation. A complementary insight into the principles and mathematical foundation of DSP for elastic wave signals can be found elsewhere [2]. As a result of intensive efforts over the years a variety of DSP approaches is available. A popular taxonomy for categorising these approaches is in terms of the domain where the processing is conducted, i.e., time domain, frequency domain and joint time-frequency domain analyses. 5.2.1 Time Domain Analysis In most cases, a captured Lamb wave signal is presented in the time domain. A time-series signal inherently records the propagation history of Lamb waves travelling in a structure, thereby providing the most straightforward information about the waves, such as existence of various wave modes, propagation velocity, attenuation and dispersion with distance, scattering from a structural boundary or damage. The characteristics contained in a time-series Lamb wave signal, f (t ) , that may be beneficial to damage identification include the absolute value of magnitude ( f (t ) ), the root mean square (RMS) of the signal (

1 T2 − T1

T2

∫f

2

(t ) ⋅dt ,

T1

where T1 and T2 are the starting and ending time moments for signal acquisition, respectively), standard deviation, kurtosis, characteristic time moment, trend, cyclical component, time-of-flight (ToF, i.e., the time consumed for a specific wave mode to travel a certain distance), etc. All these characteristics can be modulated to a greater or lesser degree in the presence of structural damage. In view of the fact that the propagation of Lamb waves is continuous transportation of energy in kinetic and potential forms, a time-series Lamb wave signal f (t ) is often examined in accordance with its energy distribution in the time domain, defined as [3]

E=

∫

2

f (t ) dt ,

(5.1)

t ≥0 2

2

where f (t ) is the energy density per unit time at moment t , and thus f (t ) ⋅ Δt denotes the fractional energy within the time interval Δt at that moment. Mathe2

matically, f (t ) has a higher sensitivity than amplitude f (t ) to changes or singularities in the signal. DSP in the time domain is typified by the Hilbert transform, correlation, time reversal, exponential smoothing, regression (curve-fitting), extrapolation, differencing

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and decomposition. All of these approaches can globally or locally extract the aforementioned characteristics from a time-series Lamb wave signal. 5.2.1.1 Hilbert Transform The Hilbert transform is an approach aimed at canvassing a Lamb wave signal in the time domain in terms of its energy distribution [4-11], defined as [2] H (t ) =

1

π

+∞

f (τ )

∫ t − τ dτ .

(5.2)

−∞

H (t ) is the Hilbert transform of signal f (t ) . Equation 5.2 performs a 90° phaseshift or quadrature filter to construct a so-called analytic signal FA (t ) :

FA (t ) = f (t ) + iH (t ) = e(t ) ⋅ eiφ (t ) , e(t ) =

f 2 (t ) + H 2 (t ) , and

φ (t ) =

(5.3a) 1 d H (t ) , ⋅ arctan f (t ) 2π dt

(5.3b)

whose real part is the signal f (t ) itself and whose imaginary part is its corresponding Hilbert transform, H (t ) . e(t ) is the module of FA (t ) and φ (t ) is the instantaneous frequency of FA (t ) . The envelope of e(t ) depicts the energy distribution of f (t ) in the time domain. The Hilbert transform can be fulfilled using a fast Fourier transform (FFT), detailed in a subsequent section. Using Equation 5.3, the energy envelope of a Lamb wave signal captured in a carbon fibre-reinforced epoxy (CF/EP) composite laminate containing delamination is displayed in Figure 5.1, from which the energy distribution of the signal becomes explicit and global or local features such as instantaneous frequency, magnitude and damping characteristic can further be extracted. As another example, Figure 5.2(a) shows a Hilbert transform-processed Lamb wave signal captured in an aluminium plate with a crack, and the instantaneous frequency of the signal, φ (t ) , is displayed in Figure 5.2(b). The sudden change in

φ (t ) at the time moment of 14.5 s implies that damage may have occurred at that moment and the degree of change in φ (t ) can further be used to quantify the severity of the damage. However, the processing of a Lamb wave signal solely in the time domain can be effectively accomplished only if the signals contain pure Lamb mode and the structure under inspection is geometrically simple. The task can become highly intractable if a captured signal is rich in Lamb modes overlapping with each other or is obscured by broadband ambient noise.

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1.0

1.0

Benchmark Plate

Benchmark Plate

Normalised amplitude

Normalised amplitude

0.8

0.5

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a

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Fig. 5.1. a. A Lamb wave signal captured in a CF/EP composite laminate containing delamination; and b. the envelope of energy distribution of the signal in a. obtained using the Hilbert transform [12] 30

1.5 23 mm crack 50 mm crack

20

Frequency [MHz]

Relative amplitude

1.0 10

0

Sudden change in frequency at 14.50 s 0.5

0 -10

-20

-0.5 0

5

15

10

Time [ s]

a

20

25

0

5

10

15

20

25

Time [ s]

b

Fig. 5.2. Hilbert transform for identifying crack in an aluminium plate: a. Lamb wave signal captured in an aluminium plate; and b. its corresponding instantaneous frequency curve obtained using the Hilbert transform [2]

5.2.1.2 Correction ‘Damage’ is a structural state different from the pristine state that is supposed to be ‘healthy’; that is to say, the states of ‘damage’ and ‘health’ are defined relatively. Implicit in this definition, a damage event is not meaningful without a comparison between two different states. To facilitate such a comparison and to highlight the difference, a Lamb wave signal captured in a structure under inspection is often evaluated against its counterpart signal in the benchmark structure by using correlation in the time domain. An abnormality such as damage in the

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147

structure can thus be detected and quantified with respect to the healthy state. In such a correlation processing, the correlation coefficient, λxy , of two discrete time-series Lamb wave signals of the same length (i.e., both having N sampling points), xi and yi , ( i = 1, 2, A , N ), is defined as [13-15]

λxy =

N

N

i =1

i =1

N

N ∑ xi yi − ∑ xi ∑ yi i =1

,

N

N

N

N

N ∑ xi − (∑ xi ) ⋅ N ∑ yi − (∑ yi ) 2

2

2

i =1

i =1

i =1

(5.4a)

2

i =1

or N

λxy =

C xy

σ x ⋅σ y

∑ ( x − µ )( y − µ i

=

x

i

y

)

i =1

∑ (x − µ ) i

i =1

x

,

N

N

2

⋅

∑(y − µ i

y

)

(5.4b)

2

i =1

where Cxy , µ and σ are the covariance, mean and standard deviation of xi and yi , distinguished by subscripts for two signals. When signal xi is very close to signal yi , the correlation coefficient in Equation 5.4 reaches unity; the greater the similarity between two signals the closer to unity is the coefficient. If a signal is correlated with itself, which can be realised by sliding its mirrored signal along the time axis, the correlation is auto-correlation. For illustration, two Lamb wave signals, captured in a CF/EP composite laminate before (i.e., the benchmark) and after the presence of delamination, in Figure 5.3(a) and (b), respectively, are auto-correlated with regard to themselves from i = 1 in Equation 5.4, and the results are shown in Figure 5.3(c). To emphasise the discrepancy between them, the correlation coefficients of the damaged laminate are divided by those of the benchmark to obtain the ratio curve, in Figure 5.3(d). In the ratio curve, the singularity contributed by the delamination-induced extra wave energy (the peak in magnitude) becomes pronounced (circled in the figure), and its corresponding time moment can thus be used to locate the damage. One great advantage offered by such correlation processing is the weakening of the boundary effect, since the same or similar boundary reflection of waves exists in all signals regardless of the presence of damage, and no singularity would be incurred in the ratio curve. 5.2.1.3 Time Reversal – for Improving Quality of Signal Time reversal is a signal processing approach originating from the scenario based on reciprocity of the wave equation (Equation 2.1), which is mathematically guaranteed by the fact that the wave equation contains only even order derivatives. Reciprocity presumes that if there is a solution to a wave equation, then the time

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reversal of that solution is also a solution to the wave equation [16, 17]. In other words, for a given process, the solution to the wave equation at time t is the same as that at time −t , even though the waves may be reflected, refracted or scattered by inhomogeneities in the medium where waves travel. However, this paradox does not hold for macroscopic processes in the real world that are irreversible and dissipative in nature. Some media are not reciprocal (e.g., very lossy or noisy media), but many are approximately so. For example, sound waves in water or air, ultrasonic waves in human bodies, alloy or composites, and electromagnetic waves in free space are all approximately reciprocal examples. Detailed theory concerning time reversal can be referred to elsewhere [16]. 1.0

1.0

Delaminated Plate

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1.0

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0.6

0.4

0.2

Delaminated Plate 0.0 0.0

50.0µ

100.0µ

150.0µ

200.0µ

Ti Diff Time difference

c

250.0u

300.0u

350.0u

300.0µ

350.0µ

T [s]

b Ratio of correlation coefficients

a

0.8

200.0u

Ti [ ] Time difference

T [s]

250.0µ

[ ] TT[s]

300.0µ

350.0µ

1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 0.0

50.0µ

100.0µ

150.0µ

200.0µ

Diff TimeTidifference

250.0µ

ΔT ] T[[s]

d

Fig. 5.3. Lamb wave signals captured in a CF/EP laminate: a. before (benchmark); and b. after introduction of delamination (after being normalised by magnitude extremum of the signal in benchmark laminate; excitation frequency: 250 kHz); c. correlation coefficient curves of two signals in a. and b.; and d. ratio of signal correlation coefficients of delaminated to benchmark laminate [12]

In accordance with the time reversal concept, an input signal, f (t ) , can be reconstructed at excitation point A, if the output signal recorded at point B is re-emitted

Processing of Lamb Wave Signals

149

back to Point A after being reversed in the time domain, f (−t ) , i.e., the waveform is reversed. In this procedure, the sensor and actuator exchange their role, i.e., sending back the time-reversed signal from the sensor to the actuator. This process can be better understood with the aid of Figure 5.4. The time reversal technique was introduced into Lamb-wave-based damage identification for two main purposes: (i) it is used as a signal processing tool for improving the quality of Lamb wave signals [16, 18-21] or compensating for wave dispersion [16, 19, 22], particularly when the damage is small, the captured signal is weak, environmental noise is strong or strengthening of signal-to-noise ratio (SNR) is required; and (ii) it is used as an inverse inference algorithm for damage identification [19-26]. Purpose (i) falls into the category of signal processing and is elaborated in this section, whereas purpose (ii) is an identification algorithm which is described in Chapter 6.

Forward wave

(b) Response signal

(d) Restored signal

(a) Input signal

Backward wave

(c) Re-emitted signal

Fig. 5.4. Concept of time reversal: a. actuator A sends an input Lamb wave signal; b. sensor B captures the response signal; c. sensor B (now serving as an actuator) sends the reversed waveform of the signal that is captured in step b; and d. actuator A (now serving as a sensor) captures the response signal [25]

Being dispersive, a Lamb wave signal captured by a sensor, particularly in a remote position, exhibits certain dispersion and distortion of the waveform. This effect can be compensated efficiently by using time reversal. When a Lamb wave signal is excited, the component in the wave packet with the highest velocity is at the wavefront, arriving at the sensor position earlier, followed by components of lower velocities. During the time reversal process, the captured signal is reversed first in the waveform, and then re-emitted from the sensing location. After the reversal, the wave component, which originally travelled at the slowest speed and arrived last at the sensor location, will arrive at the original source location first. Therefore, all the components in the wave packet travelling at different speeds precisely retrace and converge concurrently at the original source location, compensating for the dispersion and distortion. These wave signals after time reversal (i.e., after compensation)

150

Identification of Damage Using Lamb Waves

can be treated as though they were the actual signals captured by the sensor, and used for subsequent damage identification. In this way, the characteristics of the wave signals such as magnitude, energy, and ToF, can be more effectively ascertained without interference from wave dispersion and distortion. For illustration, Figure 5.5(a) shows narrowband tonebursts at a central frequency of 100 kHz, activated by a piezoelectric actuator. Propagating in a composite plate, the signal received by a piezoelectric sensor far away from the actuator is shown in Figure 5.5(b). In the signal, pronounced wave dispersion can be seen. With application of time reversal processing, the sensor-captured signal is reversed in time and then re-emitted from the sensor location back to the actuator location, to compensate for the dispersion of the Lamb wave. The signal after compensation is shown in Figure 5.5(c), and it can be considered as the signal captured by the sensor without any dispersion. 1.0

Normalised amplitude

Normalised amplitude

1.0

0.5

0

-0.5

-1.0

0.5

0

-0.5

-1.0 0

0.1

0.2

0.3

4.7

4.8

4.9

5.0

Time [ms]

Time [ms]

a

b

Normalised amplitude

1.0 Original input signal Reconstructed signal

0.5

0

-0.5

-1.0 0

0.1

0.2

0.3

Time [ms]

c Fig. 5.5. Reconstruction of a narrowband input wave signal using time reversal: a. original input signal (100 kHz tonebursts); b. response signal captured by sensor; and c. reconstructed signal (solid) and original input signal (dotted) [21]

In the above example, when the input signal of narrowband tonebursts is replaced by a broadband Gaussian pulse, as shown in Figure 5.6(a), more severe wave dispersion is observed after the wave propagates over the same distance, Figure 5.6(b).

Processing of Lamb Wave Signals

151

Even when time reversal processing is applied, wave dispersion in the reconstructed signal, in Figure 5.6(c), is not well compensated for. This is because the components of the various frequencies involved in the broadband Gaussian pulse are differently scaled and superimposed during the time reversal process. This observation confirms the conclusion (Section 3.3.2) that a narrowband rather than broadband input signal should be selected as the diagnostic signal for damage identification.

1.0

Normalised amplitude

Normalised amplitude

1.0 0.5

0

-0.5

-1.0

0.5

0

-0.5

-1.0 0

0.1

0.2

0.3

4.7

4.8

Time [ms]

4.9

5.0

Time [ms]

a

b

Normalised amplitude

1.0 Original input signal Reconstructed signal

0.5

0

-0.5 Discrepancy

-1.0 0

0.1

0.2

0.3

Time [ms]

c Fig. 5.6. Reconstruction of a broadband input wave signal using time reversal: a. original input signal (a Gaussian pulse); b. response signal captured by sensor; and c. reconstructed signal (solid) and original input signal (dotted) [21]

With time-reversal-based signal compensation, the quality of a Lamb wave signal can be much improved, benefiting damage identification. For example, defects as small as 0.4 mm in a titanium billet of 250 mm diameter can be detected with the aid of time-reversal-based signal processing [24].

152

Identification of Damage Using Lamb Waves

5.2.2 Frequency Domain Analysis

5.2.2.1 Fourier Transform (FT) and Fast Fourier Transform (FFT) To reveal singularities induced by structural damage, which may not be clearly ascertained in the time domain, a Lamb wave signal, f (t ) , is often transferred into the frequency domain through the Fourier transform (FT), defined as [3] F (ω ) =

∫

+∞

−∞

−2π iωt

f (t ) ⋅ e

dt ,

(5.5)

where ω and i are the angular frequency and unit complex, respectively. F (ω ) is the Fourier counterpart of f (t ) in the frequency domain. Equation 5.5 mathematically defines the signal as the summation of a series of simple constituent sines and cosines, with different amplitudes F (ω ) and frequencies ω . Inversely, f (t ) can be reconstructed via the inverse Fourier transform (IFT)

f (t ) =

∫

+∞

−∞

F (ω ) ⋅ e 2πiωt dω .

(5.6)

Since a captured Lamb wave signal f (t ) is presented by N discrete sampling points in DSP, xi ( i = 1, 2, A, N ), Equation 5.5 is often expressed in a discrete form, called the discrete Fourier transform (DFT) N

X k = ∑ xn e

−

2π i kn N

( k = 1, 2, A, N ),

(5.7)

n =1

where X k is the Fourier counterpart of x k in the frequency domain. The FFT is a mathematic tool for computing the DFT and its inverse. With enhanced efficiency, FFT reduces the number of computations needed from 2N 2 to 2 N log 2 N , in obtaining the DFT of a signal containing N sampling points. The improvement in calculation speed can be substantial, especially for a Lamb wave signal recorded within a long time period in practical applications where N may be in the thousands or millions. The most common FFT algorithm is the CooleyTukey algorithm; other algorithms include the prime-factor, Bruun’s, Rader’s and Bluestein’s FFT algorithms [3]. In a similar fashion to that in Equation 5.1, the energy of signal f (t ) in the frequency domain can be described as E=

1 2π

∫

+∞

−∞

2

F (ω ) dω .

(5.8)

Processing of Lamb Wave Signals

Likewise, F (ω )

2

153

in the above equation is the energy density per unit fre2

quency at ω , and thus F (ω ) ⋅ Δω is the fractional energy within the frequency interval Δω at ω . Considering conservation of energy and combining Equations 5.1 and 5.8, we obtain E=

∫

2

f (t ) dt =

t ≥0

1 2π

∫

+∞

−∞

2

F (ω ) dω .

(5.9)

5.2.2.2 Digital Signal Filter A Lamb wave signal usually contains a variety of components in a wide frequency range, of which only certain bands are of interest for damage identification, such as bands whose central frequency is the same as that of activation. A digital filter developed using FT and FFT is the major approach used for extracting the components of interest from raw Lamb signals. In a mathematical expression, a digital filter is a linear transfer function, to convolve and weight a discretised Lamb wave signal, f (n) , ( n = 1, 2, A , N ), described by N sampling points, [27] f ′(n) = δ (n) ∗ f (n) ,

(5.10)

where f ′(n) is the filtered signal and δ (t ) is the filter function. The counterpart of Equation 5.10 in the frequency domain is [27] F ′(ω ) = Δ(ω ) ⋅ F (ω ) =

b1 + b2 e − iω (1) + b3e − iω ( 2 ) + A + bn e − iω ( n−1) ⋅ F (ω ) , a1 + a2 e −iω (1) + a3e −iω ( 2) + A + a m z −iω ( m−1)

(5.11)

where F ′(ω ) , F (ω ) and Δ (ω ) are the Fourier transform pairs of f ′(n) , f (n) and δ (n) , respectively. ai , ( i = 1, 2, A, m ) and bi , ( i = 1, 2, A, n ) are the filter coefficients. Digital filter design is actually the process that seeks the most suitable filter coefficients, ai and bi , to cater for certain filtering requirements. By setting the filter coefficients, i.e., ai and bi , as different values in Equation 5.11, a digital filter for a Lamb wave signal can be one of following, in terms of the filtering effect [27]: (i) low-pass filter (transmitting wave components with frequencies below a threshold and excluding others); (ii) high-pass filter (transmitting wave components with frequencies above a threshold and excluding others); (iii) bandpass filter (transmitting wave components within a particular range of frequencies and excluding others); and (iv) band-stop filter (stopping components between a lower and a higher cut-off frequencies).

154

Identification of Damage Using Lamb Waves

However, when the wave components of interest are in the same frequency band as those not of interest, FT- or FFT-based filtering becomes inefficient to isolate them. It should also be noted that the use of the FT and FFT to transfer a wave signal from the time to frequency domain comes at the cost of loss of temporal information of the signal such as magnitude of signal amplitude and ToF. 5.2.2.3 Two-dimensional FT and FFT (2D-FT/FFT) To separate different wave components or multiple wave modes which share the same frequency range in a Lamb wave signal, two-dimensional FT (2D-FT) [2834] is one among a number of diverse applicable methods. 2D-FT assumes that in a harmonic regime the surface displacement u ( x, t ) induced by the propagation of Lamb waves along a plate in the x direction is a function of spatial location, x , and time, t [28, 29],

u ( x, t ) = A(ω )ei ( kx −ωt −ϕ ) ,

(5.12)

0

where A(ω ) is the frequency-dependent amplitude of the wave, ϕ0 denotes the phase and ω is the angular frequency ( ω = 2π f ). The wavenumber, k , inversely proportional to the wavelength, is given by k = ω c p ( c p is the phase velocity). Equation 5.12 implies that Lamb waves have harmonically varying components in both time and space (in the propagation direction). It also indicates that, based on the responses of the plate captured at a series of equally spaced positions along the plate surface, the magnitudes of different Lamb wave modes at different frequencies can be discerned in a frequency-wavenumber domain by H (k , f ) =

∫∫ u ( x, t )e

−i ( kx −ωt )

dx ⋅ dt .

(5.13)

This process, named 2D-FT, links the magnitudes of different Lamb modes in a wave signal with wavenumber and frequency. More often, a two-dimensional FFT (2D-FFT) algorithm is used [29-32, 35] because of the improved capacity of calculation of FFT previously described. This algorithm can present a Lamb wave signal in a two-dimensional contour plot or a three-dimensional plot of magnitude versus wavenumber and frequency, as in the example shown in Figure 5.7. In the figure, various Lamb modes propagating in a thin copper plate can be isolated, allowing clear recognition of multiple wave modes even within the same frequency band.

Processing of Lamb Wave Signals

155

20

Frequency [MHz]

16

12

8

4

0 0

4000

2000

6000

Wavenumber [m-1]

Fig. 5.7. Spectrum of a Lamb wave signal obtained using 2D-FFT [29]

Since 2D-FT/FFT needs Lamb wave signals captured at different locations, a great number of sensors are required. Laser-based ultrasonics (Section 3.2.3) may help to avoid excessive consumption of sensors. 5.2.3 Joint Time-frequency Domain Analysis

It is a corollary to combine the analyses in the sole time and sole frequency domains so as to avoid any potential loss of information carried by a Lamb wave signal, leading to the joint time-frequency domain analysis. The joint timefrequency domain analysis is exemplified by the short-time Fourier transform (STFT), Wigner-Ville distribution (WVD) and wavelet transform (WT), all of which can be generalised as [3] S (t , ω ) =

∫∫∫e

δ τ θ

τ τ φ (θ , τ ) ⋅ f * (δ − ) ⋅ f (δ + ) ⋅ dδ ⋅ dτ ⋅ dθ ,

−2π i (θt +τω +θδ )

2

2

(5.14)

where S (t , ω ) is the energy intensity at time moment t and frequency ω of a Lamb wave signal f (t ) , and f * denotes its complex conjugate. φ (θ ,τ ) is a function depending on f (t ) . Equation 5.14 two-dimensionally deploys a time-series Lamb wave signal in a time-frequency space, as in the example shown in Figure 5.8, where features concerning ‘when’ (time) and ‘who’ (component of a specific frequency) of the signal are exhibited simultaneously. Such a plot reflecting information of spectral amplitude in the time-frequency domain is called spectrogram [36].

Identification of Damage Using Lamb Waves

Time [ s]

156

Energy concentration

Amplitude

Frequency [MHz]

Fig. 5.8. Spectrum of a Lamb wave signal captured in an aluminium plate obtained using joint time-frequency analysis [14]

5.2.3.1 Short-time Fourier Transform STFT applies the basic FT on a small signal segment about time moment t , by multiplying a time window function (i.e., ‘short time’), r (t ) (commonly a Hanning or Gaussian window) and neglecting the rest of the signal. This operation is then continued by moving the short time window along the entire time axis, to obtain the energy spectrum of the full signal, as [3] S STFT (t , ω ) =

∫

+∞

−∞

f (τ ) ⋅ r (τ − t )e −2π iωτ dτ ,

(5.15)

where t and ω are the time and angular frequency, respectively. S STFT (t , ω ) is actually the FT of f (τ ) ⋅ r (τ − t ) (referring to Equation 5.5) over the period of the applied short time window. With its ability to simultaneously unveil features as to the time and frequency of a signal, STFT has found a great number of applications in Lamb wave signal processing [36-40]. As an illustration, upon application of STFT to Lamb wave signals captured within a frequency range from 60 to 580 kHz in Figure 5.9(a), the energy distribution of various Lamb wave modes in the signals at different time moments and frequencies can be obtained, presented two-dimensionally in Figure 5.9(b). Thus the approach assists in selecting an optimal excitation frequency at which the activated signal has a high SNR. However, because of the unalterable window size, satisfactory precision cannot be obtained along the time- and frequency-axes synchronously. Therefore STFT may not be the optimal choice for analysing wave signals whose instantaneous frequency varies rapidly.

157

Frequency [kHz]

Frequency [kHz]

Processing of Lamb Wave Signals

Time [ s]

Time [ s]

a

b

Fig. 5.9. a. Collected Lamb wave signals within a frequency range from 60 to 580 kHz; and b. the corresponding spectrum obtained using STFT [36]

5.2.3.2 Wigner-Ville Distribution Transform Accordingly, a flexible choice of window size becomes attractive, and this can be achieved by the WVD transform [38, 41-44], formulated as [42] +∞

τ

τ

SWVD (t , ω ) = ∫ f (t + ) ⋅ f * (t − )e −2π iωτ dτ . −∞ 2 2

(5.16)

τ τ Equation 5.16 is actually the FT of f (t + ) ⋅ f * (t − ) (referring to Equation 5.5) 2

2

at time moment t , and as a result, SWVD (t , ω ) is a measure of the local timefrequency energy of the signal. Figure 5.10 presents the WVD transform of a Lamb wave signal, demonstrating that the WVD transform does a fairly good job in resolving the S0 and A0 modes over a wide frequency range. With a flexible transform window size, the WVD transform can offer a better resolution than STFT [42]. Nevertheless, because of the need to avoid mathematic aliasing, the computation involved in a WVD transform is usually at least four times as high as the number of the sampling points of the signal to be processed, which may incur high computational cost. In addition, erroneous transform often occurs between two strong signal components or between strong and weak components in the signal [45]. Furthermore, a WVD analysis may lose sensitivity when applied directly to a raw wave signal exacerbated by ambient noise. Signal changes within a short time duration or small changes in wave magnitude may not be detected using such a signal processing technique. Although some variants have been introduced to overcome these disadvantages, e.g., Choi-Williams analysis [38, 46], the sole use of the WVD transform for Lamb wave analysis is debatable [42, 43].

Identification of Damage Using Lamb Waves

Scaled amplitude

158

2.0

0

-2.0 0

10

30

20

40

50

60

Time [ s]

a 60

50

Time [ s]

A0 40

30

20

0

2

6

4

8

10

Frequency [MHz]

b Fig. 5.10. a. A Lamb wave signal captured in the time domain; and b. the corresponding spectrum over the time-frequency domain obtained using the WVD transform [42]

Other representative signal processing tools in the time-frequency domain that can be employed for Lamb wave signals include matching-pursuit (MP)-based processing [47-53], four dimensional space-time-wavenumber-frequency representation [54], and S-transformation [55]. These approaches have demonstrated efficiency in processing Lamb wave signals in specific cases.

5.3 Wavelet Transform As an improvement on direct time-frequency analysis, WT is a tool for processing dynamic signals or images. With its rationale established in the 1950s, WT has claimed a wide application domain ranging from geophysics and biomedicine to offshore petroleum exploration and movie industry; indeed, wherever signal and image processing is necessary. Since introduced to the analysis of vibration signals by Daubechies [56] and Newland [57, 58] in the 1990s, this signal processing

Processing of Lamb Wave Signals

159

technique has enjoyed burgeoning popularity in the NDE community [38, 56, 5975]. A detailed description of the mathematical theory of WT can be found elsewhere [45, 76, 77]. In brief, the wavelet is a waveform with a limited duration or window, whose average amplitude equals zero. During the transform, a dynamic signal is represented using dual parameters, scale and time, denoted by a and b respectively in what follows. Scale is inversely proportional to frequency as [45] Fa =

Δ ⋅ Fc , a

(5.17)

where a , Δ , Fc and Fa are scale, sampling period, centre frequency of the wavelet and the frequency corresponding to scale a , respectively. WT is substantially a window technique featuring a window of variable size. A large value of scale stands for a big window, a global view of the signal and accordingly low resolution; a small value of scale represents a small window, a detailed view of the signal and accordingly high resolution. Representation of a dynamic signal over the time-scale domain rather than the direct time-frequency domain is not a degradation or compromise; rather it enhances the resolution of illustration and recognisability of a signal [45]. It allows detailed interpretation of a localised signal fragment so as to canvass hidden characteristics such as singularity or discontinuity in signals. Compared with other time-frequency approaches previously introduced, WT features conservation of energy during the transform, provision of full signal information, localisation in both the time and frequency domains, and deployment of the signal with multiresolution. Two types of WT are available: continuous wavelet transform (CWT) and discrete wavelet transform (DWT). 5.3.1 Continuous Wavelet Transform +∞

Windowed by an orthogonal wavelet function, Ψ(t ) , (

∫ Ψ(t )dt = 0

and

−∞ +∞

∫ Ψ (t )

2

dt < ∞ ), a Lamb wave signal, f (t ) , can be converted to a quadratic form

−∞

as [78] CWT (a, b) =

1 a

+∞

∫ f (t ) ⋅ Ψ ( *

−∞

t −b ) ⋅dt , a

(5.18)

where Ψ * (t ) denotes the complex conjugate of Ψ(t ) . CWT (a, b) is termed the CWT coefficient, i.e., the output of the CWT, which can be understood as a series of band-pass filters whose central frequencies and bandwidths are dependent on

160

Identification of Damage Using Lamb Waves

scale and Ψ(t ) [79]. It depicts the energy distribution of signal f (t ) over the time-scale domain, i.e., the energy spectrum of f (t ) . Therefore, the signal energy in total is [80] +∞ +∞

E=

∫ ∫ CWT (a, b)

2

⋅ da ⋅ db ,

(5.19)

b ≥ 0 a ≥0

2

where CWT ( a, b) is the density of the energy spectrum. Two raw Lamb wave signals, captured in a CF/EP composite plate before and after introducing delamination, and their corresponding energy spectra in the three-dimensional form obtained in terms of Equation 5.18 are shown in Figure 5.11. 1.0

1.0

S0-boundary

S0-boundary

S0

0.5

Normalised Normalised amplitude Amplitude

NormalisedAmplitude amplitude Normalised

S0

0.0

-0.5

0.5

0.0

-0.5

SH0 -1.0

-1.0 4500

5000

5500

6000

6500

Sampling SamplingPoints points

4500

5000

5500

6000

6500

Sampling Points Sampling points

a

b

S0

S0

S0-boundary

S0-boundary

SH0

c

d

Fig. 5.11. Lamb wave signals captured in a CF/EP laminate: a. without; and b. with delamination; c. energy spectrum of the signal in a.; and d. energy spectrum of the signal in b. [81]

Processing of Lamb Wave Signals

161

In the spectra, Figures 5.11(c) and (d), energy concentrations of various Lamb modes are calibrated by the CWT coefficients. The incident S0 mode and its reflection from the boundary, S0 − boundary , are clearly observed in both spectra. In addition, the delamination-induced SH 0 mode (Section 2.2.3), an extra wave mode converted from the incident S0 mode upon interaction with delamination, can be identified in the spectrum for the delaminated plate by virtue of its propagation speed, Figure 5.11(d). Signal f (t ) can also conversely be reconstructed via the inverse continuous wavelet transform (ICWT) [78]

+∞

where Cψ =

∫

+∞ +∞

1 CΨ

f (t ) =

∫ ∫ CWT (a, b) ⋅

b ≥0 a ≥0

Ψ (t )

−∞

t

⎛t −b⎞ 1 ⋅ Ψ⎜ ⎟ ⋅ 2 da ⋅ db , ⎝ a ⎠ a

1 a

(5.20)

2

dt < ∞ is a constant depending on Ψ(t ) .

5.3.2 Discrete Wavelet Transform

To calculate CWT coefficients at every single scale point is computationally expensive. To simplify the task, Equation 5.18 is executed at discretised scales and time moments only using two dyadic variables, m and n [77]

a = a0m

and

b = na0m b0 ,

DWT ( m , n ) = a

m − 2 0

∫ f (t ) ⋅ Ψ

m, n ∈ Z , *

( a 0− m t − nb 0 ) ⋅dt ,

(5.21a) (5.21b)

where a0 and b0 are two constants determining sampling intervals along the scale and time axes, respectively. DWT (a, b) is termed the DWT coefficient. Equation 5.21 decomposes a signal into associated sub-bands of relatively higher and lower frequencies. The more dense the decomposition is, the higher the resolution that can be achieved. It is the orthogonality of the WT that insures the uniqueness of such decomposition. To assist understanding, the decomposition of signal f (t ) in a three-level hierarchy is outlined in Figure 5.12. In this example, f (t ) is hierarchically separated into a series of approximations (low-frequency components of the signal, denoted by Ai ) and details (high-frequency components of the signal, denoted by Di ). Theoretically, the decomposition can proceed successively until the part consists of only a single sampling point or pixel. Taking advantage of this property, DWT is often used to design high-pass or low-pass digital filters, making it possible to isolate the damage-induced waves from others in a captured Lamb wave signal.

162

Identification of Damage Using Lamb Waves

Original signal f(t)

D1

A1

D2

A2

A3

D3

Fig. 5.12. Principle of DWT-based signal decomposition [45]

The lower and upper frequency limits of a specific sub-band are determined by both the sampling rate χ and the DWT level number. In accordance with the Nyquist sampling theorem [45], the maximum and minimum effective sampling frequencies of a signal which is captured with a sampling rate of χ are χ / 2 and 1 1 , respectively, where T is the sampling duration and M is the num= T (M / χ ) ber of sampling points. DWT decomposes a signal into a series of Ai and Di , with the lower and upper frequencies being: The 1st level:

approximation:

1 χ 1 ~ ⋅ ; (M / χ ) 2 2

detail:

1 χ χ ⋅ ~ ; 2 2 2

The 2nd level: (successive decomposition of the approximation in the 1st level)

approximation:

1 1 1 χ ~ ⋅ ⋅ ; (M / χ ) 2 2 2

detail:

1 1 χ 1 χ ⋅ ⋅ ~ ⋅ ; 2 2 2 2 2

The 3rd level: (successive decomposition of the approximation in the 2nd level)

approximation:

1 1 1 1 χ 1 1 1 χ 1 1 χ ~ ⋅ ⋅ ⋅ ; detail: ⋅ ⋅ ⋅ ~ ⋅ ⋅ ; (M / χ ) 2 2 2 2 2 2 2 2 2 2 2 ……

Processing of Lamb Wave Signals

163

The nth level: (successive decomposition of the approximation in the n-1th level)

approximation:

1 1 χ ~ ( )n ⋅ ; (M / χ ) 2 2

….

χ χ 1 1 detail: ( ) n ⋅ ~ ( ) n−1 ⋅ ; 2 2 2 2 (5.22)

For example, if the sampling rate χ is 20.48 MHz and there are 8192 sampling points ( M = 8192 ) to define a signal in signal acquisition, the lower and upper frequency limits of each sub-band are, in terms of Equation 5.22: The 1st level: The 2nd level: The 3rd level: The 4th level: ….

approximation: 2500 Hz~5.12 MHz; detail: 5.12MHz~10.24MHz; approximation: 2500 Hz~2.56 MHz; detail: 2.56MHz~5.12MHz; approximation: 2500 Hz~1.28 MHz; detail: 1.28MHz~2.56MHz; approximation: 2500 Hz~0.64 MHz; detail: 0.64MHz~1.28MHz;

By the reverse process, signal f (t ) can also be conversely reconstructed via the inverse discrete wavelet transform (IDWT) [78] m

f (t ) = c∑∑ Cmn (t ) ⋅ DWT ( m, n) , Cmn (t ) = a0 2 Ψ (a0−m t − nb0 ) , −

m

(5.23)

n

where c is a constant in correlation with Ψ(t ) . Expanding DWT analysis, the wavelet packet (WP) delivers a multi-resolution decomposition, where both Ai and Di are split into sub-bands. One example, decomposition of signal f (t ) in a three-level hierarchy using WP, is shown schematically in Figure 5.13.

f(t)

f(t)=AAA3+DAA3+ADA3+DDA3+AAD3+DAD3+ADD3+DDD3

Fig. 5.13. Architecture of a three-level WP-based signal decomposition [45]

164

Identification of Damage Using Lamb Waves

5.3.3 Selection of Wavelet Function

In both CWT and DWT, the orthogonal wavelet function, Ψ(t ) , is a key factor that can affect the accuracy and efficiency of the transform substantially. Gabor, Gaussian, Haar, Daubechies, bi-orthogonal, Coiflets, Symlets, Morlet, Mexican Hat and Meyer are the names of some popular wavelet functions in practice. Although the wavelet function is normally selected case by case, a basic consideration is that the waveform of a selected wavelet function should be as similar as possible to the waveforms of major components of the signal to be transformed. This is because the wavelet coefficient actually indicates the similarity between the wavelet function and the signal to be processed, and a large value of the coefficient, meaning a high level of similarity between the wavelet function and the signal, can improve the efficiency of transform. For example, if a diagnostic Lamb wave signal is excited in the waveform shown in Figure 5.14(a), the best wavelet function among the four candidate functions in Figure 5.14(b) would be the Morlet or the 4th level Daubechies function family (db4), due to their closest similarity to the wave signal to be transformed. For the same reason, the Haar wavelet would be the least suitable for WT of the signal. More strictly from the perspective of mathematics, the best wavelet function for a particular signal can be determined using a matching pursuit approach [52]. The matching pursuit approach is a ‘greedy’ algorithm that iteratively projects a signal onto a large and redundant dictionary of waveforms. At each step, the algorithm chooses the waveform from the dictionary that is best adapted to approximate part of the signal. WT has ushered in a new avenue for examining and interpreting Lamb wave signals, and successful applications are formidable in number. It has been demonstrated that, by using the WT technique to canvass the Lamb wave signals captured from a composite laminate [70], damage as small as 0.1% of the total area of the laminate can be detected, whereas this value is normally over 10% when other signal processing techniques are adopted. Generally speaking, CWT is particularly effective for signal energy visualisation, and DWT is more efficient for signal de-noising, filtration, compression, and extraction of characteristics. Two representative applications of the use of WT to extract features of captured Lamb wave signals are presented as follows. 5.3.4 Extracting Signal Features Using Wavelet Transform

5.3.4.1 Ascertaining the Arrival Time of Wave Determining the exact arrival time of a damage-scattered wave component in a captured signal is a key step to triangulate the damage. In the majority of studies, the arrival time or ToF of a wave component is determined by measuring the time difference between the moment at which the concerned wave packet reaches its maximum in magnitude in the time domain and the moment at which the diagnostic wave is activated (initial time moment).

Processing of Lamb Wave Signals

165

Normalised amplitude

1.0

0

-1.0 0

5

10

15

20

Time [ s]

a

Haar wavelet

db4 wavelet

db2 wavelet

Morlet wavelet

b Fig. 5.14. a. A Hanning windowed Lamb wave signal; and b. some candidate wavelets

However, wave propagation is in fact the transportation of the energy contained in the wave packet, and ideally the arrival time or ToF should be ascertained in terms of the time difference between the moment at which the wave packet reaches its maximum in the energy spectrum over the time-frequency domain and the initial time moment [82]. To determine exactly the energy peak of the wave packet in

166

Identification of Damage Using Lamb Waves

signal f (n) , ( n = 1, 2, A, N ), described by N sampling points, one can use the CWT-based scale-averaged wavelet power (SAP), which is defined as [82, 83] SAP 2 (n) =

1 M

2

M

∑

( i = 1, 2, A , M ) ,

CWT (ai , n)

(5.24)

i =1

where M is the largest scale during CWT. Therefore, the mean value of the translated wave energy, E , over the entire time period concerned is E=

1 N

N

∑ SAP (n)

( n = 1, 2, A, N ) .

2

(5.25)

i =1

From the viewpoint of energy, the time corresponding to the peak of the energy packet determined in terms of Equation 5.25 is the actual arrival time of the wave packet. By way of illustration, a Lamb wave signal, its energy spectrum over the time-scale domain obtained via CWT, and the SAP 2 spectrum established via Equation 5.25 are displayed in Figures 5.15(a-c). From the SAP 2 spectrum, Figure 5.15(c), the arrival time of the wave packet is determined as at the 396th sampling point, at which the wave energy reaches its extremum, rather than at the 412th sampling point, at which the signal amplitude reaches its extremum in the time domain [84]. 5.3.4.2 Calculating Reflection/Transmission Coefficients Evaluation of damage severity in many damage identification approaches has been achieved by calibrating (i) the reflection coefficients of a wave signal (ratio of the largest magnitude of the damage-reflected first wave component captured by the sensor to that of the incident wave) [85-95]; or (ii) the transmission coefficients of a wave signal (ratio of the largest magnitude of the first wave component after the wave propagating across the damage, captured by the sensor, to that of the incident wave) [91, 95-97]. Consistent with the fact that wave propagation is the transportation of the energy contained in the wave packet, a more accurate determination of the reflection and transmission coefficients is expected to be achieved in the energy spectrum of signals over the time-frequency domain. Consider a signal, f (n) , ( n = 1, 2, A, N ), described by N sampling points, and focus on an energy ridge in its energy spectrum obtained via CWT. The magnitude of this energy ridge, Aridge , along the scale axis at a specific time, t 0 , is defined in terms of its RMS as [98]

W1 + W2 + A + Wi + A + WN N 2

Aridge

t0

=

2

2

2

( i = 1, 2, A, N ),

(5.26)

where Wi is the i th CWT coefficient along the scale axis at time t0 of the signal.

Processing of Lamb Wave Signals

412th point

1 .0

Normalised amplitude Normalised Amplitude

167

0 .5

0 .0

-0 .5

-1 .0 0

100

200

300

400

500

600

700

800

S am p lin g P o in t

Sampling points

a

396th point

1.0

Scale

Normalised SAP

2

0.8

0.6

0.4

0.2

0.0 0

100

200

300

400

500

600

700

800

Sampling Samplingpoints Point

Sampling points

b

c

Fig. 5.15. a. A Lamb wave signal; b. contour presentation of the energy spectrum of the signal in a. obtained using CWT; and c. SAP2 spectrum of the signal in a.

Expanding the above discussion for two energy ridges, A ridge1 and A ridge2 , at two individual time moments t1 and t 2 , respectively (for example one is for the incident wave and the other for the damage-reflected or transmitted wave), the amplitude ratio, A ridge1 A ridge2 , if the same wavelet function selected, is

(

A ridge1 A ridge2

W1 + W2 + A + Wi + A + WN |t =t 2

)=

2

2

2

1

W1 + W2 + A + Wi + A + WN |t =t 2

2

2

2

( i = 1, 2, A, N ). (5.27)

2

When N is sufficiently large, Equation 5.27 becomes

168

Identification of Damage Using Lamb Waves Smax

(

A ridge1 |t

1

A ridge2 |t

2

∫W

2

) =

2

|t =t ⋅da 1

S min Smax

∫W

, 2

(5.28)

|t =t ⋅da 2

S min

where S min and S max are the lower and upper limits of the scale range of interest. Provided one of the above two ridges is that of the wave energy reflected from or transmitted through the damage, Equation 5.28 can be used to determine the reflection or transmission coefficients more accurately than methods based on calculation directly using the maximum magnitudes of wave components in the time domain, as demonstrated by a study of evaluating crack length in an aluminium beam in terms of the reflection coefficients [94].

5.4 Processing of Lamb Wave Signals Since measurement is often volatile, a Lamb wave signal captured in field by a piezoelectric sensor presents the following features: (i) the signal is inevitably exacerbated by a diversity of contaminations including random electrical and magnetic interferences, mechanical noise, temperature and humidity fluctuation; (ii) the damage-scattered waves in the signal are prone to interferences from the vibration of the host structure under inspection; (iii) multiple Lamb modes exist simultaneously in a signal with complex and unique dispersion behaviours; and (iv) a high sampling rate is often used for signal acquisition, which produces a huge amount of dataflow to serialise the sampling. Allowing for the above features, appropriate processing of a captured Lamb wave signal is of vital importance and necessity. In principle, the processing of a Lamb wave signal includes the following key steps. 5.4.1 Averaging and Normalisation

5.4.1.1 Averaging and Smoothing for Uncertainty Reduction Robustness of signal acquisition is important for minimising the uncertainties and random variations potentially included in a Lamb wave signal. Averaging a set of signals received repeatedly by an actuator-sensor path can reduce the data sensitivity with respect to uncertain fluctuation. Two basic averaging approaches that can be used for Lamb wave signals are synchronous averaging and asynchronous averaging [99]. The former is often adopted when there is a reference/benchmark signal, whereas the latter is used when there is no reference/benchmark signal, as usually occurs in practice. Cyclic averaging [99], a sort of asynchronous averaging based on statistics, is popularly employed to reduce random variations and bias errors of measurement. In this

Processing of Lamb Wave Signals

169

Normalised amplitude

Normalised amplitude

approach a blocksize is selected to emphasise a particular signal segment within a certain time period and meanwhile de-emphasise the rest of the signal. As an example, a raw wave signal and its form with uncertainty reduced by cyclic averaging are compared in Figure 5.16, where the magnitude of the signal at each individual sampling point is averaged by its ten neighbouring magnitudes (i.e., a blocksize of data, five on each side). The averaged signal has a comparatively straightforward appearance, with random noisy components having been removed. To reduce the direct current (DC) deviation of the signal that is commonly included in an in-field signal, the mean value of the signal, which can be obtained by averaging magnitudes at all sampling moments, should further be excluded from the raw signal.

Sampling points

a

Sampling points

b

Fig. 5.16. a. A captured signal; and b. the noise-reduced signal shown in a. using cyclic averaging

However, no matter which averaging approach is adopted, there is no way to eliminate serious measurement errors. 5.4.1.2 Normalisation Because Lamb wave signals are often activated and captured under varying working conditions and subject to a number of factors, normalisation of signals can be very important for correct interpretation of signals. In the field of NDE and SHM, data normalisation is the process of enlarging differentiation between the changes in sensor readings caused by damage and those caused by varying operational and environmental conditions. A common procedure is to normalise the captured Lamb wave signal with respect to the input incident signal, to the varying working conditions or to the reference/benchmark signal, so as to scale the captured signal to fall within a specified range such as [−1, 1] . This signal normalisation can effectively avoid data distortion and make different signals more comparable. Most basically, a Lamb wave signal can be normalised

170

(i)

Identification of Damage Using Lamb Waves

by the maximum magnitude of its amplitude via f new = f old max( f old ) , where max( f old ) is the maximum magnitude of the original signal f old , and f new is the normalised signal); or

(ii) by a decimal scaling, f new = f old 10 j , where j is the smallest integer such that max( f new ) < 1 ; or (iii) by its concomitant signal in the benchmark structure. More generally, a Lamb wave signal can be normalised using one of the following approaches: Min-Max Normalisation

f new = (

f old − Minold )(Maxnew − Minnew ) + Minnew , Maxold − Minold

(5.29)

where Max and Min stand for the maximum and minimum magnitudes of the original and normalised signals, f old and f new , respectively. Subscripts ‘new’ and ‘old’ indicate the states after and before the normalisation. Since the min-max normalisation is a linear transformation, it preserves all the information and relationships contained in the original signal. Zscore Normalisation f new =

f old − mean , STD

(5.30)

where ‘mean’ and STD denote the mean and standard deviation of the original signal, f old , respectively. The Zscore normalisation can be used when the minima and maxima of the original signal are unknown in Equation 5.29. Sigmoidal Normalisation

f new =

1 − e −α , 1 + e −α

(5.31)

f old − mean . This algorithm is particularly suitable for signals whose STD outliers have large values.

where α =

5.4.2 De-noising

Noise, measurands in a signal that are not a part of the phenomena of interest, is unavoidable even though precautions are taken. The magnitude of a captured

Processing of Lamb Wave Signals

171

Lamb wave signal, activated by a surface-mounted piezoelectric wafer driven by an electrical field of 5-10 V, falls in the range of 10-25 mV, being in the same range as ambient noise. As a result, the damage-scattered wave components can easily be masked by the noise from a diversity of sources (Section 4.2.1.2). Although increasing the magnitude of excitation can improve the SNR, signal denoising using various noise filters is of vital importance. Figure 5.17(a) shows a raw Lamb wave signal captured in a CF/EP composite laminate containing delamination, using a piezoelectric wafer driven by five-cycle Hanning windowed tonebursts at a central frequency of 500 kHz and with a peak-peak magnitude of 50 V. Containing a rich number of wave components in different frequency bands, the signal is overwhelmed in appearance. When DWT analysis as previously described is applied, the signal is decomposed into subbands of different frequencies, and the first seven details (d1-d7) are displayed in Figure 5.17(b). In terms of Equation 5.22, the calculated central frequency of d5 is 480 kHz, which is closest to the excitation frequency of 500 kHz, and therefore the wave component in d5 is the ‘actual wave component’ of interest for further damage identification, assuming that the waves scattered by damage, a boundary or structural inhomogeneity such as a stiffener share the same frequency as that of the incident wave activated by the actuator. In this way, the actual wave component is isolated from others including high-frequency noise at low DWT levels and lowfrequency interference at high DWT levels. In this example, the signal is decomposed into sub-bands with certain lower and upper cut-off frequencies. It is acknowledged that decomposing a Lamb wave signal exactly at a specified frequency is also feasible by properly selecting the sampling rate in Equation 5.22, although that is subject to the signal acquisition hardware. 5.4.3 Feature Extraction and Damage Index

The greatest challenge in signal-based identification is to ascertain what changes are sought in the signal, before and after the presence of damage. These changes are associated with the essential features of a Lamb wave signal, which can be used, through appropriate identification algorithms (Chapter 6), to calibrate the difference between damaged and undamaged states or between two different damage states of a structure. Feature extraction is therefore a key step in the processing of Lamb wave signals. That is the reason why some researchers have described damage identification and SHM as feature recognition [99]. Strictly speaking, feature extraction is the process of identifying and picking up the damage-modulated properties and parameters in a signal which are called the features or characteristics of the signal. The features of a Lamb wave signal include ToF, magnitude, attenuation, frequency, phase, spectrum and others. These parameters can change to different degrees in signals captured before and after the presence of damage in structures. Though application-specific, the basic principle in selecting signal features for damage identification is to extract those that are most sensitive to variation in damage parameters.

172

Identification of Damage Using Lamb Waves 0.6

Amplitude [V]

0.4 0.2 0 -0.2 -0.4 -0.6

0

2000

4000

6000

8000

10000

Sampling points

a

d7

d6

d5

d4

d3

d2

d1 0

2000

4000

6000

8000

10000

Sampling points

b Fig. 5.17. DWT-based signal de-noising: a. original Lamb wave signal; and b. signal components in the first seven frequency sub-bands upon decomposition [81]

There are two basic approaches of feature extraction: model-based and signalbased [99, 100]. The former approach uses certain pre-established models to extract signal features; the latter extracts features directly from signals without applying any sort of deterministic model to the signal. The feature extraction most commonly used for Lamb wave signal processing falls into the second category. In this aspect, various approaches have been developed to define and extract signal features in different domains for identifying structural damage, and these extracted features are often termed the damage index (DI) or damage indices (DIs), serving as an indicator to describe the damage.

Processing of Lamb Wave Signals

173

5.4.3.1 DIs in Time Domain Features of a Lamb wave signal that can be used for developing DIs in the time domain include ToF [6, 9, 11, 37, 75, 93, 101-103], RMS [104-107], signal variance [107], peak-to-peak amplitude [11], attenuation rate of wave energy [6, 18, 108-112], local statistical features [113], etc. Among the above signal features, the difference in the ToFs between two wave components in a signal, i.e., the time lag between two wave components in a signal (for example one being the incident diagnostic wave that the sensor first captures and the other being the damage-scattered wave that the same sensor subsequently captures, as illustrated in Figure 5.18), is one of the most straightforward and important features of a Lamb wave signal. Such a signal feature describes the relative distance between the sensor and the damage. 1.0

Delaminated laminate

Normalised amplitude

Time lag Incident wave

0.5

0

-0.5

Damage-scattered wave -1.0 0

20

40

60

80

100

120

Time [ s]

Fig. 5.18. Definition of difference in the ToFs between the incident diagnostic wave and the damage-scattered wave

In addition, the change in magnitude of signal amplitude is another observable signal feature, since the Lamb wave attenuates to a significant level when passing through damage, as introduced in Section 2.5. To take advantage of both, one can use a DI such as [114] DI = ( A1 − A2 ) × (T1 − T2 ) ,

(5.32)

where A and T stand for the magnitude and the difference in ToFs extracted from signals. Subscripts 1 and 2 represent two states, e.g., before and after the presence or change of damage. RMS-based DI, DI RMS [107], variation-based DI, DIVariance [107], and a combination of both (called the root mean square deviation (RMSD))-based DI [115], DI RMSD , are defined as, respectively,

174

Identification of Damage Using Lamb Waves N

∑x

2 i

i =1

DI RMS =

,

N 1 N −1

DIVariance =

(5.33a)

N

∑(x

− x)2 ,

i

(5.33b)

i =1

N

∑( y

i

− xi ) 2

i =1

DI RMSD (%) =

× 100 ,

N

∑x

(5.33c)

2 i

i =1

where x represents the mean magnitude of a discretised Lamb wave signal containing N sampling points, xi , ( i = 1, 2, A , N ); yi , ( i = 1, 2, A , N ), is the signal captured under another state of the structure such as after the presence of damage. In the above, DI RMS and DI RMSD are two DIs associated with the signal energy, whereas DIVariance indicates the variability of the signal with regard to the mean value of the magnitude. In recognition of the fact that the propagation of wave is the transportation of the energy contained in the wave packet, the DIs relating the signal energy can be one of the following [5, 111, 112]: a

t ⎞ ⎛t ⎜ f1 (t ) 2 ⋅ dt − f 0 (t ) 2 ⋅ dt ⎟ ⎟ ⎜t t ⎟ , DI = ⎜ t ⎟ ⎜ 2 f 0 (t ) ⋅ dt ⎟⎟ ⎜⎜ t ⎠ ⎝ 1

1

∫

∫

0

0

or

(5.34a)

1

∫ 0

a

⎛t ⎞ ⎜ f1 (t ) − f 0 (t ) 2 ⋅ dt ⎟ ⎜t ⎟ ⎟ , DI = ⎜ t ⎜ ⎟ 2 f 0 (t ) ⋅ dt ⎜⎜ ⎟⎟ t ⎝ ⎠ 1

∫ 0

or

(5.34b)

1

∫ 0

a

⎞ ⎛t ⎜ f (t ) 2 ⋅ dt ⎟ 1 ⎟ ⎜t ⎟ , DI = ⎜ t ⎟ ⎜ 2 ⎜⎜ f 0 (t ) ⋅ dt ⎟⎟ ⎠ ⎝t 1

∫ 0

1

∫ 0

(5.34c)

Processing of Lamb Wave Signals

175

where f1 (t ) and f 0 (t ) are two Lamb wave signals, containing the selected wave mode for damage identification (the S 0 or A0 mode for example), captured in the structure with damage and in the one without damage (benchmark structure), respectively; exponential a is a constant subject to the case and is often set as 1.0; t 0 and t1 are the starting and ending time moments for signal acquisition, respectively. In terms of the correlation of two signals (Section 5.2.1.2), the DI can be established as [5, 13] n

∑ (x

i

− µ x )( yi − µ y )

i =1

DI = 1 − λ xy = 1 −

∑ (x

,

n

n

2

i

− µx ) ⋅

i =1

∑( y

i

− µy)

(5.35)

2

i =1

where all the variables have the same meaning as those in Equation 5.4 for defining the correlation. Two discretised signals, xi and yi , are the captured signals in the structure before and after the presence of damage. If the value of DI defined by Equation 5.35 is clearly lower than unity, it shows poor correlation between the two signals, indicating the presence of damage in the structure. Making use of the concept of time reversal, a DI in the time domain is proposed as [21, 25] t1

∫

( I (t ) ⋅ V (t ) ⋅ dt ) 2 DI = 1 −

t0

t1

∫

,

t1

2

∫

(5.36)

2

( I (t ) ⋅ dt ) ⋅ ( V (t ) ⋅ dt ) t0

t0

where I (t ) and V (t ) are the input and reconstructed Lamb wave signals after the time reversal; t0 and t1 are the starting and ending time moments for signal acquisition, respectively. This DI becomes zero when the reversibility of Lamb waves is preserved, indicating a state of absence of damage; on the other hand, if the reconstructed signal deviates from the input signal, DI becomes non-zero, indicating the existence of damage in the structure near the direct wave path. 5.4.3.2 DIs in Frequency Domain Features of a Lamb wave signal that can be used for developing DIs in the frequency domain include figure-of-merit (FoM) [116-118], spectral density [119], peak of FFT amplitude, FFT coefficient [120], variance and kurtosis [121, 122], etc.

176

Identification of Damage Using Lamb Waves

In particular, the FoM [116, 117] is defined as ⎤ ⎡ N − frequency log g iI FoM = Max fom j = Max ⎢ Wi ( − 1) 2 ⎥ II log g i ⎦ ⎣ i =1 ( i = 1, 2, A, N ),

[

∑

]

(5.37)

where g iI and g iII are the magnitudes of the Fourier-transformed signals in the frequency domain, in terms of Equation 5.5, at the i th frequency of N frequencies of interest in total for two states of a structure, I and II (e.g., before and after the presence of damage or with two different severities of damage), respectively. Wi is a weighting factor used to reduce the noise sensitivity (often set as 1.0 ); fom j is a single scalar associated with the response from the j th actuatorsensor path in a sensor network. With FFT analysis, the DI in the frequency domain can be defined in another form as [120] N

∑F

I

i

DI =

− Fi II ( i = 1, 2, A , N ),

i =1

N

∑

(5.38)

Fi I

i =1

where Fi I and Fi II are the FFT coefficients ( N in total) in the FFT spectra of two wave signals captured in a structure when it is at the initial and later states, I and II , respectively. Thus, this DI represents the normalised difference in the moduli between two Lamb wave signals in a given frequency band captured at two different structural states, able to highlight presence of damage or evolution of damage in comparison to the healthy or anterior state. This DI can further be modified as [17, 123, 124] DI = 1 −

( FRFi II )T ∗ FRFi II ( FRFi I )T ∗ ( FRFi I )

( i = 1, 2, A , N ),

(5.39)

where FRFi I and FRFi II are the frequency response functions ( N in total) of Lamb wave signals captured in a structure when it is at the prior and posterior states, I and II , respectively. Such a DI becomes zero if no damage exists, i.e., FRFi I = FRFi II . 5.4.3.3 DIs in Joint Time-frequency Domain The main features of a Lamb wave signal that can be used for developing DIs in the joint time-frequency domain are the characteristics extracted from signal energy spectrum obtained using either STFT or WT. A representative DI is [40]

Processing of Lamb Wave Signals

⎡t ⎤ 2 ⎢ ∫ S I (ωi , t ) dt ⎥ ⎥ 1 N ⎢t DI = ∑ ⎢ t ⎥ N i =1 ⎢ 2 S (ω , t ) dt ⎥ ⎢ ∫ II i ⎥ t ⎣ ⎦

177

k

2

1

2

( i = 1, 2, A , N ),

(5.40)

1

where S (ω , t ) denotes the magnitude of energy spectrum of a Lamb wave signal over the frequency-time domain obtained using STFT (Section 5.2.3.1). Subscripts I and II indicate two states of the structure, such as before and after the presence of damage or with damage of different severities, and superscript k is a gain factor in the range of [0,1] which can be chosen empirically depending on the type of damage [40]. N is the number of frequencies in total included in signals that are of interest; t1 and t2 are the starting and ending time moments for signal acquisition. This DI depicts the ratio of the energy of the Lamb waves in the structure with damage to that of the waves when the structure is healthy. The DI described by Equation 5.40 has been applied to the identification of structural damage using different Lamb modes [36, 125], and it has been demonstrated that using the damage-scattered S0 or A0 mode to develop this DI is most effective for evaluating a crack in an aluminium structure or delamination in composite laminates, respectively. To calibrate changes in the energy of Lamb wave signals before and after the presence of damage, a DI is defined in terms of CWT [126] ⎛t ⎞ ⎜ CWT (ω , t ) dt ⎟ I 0 ⎜ ∫t ⎟ ⎟ , DI = 1 − ⎜ t ⎜ ⎟ CWTII (ω0 , t ) dt ⎟ ⎜⎜ ∫t ⎟ ⎝ ⎠ 2

1

(5.41)

2

1

where CWT (ω0 , t ) represents the CWT coefficient of the Lamb wave signal at a specific frequency ω0 . Other variables I , II , t1 and t 2 share the same meaning as those in Equation 5.40. The DI, ranging from 0 to 1, becomes zero when there is no attenuation in the captured signal in comparison with a benchmark signal, and it deviates from 0 as a result of the existence of damage since damage attenuates a Lamb wave significantly, as introduced in Section 2.5. This DI can be further simplified by using the peak values of the wavelet coefficients rather than integrating the coefficients along the entire time span [115, 127], at the l th stage ( l = 1, 2, A , M ) provided that the structural damage evolves in M stages,

178

Identification of Damage Using Lamb Waves N

∑ (C DI (l ) =

II i

(l ) − CiI ) 2 ( i = 1, 2, A , N ),

i =1

N

∑ (C

(5.42)

I 2 i

)

i =1

where CiI and CiII (l ) are the peak values (maximum) in wavelet coefficients of a specific Lamb mode captured from the healthy and unknown states of a structure (when the damage evolves at the l th stage), respectively. Subscript i denotes that the signal is captured via the i th actuator-sensor path ( i = 1, 2, A , N ) of a sensor network. This DI actually indicates the RMS changes in the wavelet coefficients over the time-scale domain of a specific Lamb mode due to the existence of damage. In the above, various DIs in different domains have been introduced. It may be perplexing to decide which DI should be selected for a particular case of damage identification. Though there is no an explicit criterion in this respect, it should be appreciated that (i) an efficient DI, whatever its form, must be sensitive to the presence and evolution of damage but robust against ambient noise (insensitive to background noise); and (ii) selecting signal features normally involves a trade-off between the desired sensitivity and computational feasibility, where high sensitivity and high precision demand high-level signal features, incurring high cost as a result. With a selected DI, a qualitative or in particular a quantitative relationship between changes in DI and damage parameters such as location, size and shape can be further established, whereby the damage can inversely be identified, to be detailed in Chapter 6. 5.4.4 Compression

As discussed previously, for quantifying damage, it is important not only to extract essential features from captured signals, but also to limit the signal capacity to a reasonable and manageable level before it is used for damage identification, as accuracy, sensitivity and efficiency of identification may be jeopardised when high-dimensional data are involved. As a result of feature extraction, the original signal is condensed, but that does not mean that the extracted signal features are sufficiently low-dimensional. On the other hand, implementation of a SHM technique normally produces a huge amount of data, since monitoring often occurs across the lifetime of a structure. The above two issues have necessitated considerably the robust condensation and compression techniques for captured Lamb wave signals. There are several data condensation and compression methods, typified by predictive coding, transform coding, entropy coding, vector quantization and pyramid technique [128]. All these approaches can be roughly grouped into two

Processing of Lamb Wave Signals

179

categories: lossless and lossy [128]. Those in the former category do not introduce any distortion or loss of information contained in the original signal during compression, whereas the latter approaches allow a certain level of distortion or loss of information in the reconstructed signals, which, however, may be done intentionally for purposes such as de-noising and filtering. Most compression techniques for Lamb wave signals fall into the latter category, including mainly thresholdbased linear compression [78, 129], Sammon mapping and principal component analysis (PCA) [2] . 5.4.4.1 Threshold-based Linear Signal Compression Threshold-based compression is a linear compression technique that transfers a discretised signal X (vector) into another vector Y . For example, from the time domain to the time-frequency domain using the WT, compression can be achieved by discarding all elements in the new vector in the time-frequency domain that are below a specific threshold, c , and then reconstructing the vector back to the time domain using an inverse transformation such as inverse WT. The threshold can be defined in different ways, depending on the case, such as c = 2σ ( σ is the standard deviation of the signal) and c = σ ln N ( N is the number of sampling points in the signal) [2]. It is obvious that the higher the threshold, the higher the compression ratio (i.e., the ratio of capacities of the signals after compression to before compression). Two Lamb wave signals acquired in a CF/EP composite plate with/without delamination are displayed in Figure 5.19, which are then compressed using a WT-based compression approach, where the 16 highest wavelet coefficients are retained and all the other coefficients are set to zero (i.e., discarded). Then, via the inverse WT, the signals are reconstructed. Upon compression, non-essential information and noise in the signal are removed and the damage-scattered waves become explicit in the reconstructed signals. 5.4.4.2 Principal Component Analysis PCA is a classical multivariate statistical data compression and feature extraction method which linearly converts an original signal containing correlated variables into a substantially smaller set of data containing only uncorrelated variables, called the principal components, which represent the essential (eigen) information of the original signal [15, 130]. The rationale of PCA is based on the second order statistics, orthogonal decomposition and eigenvalue analysis of the covariance matrix of a signal. Mathematically, PCA attempts to express a discretised signal, T X = {x1 , x1 , A, xi , A, x N } , ( xi ∈ R , i = 1, 2, A, N ; T denotes transposition),

with

another

vector Y = {y1 , y1 , A, yi , A, y M }

j = 1, 2, A, M ), where M << N [131],

T

,

( yj ∈R ,

Identification of Damage Using Lamb Waves Relative Amplitude

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4 2 0 -2 -4 0

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d Fig. 5.19. Threshold-based linear compression for a Lamb wave signal captured in a CF/EP laminate: a. before; and b. after introducing delamination; c. compressed and then reconstructed form of the signal shown in a.; and d. compressed and then reconstructed form of the signal shown in b. (small figure: difference between signals in c. and d.) [128]

Processing of Lamb Wave Signals

⎡ x1 ⎤ ⎡ f1 ( y1 , A , yM ) ⎤ ⎢x ⎥ ⎢ f ( y ,A, y ) ⎥ M ⎥ X=⎢ 2⎥ =⎢ 2 1 , ⎢B ⎥ ⎢ ⎥ B ⎢ ⎥ ⎢ ⎥ ⎣ x N ⎦ N ×1 ⎣ f N ( y1 , A , yM )⎦ N ×1

181

(5.43)

where f i , ( i = 1, 2, A , N ), are N linear correlations. N is called the superficial dimension of the signal and M is the intrinsic dimension. X is expressed as a linear combination of y1 , y2 , …, yM . Since all f i are linear, Equation 5.43 can be simplified as X N ×1 = FN ×M ⋅ YM ×1 or

YM ×1 = F −1 M × N ⋅ X N ×1

( M << N ),

(5.44)

where F −1 M × N = [e1 , e 2 , A,e M ]T and e i , ( i = 1, 2, A , M ), are the first M eigenvectors of the covariance matrix of the signal, each containing N eigenvalues, λi ( i = 1, 2, A , N , and λ1 > λ2 > λ1 > A > λN ). y1 , y2 , …, yM in Equation 5.44 are termed the principal components of the original signal. With an increase in the order, the essentiality of an eigenvalue, λi , for describing a signal, decreases. Signal compression can thus be achieved by retaining these lower-order principal components and discarding higher-order ones, to reduce the capacity of a signal from N-dimensional to M-dimensional. PCA has been used for de-noising and compressing Lamb waves for damage identification [130]. In this approach, a series of captured Lamb wave signals was processed to build up a baseline dataset. PCA-based compression approach was then applied on this dataset to highlight the critical signal features by truncating high-order eigenvectors of the covariance matrix of signals (based on the above discussion, the high-order eigenvectors are not the essential parts of a signal, and may be contributed by noise). By this process, the noise in Lamb wave signals was filtered and consequently the signals were compressed into a compact capacity.

5.5 A Signal Processing Approach for Lamb Waves: Digital Damage Fingerprints Designed to extract essential features from captured raw Lamb wave signals, with the aim of establishing particular patterns as the ‘fingerprints’ for individual damage cases and subsequently reducing the signal capacity, a Lamb wave signal processing approach called the digital damage fingerprints (DDF) [132, 133] was developed in conjunction with an inverse pattern recognition technique (artificial neural network, addressed in Chapter 6). To explain in a nutshell, DDF are a set of optimised and digitised characteristics extracted from raw Lamb wave signals, to quantitatively define a certain damage status of the structure under inspection (e.g., location and severity). The approach includes sequentially

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(i) DWT-based signal purification; (ii) CWT-based signal characteristic extraction; (iii) threshold-based linear data compression; and (iv) information mapping. The whole procedure of damage identification using DDF is flowcharted schematically in Figure 5.20.

A Lamb wave signal provided

Information mapping

Pattern

by a sensor network

(if applicable)

recognition

Signal pre-processing

Damage

e.g., DC offset, averaging,

Threshold-based linear

dispersion compensation

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purification (de-noising)

feature extraction

identification

Fig. 5.20. Flowchart of DDF-based signal processing for Lamb-wave-based damage identification

Purification

To remove noise from a raw Lamb wave signal captured in a structure under inspection and to minimise uncertainties of measurement, a series of digital bandpass filters with the preset frequency thresholds is designed using DWT (Section 5.2.2.2 for digital filter and Section 5.3.2 for DWT). These filters can decompose signals into different frequency bands, whereby the damage-scattered Lamb waves in the frequency band of the incident diagnostic waves activated by actuators are isolated from interference from a variety of noise in other frequency bands. Characteristic Extraction and Signal Compression

For a filtered Lamb wave signal, like the example shown in Figure 5.21(a), only the time moments at which magnitudes of the signal reach their local extrema are the key features of the signal in the time domain which dominate the description of the signal; similarly, in the corresponding energy spectrum of the signal obtained using CWT (Section 5.3.1 for CWT), in Figure 5.21(b), only the time moments and frequencies at which magnitudes of the signal energy reach their local maxima are the key features of the signal in the time-scale domain. All these features are termed the characteristic points in the DDF approach, and their

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corresponding magnitudes in the time and time-scale domains are characteristic magnitudes, both of which are characteristic components of the signal; the rest are non-characteristic components of the signal. In this way, characteristic components (time, frequency and magnitude) are extracted from a filtered signal in the time domain and from its energy spectrum in the time-scale domain. Characteristic Non-characteristic

components

Amplitude [mV] Voltage [mV]

components

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components

components

0

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5.6x10

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a

b

Fig. 5.21. Characteristic components of a Lamb wave signal in the a. time; and b. timescale domains [132]

A feature vector pair, {time, magnitude} and {time, frequency, magnitude}, is created to accommodate the extracted characteristic components. For an active sensor network consisting of a certain number of actuators and sensors, a series of feature vector pairs can be established for all the signals captured by the sensor network, using the same principle. These feature vector pairs are arranged in sequence, termed the digital damage fingerprints (DDF). One particular damage case is uniquely defined with one set of DDF. If we personify different damage cases as ‘crimes’ inflicted on a structure, DDF serve as the records that describe individual crimes. Signal compression can be further applied by discarding the non-characteristic components of the signal, significantly reducing the amount of data. Taking into account all the damage cases of interest, a damage parameter database (DPD) hosting all DDF can be constructed for a particular type of damage in the structure under inspection, e.g., a crack or delamination. With the extracted DDF hosted in a DPD, quantitative damage identification can further be accomplished in conjunction with an artificial-neural-network-based pattern recognition technique, detailed in Chapter 6.

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Information Mapping

In practice, completely or partially symmetric conditions may exist in the geometry of structures under inspection and the sensor networks attached to them. To fully exploit these symmetric properties so as to reduce effort and cost in establishing DDF, which can be quite expensive in cases where broad data are involved, a mapping procedure is included in the DDF approach. Wherever symmetric conditions are applicable, the DDF stored in the DPD for damage cases in partial regions of the structure (sub-DPDs) are mirrored into other regions with regard to all the available symmetric points, axes or planes of the structure, to obtain the DDF for damage cases in those regions. A full database comprised of several sub-DPDs for the entire structure can thus be built. Without sacrificing information that could possibly be acquired, such a mapping endeavour using limited information minimises the effort of developing DDF for the entire structure. For illustration, a Lamb wave signal processed with the DDF approach is shown in Figures 5.22(a)-(e), with interim results and final DDF extracted. In this procedure, applied with digital bandpass filters, the wave components in the frequency band of wave excitation are isolated from broadband noise, Figure 5.22(b). The energy spectrum of the filtered wave signal obtained using CWT analysis and its compressed form using the threshold-based linear signal compression are displayed in Figures 5.22(c) and (d), respectively. DDF of the signal are sequentially extracted, exhibited in Figure 5.22(e). From (a) to (e), the original Lamb wave signal is seen to be re-defined in a concise form but without losing connatural characteristics, and meanwhile the noise is removed. The DDF approach works as a generic technique, applicable to other dynamic signals as well.

5.6 Summary With the aim of extracting substantial yet concise features from captured raw Lamb wave signals for damage identification, various DSP techniques have been developed in the time, frequency, and joint time-frequency domains, represented by the Hilbert transform, correlation, time reversal, FFT, STFT and WT. Extracted signal features can be examined to establishing various DIs, serving as indicators to describe the structural damage. In particular, the WT has proved effective in simultaneously exploring the frequency and time information of a Lamb wave signal. Generally speaking, the CWT analysis can be used for energy visualisation of a Lamb wave signal, while the DWT analysis has advantages in signal denoising, filtration, compression and characteristic extraction. To assist in the interpretation of a captured Lamb wave signal, some basic steps of processing include averaging, normalisation, de-noising, feature extraction, and compression. In particular, a signal characteristic extraction approach for Lamb-wave-based damage identification, termed the DDF, was introduced in this chapter. DDF are a set of optimised and digitised characteristics of signals, able to exactly describe the healthy state of a structure. With the extracted signal features, the next step in damage identification is to quantitatively identify damage parameters (e.g., location and severity) using appropriate algorithms, as detailed in the next chapter.

Processing of Lamb Wave Signals

1.0

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e Fig. 5.22. Procedure of DDF extraction for a Lamb wave signal: a. raw signal; b. filtered signal in the excitation frequency band; c. energy spectrum; d. compressed spectrum in the time-scale domain; e. extracted DDF in time-scale domain [132]

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86. Pine, D.J.: Detection of utility pole rot damage by measuring the reflection coefficient. Journal of Nondestructive Evaluation 16(1), 43–56 (1997) 87. Gilchrist, M.D.: Attenuation of ultrasonic Rayleigh-Lamb waves by small horizontal defects in thin aluminium plates. International Journal of Mechanical Sciences 41, 581–594 (1999) 88. Culshaw, B., Pierce, S.G., Staszewski, W.J.: Condition monitoring in composite materials: an integrated systems approach. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 212, 189– 202 (1998) 89. Karunasena, W.M., Liew, K.M., Kitipornchai, S.: Hybrid analysis of Lamb wave reflection by a crack at the fixed edge of a composite plate. Computer Methods in Applied Mechanics and Engineering 125, 221–233 (1995) 90. Crane, L.J., Gilchrist, M.D., Miller, J.J.H.: Analysis of Rayleigh-Lamb wave scattering by a crack in an elastic plate. Computational Mechanics 19, 533–537 (1997) 91. Maslov, K., Kundu, T.: Selection of Lamb modes for detecting internal defects in composite laminates. Ultrasonics 35, 141–150 (1997) 92. Chimenti, D.E., Yang, C.-H.: Guided wave mode crossing/grouping studied in an image representation of the reflection coefficient. In: Thompson, D.O., Chimenti, D.E. (eds.) Review of Progress in Quantitative Nondestructive Evaluation, vol. 13, pp. 117–124. Plenum Press, New York (1994) 93. Diamanti, K., Hodgkinson, J.M., Soutis, C.: Detection of low-velocity impact damage in composite plates using Lamb waves. Structural Health Monitoring: An International Journal 3(1), 33–41 (2004) 94. Su, Z., Ye, L., Bu, X., Wang, X., Mai, Y.-W.: Quantitative assessment of damage in a structural beam based on wave propagation by impact excitation. Structural Health Monitoring: An international Journal 2(1), 27–40 (2003) 95. Seemann, W.: Transmission and reflection coefficients for longitudinal waves obtained by a combination of refined rod theory and FEM. Journal of Sound and Vibration 197(5), 571–587 (1996) 96. Diligent, O., Lowe, M.J.S.: Reflection of the S0 Lamb mode from a flat bottom circular hole. Journal of the Acoustical Society of America 118(5), 2869–2879 (2005) 97. Benmeddour, F., Grondel, S., Assaad, J., Moulin, E.: Study of the fundamental Lamb modes interaction with symmetrical notches. NDT&E International (in press) 98. Kim, Y.Y., Kim, E.H.: A new damage detection method based on a wavelet transform. In: Proceedings of the 18th International Modal Analysis Conference (IMAC), San Antonio, TX, USA, February 7-10, 2000, pp. 1207–1212 (2000) 99. Adams, D.E.: Health Monitoring of Structural Materials and Components: Methods with Applications. John Wiley & Sons, Inc, Hoboken (2007) 100. Sohn, H.: Statistical pattern recognition paradigm applied to defect detection in composite plates. In: Inman, D.J., Farrar, C.R., Lopes Jr., V., Steffen Jr., V. (eds.) Damage Prognosis: for Aerospace, Civil and Mechanical Systems, ch. 14, pp. 293– 303. John Wiley & Sons, Inc., Chichester (2005) 101. Diaz Valdes, S.H., Soutis, C.: A structural health monitoring system for laminated composites. In: Chang, F.-K. (ed.) Proceedings of the 3rd International Workshop on Structural Health Monitoring, Stanford, CA, USA, September 12-14, 2001, pp. 1476–1485. CRC Press, Boca Raton (2001)

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102. Quek, S.T., Tua, P.S., Jin, J.: Comparison of plain piezoceramics and inter-digital transducer for crack detection in plates. Journal of Intelligent Material Systems and Structures 18, 949–961 (2007) 103. Fromme, P.: Monitoring of plate structures using guided ultrasonic waves. In: Thompson, D.O., Chimenti, D.E. (eds.) Review of Progress in Quantitative Nondestructive Evaluation, vol. 27, pp. 78–85. American Institute of Physics, New York (2008) 104. Dupont, M., Osmont, D., Gouyon, R., Balageas, D.L.: Permanent monitoring of damaging impacts by a piezoelectric sensor based integrated system. In: Chang, F.-K. (ed.) Proceedings of the 2nd International Workshop on Structural Health Monitoring, Stanford, CA, USA, September 8-10, 1999, pp. 561–570. Technomic Publishing Co (1999) 105. Wolfinger, C., Arendts, F.J., Friedrich, K.: Health-monitoring based on piezoelectric transducers. Aerospace Science and Technology 6, 391–400 (1996) 106. di Scalea, F.L., Matt, H., Bartoli, I., Coccia, S., Park, G., Farrar, C.: Health monitoring of UAV wing skin-to-spar joints using guided waves and macro fiber composite transducers. Journal of Intelligent Material Systems and Structures 18, 373–388 (2007) 107. Rizzo, P., di Scalea, F.L.: Feature extraction for defect detection in strands by guided ultrasonic waves. Structural Health Monitoring: An International Journal 5(3), 297– 308 (2006) 108. Michaels, J.E., Michaels, T.E.: An integrated strategy for detection and imaging of damage using a spatially distributed array of piezoelectric sensors. In: Proceedings of the SPIE (Conference on Health Monitoring of Structural and Biological Systems), vol. 6532 (2007), Paper No.: 653203 109. Michaels, J.E., Michaels, T.E.: Enhanced differential methods for guided wave phased array imaging using spatially distributed piezoelectric transducers. In: Thompson, D.O., Chimenti, D.E. (eds.) Review of Progress in Quantitative Nondestructive Evaluation, vol. 25B, pp. 837–844. American Institute of Physics, New York (2006) 110. Leonard, K.R., Hinders, M.K.: Lamb wave tomography of pipe-like structures. Ultrasonics 43, 574–583 (2005) 111. Qing, X.P., Chan, H.-L., Beard, S.J., Kumar, A.: An active diagnostic system for structural health monitoring of rocket engines. Journal of Intelligent Material Systems and Structures 17, 619–628 (2006) 112. Wu, Z., Qing, X.P., Ghosh, K., Karbhar, V., Chang, F.-K.: Health monitoring of bonded composite repair in bridge rehabilitation. Smart Materials and Structures (in press) 113. Trendafilova, I., Manoach, E.: Vibration based damage detection in plates by using time series analysis. Mechanical Systems and Signal Processing (in press) 114. Yuan, S., Liang, D., Shi, L., Zhao, X., Wu, J., Li, G., Qiu, L.: Recent progress on distributed structural health monitoring research at NUAA. Journal of Intelligent Material Systems and Structures 19, 373–386 (2008) 115. Park, S., Yun, C.-B., Roh, Y., Lee, J.-J.: PZT-based active damage detection techniques for steel bridge components. Smart Materials and Structures 15, 957–966 (2006) 116. Keilers Jr., C., Chang, F.-K.: Identifying delamination in composite beams using built-in piezoelectrics: part I - experiments and analysis. Journal of Intelligent Material Systems and Structures 6(5), 649–663 (1995)

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117. Choi, K., Keilers Jr., C., Chang, F.-K.: Impact Damage detection in composite structures using distributed piezoceramics. In: Proceedings of the 35th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, April 18-20, 1994, pp. 118–124 (1994) 118. Tracy, M., Chang, F.-K.: Identifying impacts in composite plates with piezoelectric strain sensors, part I: theory. Journal of Intelligent Material Systems and Structures 9, 920–928 (1998) 119. Halabe, U.B., Franklin, R.: Ultrasonic signal amplitude measurement and analysis techniques for nondestructive evaluation of structural members. In: Proceedings of the SPIE, vol. 3396, pp. 84–94 (1998) 120. Monnier, T.: Lamb waves-based impact damage monitoring of a stiffened aircraft panel using piezoelectric transducers. Journal of Intelligent Material Systems and Structures 17, 411–421 (2006) 121. Staszewski, W.J., Boller, C., Tomlinson, G.R.: Health Monitoring of Aerospace Structures: Smart Sensor Technologies and Signal Processing. John Wiley & Sons, Inc, Chichester (2004) 122. Sohn, H., Farrar, C.R., Hunter, N.F., Worden, K.: Structural health monitoring using statistical pattern recognition techniques. ASME Journal of Dynamic Systems, Measurement and Control 123, 706–711 (2001) 123. Banerjee, S., Ricci, F., Monaco, E., Mal, A.: A wave propagation and vibration-based approach for damage identification in structural components. Journal of Sound and Vibration 322(1-2), 167–183 (2009) 124. Banerjee, S., Ricci, F., Monaco, E., Lecce, L., Mal, A.: Autonomous impact damage monitoring in a stiffened composite panel. Journal of Intelligent Material Systems and Structures 18, 623–633 (2007) 125. Ihn, J.-B., Chang, F.-K.: Pitch-catch active sensing methods in structural health monitoring for aircraft structures. Structural Health Monitoring: An International Journal 7(1), 5–19 (2008) 126. Sohn, H., Park, G., Wait, J.R., Limback, N.P.: Wavelet based analysis for detecting delamination in composite plates. In: Chang, F.-K. (ed.) Proceedings of the 4th International Workshop on Structural Health Monitoring, Stanford, CA, USA, September 15-17, 2003, pp. 567–574. DEStech Publications, Inc. (2003) 127. Park, S., Yun, C.-B., Roh, Y.: Damage diagnostics on a welded zone of a steel truss member using an active sensing network system. NDT&E International 40, 71–76 (2007) 128. Staszewski, W.J.: Wavelet based compression and feature selection for vibration analysis. Journal of Sound and Vibration 211(5), 624–659 (1998) 129. Levin, R.I., Lieven, N.A.J.: Dynamic finite element model updating using neural networks. Journal of Sound and Vibration 210, 593–607 (1998) 130. Lu, Y., Wang, X., Tang, J., Ding, Y.: Damage detection using piezoelectric transducers and the Lamb wave approach: II. robust and quantitative decision making. Smart Materials and Structures (in press) 131. Jolliffe, I.T.: Principal Component Analysis. Springer, New York (2002) 132. Su, Z., Ye, L.: Digital damage fingerprints (DDF) and its application in quantitative damage identification. Composite Structures 67, 197–204 (2005) 133. Su, Z., Ye, L.: An intelligent signal processing and pattern recognition technique for defect identification using an active sensor network. Smart Materials and Structures 13(4), 957–969 (2004)

6 Algorithms for Damage Identification Signal Features

Fusion of

6.1 Introduction Damage identification and structural health monitoring are somewhat like detective work to catch the ‘criminal’ damage committed to a structure. In this procedure, signals are acquired by sensors (introduced in Chapter 4) and processed with appropriate signal processing tools (introduced in Chapter 5) with the aim of extracting signal features, which are then aggregated, interpreted and subsequently linked with damage parameters. From the linkages established between signal features and damage, damage parameters of interest such as location, shape and severity can be inferred. This inferential process for identifying structural damage is a typical inverse endeavour, in which the outcome (e.g., a damage-scattered wave signal) is known beforehand whereas the reason leading to such an outcome (e.g., the damage) is unknown. In other words, we attempt to inversely infer the damage (reason) based on the captured signals (outcomes). Inverse (deductive) identification is opposite to forward (inductive) analysis. In the latter, the reason (e.g., the damage) is perspicuous beforehand, and on that basis we can logically obtain the outcomes (e.g., structural responses). An inverse problem is often notably ill-posed and is difficult to solve by rational and logical means. In most cases, solutions are uncertain or ambiguous. For example, with a captured wave signal, there may be an infinite number of combinations of damage location, shape and extent that may result in such a wave signal. Most inverse problems can be resolved only through appropriate inverse algorithms. Algorithms for detection, classification and identification, as a generic interest in engineering practice, have been extensively examined in recent years, and a popular taxonomy is shown in Figure 6.1, including mainly physical models, feature-based inference techniques and cognitive-based models. In particular, feature-based inference plays a dominant role in solving an inverse problem and is widely adopted for damage identification using Lamb waves, in line with the fact that damage identification is substantially based on the features extracted from Lamb wave signals. Z. Su and L. Ye: Identification of Damage Using Lamb Waves, LNACM 48, pp. 195–254. springerlink.com © Springer-Verlag Berlin Heidelberg 2009

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Fig. 6.1. Taxonomy of algorithms for detection, classification and identification [1]

This chapter describes the principles of major algorithms commonly used in Lamb-wave-based damage identification. For better understanding, selected case studies using some of these algorithms are detailed in Chapter 7.

6.2 Data Fusion and Damage Identification Algorithms The aggregation and interpretation of features extracted from captured signals with the aim of defining damage is the core of an inverse inferential procedure, and such a process is termed data fusion. Literally, data fusion is a multilevel and multifaceted process of combining multiple features extracted from a multitude of spatially distributed independent sources (e.g., sensors), so as to provide capabilities in automatic detection, classification and identification [1]. Through appropriate fusion procedures, the features extracted from Lamb wave signals can be related to the damage parameters at a qualitative or quantitative level. Data fusion thus plays a pivotal role in pursuing accuracy and precision of identification. In addition, a proficient fusion process can also help reduce imprecision, uncertainty and incompleteness of signal acquisition, thereby increasing identification robustness and reliability.

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Damage is a structural state different from the pristine state that is supposedly ‘undamaged’ or ‘healthy’, that is to say, the states of damage and health are defined relatively. Implicit in the definition, a damage event can only become evident by comparing the state to be evaluated with the benchmark state, or more generally speaking by comparing the state to be evaluated with an anterior structural state at a specific moment, which serves as the benchmark for a posterior state at a subsequent moment. In accordance with this understanding, the majority of damage identification approaches, using not only Lamb waves but also other dynamic signatures such as impedance or modal data, have been developed by making reference to a benchmark state supposed to be healthy. Accordingly, a damage identification exercise is often termed benchmarking or referencing. In an exercise of damage identification using Lamb waves, actuator(s) and sensor(s) are often placed in accordance with either (i) pitch-catch or (ii) pulseecho configuration (a tandem arrangement of an actuator-sensor pair), as briefed in Chapter 1 (Figure 1.1), (i) in a pitch-catch configuration [2-6], sketched in Figure 6.2(a), a diagnostic Lamb wave signal is emitted from an actuator to travel across the inspection area while a sensor on the other side of the area receives the wave signal propagated through the inspection area (forward-scattering wave). Such an approach cannot locate the damage unless a network of transducers is used to offer multiple forward-scattering wave signals; and (ii) in a pulse-echo configuration [6-11], sketched in Figure 6.2(b), the actuator and sensor are placed on the same side of the inspection area, and the sensor receives the wave signal echoed back from the damage (back-scattering wave). One caveat of the pulse-echo configuration is that the captured signal may not be sufficiently sensitive to damage at a remote site, because the waves echoed from remote damage travel relatively long distance before received by the sensor in comparison with a pitch-catch configuration, and the signal may lose substantial information concerning damage during longdistance propagation. Furthermore, there may be a blind zone area close to the collocated actuator and sensor, which is a result of the interference between the damage-echoed waves received by the sensor and the outgoing diagnostic waves generated by the actuator [12]. In either configuration, various characteristics can be extracted from the transmitted or reflected signals, including time-of-flight (ToF), magnitude and frequency, which contain essential information about the damage. The damage can then be defined qualitatively or quantitatively by aggregating these signal characteristics via appropriate fusion algorithms. Arguably the most important difference between the pitch-catch and pulseecho configurations is: the sensitivity of the former configuration is governed by the magnitude of the forward-scattering wave signal across the inspection area, whereas the sensitivity of the latter is mainly governed by the magnitude of the wave back-scattered from the damage. This then makes the choice of a configuration dependent on the anticipated damage. For example, For the same damage, the S0 mode often provides a better reflection (more pronounced magnitude) than the

A0 mode does [13], which suggests that if the S0 mode is employed for damage

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Identification of Damage Using Lamb Waves

identification the actuator and sensor should preferably be arranged in a pulseecho configuration to explore the damage-reflected wave signals rather than the transmitted signals. That is why the S0 mode and pulse-echo configuration are often employed together to identify a through-thickness crack.

Forward-scattering wave

Sensor

Damage

Diagnostic wave

Actuator

a

Back-scattering wave

Damage

Sensor

Diagnostic wave

Actuator

b Fig. 6.2. Arrangement of a pair of actuator and sensor in a. pitch-catch; and b. pulse-echo configurations

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The principles of the primary fusion algorithms commonly used for Lamb-wavebased identification are introduced briefly in the following sections. 6.2.1 Damage Index The DI (Section 5.4.3) is a series of features extracted from the captured signal that can be linked with damage at different states. An efficient DI can serve as an indicator to depict the damage. The cardinal steps of damage identification in terms of DIs are: (i) establishing a relationship between changes in DIs extracted from wave signals (e.g., reflection coefficients, ToF, figure-of-merit and root mean square) and known damage parameters (e.g., location, size and shape) using a sufficiently large number of cases obtained beforehand from experiments and/or simulations; (ii) extracting DIs from signals captured in the structure under inspection whose state is unclear, in accordance with the same DI extraction procedure as in step (i); and (iii) interpolating or extrapolating the DI obtained in step (ii) in the established relationship to determine the unknown damage parameters. Figure 6.3 presents two representative relationships between DIs extracted from Lamb wave signals and a specific damage parameter (e.g., crack/notch length). In Figure 6.3(a), the length of a rivet crack in an aircraft panel is linked with a correlation-coefficient-based DI, and in Figure 6.3(b), the size of a notch in a laminate beam is associated with a reflection-coefficient-based DI. However, such interpolation-based identification, by linking a particular DI with a particular damage parameter (e.g., the damage location in a onedimensional beam OR crack length) is generally unable to define multiple parameters of damage at the same time. Moreover, the nature of such an approach implies that, ideally, the selected DI must be most sensitive to the particular damage parameter to be linked, and such correlation must not be prominently influenced by other parameters. If a DI is sensitive to multiple damage parameters (e.g., location, size and shape) rather than just one, theoretically there may exist an infinite number of combinations of multiple damage parameters, resulting in ambiguous identification results. As a consequence, DI-based interpolation is normally effective in some relatively simple cases only, such as evaluating the size of through-width delamination in a one-dimensional laminate beam using the pitch-catch configuration, in which the damage is located in the actuator-sensor path. 6.2.2 Time-of-flight The difference in ToFs (difference in ToFs is defined as the time lag between the incident wave that the sensor first captures and the wave scattered by damage that the same sensor subsequently captures) is one of the most straightforward features of a Lamb wave signal for damage identification. In substance it suggests the relative positions among the actuator, sensor and damage. From the difference in the ToFs between the damage-scattered and incident waves extracted from a certain number of signals, damage can accordingly be triangulated [3, 14-17].

Identification of Damage Using Lamb Waves

Correlation-coefficient-based DI

200

0.98

0.94

0.9

3 mm crack

1 mm crack

Loose rivet

Normal

Damage case

a

Reflection-coefficient-based DI

0.36

0.24

0.12

0 0

2

4

6

8

10

Notch length [mm]

b Fig. 6.3. Relationships between selected DIs and damage parameters of interest: a. signal correlation-coefficient-based DI vs. crack length near a rivet in an aircraft panel [18]; and b. wave reflection-coefficient-based DI vs. notch length in a composite beam [19]

6.2.2.1 One-dimensional Scenario In a one-dimensional case (e.g., a structural beam or rod), the actuator, sensor and damage are in a straight line with two possible scenarios as shown in Figures 6.4(a) and (b). For the former, the sensor captures the incident wave from the actuator first and then the wave scattered back from the damage. The damage can

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201

thus be located with regard to the position of the sensor in terms of the difference in the ToFs between the damage-scattered and incident waves, Δt ,

L=

V ⋅ Δt , 2

(6.1)

where L is the distance between the damage and the sensor; V is the group velocity of the diagnostic Lamb wave. The underlining assumption of Equation 6.1 is that the group velocity is the same for the forward and echoed waves. The echoed wave signal can further be used to estimate the extent of the damage using DIbased interpolation, based on the observation that the magnitude of the echoed wave signal is relevant to the damage size. Incident wave

Wave echoed back from damage

Difference in ToFs

Incident diagnostic signal

Signal captured by sensor

Damage Actuator

Sensor

L

a Wave transmitted through damage

Incident diagnostic signal

Signal captured by sensor Damage

Actuator

Sensor

b Fig. 6.4. ToF-based identification of damage in a one-dimensional beam with an actuatorsensor pair: a. sensor capturing the damage-reflected wave to locate damage; and b. sensor capturing the transmitted wave to evaluate damage severity

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Identification of Damage Using Lamb Waves

For the case shown in Figure 6.4(b), in recognition of the observations that damage attenuates Lamb waves passing through it (Section 2.5) and the degree of attenuation is associated with the size of damage, the transmitted wave signal can be used to evaluate the size of the damage using DI-based interpolation, although this configuration of actuator and sensor is an unwieldy way of locating the damage.

6.2.2.2 Two-dimensional Scenario with Two Actuator-sensor Pairs Expanding the above discussion to a two-dimensional plate with an actuatorsensor pair (an sensing path), Figure 6.5(a), Equation 6.1 is then extended to t A− D − S − t A− S = (

L L A− D LD − S + ) − A− S = Δt , V1 V2 V1

(6.2)

where L A− D = ( x D − x A ) 2 + ( y D − y A ) 2 ,

LD −S = ( x D − x S ) 2 + ( y D − y S ) 2 ,

L A− S = ( x A − x S ) 2 + ( y A − y S ) 2 .

In the above equation, t A − D − S is the ToF of the incident wave propagating from the actuator to the damage and then to the sensor, and t A − S is the ToF of the incident wave propagating directly from the actuator to the sensor. Δt is the difference between the above two ToFs, which can be extracted from the captured Lamb wave signal. L A− D is the distance between the actuator located at ( x A , y A ) , and the damage centre, presumed at ( x D , y D ) and to be determined; LD− S is the distance between the damage centre and the sensor located at ( x S , y S ) ; L A− S is the distance between the actuator and sensor (see Figure 6.5(a) for the coordinate system). V1 and V2 are the group velocities of the incident Lamb wave activated by the actuator and the wave scattered by the damage ( V1 and V2 need not be the same, provided that mode conversion occurs upon interaction of the incident wave with the damage). Theoretically, the solutions to Equation 6.2 configure a locus, a dotted line in Figure 6.5(a), indicating possible locations of the centre of the damage. With ToF extracted from another actuator-sensor pair (sensing path), an equation similar to Equation 6.2 can be obtained, and a nonlinear equation group, containing two equations contributed by two actuator-sensor pairs and involving the position of the damage centre ( xD , y D ) (two unknown variables), is available. Two loci established by the two equations lead to intersection(s), i.e., the solution(s) to the equation group, sketched in Figure 6.5(b), which is(are) the location of the damage centre ( xD , y D ) .

Algorithms for Damage Identification

y

203

Plate under inspection

Sensor

Damage

( xD , y D )

( xS , y S )

Actuator

(xA , yA ) x

a y

Plate under inspection

Actuator Intersection of loci

( xD , y D )

Sensor

Sensor

Actuator

x Intersection of loci

b

( xD , y D )

Fig. 6.5. ToF-based triangulation of damage in a two-dimensional plate with two actuatorsensor pairs: a. locus established by a sensing path; and b. two loci established by two paths (when V1 and V2 are not the same, the locus is not exactly an ellipse)

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Identification of Damage Using Lamb Waves

The damage severity can further be calibrated in terms of changes in the magnitude of damage-scattered waves, although such changes may not be linearly subject to damage severity. In the case that the damage is located exactly on the projection of connection between the actuator and sensor, the case is simplified to the aforementioned one-dimensional scenario. Mathematically, the locus defined by Equation 6.2 is an ellipse with the actuator and sensor being its two foci, provided V1 and V2 are the same, otherwise the locus is not exactly an ellipse, with one relatively dull end and one relatively sharp end, like the two loci shown in Figure 6.5(b). As a special case of the above discussion, one actuator and two sensors are also able to configure two sensing paths. In such a scenario, the incident wave activated by the actuator propagates to the damage, and then the damage-scattered waves are captured by two sensors sequentially. The difference in the ToFs between the damage-scattered waves captured by the two sensors S 1 , located at ( x S , y S ) , and S 2 , located at ( x S , y S ) , respectively, Δt12 , is 1

1

2

2

t A− D − S − t A − D − S = Δ t12 , 1

(6.3)

2

where t A− D − S and t A− D − S are the ToFs of the incident wave propagating from the 1

2

actuator to the damage and then to sensors S 1 and S 2 , respectively. Because the time for the incident wave to propagate from the actuator to the damage is the same for both sensing paths, Equation 6.3 becomes t D − S 1 − t D − S 2 = Δ t12 ,

or

LD − S

1

V2

−

LD − S

2

V2

= Δt12 ,

(6.4)

where LD − S = ( x D − x S ) 2 + ( y D − y S ) 2 , LD − S = ( x D − x S ) 2 + ( y D − y S ) 2 . 1

1

1

2

2

2

In the above equations, LD − S1 and LD − S2 are the distances from the damage to S1 and from the damage to S 2 , respectively. Theoretically, the solutions to Equation 6.4 configure a locus, and the difference between the distances from any point on the locus to two sensors is a constant ( Δt12 ⋅ V 2 ), i.e., a hyperbola with S1 and S 2 being its two foci, the dotted lines in Figure 6.6(a). The hyperbola suggests possible locations of the centre of the damage. The shape of the hyperbola is defined by the distance between the two sensors and V2 . A typical hyperbola defined by Equation 6.4 has two arms, and the possible damage is located on the arm close to the sensor that receives the signal early. As with the aforementioned triangulation procedure using two actuator-sensor pairs, two sets of hyperbolae can thus be established in conjunction with another actuator. The intersection(s) of the two sets of hyperbolae is(are) the location of damage centre ( xD , y D ) .

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205

Plate under inspection

y

Damage

( xD , y D ) Sensor S1

( xS , yS ) 1

Sensor S2

1

( xS , y S ) 2

2

Actuator

(xA , yA ) x

a Plate under inspection

y Ellipse

Hyperbola established

established by

by the actuator and two

the actuator

sensors (S1 and S2)

and S1

Sensor S1

Ellipse

( xS , yS ) 1

1

established by Sensor S2

Intersection of

two ellipses

the actuator

( xS , y S ) 2

hyperbola and

and S2

2

Actuator

(xA , yA ) x

b Fig. 6.6. ToF-based triangulation of damage in a two-dimensional plate with one actuator and two sensors: a. hyperbola established; and b. integrated diagram showing two ellipselike loci and hyperbola (if V1 and V2 are not the same, the locus is not exactly an ellipse)

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Identification of Damage Using Lamb Waves

Theoretically, if the hyperbola (defined by Equation 6.4) and two ellipse-like loci (defined by Equation 6.2) are put into one diagram, the hyperbola arm can be seen to pass the intersection(s) of the two ellipses, Figure 6.6(b).

6.2.2.3 Two-dimensional Scenario with Active Sensor Network Damage triangulation using the difference in ToFs is in principle a focusing (or fusion) process of seeking common intersections of loci (ellipses or hyperbolae) established by multiple actuator-sensors pairs. We now further expand the above discussion to a two-dimensional plate with a sensor network attached consisting of N piezoelectric elements (each being able to serve as both actuator and sensor), denoted by S i , ( i = 1, 2, A , N ), Figure 6.7(a). The actuator-sensor path, in which S i serves as the actuator and S j as the sensor ( i ≠ j ), is symbolised by Si − S j .

Considering an arbitrarily selected piezoelectric element in the network, S i , a local coordinate system can be established as in Figure 6.7(b), where S i is at the origin when it serves as the actuator, and the centre of the damage is presumed at ( xD , y D ) . In such a coordinate system, a set of nonlinear equations can be established for individual sensing paths, (

LS − D i

V1

+

LD − S V2

j

)−

LS −S i

V1

j

( i, j = 1, 2, A, N , but i ≠ j ),

= Δt i − j

(6.5)

where LD −S j = ( x D − x j ) 2 + ( y D − y j ) 2 ,

2 2 LS − D = x D + y D , i

2

2

LS −S = x j + y j , i

j

where Δt i − j is the difference between the ToF for the incident wave to propagate from actuator S i to the damage and then to sensor S j , and the ToF for the incident wave to propagate directly from actuator S i to sensor S j . LSi − D , LD − S j

and

LS −S represent the distances between actuator S i located at (0,0) and the damage i

j

centre ( x D , y D ) , the damage centre and sensor S j located at ( x j , y j ) , and S i and S j , respectively. Equation 6.5 depicts a series of ellipse-like loci with S i and S j ( i, j = 1, 2, A , N , but i ≠ j ) being two foci, indicating possible damage

locations. Therefore, each locus is the perception as to the damage in the structure from the perspective of the sensing path ( S i − S j ) that creates such a locus. Similarly, for the case using one actuator and two sensors ( S m and S k , ( m, k = 1, 2, A , N , but m ≠ k )) defined by Equation 6.4, by extending the equations to a sensor network consisting of N piezoelectric elements, we have

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207

Y

Si X

Si-Sj

Sj

S3

S2

S1

SN

a

Damage at (xD, xD)

LS − D i

Actuator Si at (0, 0)

LD − S

LS

i

−S j

j

Sensor Sj at (xj, xj)

b Fig. 6.7. a. ToF-based triangulation of damage in a two-dimensional plate with an active sensor network consisting of N piezoelectric elements; and b. relative positions among actuator si , sensor s j and damage in the local coordinate system for sensing path S i − S j

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Identification of Damage Using Lamb Waves

LD − S m V2

−

LD − S k V2

= Δt m − k

( m, k = 1, 2, A , N , but m ≠ k ),

(6.6)

where LD − Sm = ( x D − xm ) 2 + ( y D − y m ) 2 ,

LD − Sk = ( x D − xk ) 2 + ( y D − y k ) 2 ,

where L D − S m represents the distance between the damage centre ( x D , y D ) and sensor S m located at ( x m , y m ) ; LD −Sk represents the distance between the damage centre and sensor S k located at ( xk , yk ) . Δt m−k denotes the difference in the ToFs between the damage-scattered waves captured by S m and S k . Likewise, Equation 6.6 depicts a series of hyperbolae with

Sm

and

Sk

being two foci

( m, k = 1, 2, A , N , but m ≠ k ), indicating possible damage locations. Therefore, each hyperbola is the perception as to the damage in the structure from the perspective of the sensor pair ( S m and S k ) that creates such a hyperbola. Equations 6.5 and 6.6 provide a way to locate damage by seeking intersections of a series of ellipse-like loci or hyperbolae, respectively. In practice, it is often the case that these curves do not converge at one point, since damage that scatters incident waves is a spatial object with certain geometry rather than a point (in all the above derivation, we suppose that damage is a point, located at ( x D , y D ) ). The incident waves are in fact scattered at the tip/edge of the damage rather than its centre. Allowing for this fact, the region containing the majority of interactions can be deemed as a damage zone. On the other hand, it is axiomatic that the success of triangulating damage in terms of ToF is largely dependent on the accuracy of ToF extraction. (i) Mode conversion upon an incident wave encountering damage, (ii) relative positions among actuators, sensors and possible damage, and in particular (iii) wave reflection from a structural boundary are some factors that can complicate ToF extraction. To this end, appropriate signal processing tools (Chapter 5), including the Hilbert transform, wavelet analysis and time reversal can be helpful. A sensor network with relatively dense sensor allocation can also reduce the complexity of ToF extraction. Furthermore, during ToF extraction, when an additional wave packet after the incident wave packet is observed in a captured wave signal, it is in fact not possible simply to infer that the additional wave packet is due to the damage without comparing this signal with a benchmark signal or prior knowledge of the relative positions of the actuator and sensor relevant to the boundaries. That is the reason that damage identification is often termed benchmarking or referencing, as mentioned previously.

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6.2.3 Time Reversal – for Identifying Damage

The time reversal technique was previously introduced as a signal processing tool for improving the quality of a captured Lamb wave signal in Section 5.2.1.3. In addition, it can be used as an inverse inferential tool for evaluating structural damage. The keystone of time-reversal-based damage identification is that if there is any defect in or near the wave propagation path, the time reversibility of the wave signal captured via this path breaks down. Furthermore, the damage can be quantitatively assessed by calibrating the deviation of the reconstructed wave signal after applying time reversal with regard to the original incident signal, without requiring any benchmark signals (see Section 5.2.1.3 for how to time-reverse a wave signal) [20-23]. For example, in the absence of any damage in a composite laminate, the reconstructed signal coincides well with the original incident signal, Figure 6.8(a); in the presence of impact delamination, a large discrepancy between the reconstructed signal and the original incident signal is clearly evident, Figure 6.8(b), indicating the breakdown of reversibility of the signal as a result of the presence of damage. The intersections contributed by any two actuator-sensor paths of a dense sensor network, whose reversibility is interrupted, form a region which has a high probability of containing damage, illustrated schematically in Figure 6.9. This is rather like the procedure of locating damage by seeking intersections of loci in terms of ToFs, introduced in Section 6.2.2. The deviation of reconstructed signals from original input signals for the damage-influenced actuator-sensor paths can further be calibrated to evaluate the size of the damage, in conjunction with the DI-based interpolation introduced in Section 6.2.1. Since damage scatters all the wave modes contained in the incident wave signal, individual Lamb modes (e.g., S0 , A0 or S0 + A0 modes) can be used for such an algorithm [23]. 6.2.4 Migration Technique

In geophysical reconnaissance, a man-made explosion at a low energy level on the earth’s surface is a means of creating waves that are able to travel in the earth’s interior and propagate on its surface. Any inhomogeneity beneath the earth’s surface can be detected and located by examining both the initial bang and the waves scattered from the inhomogeneity captured by a number of geophones placed at different locations. In geology this method is called the migration technique. This technique has attained maturity for seismic applications over the past 50 years, and it has recently been examined to develop algorithms of Lamb-wave-based damage identification [24-28]. In such an approach, the sensor-captured wave signals are moved (‘migrate’) back by presuming that time goes back (reverses), until the wave recurs at its source (this can be accomplished based on computer simulation of the wave field step by step). During this procedure, any structural damage or boundary, which is actually the wave source scattering the incident wave, can be located. The process of propagating back the captured waves is achieved substantially by solving the

210

Identification of Damage Using Lamb Waves

wave equation based on Huygens’ principle which states that the scattered wave radiating from damage can be viewed as a new wave activated from the damage, and therefore the damage can be treated as a secondary source that generates the waves [26].

Amplitude

Input signal

Reconstructed signal

Time

a

Amplitude

Input signal

Reconstructed signal

Time

b Fig. 6.8. Principle of the time-reversal-based damage identification: input and reconstructed Lamb wave signals in a composite structure a. without; and b. with delamination [29]

The migration-based damage identification includes mainly three basic steps in sequence: (i) computation of the wave field signals: the propagation of Lamb waves activated by an actuator is calculated at each time step, to form a description of the wave field (this can be done using theoretical derivation such as Mindlin’s plate theory or finite element simulation); (ii) backward extrapolation of the scattered wave field signal: signals captured by sensors are used as the boundary conditions. Wave field signals obtained from step (i) are then extrapolated backwards in time from sensors, similar to the procedure of time reversal. Successive iterations backwards in time are

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211

performed until the initial time is reached for an actuator-sensor path. During this process, a numerical method (e.g., finite element simulation or finite difference method) can be employed to migrate backwards the wave field signals. In the presence of damage, which is the secondary source to scatter the incident waves, the wave propagating backwards will recur at the position of damage. By such an means, the damage can be located in an image of the wave field [26]; and (iii) formation of damage image: applying the same procedure to individual actuator-sensor paths of a sensor network, a series of images containing the damage can be formed. Aggregating all the images (i.e., all the images are superimposed) produces a resulting wave field image in which damage, if any, is visualised.

a

b

c

Fig. 6.9. Damage localisation procedure based on the time reversal algorithm for a composite panel: a. actual impact location in the panel (white square); b. actuator-sensor paths whose reversibility is interrupted due to the presence of delamination; and c. identified damage area that contains the majority of intersections of damage-influenced actuatorsensor paths [29]

The above procedure can be better understood using an example [26], in which a piezoelectric element actuator is surface-bonded at the centre of a quasi-isotropic carbon fibre-reinforced epoxy laminate with a configuration of [45/0/-45/90]s. The laminate contains two delamination areas (each 10 mm in diameter). Figure 6.10

212

Identification of Damage Using Lamb Waves

Plate y-dimension

Plate y-dimension

shows snapshots of the wave field at four typical moments during migrating back the wave signals to their sources (either the wave actuator or the damage), in accordance with the three aforementioned steps. Due to the quasi-isotropy of the composite laminate, the wavefront in the wave field does not strictly form a circle. As the time moves backwards, the signal scattered by the first damage (left delamination, a secondary wave source) is extrapolated and focused back to the damage, in Figure 6.10(b); then the wave field continues moving backwards until the wavefront encounters the second damage (right delamination, another secondary wave source), Figure 6.10(c); finally, the wavefront migrates back to the actuator, Figure 6.10(d). Migration technique provides an intuitive way to visualise the location and size of structural damage.

Plate x-dimension

Plate x-dimension

Right damage

Left damage

b

Plate y-dimension

Plate y-dimension

a

Plate x-dimension

c

Plate x-dimension

d

Fig. 6.10. Damage identification based on migration technique (wave is generated by actuator at t = 0 ): a. as time moves backwards, the recorded wave field is extrapolated and the wave propagates backwards (snapshot at the 150th s); b. the wave scattered by the left damage focuses back to the left damage through migration (snapshot at the 90th s); c. the wave continues moving backwards, and the wave scattered by the right damage focuses back to the right damage through migration (snapshot at the 86th s); and d. the wave continues moving backwards (snapshot at the 70th s) until it reaches the actuator [26]

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213

6.2.5 Lamb Wave Tomography

Computed tomography (CT) using X-ray radiography is widely used in clinical applications. The principle of this technique is that a radiated gamma ray passes more easily through soft tissue whereas it is somewhat blocked (‘attenuated’) by dense tissue. Any abnormality in tissue can thus be highlighted in the reconstructed image. On a similar principle, Lamb wave tomography has been developed. In the technique [30, 31], an easily interpretable image (i.e., a tomogram) concerning the damage parameters of interest (e.g., thickness loss due to corrosion) can be reconstructed using an appropriate image reconstruction technique, in which the location, size and shape of the damage, if any, can be visualised. In Lamb wave tomography, Lamb waves can be activated and received using contact, air-coupled or laser-based ultrasonic transducers. These devices are called tomographs. The object under inspection can also be immersed into water tank in accordance with the normal ultrasonic scan procedure. These implementations of using different tomographs are compared elsewhere [32, 33]. Employing a large number of transducers, Lamb wave tomography can be conducted following certain basic steps: (i) the area under inspection is meshed virtually into small cells (called grid cells); (ii) for an actuator-sensor pair of a sensor network, any feature extracted from a Lamb wave signal (activated by the actuator and captured by the sensor, termed projection data in this technique) is deemed to be the sum of contributions from all cells that lie on the straight line (called a ray) between the actuator and the sensor; (iii) since the contribution of any cell is proportional to the length of the ray in that cell, this length can be used as a weight to calibrate the contribution of individual cells; and (iv) in recognition of the fact that the presence of damage changes signal features in relation to the benchmark signal, the field value at individual cells along a ray can be defined using appropriate algorithms, in terms of changes in wave velocity [34, 35], attenuation in magnitude of the transmitted signal [33, 36, 37], difference in ToF [30, 38, 39] (in some Lamb wave tomography techniques it is called arrival time or time-of-arrival), etc. Aggregation/fusion across the inspection area of the corresponding field values established by all the available rays in a sensor network reconstructs a tomogram for the damage that has caused the changes in the signal features. In step (iv), if the changes in the propagation velocity of a Lamb wave signal within each grid cell are used to establish the field value, the algorithm for tomographic reconstruction is [34] T [i , j ] =

∑ t[i, j, m, n] = ∑

m , n∈ray [ i , j ]

d [i , j , m , n ] v[m, n] m , n∈ray [ i , j ]

( i, j = 1, 2, A , N , but i ≠ j ),

(6.7)

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Identification of Damage Using Lamb Waves

where [m, n] is the grid cell with its coordinates being (m, n) , Figure 6.11, and [i, j ] denotes the ray connecting the i th actuator and the j th sensor; T [i, j ] is the experimentally measured ToF, i.e., the total time for the Lamb wave to travel from the i th actuator to the j th sensor, and t[i, j , m, n] is the time for the Lamb wave to travel the distance of ray [i, j ] within cell [m, n] . Therefore we have d [i, j , m, n] t[i, j , m, n] = where d [i, j , m, n] is the distance in cell [m, n] that the v[m, n] wave travels through along ray [i, j ] ; v [ m, n ] is the wave propagation velocity in

the cell (termed cell velocity); d [i, j , m, n] can be determined once the mesh for defining the grid cell is specified. Cell [m,n]

jth sensor

ith actuator

Fig. 6.11. Principle of Lamb wave tomography

A sensor network offering N p actuator-sensor paths (rays) contributes N p equations described by Equation 6.7, and the solutions to these equations reconstruct a tomogram reflecting changes in the wave velocities. In this regard, the iterative algebraic reconstruction technique (ART) [33] and simultaneous iterative reconstruction technique (SIRT) [34, 37] are two algorithms that can be used to reconstruct such a tomogram, including mainly four basic steps in sequence [34]: (i) with initial estimated cell velocities, v 0 [m, n] (in what follows, superscript ‘0’ stands for the initial value in an iterative procedure), the initial estimated ToF for individual ray is

Algorithms for Damage Identification

T 0 [i, j ] =

∑

d [i, j , m, n] . 0 m ,n∈ray [ i , j ] v [ m, n ]

215

(6.8)

In subsequent iterations, the estimated ToF is calculated with the updated cell velocities as T k [i , j ] =

∑

d [i , j , m, n ] , k m ,n∈ray [ i , j ] v [ m, n]

(6.9)

where k is the iteration number; (ii) for every single ray, the difference between the wave velocities in the current iteration and those in the previous iteration is calculated for each cell through which the ray passes as Δ

1 vm ,n∈ray [ i , j ] [m, n]

=

T k [i, j ] − T k −1[i, j ] , L[i, j ]

(6.10)

where L(i, j ) is the length of ray [i, j ] . During each iteration, the above calculation is cycled through each ray and the changes in velocity for each individual cell are recorded; (iii) each cell’s velocity is updated by taking the average of the differences 1 ( Δ average ) recorded for that cell in step (ii) and adding it to the cell’s v[m, n] current velocity as 1 1 1 ; = + Δ average v[ m, n] v k +1[m, n ] v k [m, n ]

(6.11)

(iv) the above three steps are repeated until the required accuracy is reached when T k [i, j ] converges to the measured ToF. The above four steps are then applied to all the available actuator-sensor paths (rays) of the sensor network, to obtain the field value, v[ m, n] , at each grid cell of the inspection area. The reconstructed tomogram thus represents changes in velocity of the Lamb wave across the entire inspection area. In step (iv), if the changes in the magnitude of a Lamb wave signal, contributed by attenuation of the wave within each grid cell, are used to establish the field value, the algorithm for tomographic reconstruction is [37] A[i, j ] = Aini

∑

m,n∈ray[i , j ]

EXP(−

1 (µ[m, n] ⋅ d[i, j, m, n])) C

( i, j = 1, 2, A , N , but i ≠ j ).

(6.12)

216

Identification of Damage Using Lamb Waves

In the above equation, A[i, j ] is the magnitude of the measured wave signal upon travelling from the i th actuator to the j th sensor, which can be experimentally measured; Aini is the initial amplitude of wave; µ[m, n] represents the attenuation of waves in cell [m, n] along ray [i, j ] ; and C is a constant related to the attenuation. The field value based on the attenuation of waves in individual cells, µ[m, n] , from the measured A[i, j ] and known cell distances d [i, j , m, n] can be obtained by solving Equation 6.12 for all the rays of the sensor network, adopting an iteration procedure similar to that based on changes in the propagation velocity [37] mentioned previously. Starting with an initial estimated attenuation of waves in cells, µ 0 [m, n] , we have Δµ m, n∈ray[ i , j ] [ m, n] =

[

]

C ln( A k −1 [i, j ]) − ln( A k [i , j ]) , L[i, j ]

(6.13)

where k is the iteration number. A single iteration is completed when all the measured rays have been cycled through and the corresponding changes in wave attenuation for each individual cell have been recorded. Then each cell’s attenuation is updated by taking the average of the differences ( Δ average µ[m, n] ) recorded for that cell and adding it to the cell’s current attenuation as

µ k +1[ m, n] = µ k [m, n] + Δ average µ[ m, n] ,

(6.14)

and the above steps are repeated until the required accuracy is reached when Ak [i, j ] converge to the measured magnitudes. The above steps are then applied to all the available actuator-sensor paths (rays) of the sensor network, to obtain the field value, µ[m, n] , at each grid cell of the inspection area. The reconstructed tomogram thus reflects changes in wave signal magnitude due to attenuation across the entire inspection area. Parallel beam projection (also called fan beam projection) and crosshole projection are two major schemes for implementing Lamb wave tomography, with configurations compared in Figure 6.12. In the former, only one actuator-sensor pair is employed to form a pitch-catch configuration. With this transducer pair mounted on an X-Y positioning stage that moves over the object, the entire inspection area of the object can be scanned by sliding/rotating the object, Figure 6.12(a). In this case, all the activated Lamb wave signals propagate the same distance, and changes in signals such as velocity or magnitude are captured. Rather than rotating the object, one can also employ a large number of fixed transducers surrounding the inspection area to form multiple parallel actuator-sensor pairs for tomographic reconstruction. In the crosshole projection scheme, a certain number of transducers are allocated along two parallel lines relative to the object under inspection, Figure 6.12(b).

Algorithms for Damage Identification

217

One can also employ one actuator-sensor pair to move relatively to each other along these two parallel lines to form a similar configuration. In this case, Lamb waves propagate different distances along different actuator-sensor paths, depending on their relative positions.

90º scan

135º scan

Receiving

Sending

transducer

transducer

Sample on rotary table 45º scan Stepper motor for 0º scan

linear scanner

a Receiving transducer

Sending transducer

Stepper motor for linear scanner

b Fig. 6.12. Schemes of Lamb wave tomography: a. parallel projection scheme (right: setup for implementation) where all the actuator-sensor paths are of the same length; and b. crosshole scheme (right: setup for implementation) where individual actuator-sensor paths are of different lengths [31]

A study [30] thoroughly compared the two schemes in terms of their merits and limitations, concluding that (i) ray density is critical to the quality of the tomogram reconstruction. The ray density is uniform in the parallel beam projection scheme but non-uniform in the crosshole projection scheme; (ii) rays in the parallel beam projection scheme cover all angles since projections can be evenly spaced over 180°. But this can be a challenge in practice

218

Identification of Damage Using Lamb Waves

because during the operation the area of the object under inspection needs to be free of obstructions to ensure access by the transducers from different angles. This condition may not apply for the crosshole projection scheme which can accept any geometry of the object; and (iii) in the parallel beam projection scheme each ray contributes substantially to the tomogram reconstruction and as a result such a scheme is susceptible to incompleteness of scanning and noise corruption. In contrast, the crosshole projection scheme allows certain incompleteness of data, and has better tolerance to measurement noise and uncertainty because it can take advantage of an active sensor network in which all sensing pairs are interactive. Generally speaking, the crosshole projection scheme is more flexible and practical than the parallel beam projection scheme. For comparison of precision, both schemes were employed to evaluate invisible impact delamination in a multi-layer woven graphite/epoxy laminate with a Cartesian grid pattern of through-thickness Kevlar stitching [30], and the identification results are shown in Figures 6.13(a) and (b), respectively, demonstrating that both schemes are able to pinpoint the damage in the laminate. In another example [33], with ART, two throughthickness holes each 7 mm in diameter only 14 mm apart in a composite plate measuring 100 mm × 100 mm can be clearly identified, but it is achieved at the cost of using 400 Lamb wave signals for tomographic reconstruction. However, no matter which scheme is adopted, there is the requirement of a large number of rays to cover the entire inspection area for tomographic reconstruction, leading to either rotation of the object by very tiny increments or a large number of appropriately arranged transducers. Under these conditions, application of Lamb wave tomography for rapid damage assessment is accordingly restricted. Moreover, most approaches based on crosshole projection scheme have been demonstrated to be particularly effective only when the major length of the damage is between 15% and 35% of the dimension of inspection area [36]. To improve efficiency, some modified schemes have been introduced such as the double crosshole scheme [30, 38].

a

b

Fig. 6.13. Identification results for delamination in a multi-layer woven graphite/epoxy laminate using a. parallel projection scheme; and b. crosshole scheme [30]

Algorithms for Damage Identification

219

6.2.6 Probability-based Diagnostic Imaging

There has been increasing interest in visualising a structural damage event intuitively in a two- or three-dimensional image whose pixels correspond exclusively to spatial points of the structure under inspection. In addition to the migration and Lamb wave tomography introduced previously, some more generic imaging approaches have been developed in conjunction with active-sensor network techniques, termed diagnostic imaging [5, 18, 21, 40-46]. A probability-based diagnostic imaging attempts to describe a damage event using a greyscale image to indicate the probability of the presence of damage at a specific point of the structure. The region of greyscale area where the probabilities are above a certain threshold may further be assumed to represent the shape and size of the damage. Considering of the many uncertainties encountered during the practical implementation of a damage identification exercise, it is probably unrealistic to achieve definitive identification results based on information provided by few actuator-sensor paths. Presenting the identification results in terms of the probability of the presence of damage, based on the fusion of signals rendered by a number of actuator-sensor paths, is an advantage over identification approaches based on the isolated actuator-sensor path. The underlying concept of probability is more consistent in nature with the implication of predicting or estimating damage. As addressed in Section 5.4.3, a DI is often defined in terms of the comparison of extracted signal features between different states of the structure under inspection (i.e., the benchmark and present states, or more generally speaking an anterior state at a specific moment and a posterior state at a subsequent moment). The presence of damage is the exclusive reason that leads to changes in the DI. On the basis of this philosophy, the probability of the presence of damage at a specific pixel of the image (one pixel of the image corresponding exclusively to a spatial point of the structure) can be calculated or defined using an appropriate DI extracted from captured Lamb wave signals, such as ToF, signal magnitude, signal energy, and others introduced in Section 5.4.3. The value of the probability image at a specific pixel is more often termed field value. Selecting and establishing an appropriate field value at each single pixel from captured wave signals rendered by individual actuator-sensor paths, so as to calculate the probability of the presence of damage at this pixel, is the core step in all the probability-based diagnostic imaging approaches. Various imaging approaches have been developed, which can be grouped roughly into four major categories in terms of the DI extracted from the Lamb wave signals in defining the field values. 6.2.6.1 ToF Following the discussion in Sections 6.2.2.2 and 6.2.2.3 concerning ToF, first, a locus can be obtained in terms of the difference in the ToFs between the damagescattered wave and the incident diagnostic wave in a captured Lamb wave signal. The locus may be ellipse-like if an actuator-sensor path is used (described by Equation 6.5) or a hyperbola if a pair of sensors is used (Equation 6.6). The locus implies possible locations of damage centre, reflecting the perception as to the

220

Identification of Damage Using Lamb Waves

damage in the structure from the perspective of the actuator-sensor path or sensor pair that creates such a locus. Traditional ToF-based identification, introduced in Section 6.2.2, triangulates damage by seeking intersection(s) of the above loci established by a numbers of actuator-sensor paths or sensor pairs. It must particularly be emphasised that in order to develop probability-based diagnostic imaging, no identification of damage is carried out at this step by finding intersections of two or more loci. Second, the field value at a specific pixel of the image is calculated in terms of the shortest distance between this pixel and the locus established by an actuatorsensor path or a sensor pair, using an appropriate scaling algorithm. In principle, the pixels right on the locus have the highest degree of probability (100%) as to the presence of damage, and for other pixels, the greater the distance to the locus, the lower the probability that damage exists there. Third, theoretically N probability images can be obtained if N actuator-sensor paths or sensor pairs are involved. In each image, the field value at each pixel is linked with the probability of the presence of damage at this pixel, from the perspective of the actuator-sensor path or sensor pair that creates such an image. Finally, these images are aggregated to produce a superimposed image, wherein damage, if any, can be highlighted at pixels whose probabilities are greater than a preset threshold. To summarise the above, creating a probability image in terms of ToFs extracted from Lamb wave signals includes four key steps: (i) to develop a perception as to the existence of damage such as an ellipse-like locus using an actuator-sensor path (Equation 6.5) or a hyperbola using a pair of sensors (Equation 6.6); (ii) to establish the probability (i.e., a field value between 0% and 100%) of the presence of damage at every single pixel with regard to the developed perception (i.e., the locus); (iii) to repeat the above two steps for all the available actuator-sensor paths or sensor pairs of the sensor network, and establish the probability of the presence of damage at every pixel for individual actuator-sensor paths or sensor pairs (each path or pair creating an image); and (iv) to aggregate all images through appropriate image fusion algorithms, leading to a resulting image of scaled probability as to the presence of damage throughout the area under inspection. Figure 6.14 presents such a probability image, established by a signal actuatorsensor path of a sensor network, where the lighter the greyscale image, the greater the possibility of damage existing at the pixel. 6.2.6.2 Signal Magnitude As detailed in Section 6.2.2, if damage exists at a location near an actuator-sensor pair (a sensing path), the wave signal captured via this sensing path normally presents an additional wave packet, scattered from the damage, following the incident diagnostic wave. If the damage-scattered wave can be extracted from a Lamb wave signal by benchmarking the baseline signal, the field value can be defined in terms of the magnitude of the damage-scattered wave signal.

221

Probability of damage presence

Plate y-dimension [mm]

Algorithms for Damage Identification

Plate x-dimension [mm]

Fig. 6.14. A probability image of the presence of damage established by an actuator-sensor path in terms of ToF extracted from Lamb wave signals (ellipse representing perceptions as to the presence of damage from the perspective of the actuator-sensor path; greyscale at each pixel is associated with the probability of the presence of damage at this pixel; diagram shows only the inspection area enclosed by sensors) [47]

Suppose that the signals captured via an actuator-sensor path before and after the presence of damage in a structure are f 0 (t ) and f (t ) , respectively. In principle, the difference between them, i.e., r (t ) = f (t ) − f 0 (t ) , is the damage scatteredwave. In practice, the benchmark signal, f 0 (t ) , may be obtained via computer simulation or experiment from a healthy structure with the same geometry and actuator-sensor configuration as those of the structure under inspection. Supposing that (i) an active sensor network consists of N piezoelectric elements, (ii) the group velocity of the wave mode selected for identification is c g ( c g is the same for both the incident and the damage-scattered waves in the following discussion; the wave mode can be the S0 [42] or A0 [41] mode), and (iii) there is damage at ( x, y ) within the inspection area, then the time, t , for the incident wave to travel from the i th actuator (located at ( xi , y i ) ) to the damage (located at ( x, y ) ), and then to the j th sensor (located at ( x j , y j ) ), based on Equation 6.2, is t=

(x − xi )2 + ( y − yi )2 + (x − x j )2 + (y − y j )2 cg

( i, j = 1, 2, A, N , but i ≠ j ).

(6.15)

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Identification of Damage Using Lamb Waves

In the imaging approach using signal magnitude, the field value at pixel ( x, y ) is calibrated by r (t ) . Generally speaking, this field value is a function subject to t , x and y , as seen in Equation 6.15. Mathematically, pixels defined by Equation 6.15 fall on an ellipse with the actuator and sensor being its two foci, as discussed in Section 6.2.2.2. All the pixels which produce the same arrival time (Equation 6.15) locate on one locus. There exist an infinite number of such loci, calibrated by r (t ) , and those with the highest field value (i.e., the maximum magnitude corresponding to the peak of the damage-scattered wave) highlight possible damage locations. Actually, this locus is the same as that defined by Equation 6.2 using the difference in the ToFs between the incident and damage-scatted waves. For the active sensor network of N piezoelectric elements, there are in total N p = N ( N − 1) possible actuator-sensor paths. The field value, I ( x, y ) , at each pixel ( x, y ) of the image can be defined, after fusion of all the images established by individual actuator-sensor paths, as [5, 21, 41, 42, 45, 46] I ( x, y ) =

1 NP

NP

∑ r (t , x , y ) k

k =1

( k = 1, 2, A , N P ; i, j = 1, 2, A , N , but i ≠ j ).

(6.16)

rk (t , x, y ) represents the damage-scattered wave signal captured by the k th actuator-

sensor path (from the i th actuator to the j th sensor). The symbol in Equation 6.16 indicates the aggregation of images created by all the available actuator-sensor paths, which is a kind of image fusion algorithm for obtaining a resulting image, i.e., the common perceptions of all the sensing paths. By changing ( x, y ) in Equation 6.16, the field values at all pixels enclosed within the inspection area can be established. When damage exists at a specific pixel, the field value therein becomes pronounced. After image fusion, the pixels with maximum field values highlight the location of damage in the image. Actually, from the perspective of ToF-based damage triangulation (Section 6.2.2), such a highlighted region, in principle, contains the most intersections of ellipse-like loci established by individual actuator-sensor paths. Figure 6.15 presents the identification results for a through-thickness hole (6 mm in diameter) in an aluminium plate (610 mm × 610 mm × 4.76 mm) using probability-based diagnostic imaging in terms of signal magnitude. As with the other algorithms already introduced, the more sensing paths or sensor pairs involved, the higher the identification precision expected.

223

Plate y-dimension [mm]

Plate y-dimension [mm]

Algorithms for Damage Identification

Plate x-dimension [mm]

Plate x-dimension [mm]

b

Plate y-dimension [mm]

a

Plate x-dimension [mm]

c Fig. 6.15. Identification results for a through-thickness hole (diameter: 6 mm) in an aluminium plate (610 mm × 610 mm × 4.76 mm) based on probability-based diagnostic imaging in terms of signal magnitude, using different numbers of transducers for image construction: a. 3; b. 4; and c. 5 (+: transducer location; ×: actual hole location; white circle: identified damage) [42]

During practical implementation the incident diagnostic wave is often designed as tonebursts with multiple cycles confined by a window function (e.g., a Hanning window function), so as to reduce dispersion of the wave (Section 3.3.2). As a result there may be multiple peaks in the damage-scattered wave packet, leading to multiple ellipse-like loci (all sharing the same foci, i.e., the actuator and sensor) which spatially span the bandwidth of the wave packet. In terms of Equation 6.16, all pixels included in these loci are assumed to bear damage since their field values are non-zero, resulting in ambiguous identification results. In addition, the principle of the approach in fact assumes that wave reflections from boundaries do

224

Identification of Damage Using Lamb Waves

not interfere with the damage-scattered waves. When either the damage or the sensors are close to the structural boundaries, the captured wave signals may contain, before or after the damage-scattered wave packet, reflections from boundaries or other wave modes converted from the incident wave upon interaction with the damage. All these features can reduce the accuracy and resolution of the image. Taking these complications into account, to improve the accuracy of the imaging approach, the damage-scattered wave signal, r (t ) , can be pre-processed using signal processing techniques introduced previously, such as discrete-wavelettransform-based de-noising (Section 5.3.2) and beam spreading compensation (Section 2.5). In particular, the Hilbert transform (Section 5.2.1.1) and short-time Fourier transform (STFT) (Section 5.2.3.1) are two effective tools to produce an envelope of signal magnitude associated with energy. They can be used to enhance the recognisability of damage-scattered wave signals in order to establish the field values. In this way, the ellipse that corresponds to the peak of the signal envelope can be picked up from multiple loci. With the Hilbert transform [42] and STFT [5], Equation 6.16 can be re-written, after fusion of all images established by individual actuator-sensor paths, as I ( x, y ) =

NP

1 NP

∑H

1 NP

∑S

(t , x , y ) ,

(6.17a)

(ω 0 , τ , x, y ) .

(6.17b)

k

k =1

and I ( x, y ) =

NP

k

k =1

In the above equations ( k = 1, 2, A , N P ; i, j = 1, 2, A , N , but i ≠ j ), H k (t , x, y ) is the Hilbert transform of rk (t , x, y ) and S k (ω0 ,τ , x, y ) is the STFT of rk (t , x, y ) where τ and ω 0 are the time and angular frequency of the wave excitation, respectively. 6.2.6.3 Signal Energy As addressed in Sections 2.5 and 5.2.1, the propagation of Lamb waves is continuous transportation of energy. Therefore the field value can be defined in terms of the signal energy. Suppose there is damage at ( x, y ) within the inspection area,

the energy, Ek ( x, y ) , of the damage-scattered signal, rk (t , x, y ) , captured by the k th actuator-sensor path is T2

E k ( x, y ) =

∫ [r (t, x, y)] k

T1

2

⋅ dt ,

(6.18)

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where T1 and T2 are set to ensure that the range of integration is centred on the scattered wave echoes when ( x, y ) is an actual damage location. The field value, I ( x, y ) , at each pixel ( x, y ) of the image can be defined, after fusion of all the images established by individual actuator-sensor paths, as [43, 48, 49],

I ( x, y ) =

1 NP

NP

∑ E ( x, y ) k

k =1

( k = 1, 2, A , N P ; i, j = 1, 2, A , N , but i ≠ j ).

(6.19)

Plate y-dimension [mm]

All the variables in Equation 6.19 have the same denotations as those in Equation 6.16. After fusing all the images from available actuator-sensor paths, a resulting image is produced. When damage exists at point ( x, y ) , the field value at this point becomes prominent, and all the pixels with high field values highlight the damage in the resulting image. As an example, such a probability image for an aluminium plate (610 mm × 605 mm × 0.79 mm) containing a through-thickness hole (6.35 mm in diameter), obtained using a sensor network consisting of four piezoelectric elements, is shown in Figure 6.16, where the hole is visualised.

Plate x-dimension [mm]

Fig. 6.16. Identification result for a through-thickness hole (diameter: 6.35 mm) in an aluminium plate (610 mm × 605 mm × 0.79 mm) based on probability-based diagnostic imaging in terms of signal energy (×: transducer location; white square: actual hole location) [48]

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Identification of Damage Using Lamb Waves

6.2.6.4 Signal Correlation In recognition of the observation that the extent of signal change for a sensing path before and after presence of damage clearly increases if the sensing path is close to the damage, and vice versa. After benchmarking, the correlation coefficients for paths, which are closer to the damage and are therefore more modulated by damage, are lower than those for paths, which are further from the damage. Therefore, the probability of the presence of damage at a specific point of the structure can be calculated in terms of the correlation coefficient between captured and benchmark signals. The field value, I ( x, y ) , at each pixel ( x, y ) of the image can be defined, after fusion of all the images established by individual actuator-sensor paths [18, 32], as NP

I ( x, y ) = ∑ (1 − ρ k )( k =1

−1 β ) ⋅ R ( x, y ) + β −1 β −1

( k = 1, 2, A, N P ; i, j = 1, 2, A, N , but i ≠ j ),

(6.20)

where ⎧ ( x − x ) 2 + ( y − y )2 + ( x − x )2 + ( y − y )2 i i j j ⎪⎪ R( x, y) = ⎨ 2 2 ( xi − x j ) + ( yi − y j ) ⎪ ⎪⎩ β,

when R( x, y) < β when R( x, y) ≥ β .

All the variables in Equation 6.20 have the same denotations as those in Equation 6.16. In addition, ρ k ( k = 1, 2, A , N P ) is the correlation coefficient (see Equation 5.4 for definition) between signals received by the k th actuator-sensor path (i.e., from the i th actuator located at ( xi , y i ) to the j th sensor located at ( x j , y j ) ) before and after presence of damage. β is a scaling parameter controlling the area influenced by actuator-sensor paths, and is often set to 1.05 [32]. Equation 6.20 implies that the field values at all pixels along an actuatoractuator path have the same magnitude, being the highest of the field values defined by this path. The lower the value of coefficient ρk for a particular actuator-sensor path, the higher the probability of the presence of damage at the pixels near the path. After the images contributed by all available actuator-sensor paths are aggregated, a resulting image is produced. In the image, a ‘hotspot’ with field values higher than a preset threshold becomes intuitive, and represents the damage in the structure. This hotspot is the common perceptions of sensing paths, which have low correlation coefficients, as to the damage. Using such an algorithm, the probability image as to the presence of corrosion in an aircraft wing skin (200 mm × 200 mm) is exhibited in Figure 6.17, where corrosion is highlighted when a field value of 0.25 is set as the threshold for drawing the conclusion that corrosion is present.

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Identified

Plate y-dimension

corrosion

Plate x-dimension

Fig. 6.17. Identification results for corrosion in an aluminium aircraft skin based on probability-based diagnostic imaging in terms of correlation coefficients of captured Lamb wave signals [18]

The complexity of structural geometry or boundary conditions does not affect the capability of the approach for damage detection, as these influences are implicitly included in both the present and the reference signals. 6.2.6.5 Additional Notes In the diagnostic imaging approach, the field value, defining the probability of the presence of damage at a point of a structure under inspection, may not lie within the range of [0,1] after the image fusion process. Accordingly, to properly identify the presence of damage in terms of probability, the field value needs to be normalised to insure that I ( x, y ) falls in the range of [0,1] . In addition, in such an approach, damage is pinpointed in terms of the colour (i.e., the field value) of the image. So a commendable diagnostic imaging approach would therefore present a low field value maximum when the structure is defect-free but show a marked increase in the field value in the presence of a defect. It is debatable whether information based solely on the ToFs extracted from captured Lamb wave signals can be used to effectively depict the shape or size of damage. It may be unachievable if using the algorithms introduced previously such as ToF-based damage triangulation (Section 6.2.2). However, with a probabilitybased diagnostic image approach, an estimate of the shape or size of a damaged zone can always be delivered by properly selecting a threshold of field value. When the probability at a specific pixel is greater than the threshold, it is estimated that this pixel is contained in the damaged zone, and by this means the size and shape of the damaged zone can be approximately defined. For detecting dimension-specific damage such as a long crack (i.e., a couple of times larger than the wave length), the image is most likely able to highlight the locations of both crack tips only, since the crack tip is the major point-like source of wave scattering. Under such a

228

Identification of Damage Using Lamb Waves

circumstance, the crack length can be defined by calculating the distance between two major scattering sources highlighted in the resulting image. For detecting damage with a certain area such as delamination, added mass or debonding, the image possibly highlights the edges (or boundary) of the damage [5], and the damaged area can be approximated by drawing the smallest circle that connects the scattering sources highlighted in the resulting image by assuming that the damage is circular. Accurate ascertainment of ToFs, scattered-signal magnitude and energy from captured Lamb wave signals can therefore be seen as a prerequisite to deliver a correct and precise probability image. To enhance the signal-to-noise ratio (SNR) of a signal for extracting these features precisely, captured raw Lamb waves can be pre-processed using noise filtering based on the Hilbert transform (Section 5.2.1.1) [42], STFT (Section 5.2.3.1) [5], wavelet transform (Section 5.3), or applying compensation for wave attenuation with distance [41]. A probability-based diagnostic imaging approach works regardless of the number of damage instances in the area covered by the sensor network. It therefore has the potential to be used for identifying multiple instances of damage, with enhanced tolerance to measurement noise and uncertainties. Being different from Lamb wave tomography which usually requires a relatively large number of transducers and dense cells for reconstruction of a fine tomogram, probability-based imaging approaches use a sensor network with a few sensors. 6.2.7 Phased-array Beamforming

A phased-array is a device consisting of a multitude of transducer elements, usually piezoelectric elements (called array elements), which can be individually and sequentially activated with programmable time delays. As a result of the time delays, phase differences in the wavefronts activated by individual array elements are created, and the resulting wave generated by the phased-array is therefore the synchronisation of waves (i.e., beamforming) generated by individual array elements. By appropriate adjustment of the time delays and therefore the phase differences in the wavefronts generated by individual elements, the resulting wave can be dominant in a particular propagation direction (i.e., having strong directionality of propagation). Phased-array beamforming is a process of spatio-temporal filtering, through which a high SNR can be achieved by virtue of the synchronisation of wavefronts coming from individual array elements, i.e., an aggregation of a series of waves with weighted phase shifts from different directions [50]. This technique was developed in the 1940s for radar positioning and tracking, and soon found applications in sonar techniques, medical imagery, seismology, oceanography and nondestructive evaluation for engineering structures. Phased-array beamforming has recently been introduced in Lamb-wave-based damage identification [50-55]. The approach using piezoelectric wafer active sensors (PWASs) (Section 4.5.2) is a representative of the phased-array beamforming technique [56], in which a group of piezoelectric elements are aligned in a straight line (as the simplest configuration). When individual elements are sequentially fired in accordance with a specified sequence, the resulting wavefront

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generated by the array can be focused (enhanced or steered) in a specific direction. In this way, a broad region of a structure can be scanned by sweeping the resulting waves in different directions. If piezoelectric elements are used in the array, they can be immediately switched to serve as sensors after activating wave signals, to capture the echoed waves from damage, if any, and from a boundary. Such an actuator-sensor configuration is similar to the pulse-echo configuration, although the major difference is that the pulse-echo configuration is based on one pair of actuator and sensor which are separate, whereas phased-array beamforming uses a group of closely placed transducer elements to activate and then receive SNRenhanced wave signals. Such an approach forms the core concept of ‘embedded ultrasonics structural radar’ (EUSR), which has been well elaborated elsewhere [27, 51, 57]. Damage identification based on phased-array beamforming includes three major steps: (i) transmitter beamforming (also called transmitter focusing): individual array elements are fired sequentially, and superposition of the waves generated by all elements forms a resulting wavefront with enhanced SNR in a specific direction, to serve as the diagnostic wave signal (i.e., beamforming); (ii) receiver beamforming: individual array elements receive wave signals echoed back from damage, and superposition of the waves captured by all elements forms a resulting signal with further enhanced SNR; and (iii) wave steering: the whole structure under inspection is scanned by repeating the steps (i) and (ii) but in other specific directions. When damage exists, the ToF (time for the diagnostic signal to travel from an element of the array to the damage and then travel back to the element) can be extracted from the echoed signals, allowing to precisely locate the damage. The shape, size and orientation of the damage can be further defined from the echoed signals by sweeping the direction of the wave beam. 6.2.7.1 Transmitter Beamforming Consider a uniform linear array consisting of M piezoelectric elements, in which the distance between any two neighbouring elements (sensor spacing), d , is set as λ / 2 ( λ is the wavelength of the Lamb wave mode to be activated), which is much smaller than the distance from the array to a generic spatial point, P , of the structure under inspection, denoted by r , Figure 6.18. Each element of the array acts as a pointwise omnidirectional wave actuator in this step. Since d << r , the waves coming from the array to point P can be assimilated with a parallel fascicle with azimuth φ . If all the elements are fired m th element the d ( m = 0, 1, A , M − 1 ) arrives at P faster by Δ m (φ ) = m ⋅ (cos φ ) than the c wave signal activated by the first element ( m = 0 ), where c is the group velocity of the Lamb wave mode activated. If the elements are not fired simultaneously but with a certain time delay, δ m , for the mth element, then the resulting signal arriv-

simultaneously,

the

wave

ing at P , f P (t ) , is [27, 51]

signal

activated

by

230

Identification of Damage Using Lamb Waves

Point source P

Activated wave

r0 = r

r1 = r − d cos φ

rm = r − m(d cos φ )

φ Element 0

d

Element 1

Element m

Element (M-1)

Fig. 6.18. Principle of transmitter beamforming [51]

f P (t ) =

M −1

∑s r

1

T

m=0

(t −

r + Δ m (φ ) − δ m ) c

( m = 0, 1, A, M − 1 ),

(6.21)

where 1 r represents the decrease in the wave magnitude due to wave attenuation where r is the distance between the first actuator ( m = 0 ) and point P , and r c represents the time for the wave to travel the distance r . sT (t ) is the signal generated by each array element, having the same waveform but different phase. If d we set δ m = m ⋅ (cos φ0 ) for the mth element, Equation 6.21 can be simplified to c

f p (t ) = M

r sT (t − ) . c r

1

(6.22)

The resulting signal, f p (t ) , can thus be seen to have been enhanced M times in magnitude in a specific direction, φ0 (also along −φ 0 ), in comparison with the

Algorithms for Damage Identification

231

signal activated by a single actuator ( sT (t ) ). The above procedure is called transmitter beamforming. 6.2.7.2 Receiver Beamforming Receiver beamforming is a procedure reciprocal to transmitter beamforming. In this process, the spatial point P (defined by azimuth φ0 and distance r ) is an omnidirectional wave source, and if any damage exists at point P , it scatters incident waves. The arrival of the scattered wave signal from P is not synchronised at individual sensors. It arrives at the mth element faster by d mΔ 0 (φ0 ) = m ⋅ (cos φ0 ) than it arrives at the first element ( m = 0 ). Therefore, the c resulting signal, f R (t ) , backscattered from point P and captured by the array, is the superposition of waves received by individual array elements, illustrated in Figure 6.19, as f R (t ) =

A⋅ M r

M −1

∑s

T

m=0

(t −

2r + Δ m (φ ) − δ m ) c

( m = 0, 1, A , M − 1 ),

(6.23)

Fig. 6.19. Principle of receiver beamforming [51]

where A is a coefficient related to wave attenuation, and 2r c represents the time for the wave to travel from the actuator to point P and then back to the send sor. If we set δ m = m ⋅ (cos φ0 ) for the mth element, Equation 6.23 can be simc plified, as highlighted in Figure 6.19, to

232

Identification of Damage Using Lamb Waves

f R (t ) =

A⋅ M 2 r

M −1

∑s

T

m= 0

(t −

2r ). c

(6.24)

The above procedure is called receiver beamforming. In this way, all the waves captured by individual array elements will be synchronised and thus the resulting wave signal, f R (t ) , scattered from point P , can be seen to have been boosted M times again, i.e., M 2 in total, through the transmitter and receiver beamforming, in comparison to the case when only one actuator-sensor pair is used. To this point, it can be seen that the first two steps of phased-array beamforming are aimed at improving the SNR of the incident and received signals, respectively. In the procedure, a phased-array transfers two-dimensional planar wave propagation into quasi-one-dimensional propagation with much enhanced SNR. These two steps are particularly helpful when damage to be detected is small in size or when the material considerably attenuates waves.

Panel y-dimension (half)

6.2.7.3 Wave Steering In principle, by progressively changing r (for focusing) and φ (for sweeping) by a small increment, it is possible to scan the whole area surrounding a phasedarray, an operation called wave steering. If any damage exists, an extra wave component, prior to those reflected from the structural boundary, can be identified in the SNR-enhanced signal, f R (t ) , and the ToF of this extra wave, τ ( τ = 2r c ), can be used to locate the damage in accordance with the ToF-based identification algorithms introduced previously. Through wave steering, a two-dimensional map (half-plane usually, i.e., φ in the range of [00 , 1800 ] ) is plotted, in which the damage can be highlighted. As an example, one such two-dimensional map is shown in Figure 6.20 for identifying a crack in a large aluminium plate (1220 mm × 1200 mm). Damage identification based on phased-array beamforming has in particular proven effectiveness for large panels when the array is distant from the structure boundaries.

Panel x-dimension

Fig. 6.20. Identification results for a broadside crack in a large aluminium plate (1220 mm × 1200 mm, half of the plate shown) based on phased-array beamforming [51, 57]

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233

The quality of phased-array beamforming can be described by the main beam, called main lobe, steered in the desired direction, which is the wave field that contains the majority of energy of the resulting wave signal, exhibiting the greatest field strength centred around the direction in which it is steered, illustrated in Figure 6.21 [56]. In contrast, the grating lobes (or side lobes) are those with minor energy of the resulting wave signal. For phased-array beamforming using the PWAS technique, optimisation of the main lobe to attain its greatest strength in the steered direction can be achieved by adjusting several parameters of the PWAS array: (a) number of sensors in the array, M ; (b) sensor spacing, d ; (c) the ratio d λ ; and (d) the weight of individual wafers. All these parameters can be used to tune the main lobe and its width in particular. For a linear PWAS array, the objectives of beamforming optimisation should include: (i) minimising the main lobe width; (ii) eliminating grating lobes; and (iii) suppressing magnitudes of side lobes. Main lobe at 90°

Main lobe at 45°

Side/grating lobes

Fig. 6.21. Beamforming of a PWAS array consisting of eight wafers in a straight line [57]

The steering angle φ also affects the beamforming of a linear phased-array. There is a range of φ , within which the beam can be steered without producing any detrimental grating lobes. Moreover, the ratio d λ significantly influences both the steerability and main lobe width. When d << λ , grating lobes are suppressed but the directivity is rather poor; when d >> λ , the directivity is superior at the intended steering angle, but the existence of additional grating lobes may obfuscate the main lobe, and eventually the beam is no long steerable. A few general guidelines for tuning the main lobe, as elaborated in detail elsewhere [56], are as follows: (i) the width of the main lobe will change with φ , and grating lobes will appear within a certain range of φ ; (ii) an increase in number of the array element, M , will improve the directivity, achieving a sharper main lobe;

234

Identification of Damage Using Lamb Waves

(iii) sensor spacing, d , is kept at a half of the wavelength, i.e., d = 0.5λ , in most phased-array designs, which has proved effective; and (iv) if the size of the array, D = ( M − 1) ⋅ d (termed the array aperture in the PWAS technique), remains constant, the main lobe width will remain unchanged as well. 6.2.8 Artificial Intelligence

During the implementation of most of the identification algorithms introduced in previous sections, extraction of signal features of interest for defining DI, such as ToF, and subsequently establishment of relationships between variations in DI and damage parameters are pivotal steps for the success of identification. However, such an endeavour often involves some subjective discretion of an operator, and the identification results may vary from one operator to another. When applied to complex structures such as those with complex boundary conditions and geometries or when applied to quantitative evaluation of damage parameters including location, shape, size and orientation, these algorithms may become blocked. This problem has promoted research and development of advanced inverse algorithms with the capacity of avoiding manual canvassing of individual wave signals. As an example of advanced inverse algorithms, artificial intelligence (AI), a burgeoning technology, has been increasingly introduced in Lamb-wave-based damage identification in recent years. The phrase AI, coined three decades ago, evades an explicit definition to date, perhaps because of the abstract word ‘intelligence’, although a well accepted definition is ‘the simulation of human intelligence so as to efficiently use the right knowledge toward solving a problem’ [58]. AI technology is interdisciplinarily based on computer science, psychology, philosophy, neuroscience, cognitive science, linguistics, ontology, control theory, probability, optimisation, logic, etc. Boosted by recent advances in neuroscience and high capability computing devices, AI has consolidated its superb capacity for solving complex inverse problems, ranging from game-playing through fingerprint identification to pattern classification and recognition (damage identification falls in the category of pattern recognition†). This technique is particularly effective for describing a system that is very difficult to define using an explicit mathematic expression. There is a variety of identification algorithms based on AI techniques in practice, typified by searching (e.g., heuristic and hill climbing searching, genetic algorithm (GA) and evolution), logic (e.g., propositional and fuzzy logic) and probabilistic (e.g., Bayesian inference (BI)) approaches, classifiers and statistical learning (e.g., Gaussian mixture model and naive Bayes classifier) and artificial

†

Pattern recognition is the identification of an individual object, such as damage, based on either a priori knowledge or statistical information extracted from a series of patterns, where ‘pattern’ refers to as an entity representing an abstract concept or a physical object. Since diverse damage cases can be regarded as patterns that present various symptoms in a structure, identification of damage falls into area of pattern recognition.

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235

neural networks (ANN). In particular, ANN, GA and BI are three proven tools for developing Lamb-wave-based damage identification algorithms. 6.2.8.1 Artificial Neural Network The human nervous system consists of a huge number of small cellular units (neurons) connected by nerve fibres, to form a neural net. A neuron receives biological stimuli (input signals), processes signals, generates new signals and passes them to neighbouring neurons. The output signals of the neural net are therefore subject to the perceptions of all neurons. To mimic this way of processing information and perceiving an event, the ANN technique has been developed as a computational model based on a loose neural construction. With strong capabilities in adaptability and parallelism, an ANN is able to mathematically establish a nonlinear and high-order connection between a series of inputs and the corresponding outputs for a given system, and, via such a connection, to further predict the output/consequence of an unknown input that has not been involved in establishing the connection. In other words, in damage identification, the signatures of structures (e.g., extracted DI from captured Lamb wave signals) under a certain number of known damage states are the inputs, and the damage parameters under these known structural states are outputs. These inputs and outputs, which are known beforehand and stored in a training database, are then connected via an ANN. When signals, captured from the structure under inspection with unclear damage state, are available, signal features are extracted and used as new input to feed into the ANN. The ANN can accordingly predict the corresponding damage parameters using the established connection. At a rudimentary level, a typical ANN is comprised of an input layer, single or multiple processing (neural) layers, and an output layer. Each neuron is weighted individually using an adjustable variable (weight), and is offset using a constant (bias). Individual layers are connected by transfer functions. For illustration, an ANN developed for Lamb-wave-based damage identification [59] is displayed in Figure 6.22. This ANN features an input, an output and two processing layers, hosting M input elements, N output elements, and J and K computing units (neurons) in two neural layers, respectively. The i th neuron in a neural layer summates all the weighted inputs and biases to generate a scalar output, which subsequently serves as the input for the next layer. The final output of the i th output element of the ANN, oi , is oi = T3 (ni3 )

( i = 1, 2, A, N ),

where K

ni3 = ∑ T2 (nq2 ⋅ wq3−i ) + bi3 q =1

( i = 1, 2, A, N ),

(6.25)

236

Identification of Damage Using Lamb Waves J

nq2 = ∑ T1 (nl1 ⋅ wl2− q ) + bq2

( q = 1, 2, A, K ),

l =1

M

nl1 = ∑ in p ⋅ w1p −l + bl1

( l = 1, 2, A , J ),

p =1

where nl1 ( l = 1, 2, A, J ) and nq2 ( q = 1, 2, A, K ) are the outputs of the first and second neural layers. in p denotes the p th input ( p = 1, 2, A, M ); wrp −q represents the weight joining the p th element/neuron in the r th layer ( r = 1, 2, 3 standing for the input, first and second neural layer, respectively) with the q th element/neuron in the succeeding layer; bqr is the bias for the q th element/neuron in the r th layer ( r = 1, 2, 3 standing for the input, first and second neural layer, respectively); Tr ( r = 1, 2, 3 ) is the transfer function connecting the r th layer ( r = 1, 2, 3 standing for the input, first and second neural layer, respectively) and the succeeding layer. 1 w1− 1

n11

in1

n12

2 w1− 1

Σ

Σ

T1 b11

T2

Σ

T1 b21 n

Σ

T1

w

T1

w J2 − k

b 1J

T3

oN

b

n 3N

Σ n

Σ

oi

T2

n1J 1 M −J

T3 3 i

bq2

bl1

o1

ni3

Σ n q2

1 l

T3 b13

T2 b22

Σ

inM

Σ n 22

Σ

in3

n13

b12 n 12

in2

3 w1− 1

Σ

2 K

T2

w K3 − N

b N3

bK2

Fig. 6.22. An ANN designed for Lamb-wave-based damage identification [59]

Equation 6.25 can also be written in a compact form as K

J

M

q =1

l =1

p =1

oi = T3 (∑ T2 ((∑ T1 ((∑ in p ⋅ w1p−l + bl1 ) ⋅ wl2−q ) + bq2 ) ⋅ wq3−i ) + bi3 ) ( i = 1, 2, A , N ).

(6.26)

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237

The procedure of iteratively adjusting the weights and biases in neural layers is called training or personified ‘learning’ of the ANN. Through training an overall balanced and optimised connection between all the outputs (i.e., known damage parameters) and their corresponding inputs (i.e., features extracted from Lamb wave signals captured under known damage parameters) can be eventually achieved for all the training cases (i.e., a number of structural states with different damage parameters known beforehand) in the database. Since an ANN must balance the inputs and outputs for all the training cases selected, the output of the trained ANN for a specific input used for the training can become slightly different or deviate from its original value used for the training. Such a deviation is often calibrated using mean square error (MSE) 1 MSE = N

2

N

∑ [o

i −origin

− oi−temp

]

( i = 1, 2, A , N ),

(6.27)

i =1

where oi −origin and oi − temp are the original outputs used for training and interim outputs after each iteration for the i th output element of the ANN, respectively. The training of an ANN is essentially a procedure with attempt to minimise such deviation for all the selected training cases, and therefore MSE can be used to monitor the training procedure. The ANN training governed by Equation 6.27 is called supervised training, contrasting with unsupervised training where weights and bias are modified subject to the inputs only (when the original outputs are not available) [60]. Under a supervised scheme, training is not terminated until the MSE is below a preset threshold. Supervised training outperforms unsupervised training in terms of accuracy and precision, although it takes much longer to achieve convergence of training. In terms of the selected transfer functions for connecting different layers, an ANN can be one of three modalities: perception (using hard-limit transfer function), linear filter (using linear transfer function), and backpropagation (using sigmoid transfer function). The three transfer functions are compared in Figure 6.23. The choice of a transfer function can be case-specific. The hard-limit transfer function sets the output of each neuron as either 0 or 1, which works well for an ANN with a single neural layer; the linear transfer function forces the output to be equal to the input, which can be far greater than 1 depending on the input; the sigmoid transfer function, including tan-sigmoid and log-sigmoid functions, squashes the output into the range of [−1, 1] and [0, 1] , respectively. In particular, backpropagation has proven effectiveness for most engineering applications. Feedforward backpropagation ANN (BP-ANN) has the closest similarity to human behaviour [61], and a well-trained BP-ANN is able to infer general rules or predict consequences from specific damage cases that have never been used for training, making it possible to train an ANN using just a limited number of representative damage cases which may be obtained via computer simulation or experiment. In a simplified expression, a trained ANN is in fact a high-order and nonlinear correlation between given inputs and the outputs. With such a correlation, the

238

Identification of Damage Using Lamb Waves

process of inferring or predicting, in analogy, is a sort of interpolation or extrapolation with the new inputs. Therefore, as may be expected, the more inputs for training the more accurate the outputs.

Hard-limit 1

Output

Log-sigmoid 0 Tan-sigmoid

-1

Linear

Input

Fig. 6.23. Transfer functions used in ANNs [61]

For damage identification using non-wave-based information, various signatures of the structure under inspection have been selected for ANN training, including mode shapes [62, 63], natural frequencies [63-68], combined modal data [69], displacement [70-72], acceleration spectra [73] or combined displacement, velocity and acceleration [74], applied force [75], static strain [76, 77] or strain history [78], auto-correlation function [79], and impedance [80]. However, most of the above structural signatures have relatively low sensitivity to undersized damage and damage evolution. More recently, signal features extracted from Lamb wave signals have been employed as training data, and were soon found particularly effective for evaluating debonding in adhesively-bonded joints [81, 82], locating cracks in aluminium alloys [83] and predicting delamination in composite laminates in conjunction with the concept of digital damage fingerprints (DDF) (Section 5.5) in particular [84]. 6.2.8.2 Genetic Algorithm Resting on Darwinism (‘survival of the fittest’) and natural genetic evolution, GAs are stochastic and highly adaptable global optimum searching algorithms used in computing science. They take advantage of random selection in an optimisation process, to find exact or approximate solutions to an optimisation or searching problem [85]. Because of their flexibility, globality, parallelism, simplicity and good problem-solving capability, GAs have found increasing application in damage identification [85-96]. Assisted by a pre-established objective function, most

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GA-based damage identification attempts to define the structural damage by finding the damage-induced local minima or maxima in structural responses such as a Lamb wave signal. A deeper and more profound elaboration of the mathematical basis of GAs can be found elsewhere [97]. A typical GA includes five major steps in sequence: encoding, evaluation, selection, crossover and mutation [97]. In this procedure, a selected GA is initialised with a randomly or heuristically generated number of populations which serve as a set of candidate solutions to the concern problem. Each individual in the population is known as a chromosome. The algorithm evaluates chromosomes based on a designed objective function (or called fitness function) and calculates the fitness of each individual. Individuals with higher fitness have a greater chance of being selected to reproduce the offspring. The next generation of the chromosomes is then created using genetic operators, crossover and mutation. When convergence criteria are met, the above operation is terminated and an optimal solution becomes available. In accordance with the above key steps, GA has been employed as a tool to develop wave-based damage identification strategies [92, 95, 98]. As an example, a hybrid GA [92] has been developed to examine the Lamb wave signals reflected by cracks in composite beams. This method formulates the damage detection as an optimisation problem of linking the scattered Lamb wave signals with damage parameters (crack location and length). The objective function in this case is defined as [92] Np

E ( ac , d c , l c ) = ∑ f i ( ac , d c , l c ) − f i m

or

i =1

Np

E ( a c , d c , l c ) = [∑ f i ( a c , d c , l c ) − f i m

2

i =1

( i = 1, 2, A, N P ),

(6.28)

where ac , d c and lc are three parameters to define a crack in a composite beam ( ac : location along beam axis; d c : location along beam thickness; lc : length of crack). f i and f i m are the calculated (using a strip element method) and measured Lamb wave signals at the i th point, respectively. N p is the number of points on the surface of the beam used for calculation. Equation 6.28 calibrates the difference between the theoretically calculated and experimentally measured Lamb wave signals, and minimising that difference leads to determination of the three crack parameters. The maximum error in identifying a crack in a composite beam using this method is 4.3% with only 60 generations. Conclusively, damage identification based on GA is flowcharted in a nutshell in Figure 6.24. In practice, GA has proven effectiveness for identifying damage in relatively simple cases such as predicting cracks in one-dimensional structural beams, but it becomes less effective in handling complex cases such as identifying damage in two-dimensional panels due to the difficulty in proposing an objective function to describe the system appropriately.

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Fig. 6.24. Flowchart of damage identification based on GA [89]

6.2.8.3 Bayesian Inference BI is a statistical learning approach which uses a priori knowledge to estimate and update the posterior probability of a hypothesis or to identify an event with given supporting evidence [99]. As evidence accumulates or additional information becomes available, BI consistently modifies the perceptions of a multitude of sensors in a sensor network, and as a result the degree of belief in the hypothesis increases or decreases. The hypothesis is accepted as being true with a very high degree of belief, or rejected as false when the degree of belief becomes very low, in a manner similar to the human procedure of making judgments. The BI theorem is described by [99] P ( H i | Ev ) =

P(Ev | H i )P(H i ) = P ( Ev )

P(Ev | H i )P(H i ) [P(Ev | H i )P(H i )]

∑ i

( i = 1, 2, A, N ),

(6.29)

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where P(H i | Ev ) is the posterior probability that hypothesis H i ( N in total) is true for the given evidence Ev . P(Ev | H i ) is the probability of evidence Ev given that H i is true, defined as the likelihood function. P(H i ) is the prior probability given that hypothesis H i is true and satisfies

∑ P(H ) = 1. ∑ P(E i

i

v

| H i )P(H i ) is

i

the sum of the probability of evidence Ev when all mutually exclusive hypotheses H i ( i = 1, 2, A , N ) are true. The factor P(Ev | H i ) / P(Ev ) represents the impact of a piece of new evidence on the degree of belief in the hypothesis; if the new evidence supports the hypothesis, this factor becomes greater than one; in other words, the hypothesis becomes more possible or P(H i | Ev ) > P(H i ) . The BI-based identification algorithm has been successfully applied to quantitative detection of a through-thickness hole in composite panels [100].

6.3 Architecture and Scheme of Data Fusion The implementation of a damage identification algorithm, whichever algorithm is used, is basically a process of aggregating features extracted from multiple signals so as to infer damage parameters of interest, i.e., a process of data fusion as addressed at the beginning of Section 6.2. 6.3.1 Fusion Architecture

At a basic level, to fuse multiple signals for damage identification one can take advantage of the whole or part of a sensor network and adopt one of three architectures as depicted in Figure 6.25, which are distinguished by whether the steps of signal feature extraction and data fusion (for defining damage parameters) in the overall flowchart are executed at the level of individual sensors or the level of the entire sensor network: (i) independent architecture: (Figure 6.25(a)) signal features (e.g., ToF or signal magnitude) are selected and extracted from signals provided by individual sensors (or actuator-sensor paths) independently, and identification is carried out at the level of individual sensors (or actuator-sensor paths). The individual fusion results are then aggregated at the entire sensor network, exemplified by the approaches based on diagnostic imaging (Section 6.2.6); (ii) centralised architecture: (Figure 6.25(b)) generic signal features with commonality are selected and extracted from pre-processed signals provided by individual sensors (or actuator-sensor paths) in parallel for subsequent data fusion at the level of the entire sensor network, exemplified by the approaches based on ANN (Section 6.2.8.1); and (iii) decentralised architecture: (Figure 6.25(c)) signal features are selected and extracted from signals provided by individual sensors (or actuator-sensor paths) independently, but the features can be in common or irrelevant from sensor to sensor. All the extracted features are then fused at the level of the entire sensor network.

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a

b

c Fig. 6.25. Data fusion for damage identification in: a. independent; b. centralised; and c. decentralised architectures

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Combinations of the above are also possible in practice to take full advantage of each architecture, represented by the Waterfall and Omnibus fusion [101]. In particular, the scenario of centralised architecture in nature tallies with the observation from the neurological study [102] that the neurons of the human neural system perceive independently and in parallel, and different perceptions are then transmitted to the brain where features are extracted and fused for identification. As illustrated in Figure 6.25(b), the centralised architecture includes three critical steps in succession: (i) distributed sensing (i.e., acquisition of signals) of individual sensors of a sensor network; (ii) extraction of certain generic features from the captured signals; and (iii) amalgamation of the extracted features to infer damage parameters. Through the first two steps, the distributed sensors form prior perceptions that represent their own interpretations of the event they sense. In the last step, an appropriate fusion process aggregates all prior perceptions to shape a consensus of the view of the event – the damage in the structure. Signal fusion can therefore be seen as a route from the prior perceptions of individual sensors or actuator-sensor paths to an ultimate consensus of a sensor network. 6.3.2 Fusion Scheme

In the above exercise of ‘aggregating perceptions’, it is possible to adopt some or all signals available, leading to different fusion schemes. Mathematically, there are three basic fusion schemes in terms of Boolean algebra, namely disjunctive, conjunctive and compromised fusion [103], or their combination, as illustrated graphically in Figure 6.26 using a Venn diagram (for simplification, only two sensors are involved). Without losing generality, assuming that there are two perceptions with degrees of x and y , respectively, established by two sensors, the posterior consensus, ℑ( x, y ) , pertaining to x and y can be (i)

ℑ is disjunctive if ℑ( x, y ) ≥ max( x, y ) ;

(ii) ℑ is conjunctive if ℑ( x, y ) ≤ min( x, y ) ; and (iii) ℑ is compromised if min( x, y ) ≤ ℑ( x, y ) ≤ max( x, y ) . We now further expand the above discussion to a sensor network consisting of N sensors, denoted by S i ( i = 1, 2, A, N ). Assuming that sensor S i holds a perception P ( S i ) as to an event such as probability of presence of damage, the posterior consensus, i.e., the probability of damage presence, is, taking into account the entire sensor network,

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Perception

Perception

from sensor A

from sensor B

a

Perception

Perception

from sensor A

from sensor B

b

Perception

Perception

from sensor A

from sensor B

c Fig. 6.26. Venn diagram for illustrating data fusion based on two sensors using a. disjunctive; b. conjunctive; and c. compromised fusion schemes

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if disjunctive scheme is used ℑ( S1 , S 2 , " , S N ) = P ( S1 ) ∪ P ( S 2 ) ∪ " ∪ P( S N −1 ) ∪ P( S N ) N

N −1 N

i =1

i =1 i < j

= ¦ P( S i ) − ¦¦ P ( Si ) ⋅P ( S j ) N − 2 N −1 N

− ¦¦¦ P ( Si ) ⋅ P ( S j ) ⋅ P( S k ) − " − P ( S1 ) ⋅ P ( S 2 ) ⋅ " ⋅ P( S N ); i =1 i< j j < k

(6.30a)

if conjunctive scheme is used ℑ( S1 , S 2 , A , S N ) = P( S1 ) ⋅ P( S 2 ) ⋅ A ⋅ P( S N );

(6.30b)

if compromised scheme is used ℑ( S1 , S 2 ,A , S N ) =

1 N

N

∑ P(S ). i

(6.30c)

i

Referring to Figure 6.26 and the above three equations, disjunctive fusion covers perceptions from all sensors, increasing certainty and yielding the largest measure; conjunctive fusion aggregates the perceptions of the two sensors to select the common part between them, reducing less certain components and yielding the smallest measure; as reflected by its name, compromised fusion yields an intermediate measure, balancing the smallest and largest measures and providing a measure between the results from the disjunctive and conjunctive fusion. The quality of a signal fusion process is substantially subject to the selection of fusion scheme, which governs the accuracy and precision of identification. For illustrative comparison, three fusion schemes were used to process the extracted ToFs from Lamb wave signals captured by a sensor network consisting of twelve piezoelectric sensors surface-mounted on a quasi-isotropic composite laminate containing delamination [104]. In line with the four steps of the probability-based diagnostic imaging approach in terms of ToF (Section 6.2.6.1), each actuatorsensor path established its prior perception first, a locus of possible damage locations (step (i)); an image for the probability of the presence of damage at each spatial point of the laminate was calibrated (step (ii)); the above two steps were extended to all available actuator-sensor paths of the sensor network (step (iii)). Two images contributed by two paths randomly selected from the sensor network are shown in Figure 6.27. Following application of the three fusion schemes (step (iv)), the resulting images for the probability of the presence of delamination across the laminate are compared in Figure 6.28. In all images shown in Figures 6.27 and 6.28, the lighter the greyscale is, the greater the possibility of damage existing at the pixel.

Plate y-dimension [mm]

Identification of Damage Using Lamb Waves

Plate y-dimension [mm]

246

Plate x-dimension [mm]

a

Plate x-dimension [mm]

b

Fig. 6.27. Greyscale image established by two actuator-sensor paths randomly selected from a sensor network where the greyscale at each pixel is associated with the probability of presence of damage at this pixel (diagram shows only the inspection area enclosed by sensors)

From this comparison, it can be concluded that the disjunctive fusion scheme may ‘pessimistically’ exaggerate the possibility of damage, whereas the conjunctive fusion scheme may ‘optimistically shrink’ the likelihood of damage. Both schemes exhibit high susceptivity to the perception from a particular sensor (or a particular actuator-sensor path), and they may render inaccurate estimation. On the other hand, the compromised fusion scheme delivers identification with relatively high robustness and reliability, by taking into account the perceptions of all sensors with a balanced contribution.

6.4 Summary In general, damage identification is an inverse problem in which an attempt is made to infer damage parameters of concern based on fusion of features extracted from a series of captured signals. A variety of damage identification algorithms has been developed, as detailed in this chapter. Identifying damage in a simple structure (e.g., a structural beam or a two-dimensional panel) using Lamb wave signals captured from an active-sensor network can be in principle fulfilled using (i) ToF-based triangulation for locating the planar position of the damage; and (ii) DI-based interpolation/extrapolation for evaluating the severity of the damage. Time reversal and phased-array beamforming are two techniques for locating damage in a structure. They also enhance the SNR of captured Lamb wave signals prior to the identification, contributing to great improvement in signal quality.

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Plate y-dimension [mm]

Probability of damage presence

Plate x-dimension [mm]

a

Plate y-dimension [mm]

Probability of damage presence

Plate x-dimension [mm]

b

Plate y-dimension [mm]

Probability of damage presence

Plate x-dimension [mm]

c Fig. 6.28. Identification results for delamination (diameter: 40 mm) in a composite laminate (500 mm × 500 mm × 3.6 mm) based on a. disjunctive; b. conjunctive; and c. compromised fusion schemes (white or dark circle: actual delamination; diagram shows only the inspection area enclosed by sensors)

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Damage identification using algorithms based on imaging approaches has increasingly been adopted for practical application due to obvious advantages including intuitive depiction of damage and potential to depict multiple damage. Representative imaging techniques include wave migration, Lamb wave tomography, and probability-based diagnostic imaging approaches. In particular, various signal features, such as ToFs, signal magnitude, signal energy and correlation coefficient, from individual actuator-sensor paths of an active sensor network can be used to construct an image presenting the probability of the presence of damage. With the aim of reducing the dependence of identification on subjective interpretation of signals and avoiding the need to establish intricate constitutive relationships between signal features and damage parameters, AI technique, an emerging technique in recent years, has been introduced to achieve quantitative damage identification, typified by the ANN, GA and BI. All these processes have proved effective for damage identification in specific cases. However, it should be emphasised that most AI-based damage identification may come at high cost for preparing sufficient training patterns, since most AI algorithms mimic the decision-making processes of human beings which are based on the accumulation of a priori knowledge from sufficient learning. This concern can become very significant when AI-based approaches are applied to large structures with complex boundary conditions. No matter which identification algorithm is adopted, to properly fuse extracted signal features from an active sensor network so as to infer damage parameters is the kernel. Generally speaking, there are three major fusion schemes: disjunctive, conjunctive and compromised fusion. As observed, identification results can be critically subject to the selection of fusion scheme. To assist comprehension, selected case studies using various damage identification algorithms introduced in this chapter are presented in the following chapter.

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74. Zu, B., Wu, Z.: Neural-networks-based structural health monitoring strategy with dynamic responses. In: Chang, F.-K. (ed.) Proceedings of the 3rd International Workshop on Structural Health Monitoring, Stanford, CA, USA, September 12-14, 2001, pp. 1418–1427. CRC Press, Boca Raton (2001) 75. Rhim, J., Lee, S.W.: A neural network approach for damage detection and identification of structures. Computational Mechanics 16, 437–443 (1995) 76. Hwu, C.B., Liang, Y.C.: Crack identification by artificial neural network. Key Engineering Materials 145-149, 405–410 (1998) 77. Liang, Y.C., Hwu, C.: On-line identification of holes/cracks in composite structures. Smart Materials and Structures 10, 599–609 (2001) 78. Staszewski, W.J., Worden, K., Wardle, R., Tomlinson, G.R.: Fail-safe sensor distributions for impact detection in composite materials. Smart Materials and Structures 9, 298–303 (2000) 79. Zubaydi, A., Haddara, M.R., Swamidas, A.S.J.: Damage identification in a ship structure using neural networks. Ocean Engineering 29, 1187–1200 (2002) 80. Lopes Jr., V., Park, G., Cudney, H.H., Inman, D.J.: Smart structures health monitoring using artificial neural network. In: Chang, F.-K. (ed.) Proceedings of the 2nd International Workshop on Structural Health Monitoring, Stanford, CA, USA, September 8-10, 1999, pp. 976–985. Technomic Publishing Co (1999) 81. Bork, U.: Non-destructive Evaluation of Adhered Metal Joints Using Ultrasonic Lamb Waves and Artificial Neural Network, Ph.D. Dissertation, Keele University, Staffordshire, UK (1995) 82. Bork, U., Challis, R.E.: Artificial neural networks applied to Lamb wave testing of Tform adhered joints. In: Saffari, N. (ed.) Proceedings of the Conference on the Inspection of Structural Composites, London, UK, June 9-10 (1994) 83. Lu, Y., Ye, L., Su, Z., Zhou, L.-M., Cheng, L.: Artificial neural network (ANN)based crack identification in aluminum plates with Lamb wave signals. Journal of Intelligent Material Systems and Structures 20, 39–49 (2009) 84. Su, Z., Ye, L.: Digital damage fingerprints (DDF) and its application in quantitative damage identification. Composite Structures 67, 197–204 (2005) 85. Moslem, K., Nafaspour, R.: Structural damage detection by genetic algorithms. AIAA Journal 40(7), 1395–1401 (2002) 86. Chou, J.-H., Ghaboussi, J.: Genetic algorithm in structural damage detection. Computers and Structures 79, 1335–1353 (2001) 87. Nag, A., RoyMahapatra, D., Gopalakrishnan, S.: Identification of delamination in composite beams using spectral estimation and a genetic algorithm. Smart Materials and Structures 11, 899–908 (2002) 88. Ling, H.-Y., Lau, K.-T., Cheng, L., Jin, W.: Fibre optic sensors for delamination identification in composite beams using a genetic algorithm. Smart Materials and Structures 14, 287–295 (2005) 89. Su, Z., Ling, H.-Y., Zhou, L.-M., Lau, K.-T., Ye, L.: Efficiency of genetic algorithms and artificial neural networks for evaluating delamination in composite structures using fibre Bragg grating sensors. Smart Materials and Structures 14, 1541–1553 (2005) 90. Haywood, J., Coverley, P.T., Staszewski, W.J., Worden, K.: An automatic impact monitor for a composite panel employing smart sensor technology. Smart Materials and Structures 14, 265–271 (2005)

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91. Guo, H.Y., Zhang, L., Zhang, L.L., Zhou, J.X.: Optimal placement of sensors for structural health monitoring using improved genetic algorithms. Smart Materials and Structures 13, 528–534 (2004) 92. Xu, Y.G., Liu, G.R., Xu, Z.P.: Damage detection for composite plates using Lamb waves and projection genetic algorithm. AIAA Journal 40(9), 1860–1866 (2002) 93. Kuang, K.S.C., Maalej, M., Quek, S.T.: An application of a plastic optical fiber sensor and genetic algorithm for structural health monitoring. Journal of Intelligent Material Systems and Structures 17, 361–379 (2006) 94. Chen, H.G., Yan, Y.J., Chen, W.H., Jiang, J.S., Yu, L., Wu, Z.Y.: Early damage detection in composite wingbox structures using Hilbert-Huang transform and genetic algorithm. Structural Health Monitoring: An International Journal 6(4), 281– 297 (2007) 95. Wang, X., Tansel, I.N.: Modeling the propagation of Lamb waves using a genetic algorithm and S-transformation. Structural Health Monitoring: An International Journal 6(1), 25–37 (2007) 96. Hatem, T.M., Foutouh, M.N.A., Negm, H.M.: Application of genetic algorithms and neural networks to health monitoring of composite structures. In: Boller, C., Staszewski, W.J. (eds.) Proceedings of the 2nd European Workshop on Structural Health Monitoring, Munich, Germany, July 7-9, 2004, pp. 616–623. DEStech Publications, Inc (2004) 97. Goldberg, D.E.: Genetic Algorithms in Search, Optimisation, and Machine Learning. Addison-Wesley, Boston (1989) 98. Betz, D.C., Thursby, G., Culshaw, B., Staszewski, W.J.: Structural damage location with fiber Bragg grating rosettes and Lamb waves. Structural Health Monitoring: An International Journal 6(4), 299–308 (2007) 99. Ang, A.H.S., Tang, W.H.: Probability Concepts in Engineering Planning and Design. Basic Principles, vol. 1. John Wiley & Sons, Inc., New York (1975) 100. Wang, X., Foliente, G., Su, Z., Ye, L.: Multilevel decision fusion in a distributed active sensor network for structural damage detection. Structural Health Monitoring: An International Journal 5(1), 45–58 (2006) 101. Worden, K., Dulieu-Barton, J.M.: An overview of intelligent fault detection in systems and structures. Structural Health Monitoring: An International Journal 3(1), 85–98 (2004) 102. Murphy, R.R.: Biological and cognitive foundations of intelligent sensor fusion. IEEE Transactions on Systems, Man and Cybernetics - Part A: Systems and Humans 26(1), 42–51 (1996) 103. Bloch, I.: Information combination operators for data fusion: a comparative review with classification. IEEE Transactions on Systems, Man and Cybernetics - Part A: Systems and Humans 26(1), 52–67 (1996) 104. Su, Z., Wang, X., Cheng, L., Yu, L., Chen, Z.: On selection of data fusion schemes for structural damage evaluation. Structural Health Monitoring: An International Journal 8(3), 223–241 (2009)

7 Application of Algorithms for Identifying Structural Damage Case Studies

This chapter brings together several representative case studies conducted by the authors. In these selected studies, major algorithms introduced in Chapter 6 are employed to identify structural damage of increasing complexity, ranging from identification of a notch in a simple structural alloy beam using a damage index (DI) to quantitative evaluation of delamination in composite panels using the artificial neural network (ANN) technique. Key issues addressed in the preceding chapters, including activation of Lamb waves, finite element method (FEM) simulation, mode selection, active sensor network, signal processing, data fusion and identification algorithms, are further elaborated in individual case studies.

7.1 Identifying a Notch in a Structural Alloy Beam Using Damage Index Damage such as a notch or crack in a metallic structure, deteriorating progressively under cyclic loads in service, is a substantial threat to structural integrity. The capacity to continuously monitor damage expansion or growth is a key indicator of any structural health monitoring technique. With damage discerned at an early stage, the risk of its further deterioration or failure of the structure can be considerably minimised. This case study concerns identification of a notch in a long structural alloy beam of square cross-section, and assessment of its size using a DI-based identification algorithm (Section 6.2.1) [1, 2]. Strictly speaking, the guided waves confined in the long beam in this study are the superposition of a diversity of wave modes including Lamb waves, as a result of the geometrical features of the beam, but this does not limit the use of the damage identification algorithm.

Z. Su and L. Ye: Identification of Damage Using Lamb Waves, LNACM 48, pp. 255–297. springerlink.com © Springer-Verlag Berlin Heidelberg 2009

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7.1.1 Establishment of DI Consider a homogeneous Euler-Bernoulli beam, assuming that the beam axis is the X -axis and neglecting any twisting effect. The motion equation of the beam can be expressed in terms of its lateral displacement w( x, t ) and rotation angle

θ ( x, t ) [3] upon introduction of a shear correction parameter, κ ,

κ 2cs2 [

c02

∂ 2 w ∂θ ∂ 2 w − ]− 2 = 0, ∂x 2 ∂x ∂t

2 ∂ 2θ ∂ 2θ 2 cs ∂w + − − κ θ =0, [ ] q 2 ∂x ∂x 2 ∂t 2

c0 = E ρ , cs = G ρ , q = I A , κ = π

(7.1)

12 ,

where E , G , I , A and ρ are the elastic modulus, shear modulus, second moment of area of the cross-section, cross-section area and density of the beam, respectively. Taking into account the dispersion which can be described by

w = w0 ⋅ e −i ( kx−ωt ) and θ = θ 0 ⋅ e −i ( kx−ωt ) ,

(7.2)

where w0 and θ 0 are the initial lateral displacement and rotation angle ( ω is the circular frequency of the wave), eigen roots (wavenumber) of Equation 7.1 are ⎡ c2 ⎞ 1⎛ k n = ± ⎢ ⎜⎜1 + 20 2 ⎟⎟ ± ⎢ 2 ⎝ κ cs ⎠ ⎢⎣ ( n = 1, 2, 3, 4 ).

2⎤ 2 ⎛ c0 ⎞ 1 ⎛ c02 ⎞ ⎥ ⎜⎜ ⎟⎟ + ⎜⎜1 − 2 2 ⎟⎟ ⎝ qω ⎠ 4 ⎝ κ cs ⎠ ⎥⎥ ⎦

12

⋅

ω c0

(7.3)

Mathematically, the existence of the four eigen roots above ( n = 1, 2, 3, 4 ) indicates that four wave components are available synchronously in the beam. The general solution to Equation 7.1 can therefore be expressed as a summation of four terms w( x, t ) = [∑ A1e −ikx + ∑ A2 e ikx + ∑ A3e − kx + ∑ A4 e kx ] ⋅ e iω⋅t .

(7.4)

The four terms in Equation 7.4 depict four wave modes, and in terms of the propagation direction and properties they are (i) a positively propagating mode, (ii) a negatively propagating mode, (iii) a positively growing evanescent mode and (iv) a negatively exponentially decaying mode, respectively, with A1 , A2 , A3 and A4 being the amplitude of each mode which can be a complex.

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If damage exists (we limit the following discussion to a transverse notch perpendicular to the beam axis, with a depth of H d , in Figure 7.1), a partial of the incident wave coming from the left beam end is reflected from the left notch surface, denoted by w− , and the rest is transmitted, w+ , to continue the propagation. These two wave components can be defined by separating Equation 7.4 into two sub-equations w− ( x, t ) = [∑ A1e − ik x + ∑ A2 e ik x + ∑ A4 e k x ] ⋅ e iω⋅t , 1

1

(7.5a)

1

w+ ( x, t ) = [∑ B1e −ik x + ∑ B2 e − k x ] ⋅ e iω⋅t . 2

Left surface of notch

Right surface of notch

Hd

A1 A4 A2

(7.5b)

2

H B2 B1

Fig. 7.1. A wave propagation model for a structural beam with a transverse notch

The three terms in Equation 7.5a are the original incident mode, reflected propagating mode and reflected exponentially decaying mode, respectively, and the two terms in Equation 7.5b are the transmitted positively propagating mode and the growing evanescent mode, respectively. Note that the wave modes A4 and B2 disappear very quickly because of their exponentially decaying properties. Applying continuity and compatibility conditions at the left notch surface ∂w− ( x, t ) ∂w+ ( x, t ) , = ∂x ∂x ∂w2 ( x, t ) ∂w3 ( x, t ) ∂w2 ( x, t ) ∂w3 ( x, t ) EI1 − 2 , EI1 − 3 , = EI 2 + 2 = EI 2 + 3 ∂ x ∂x ∂ x ∂x

w− ( x, t ) = w+ ( x, t ) ,

yields 2

R=

A2 − iI1 k14 + 2 I1 I 2 k13 k 2 + 2iI1 I 2 k12 k 22 − 2 I1 I 2 k1k 23 − iI 22 k 24 = , A1 I12 k14 + 2 I1 I 2 k13 k 2 + 2 I1 I 2 k12 k 22 + 2 I1 I 2 k1k 23 + I 22 k 24

(7.6)

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I1 =

W ⋅ ( H − H d )3 W ⋅H3 and I 2 = , 12 12

(7.7)

where W and H are the width and depth of the cross-section of the beam, respectively. R = A2 A1 is the reflection coefficient, defined as the magnitude ratio of the incident to the damage-reflected waves, which is subject to the notch depth H d and is therefore selected as the DI. In this way, the depth of an unknown notch can be evaluated in terms of the reflection coefficient, R , extracted from the captured wave signals. By increasing the value of the notch depth from zero by a small increment in Equation 7.7, a theoretical relationship between notch depth ( H d / H ) and DI (the reflection coefficient) can be established for an aluminium beam (H = 10 mm, W= 10 mm) with a notch, in Figure 7.2.

Notch depth [% of beam depth]

100

80

60

40

20

0.0

0.2

0.4

0.6

0.8

1.0

Reflection coefficient

Fig. 7.2. Relationship between selected DI (reflection coefficient of wave) and notch depth (damage severity)

7.1.2 Assessing Changes in Notch Size Using DI

The established DI is then used to identify changes in the size of a transverse notch in a long aluminium alloy beam (cross-section: 10 mm × 10 mm; E : 72.4 GPa; ρ : 2.69 g/cm3) with two ends clamped, sketched in Figure 7.3. A transverse notch across the width of the beam, with a 0.15 mm span along the beam axis and 350 mm away from the right beam end, is introduced using a diamond saw. The notch depth, H d , increases progressively in steps of 1.0 mm until it reaches 8.0 mm. A pendulum hammer 610 mm away from the left beam end generates the

Application of Algorithms for Identifying Structural Damage

259

transverse (perpendicular to the beam axis) impact with energy of 0.4 J to the beam, to activate incident waves. A piece of piezoelectric lead zirconate titanate (PZT) element (20 mm × 10 mm × 1 mm) is surface-affixed on the beam 570 mm away from the right beam end to capture the incident wave and the wave reflected by the notch in conformity to the pulse-echo configuration (Sections 1.2 and 6.2). As a result of impact excitation, a broadband response is generated containing various wave modes travelling at different velocities. In addition, the ambient noise and in particular the low-frequency vibration of the beam are included in the captured signals. From pendulum control To signal acquisition

Impact excitation

610 mm

PZT

220 mm

220 mm

Notch

350 mm

Fig. 7.3. Experimental setup for identifying a notch in a structural beam

As an example, the captured raw wave signal when the notch is 6 mm in depth is displayed in Figure 7.4(a). Spoiled by various noise and the low-frequency vibration of the beam under impact that claims the major energy of the signal, the captured signal does not clearly show the damage-reflected wave component. The continuous-wavelet-transform (CWT)-based spectrographic analysis (Section 5.3.1) is applied to the captured signal. The energy spectrum of the signal is presented in Figure 7.4(b), in which the wave reflected by the notch becomes explicit. After clear recognition of individual wave components in the signal, the approach for determining the reflection coefficient of a wave signal using CWTbased spectrographic analysis (Section 5.3.4.2) is employed to obtain the DI for the signal. The obtained DI is subsequently interpolated into the curve in Figure 7.2, by which means the notch depth can be ascertained. Prior to discerning the notch size, the notch can be located by calculating the difference in time-of-flights (ToFs) between the incident and notch-reflected waves (for this one-dimensional case, one actuator-sensor path is sufficient to locate the damage). The identification results for changes in the size of the notch are detailed in Table 7.1. These results show that despite of the severity of the notch, the identification of its location is accurate, while the accuracy of assessing the notch size improves as the notch size increases until it reaches approximately 6 mm, around 60-70% of the beam cross-section. A large error is observed when the notch is greater than 70% of the cross-section, attributed to the invalidation of the basic hypotheses used in the Euler-Bernoulli beam theory on which the algorithm

260

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is developed. Under such a circumstance the twisting effect [3] cannot be neglected, leading to inapplicability of the continuity and compatibility conditions defined by Equation 7.6. As commented in Section 6.2.1, DI-based identification normally works well for evaluating single damage parameters (e.g., damage size only) of a simple structure, as in the case presented here.

1.0

Normalised amplitude

Normalised Amplitude

6 mm-Depth 6 mm-depth

0.5

0.0

-0.5

-1.0 0

200

400

600

800

1000

Time [ µs ] Time [ s] a Incident wave

Wavelet coefficient

Reflected wave from notch

Reflected wave from boundaries

b Fig. 7.4. The wave signal captured when the notch is 6 mm in depth: a. in the time domain; and b. in the time-scale domain obtained through CWT analysis

Application of Algorithms for Identifying Structural Damage

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Table 7.1. Identification results for a notch in a structural beam using DI-based algorithm

Actual notch depth [mm]

Identified depth [mm]

Identified location [mm] (distance to right beam end)*

abs. error [%]

abs. error [%]

1

1.073

7.25

373

6.57

2

2.100

4.90

336

4.00

3

3.150

4.69

341

2.79

4

3.832

4.17

359

2.65

5

5.115

2.30

340

2.26

6

6.123

2.05

357

2.05

7

6.404

8.52

355

1.13

8

6.200

22.5

346

1.02

* The actual location of the notch is 350 mm from the right beam end.

7.2 Locating Delamination in a Composite Panel Using Time-of-flight When subjected to excessive transverse impact, fibre-reinforced composites are highly prone to delamination. Delamination is probably the most hazardous defect in laminated composites. Often invisible, delamination is very difficult to detect. Substantial efforts have been made to pinpoint delamination at as early a stage as possible [4-10]. This case study introduces an approach for locating delamination in a composite panel using a ToF-based identification algorithm (Section 6.2.2) [11-18]. Two carbon fibre-reinforced epoxy (CF/EP) composite laminates (500 mm Ì 500 mm Ì 3.6 mm) are fabricated using orthotropic plain woven fabric prepreg following a quasi-isotropic stacking sequence of [(+/-45)/(0/90)]4s. The material properties are detailed in Table 7.2. Each laminate is embedded between the second and third layers of the prepreg with an active PZT sensor network introduced previously (Section 4.5, Figure 4.16(a)). Twelve PZT wafers in the sensor network are numbered clockwise and denoted by S i , ( i = 1, 2, A, 12 ), in Figure 7.5. Circular delamination with a diameter of 40 mm is introduced by inserting a thin Teflon®1 film of 25 m in thickness into one of the two laminates between the second and third layers of the prepreg before the autoclaving process, and the other one serves as the benchmark. All the edges of the two laminates are fixed on an anti-vibration table, shown in Figure 4.16(b), and then the embedded active sensor network is instrumented with a signal generation and data acquisition system. Fivecycle sinusoid tonebursts at a central frequency of 250 kHz modulated by a 1

Teflon® is a registered trademark of E.I. du Pont de Nemours and Company. http://www.dupont.com

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Identification of Damage Using Lamb Waves

Hanning window after being amplified to 50 V (peak-peak) are applied in turn to each PZT wafer to activate diagnostic Lamb wave signals. At this frequency, only the lowest-order symmetric ( S 0 ), anti-symmetric ( A0 ) and shear horizontal ( SH 0 ) modes are available (based on the dispersion properties of Lamb waves in this composite laminate). The captured Lamb wave signals are pre-processed with CWT (Section 5.3.1) and discrete wavelet transform (DWT, Section 5.3.2), to remove the ambient noise, and only the wave components in the excitation frequency range are examined. Table 7.2. Material properties of CF/EP orthotropic plain woven fabric (Hexcel®)2 [12] 0° tensile modulus [GPa]

0° compressive modulus [GPa]

Fibre volume [%]

Poisson’s ratio

Density [g/cm3]

59.9-62.0

55.1-57.9

62

0.2 (fibre) 0.35 (resin)

1.78 (fibre) 1.22 (resin)

330 S5

S6

S7

S8

S9

500

S4

Ø 40 121 S10

125

110

S3

110 S2

S1

S12

S11

500

Fig. 7.5. A CF/EP composite laminate containing delamination, embedded with an active sensor network consisting of twelve PZT wafers (unit: mm; delamination is invisible)

2

Hexcel® is a registered trademark of Hexcel Corporation, Stamford, Connecticut, USA. http://www.hexcel.com

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Using the signal correlation approach (Section 5.2.1.2), the ToFs for the incident diagnostic Lamb wave and the delamination-scattered Lamb wave can be extracted from captured signals. Following the procedure of using an active sensor network to triangulate structural damage (Section 6.2.2.3), each actuator-sensor pair (i.e., a sensing path) in the sensor network contributes a locus with the extracted ToFs, indicating possible locations of the damage. Two loci from any two sensing paths in the sensor network lead to intersections. The region in the laminate containing the most intersections can be deemed the damaged zone. The identification results for the delamination in the composite laminate are shown schematically in Figure 7.6. The central position of the region containing the majority of intersections of loci is 115 mm to S 3 and 131 mm to S1 , contrasting with the actual damage centred at 121 mm to S 3 and 125 mm to S1 .

Fig. 7.6. Identification results for delamination in a composite laminate using ToF-based triangulation with an active sensor network (hollow circle: region containing most intersections of loci and deemed the damaged zone; grey circle: actual delamination (invisible); dotted curves: partial of ellipses contributed by individual actuator-sensor paths in the sensor network)

7.3 Hierarchically Locating Multiple Delamination in a Composite Panel Using Time-of-flight This case study expands the damage triangulation approach introduced in the previous section for locating multiple delamination in a composite laminate [19, 20]. With an active sensor network it is possible to conduct this identification using a group of selected sensors or sensor paths in the network, following a hierarchical procedure, which offers a way of identifying multiple instances of

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Identification of Damage Using Lamb Waves

structural damage. Such an outcome may not be achieved using a normal approach as adopted in the case study previously introduced. 7.3.1 Rationale

To hierarchically identify multiple damage instances in a structure under inspection, PZT wafers in an active sensor network are activated selectively. Note that the active sensor network does not aim to partition the structure into small sub-regions and impose the condition that each sub-region bears at most single damage, which is the method used in traditional approaches for identifying multiple damage. For the composite laminate examined in Section 7.2, regardless of the number of damage instances within the area surrounded by the twelve sensors, Level I: sensing paths of relatively short distance in the sensor network, highlighted in Figure 7.7(a), are activated to generate and capture 32 sets of Lamb wave signals; Level II: sensing paths of longer distance in the sensor network than those in Level I, highlighted in Figure 7.7(b), are activated to generate and capture another 16 sets of signals; Level III: sensing paths of longer distance in the sensor network than those in Level II, highlighted in Figure 7.7(c), are activated to generate and capture an additional 16 sets of signals; and Level IV: sensing paths of longer distance in the sensor network than those in Level III, including the longest diagonal sensing paths S2-S8/S8-S2, S5-S11/S11-S5, highlighted in Figure 7.7(d), are activated to generate and capture a further 44 sets of signals. Provided that damage exists, the signals captured by the sensing paths close to the damage will be most affected by it. This damage is then called the primary damage as to these sensing paths. In contrast, these captured signals are least influenced by distant instance(s) of damage, which is(are) accordingly called the secondary damage. Therefore, the ToFs for the incident wave and scattered wave from the primary damage can be extracted from signals captured via the selectively activated sensing paths, with minimal influence from secondary damage instance(s). Based on ToF-based triangulation in conjunction with an active sensor network (Section 6.2.2.3), multiple loci established by individual sensing paths lead to intersections, implying possible locations of the damage and reflecting the perceptions as to damage by these sensing paths. On the basis of signals captured via sensing paths in Level I, a consensus as to the damage instance(s) in the structure under inspection can be preliminarily established by aggregating all perceptions of individual sensing paths activated at this level. Subsequently, the same procedure is applied to signals rendered by Levels II, III and IV hierarchically, in which only the ToFs for the incident and primary damage-scattered waves are extracted for each sensing path. Damage identification is hierarchically conducted from low to high levels, subject to the desired precision of identification, rather than being conducted using all sensing paths at the same time. It can be expected that for long sensing paths such as the diagonal paths in Level IV, a number of wave components scattered by multiple

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265

damage (primary and secondary damage) may overlap considerably and interfere with each other in the captured signals. S6-S7

S10

S3

S4 -S 6 S4 S6 -

S1 2S1 0

S1 0S1 2

S1 2-S 9

S10

0 -S1 S1 1 0-S S1

S11-S12

S11

S2

S1

S12

S11

S7

S8

b

S6-S1

S6

S8

S5

S9

S4

S9

S10

S3

S10

S7-S12

S7

S12-S7

S6

S1-S6

S9

S12-S11 S12

a S5

6

S9 -S

S4-S3

S12-S1

S1

S3 -S1 2 S1 2-S 3

S10-S11

S1-S12

S1-S2

S11-S10

3 -S S1

S2-S1

S9 -S S3 -S 6 S6 -S3

S4

S9-S10

S10-S9

S3-S4

0 -S1 S7 7 0-S S1

S7

1 -S S3

S3-S2

S8

S6 -S9

S3

S2-S3

S7

-S7 S4 -S4 S7

S9

S4

S2

S6

S5

S8-S9

S9-S8

S9

S5-S4

S8

S7-S8 S8-S7

9 -S S7

S4-S5

S7

S7-S6

S6-S5

12

S6

S5-S6

-S4 S1 1 -S S4

S5

10 -S S6 S6 0S1

S4-S9 S4 S3 -

S7 S7 -S 3

S9-S4

S3-S10 S3 S10-S3 S1 S9 -S9 -S 1

12 -S S4 S4 2S1

S2

S12

S1

c

S11

S2

S12

S1

S11

d

Fig. 7.7. Activated sensing paths for signal acquisition in a. Level I; b. Level II; c. Level III; and d. Level IV

7.3.2 Experimental Validation

Two pieces of circular delamination (30 mm and 60 mm in diameter, respectively) are introduced into a CF/EP composite laminate (Figure 7.8) with the same configuration and material properties of the laminates used in Section 7.2, by inserting thin Teflon® films of 25 m in thickness. The active sensor network same as the one used in Section 7.2 is embedded into the panel between the

266

Identification of Damage Using Lamb Waves

second and third layers of the prepreg before the autoclaving process. The laminate is then instrumented with a signal generation and data acquisition system.

330 S6

S7

S8

120

S5

Ø 60 S9

500

S4

50

145

Ø 30 S10

90

110

S3

110 S2

S1

S12

S11

500

Fig. 7.8. A CF/EP composite laminate containing dual delamination, embedded with an active sensor network consisting of twelve PZT wafers (unit: mm; delamination is invisible)

For convenience of pinpointing intersections of loci defined by individual sensing paths, the whole inspection area (enclosed by the twelve PZT wafers and measuring 330 mm × 330 mm) is virtually and evenly partitioned using 134×134 grids, with a spacing of 2.5 mm. Following the procedure of using an active sensor network for triangulating damage (Section 6.2.2.3), the grid where the intersection of two loci established by two sensing paths is located becomes light grey in a greyscale image, and aggregation of the greyscale images contributed by all sensing paths in the sensor network leads to a resulting image showing all possible instances of damage in the laminate. Figures 7.9(a)-(c) present such resulting images obtained at the different levels of signal acquisition, where the darker the greyscale the more intersections of loci the grid contains. The image intuitionally indicates the locations of two instances of delamination in the laminate. In particular, when more sensing paths are involved at high signal acquisition levels, more perceptions as to the damage are added into the greyscale image upon aggregation, enhancing the acceptability of the identification results. However, extraction of ToFs from major wave signals in Level IV captured via the longest sensing paths in the sensor network is frustrated due to the considerable overlap and interference of the waves scattered from the multiple damage (primary and secondary damage) in the signals.

Application of Algorithms for Identifying Structural Damage

300

Plate y-dimension [mm]

Plate y-dimension [mm]

300

250 200

150

100 50 0

267

250 200

150

100 50

0

50

100

150

200

250

0

300

0

50

Plate x-dimension [mm]

100

150

200

250

300

Plate x-dimension [mm]

a

b

Plate y-dimension [mm]

300

250 200

150

100 50 0 0

50

100

150

200

250

300

Plate x-dimension [mm]

c Fig. 7.9. Identification results for dual delamination in a composite laminate using ToFbased triangulation with an active sensor network at a. Level I; b. Level II; and c. Level III signal acquisition (hollow circle: actual delamination; diagram shows only the inspection area enclosed by sensors)

As expected, the precision of identification increases (reflected by an increase of greyscale intensity in the resulting image) with an increase of activated sensing paths, from the lower-levels (short sensing paths) to the higher-levels (long sensing paths). However, a high level of signal acquisition involving long sensing paths does not necessarily contribute to improvement of the identification precision if exact extraction of ToFs from wave signals becomes problematic. A low level of signal acquisition involving short sensing paths can have the capacity to define the locations of multiple instances of damage, demonstrating the advantage of the hierarchical procedure.

268

Identification of Damage Using Lamb Waves

7.4 Evaluating Multiple Delamination in a Composite Panel Using Probability-based Diagnostic Imaging This case study applies a probability-based diagnostic imaging approach using Lamb waves to identify multiple damage in a composite laminate [21-26]. Basically, the approach fuses prior perceptions as to the presence of damage, established by individual actuator-sensor paths of an active sensor network, to form a posterior consensus on the health status of the laminate, in accordance with the principles and procedures of probability-based diagnostic imaging in terms of ToF (Section 6.2.6.1) and data fusions schemes (Section 6.3.2). 7.4.1 Establishment of Prior Perceptions from a Sensing Path in Terms of ToF

When the ToFs of the incident and damage-scattered Lamb waves are extracted from a captured signal via an actuator-sensor pair (i.e., a sensing path) in a sensor network, the accordingly established locus described by Equation 6.2 can define possible locations of the damage, which are the prior perceptions of this sensing path as to the existence of damage in the inspection area. However, for developing the probability-based diagnostic imaging, no identification of damage is carried out at this step in this case study by finding intersections of two or more loci contributed by multiple sensing paths in the sensor network, as elaborated in the previous case studies. 7.4.2 Establishment of Probability of Presence of Damage

Illustrating using the composite laminate used in Sections 7.3, the inspection area (enclosed by twelve PZT wafers) is virtually and evenly meshed using K × K nodes, in Figure 7.10. At each node, the probability of the presence of damage is defined in relation to the prior perceptions established by individual sensing paths briefed in Section 7.4.1. In principle, spatial nodes that are located exactly on the locus have the highest degree of probability (100%) of damage presence, from the perspective of the sensing path that produces such a locus. For other nodes, the greater the distance to the locus, the lower the probability that the sensing path perceives damage to exist at those nodes. Therefore, the distance from a particular mesh node to a locus can be used to scale the probability of damage presence at this node. In this case, to quantify such probability, a cumulative distribution function (CDF) [27], F ( z ) , is introduced, defined as z

F (z) =

∫ f (z

−∞

ij

) ⋅ dzij ,

(7.8)

Application of Algorithms for Identifying Structural Damage

269

y K nodes S5

S6

S7

S8

S9

S3

S10

K nodes

S4

x S2

S12

S1

S11

Fig. 7.10. The inspection area of a composite laminate enclosed by twelve PZT wafers, virtually and evenly meshed using K × K nodes

f ( zij ) =

1

exp[ −

zij

2

] is the Gaussian distribution function, 2σ ij2 σ ij 2π representing the probability density function (PDF) of the existence of damage at node ( xm , ym ) , ( m = 1, 2, A, K , for the structure that is meshed using K × K

where

nodes), perceived by the p th sensing path in which actuator Si activates the diagnostic wave signal while sensor S j captures the signal ( i, j = 1, 2, A, N but i ≠ j for the sensor network consisting of N PZT sensors, which offers in total

N p = N ( N − 1)

sensing paths;

p = 1, 2, A , N P ).

In the

above,

zij = ( xm − xij ) 2 + ( ym − yij ) 2 , where ( xij , yij ) is the location on the locus

established by sensing path Si − S j that has the shortest distance to node ( xm , ym ) , as illustrated in Figure 7.11. σ ij is the standard variance, describing the variability or dispersion of a data set, which is set as 0.44 in this case study. Given a distance, zij , the probability of the presence of damage at node ( xm , ym ) established by the

p th sensing path, I ( xm , ym ) p (i.e., the field value of the probability image at node ( xm , ym ) ), is

[

I ( xm , ym ) p = 1 − F ( zij ) − F (− zij )

]

( p = 1, 2, A, N P ; i, j = 1, 2, A, N , but i ≠ j ), as shown in Figure 7.12.

(7.9)

270

Identification of Damage Using Lamb Waves

Locus established by sensing path S i − S j

( xij , yij )

( xm , y m ) Locus established by sensing path S k − Sl

( xkl , ykl )

Fig. 7.11. Distances of mesh node located at ( xm , ym ) with regard to loci established by two sensing paths Si − S j and S k − Sl , respectively

Probability density

Probability of damage presence at node ( x , y ) m

− zij

m

zij

Fig. 7.12. Gaussian distribution of the probability density as to the presence of damage at a particular node of the structure

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271

The probabilities as to the presence of damage at all nodes across the area of inspection are then established in terms of Equation 7.9 for all available sensing paths in the sensor network, respectively, which are delineated in a set of greyscaled diagrams to indicate the likelihood of the presence of damage at one particular node of the structure. For illustration, one such diagram contributed by a sensing path arbitrarily selected from the sensor network for the laminate (500 mm × 500 mm × 3.6 mm) bearing dual delamination (30 mm and 60 mm in diameter, respectively), as used in Section 7.3, is displayed in Figure 7.13. The lighter the greyscale at a node, the greater the possibility of damage presence at this node. A sensing path can only perceive the damage near the established locus, a characteristic that is attributed to the exponential function in Equation 7.8, with which the probability of presence of damage exponentially approaches zero as the distance increases between a node and the locus.

Plate y-dimension [mm]

Probability of damage presence

Plate x-dimension [mm]

Fig. 7.13. Probability diagram as to the presence of damage established by a sensing path ( S12 − S9 ) (diagram shows only the inspection area enclosed by sensors)

7.4.3 Fusion of Probabilities for Diagnostic Imaging

By aggregating the probability diagrams established by all the available sensing paths in the sensor network across the composite laminate, the field value (overall probability of the presence of damage) at a node ( x m , y m ) in the resulting probability image, I ( x m , y m ) is NP

I ( xm , y m ) =

∏ I (x

m

, ym ) p

p =1

( p = 1, 2, A, N P ),

(7.10a)

272

Identification of Damage Using Lamb Waves

if a conjunctive fusion scheme (Section 6.3.2) is adopted; or I ( xm , y m ) =

1 NP

NP

∑ I (x

m

, ym )

p

p =1

( p = 1, 2, A, N P ),

(7.10b)

if a compromised fusion scheme (Section 6.3.2) is adopted. The images of probability as to the presence of damage across the inspection area of the composite laminate are exhibited in Figures 7.14(a) and 7.14(b) using the two fusion schemes, respectively.

Plate y-dimension [mm]

Probability of damage presence

Plate x-dimension [mm]

a

Plate y-dimension [mm]

Probability of damage presence

Plate x-dimension [mm]

b Fig. 7.14. Identification results for dual delamination in a composite laminate using probability-based diagnostic imaging with a. conjunctive; and b. compromised fusion schemes (white or dark solid circle: actual delamination; dotted area: the area with field values over 80% of the maximum field value of the diagram; diagram shows only the inspection area enclosed by sensors)

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273

The above two images provide an intuitive depiction of all the possible instances of damage in the structure under inspection. It will be observed that the highest probability in Figure 7.14(a) (circa 23%) is much lower than that in Figure 7.14(b). This is attributed to the nature of the conjunctive fusion which multiplicatively processes prior perceptions from individual sensing paths, and any perception of low possibility leads to a significantly low likelihood of the presence of damage. In contrast, the compromised fusion scheme takes into account all perceptions equally and decentralises their contribution well. If 80% of the maximum field value of the probability image is set as the threshold for drawing a conclusion that damage exists, two regions of the overall probability above that threshold are clearly visible in both images, indicating two instances of damage in the laminate. Interestingly, the sizes of these highlighted regions are similar to those of actual delamination in the laminate.

7.5 Quantitatively Predicting Delamination in Composite Beams Using an Artificial Neural Network In this case study, the damage identification algorithm based on the ANN technique (Section 6.2.8.1) is employed to quantitatively predict through-width delamination in a composite beam [28, 29]. The digital damage fingerprints (DDF) (Section 5.5) extracted from captured Lamb wave signals under different damage scenarios are used to train an ANN. Using the trained ANN it is possible to predict parameters of delamination in the beam including location, size and interlaminar position. 7.5.1 Training Data Preparation

Consider a composite beam made of eight-ply CF/EP orthotropic plain woven fabrics (Hexcel®) with raw material properties listed in Table 7.3. The effective elastic properties of the composites are derived using a three-dimensional fibre/matrix micro-mechanics model [30]. The beam is 470 mm Ì 20 mm Ì 1.78 mm in size and both ends are clamped, as shown schematically in Figure 7.15(a). The beam contains through-width delamination, defined by three damage parameters: axis-span ( a ), interlaminar position ( d ) and distance from its left tip to the left beam end ( L ), indicated in Figure 7.15(a). Two PZT elements (20 mm Ì 10 mm Ì 0.5 mm each) are assumed to be perfectly surface-bonded on the beam, 60 mm from either beam end, respectively, in conformity to the pitch-catch configuration (Sections 1.2 and 6.2), where the left PZT element functions as a wave actuator to produce a diagnostic wave signal and the right as a sensor. For the ANN training, a database hosting a certain number of damage scenarios of diverse combinations of the above three damage parameters is required. However, it can be impractical to investigate a large variety of damage scenarios experimentally. In this aspect, FEM simulation can be a practical solution, using the demonstrated modelling techniques for Lamb waves (Section 2.4.1), delamination (Section 2.4.2), surface-bonded PZT actuator and sensor (Section 3.5). In brief, the

274

Identification of Damage Using Lamb Waves

composite beam is modelled using three-dimensional eight-node brick elements, and a two-dimensional volume-split is formed in the delaminated region, as illustrated in Figure 7.15(b). There are 16 plies of brick elements in the beam thickness to simulate eight-ply plain woven fabrics, and ten nodes are allocated within one wavelength (1-1.5 mm between two neighbouring nodes). Table 7.3. Material properties of CF/EP orthotropic plain woven fabric (Hexcel®) [29] Product name

Vol. [%]

Tensile modulus [GPa]

Weight/length [g/m]

Poisson’s ratio

Density [g/cm3]

Fibre

T300/3K

45

205

0.200

0.2

1.78

Resin

F593

55

2.96

N/A

0.35

1.22

a

b

c Fig. 7.15. a. A CF/EP composite beam containing delamination, surface-bonded with a PZT actuator; b. FEM model for the delaminated region; and c. PZT actuator model for activating diagnostic Lamb wave ( S 0 )

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By imposing horizontal displacement constraints on the nodes where the PZT actuator is located (Section 3.5.1.1), Figure 7.15(c), the diagnostic Lamb wave signal (lowest-order symmetric mode S0 ), five-cycle sinusoid tonebursts modulated by a Hanning window at a central frequency of 500 kHz, is activated. At this frequency, only the lowest-order symmetric ( S0 ), anti-symmetric ( A0 ) and shear horizontal ( SH 0 ) modes are available (based on the dispersion properties of Lamb waves in this composite laminate [29]), with propagation velocities of approximately 5800 m/s, 1800 m/s and 4000 m/s, respectively, in the laminates. Upon interaction of the incident diagnostic wave with delamination, a partial of incident S0 mode is converted to the SH 0 and A0 modes that propagate following the transmitted S0 mode, Figure 7.15(a). With a calculation step less than the ratio of the minimum distance of any two adjoining elemental nodes to the maximum wave velocity (5800 m/s), the FEM simulation is fulfilled using ABAQUS®3/EXPLICIT. Two delamination parameters, a and L , are selected arbitrarily in the simulation but limited to ranges of 12 mm< a <25 mm and 90 mm< L <380 mm, and the delamination is allowed to exist between any two adjacent laminae of the eight-layer laminate (i.e., 0.1 ≤ d ≤ 0.7 if the interlaminar position of delamination is normalised with regard to the laminate thickness). Up to 60 delamination scenarios are explored individually. DDF are extracted from the captured Lamb wave signals under each damage scenario following the extraction procedure described in Section 5.5. Considering the range of L and the propagation velocity of SH 0 , DDF of only the damage-induced SH 0 mode (rather than the complete signal) between the incident S0 mode and its boundary reflection are stored in a damage parameters database (DPD) (Section 5.5) for ANN training, so as to minimise the dimension of the training database. DDF for two damage scenarios arbitrarily selected from the DPD are displayed in Figure 7.16.

a

b

Fig. 7.16. Extracted DDF for two damage cases: a. a =21 mm, L =312 mm and d =0.1; and b. a =17 mm, L =250 mm and d =0.2 3

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276

Identification of Damage Using Lamb Waves

7.5.2 ANN Training and Experimental Validation

A feedforward backpropagation ANN (Section 6.2.8.1) is designed, and it is trained with the DPD until convergence is achieved. The ANN features two neural layers with 32 and 8 neurons, respectively. Two sigmoid transfer functions and a linear transfer function are used to associate the neural, input and output layers. The concomitant output vector hosts three delamination parameters ( a , L and d ). For experimental validation, three eight-layer CF/EP laminates, made of the orthotropic plain woven fabric prepreg (Hexcel®), are cured in an autoclave, and delamination is introduced into each by inserting a thin polyimide film (Upilex®4R-25) of 25 µm in thickness during the lay-up process, summarised in Table 7.4. The material properties and configurations of the three laminates are the same as those used in the FEM simulation for DPD development. Note that the three cases of delamination were not considered during DPD development. Three beams are then instrumented with a signal generation and data acquisition system. Table 7.4. Configuration of CF/EP composite beams containing delamination for experimental validation Sample No.

Dimension [mm3]

Delamination parameters a [mm]

L [mm]

d

SP1#

470 × 20 × 1.78

21

190

0.1

SP2#

470 × 20 × 1.78

19

250

0.1

#

470 × 20 × 1.78

17

210

0.3

SP3

Two PZT elements (20 mmÌ 10 mm Ì 0.5 mm, PI®5 151) are surface-bonded on each beam as the wave actuator and sensor, respectively, with locations being consistent with the simulation. The captured Lamb wave signals are pre-processed with CWT (Section 5.3.1) and DWT (Section 5.3.2), to remove the noise, and only the wave components in the excitation frequency range are examined. DDF are extracted from the pre-processed signals, which are then fed into the trained ANN as new inputs. The identification results for the three cases of delamination are shown in Table 7.5. Excellent identification precision is achieved, particularly for predicting axial location and size ( L and a ), respectively, with relatively a large error for predicting the interlaminar position ( d ). 7.5.3 Discussion

To evaluate the capacity of using the DDF of only the damage-induced SH 0 mode for damage identification, the DDF of the complete wave signal (including those of the incident S0 mode and its reflected components from the beam ends, apart from the DDF of the SH 0 mode) are extracted for each damage scenario and then 4

5

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Application of Algorithms for Identifying Structural Damage

277

used to re-train the ANN of the same configuration. The identification results with the corresponding extracted DDF as inputs are listed in Table 7.5 for comparison. No clear improvement in identification precision can be discerned when the DDF of the complete signal are used, implying that the DDF extracted from the delamination-scattered SH 0 mode carry adequate information to quantitatively depict the delamination. Table 7.5. Identification results for delamination in composite beams using the DDFtrained ANN Sample No.

Identification results (abs. error [%]) Using ANN trained by DDF of only damage-scattered SH 0

Using ANN trained by DDF of complete signal

a

L

d

a

L

d

SP1

#

20.1 (4.3)

197 (3.7)

0.13≈0.1

22.1 (5.2)

197 (3.5)

0.11≈0.1

SP2

#

20.6 (8.4)

235 (6.0)

0.23≈0.2

19.9 (4.7)

241 (3.6)

0.13≈0.1

SP3#

18.2 (7.1)

219 (4.3)

0.37≈0.4

18.0 (5.9)

223 (6.1)

0.35≈0.4

When the delamination is located near either the actuator or sensor as well as both ends of the beam, the delamination-induced SH 0 mode can be considerably masked by the incident S0 mode and its boundary reflection, leading to difficulty in extracting DDF of the damage-induced SH 0 mode. Considering the propagation velocities of the S0 and SH 0 modes, and the dimension of the beam, the explicitly detectable region for delamination is circa 110 mm< L <350 mm, where the delamination-induced SH 0 mode can be clearly distinguished from other wave modes in the signals.

7.6 Quantitatively Estimating Through-thickness Hole and Delamination in Composite Panels Using an Artificial Neural Network By extending the approach for predicting delamination in composite beams described in the preceding section to the generic situation, the present case study has the goal of quantitatively estimating comprehensive parameters of damage (presence, location, size and orientation) in planar composite laminates. The damage considered here concerns a through-thickness hole [31-38] and delamination [35, 39, 40], which are the two most representative types of damage in fibre-reinforced composites. 7.6.1 Training Data Preparation

Consider a square quasi-isotropic ([45/-45/0/90]s) CF/EP laminate, 500 mm Ì 500 mm Ì 1.275 mm in size, which is supported on its all four sides. An active sensor

278

Identification of Damage Using Lamb Waves

network of nine PZT wafers is surface-bonded on the laminate, sensors being numbered S i , ( i = 1, 2, A, 9 ), Figure 7.17. This sensor network is able to render a total of 36 actuator-sensor pairs (viz., 72 sensing paths). To fully exploit the symmetrical properties of this square laminate, the laminate is virtually quartered into Zone-1, Zone-2, Zone-3 and Zone-4. Without losing generality, it is assumed that a single instance of damage (through-thickness hole or delamination) is within Zone-3 and elliptic, defined by six damage parameters: presence (‘0’ for ‘no’ or ‘1’ for ‘yes’), location ( ξ , ζ ), semi-major/minor axes ( α , β ) and orientation ( θ ).

Fig. 7.17. A CF/EP composite laminate containing a through-thickness hole or delamination, surface-bonded with an active sensor network consisting of nine PZT wafers (unit: mm; delamination is invisible)

The laminate with damage is simulated using the FEM modelling techniques previously introduced (Section 2.4). In particular, in the delaminated region, a three-dimensional volume-split is shaped (Figure 2.16), enveloped by two isolated surfaces sharing the same edge. The element mesh is particularly densified in the zone hosting damage (Zone-3), where more than ten nodes per wavelength are guaranteed and the laminate thickness is divided into eight layers to characterise individual unidirectional laminae. As the damage is assumed to be in Zone-3 only, Zones-1, 2 and 4 of the laminate are simplified using single layer consolidated eight-node brick elements. The effective elastic properties of individual laminae

Application of Algorithms for Identifying Structural Damage

279

are derived using a three-dimensional fibre/matrix micro-mechanics model [30], listed in Table 7.6 for the selected material T650/F584 (Hexcel®). Table 7.6. Material properties of CF/EP composites (Hexcel®) [33]: a. technical parameters; and b. estimated elastic properties for individual laminae using a fibre/matrix micro-mechanics model a Fibre name

Matrix name

Fibre volume [%]

Matrix volume [%]

Laminate density [g/cm3]

T650/3512K

F584

56

44

1.528

b E11 [GPa]

E22 [GPa]

E33 [GPa]

G12 [GPa]

G13 [GPa]

G23 [GPa]

n12

n13

n23

153.67

9.49

9.49

4.26

4.26

3.44

0.295

0.295

0.381

As an example, the ichnography of the FEM model created for a particular damage scenario (through-thickness hole) is displayed in Figure 7.18, featuring approximately 120,000 solid elements and 420,000 degrees of freedom. A Lamb wave actuator model (Section 3.5.1.1) is employed to produce the diagnostic wave signal, five-cycle sinusoid tonebursts modulated by a Hanning window at a central frequency of 500 kHz. At this frequency, only the lowest-order symmetric ( S0 ), anti-symmetric ( A0 ) and shear horizontal ( SH 0 ) modes are available (based on the dispersion properties of Lamb waves in this composite laminate). The wave signals propagating across the laminate are captured using a Lamb wave sensor model (Section 3.5.2). The FEM simulation is accomplished using ABAQUS®/EXPLICIT. Up to 120 cases of a through-thickness hole and 90 of delamination are modelled, each of which possesses a single instance of damage in Zone-3 only, with exclusive location and geometric identity randomly selected. DDF are extracted from captured Lamb wave signals for each damage scenario, and two examples are shown in Figure 7.19.

Identification of Damage Using Lamb Waves

Densified element mesh near damage

Single layer consolidated elements

280

Fig. 7.18. FEM model for the composite laminate containing a through-thickness hole

In view of the symmetry of the square laminate, a mapping approach (Section 5.5) is applied to mirror the DDF for the damage scenarios in Zone-3 into other zones of the laminate with regard to X − , Y − axes and origin of the coordinate system shown in Figure 7.17, and in this way DDF for damage in the entire laminate can be acquired. The measure of mapping dramatically reduces the effort and simulation cost required to obtain sufficient training data, but without sacrificing accuracy. Note that the applicability of mapping is guaranteed here by the assumption of dense damage cases. Hosting DDF, two DPDs are constructed for identification of a through-thickness hole and delamination, respectively, in the laminate. 7.6.2 Parameterised Modelling

Establishing a diversity of damage scenarios for ANN training can involve massive human effort and huge computational cost, which constitute a major hurdle in applying damage identification algorithms based on ANN to engineering practice. To tackle this problem, a parameterised modelling technique (PMT) is developed using the Patran®6 Command Language (PCL) [41]. PCL is a programming language for performing variational or connatural modelling. Supported by PCL, the PMT permits development of various FEM models for complex structures in terms of only few characteristic parameters provided by the user. For the composite laminates under discussion, the parameters are geometric identity, material properties and boundary conditions; for the damage (i.e., through-thickness hole and delamination), they are location, shape, size, orientation and interlaminar position (delamination only); for the PZT actuator and sensor, the required parameters include location, piezoelectric parameters, geometry and intensity of applied electrical field. Element mesh density along three dimensions and element types can also be parameters. With these 6

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Normalised CWT coefficient

Normalised CWT coefficient

parameters, the PMT is able to customise FEM models automatically and expeditiously for various damage scenarios. It has been demonstrated that over 90% of computational effort and time can be saved by using such a technique [42]. In addition, errors during modelling introduced by human-related factors can be minimised.

Normalised CWT coefficient

Normalised CWT coefficient

a

b Fig. 7.19. a. Energy spectra over the time-scale domain obtained through CWT analysis of two Lamb wave signals captured in a composite laminate containing a through-thickness hole; and b. DDF correspondingly extracted from the signal energy spectra shown in a.

7.6.3 ANN Training and Experimental Validation

Two feedforward backpropagation ANNs (Section 6.2.8.1) comprised of two neural layers, possessing 36/14 and 50/22 neurons each, are designed for predicting through-thickness hole and delamination in composite laminates, respectively. The input vector hosts 2700/3000 DDF extracted from Lamb wave

282

Identification of Damage Using Lamb Waves

Network Training Performance (MSE) MSE

signals for every single through-thickness hole and delamination scenario. The output vector accommodates the six aforementioned damage parameters. The training is fulfilled under a supervised training, and the training progress, calibrated by the mean square error (MSE, Section 6.2.8.1) versus training iteration, for the ANN used for predicting a through-thickness hole as an example is displayed in Figure 7.20. In the initial training stage (shown in the small box), an exponential acceleration in the convergence of training is observed as the number of iterations increases, indicating prompt approximation of the interim outputs of the ANN to the targets. Successive amendment continues, although slight instability is noticed locally, and then the convergence is sustained regardless of further increase in iteration, demonstrating saturation of training. 10

2

10

0

10

-2

10

-4

10

-6

10

-8

0

10

20

It

0

1

2

30

40

50

ti

3

4

5

Iteration [×(100,000] Iteration X 100,000 )

Fig. 7.20. Training progress of an ANN for predicting through-thickness holes in composite laminates (performed on a PC platform with Pentium®7 IV 1.6 GHz and 512M RAM)

The well-trained ANNs are used to quantitatively predict the actual throughthickness hole and delamination in laminates with the same material properties and geometrical dimensions as those in the FEM simulation for development of two DPDs. For this purpose, five CF/EP (T650/F584) laminates are fabricated, in three of which a through-thickness hole is introduced using a diamond grinding tool, while in the other two instances of delamination are introduced by inserting two pieces of polyimide film (Upilex®-R-25) of 25 m in thickness during the layup process. The laminates are numbered SP1# ~ SP5# and their dimensions are summarised in Table 7.7. Five laminates are then surface-bonded with a sensor network of the same configuration and properties as that used in the simulation for DPD development, and then each is instrumented with a signal generation and data acquisition system. 7

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Table 7.7. Configuration of CF/EP composite panels containing damage (through-thickness hole or delamination) for experimental validation Damage parameters Sample No. *

To Left edge [mm]

To bottom edge [mm]

[mm]

[mm]

SP1#

269

192

17

11

175

2

SP2#

172

272

19

12

135

4

SP3#

330

353

25

18

40

3

SP4#

100

192

25

19

75

1

SP5#

349

272

28

15

150

3

**

[°]

Zone

* Single through-thickness hole in SP1#~SP3#, and single delamination in SP4# and SP5#. ** Angle between the major axis of the elliptic damage and the X − axis.

The location, size and orientation angle of these cases of damage listed in the above table were not included in the scenarios for the ANN training. The experimentally captured Lamb wave signals are pre-processed with CWT (Section 5.3.1) and DWT (Section 5.3.2), to remove the noise, and only the wave components in the excitation frequency range are examined. DDF are extracted following the same procedure as in the DPD development, which are then fed into the trained ANNs for damage prediction. Figure 7.21 shows the identification results for delamination in SP4# and SP5# (results for through-thickness holes in SP1# ~ SP3# are presented in following section for discussion). Excellent prediction of delamination including presence, location, size and orientation is achieved. The results predicted by the ANN do not overlap any damage case in DPD for ANN training, implying that the results are ratiocinated rather than just finding the fittest one from the DPD. 7.6.4 Discussion: Influential Issues

As a complex high-order nonlinear inverse inferential procedure, damage identification using ANN involves a diversity of issues, typified by the quantity of training data, sensor number, and network configurations (network architecture, training functions, etc.). 7.6.4.1 Quantity of Training Cases To mimic the mechanism of human learning in which more exact deduction originates from more knowledge, an ANN behaves rationally only when trained with adequate training cases. Theoretically, the number of training cases must be sufficiently large so as to represent the system properly, although this has to be negotiated against computational cost and practicality.

284

Identification of Damage Using Lamb Waves

S5 S4

Actual delamination

Predicted delamination Zone-1 S1

S2

a

S8

S9 Zone-3 Actual delamination

Predicted delamination

S6

S5

b Fig. 7.21. Identification results for delamination in a. SP4#; and b. SP5# using the DDFtrained ANN (dotted ellipse: damage scenario in DPD; for each scenario, only single damage is considered; diagram shows only the zone where damage is present)

To explore the dependence of prediction accuracy on the quantity of training cases, 20, 50, 80, 100 and 120 scenarios of a through-thickness hole in Zone-3 of the composite laminate are modelled, using the PMT introduced previously. The corresponding DDF are extracted from Lamb wave signals under each scenario and stored in different DPDs, denoted by DPD-20, DPD-50, DPD-80, DPD-100

Application of Algorithms for Identifying Structural Damage

285

and DPD-120, respectively. The prediction results for the through-thickness hole in SP3# using an ANN (36/14 neurons in the first/second neural layers) but trained by different DPDs are integrated in Figure 7.22. Full results for the throughthickness holes in SP1# ~ SP3# are detailed in Table 7.8.

S8

S9 DPD-80

Zone-3

DPD-120

DPD-100

DPD-50 DPD-20

S6

S5 Actual through-thickness hole

Fig. 7.22. Integrated identification results for a through-thickness hole in SP3# using the ANN trained by different quantities of training cases (dotted ellipse: damage scenario in different DPDs (aggregated in one diagram); for each scenario, only single damage is considered; diagram shows only the zone where damage is present)

From Figure 7.22 and Table 7.8, it is evident that identification accuracy improves with an increase in the number of training cases until it stabilises when 80 damage cases are used for training, and thereafter no prominent improvement is further observed when more cases are added for training. This means that the more training cases taken into account the more accurate a prediction is expected, but excessive training cases do not contribute to further improvement in accuracy, i.e., training saturation is reached. For this case study, satisfactory prediction is achieved when 80-100 damage cases in one quadrant of the laminate are used for ANN training. The quantity of training cases plays the dominant role in ANN training, determining the accuracy of prediction. Insufficient training certainly leads to inability of the ANN to identify damage correctly, and excessive training with a very large number of cases does not necessarily lead to improvement in performance of the ANN (so-called over-training [43]). Moreover, excessive training comes at the cost of considerable computational requirements and much effort for database development. Both insufficient and excessive training may lead to erroneous prediction. Unfortunately, judicious determination of the appropriate

286

Identification of Damage Using Lamb Waves

quantity of training cases required for a specific application is beyond the current capability of mathematical evaluation. Table 7.8. Identification results for through-thickness holes in SP1# ~ SP3# using the ANN trained by different quantities of training cases abs. error [%] DPD

DPD20

DPD50

DPD80

DPD100

DPD120

Max. abs. error [%]

Sample No.

SP1#

21.6

23.3

21.7

27.9

32.0

32.0

SP2

#

24.8

19.9

23.0

20.4

39.5

39.5

SP3

#

26.0

17.1

19.2

25.3

35.5

35.5

SP1

#

17.5

13.5

17.4

15.5

27.7

27.7

SP2#

17.8

9.8

14.2

16.6

24.0

24.0

SP3

#

15.7

11.0

12.3

14.1

26.5

26.5

SP1

#

6.5

3.5

6.9

5.8

9.2

9.2

SP2

#

5.8

6.3

7.2

4.3

4.0

7.2

SP3

#

6.5

3.1

4.6

3.8

4.3

6.5

SP1#

5.7

3.2

6.0

5.0

8.5

8.5

SP2

#

4.7

5.2

6.1

4.8

5.5

6.1

SP3

#

5.0

3.7

2.8

3.5

4.1

5.0

SP1

#

5.3

3.7

4.8

4.8

9.1

9.1

SP2

#

4.7

5.2

6.1

4.7

5.4

5.4

SP3#

5.0

3.0

2.8

3.0

8.1

8.1

Approx. time for ANN training [hrs] *

3.2

5.1

8.3

13.5

17.2

* Based on a PC platform with Pentium® IV 1.6 GHz and 512M RAM.

7.6.4.2 Number of Sensors For each damage scenario in Zone-3, only those signals captured via sensing paths passing through this zone, including S2-S9/S9-S2, S3-S8/S8-S3, S4-S9/S9-S4, S6S7/S7-S6 and S5-S9/S9-S5, S6-S8/S8-S6, referring to Figure 7.23, are significantly influenced by the damage. For evaluation, four (S5, S6, S8, S9), six (S5, S6, S8, S9, S2 and S4) and eight (S5, S6, S8, S9, S2, S4, S3 and S7) PZT wafers in the sensor network are activated for generating diagnostic signals and capturing Lamb wave signals, using FEM simulation. DDF are accordingly extracted from signals captured via four (S5-S9/S9-S5 and S6-S8/S8-S6), eight (S5-S9/S9-S5, S6-S8/S8-S6, S2S9/S9-S2 and S4-S9/S9-S4), and twelve ( S5-S9/S9-S5, S6-S8/S8-S6, S2-S9/S9-S2, S4S9/S9-S4, S3-S8/S8-S3 and S6-S7/S7-S6) sensing paths, respectively, for each damage scenario (80 in total). For each sensing path concerned, the same numbers of DDF are extracted.

Application of Algorithms for Identifying Structural Damage

Zone-4

Zone-3

Zone-1

Zone-2

287

Fig. 7.23. Sensing paths substantially influenced by damage in Zone-3

Accordingly, three DPDs of different capacities, hosting different numbers of DDF, are established and then used to train an ANN (36/14 neurons in the first/second neural layers). The identification results for the through-thickness hole in SP3# using three DPDs are compared in Table 7.9. Obviously, more sensors (i.e., more DDF and therefore more input information) contribute to improvement in prediction accuracy. In particular, four PZT wafers are unlikely to locate damage and estimate its size; six wafers can give an approximate prediction of the presence and location of damage, but are inept at delineating the damage size exactly; eight wafers are sufficient to predict exactly all damage parameters (presence, location and size). Table 7.9. Identification results for a through-thickness hole in SP3# using the ANN trained by different numbers of sensors (i.e., different numbers of DDF)

abs. error [%]

Using DDF extracted from four sensors

Using DDF extracted from six sensors

Using DDF extracted from eight sensors

18.7

9.4

6.5

16.8

8.2

3.1

24.5

17.5

4.6

29.1

21.6

3.8

27.6

17.6

4.3

288

Identification of Damage Using Lamb Waves

7.6.4.3 Network Architecture A system might not be represented faithfully using an ANN with insufficient neurons, but the stability of an ANN is often sacrificed if an oversized ANN with surplus neurons is used (so-called over-fitting [43]). It has been substantiated that any continuous system can be portrayed smoothly using an ANN of two neural layers if the neurons of each layer are sufficient [43]. For evaluation, three ANNs possessing 20/8, 36/14 and 50/30 neurons in the first/second neural layers are comparatively trained using the DPD hosting the same number of DDF extracted from 80 damage scenarios in Zone-3. These three ANNs are labelled ANN-20/8, ANN-36/14 and ANN-50/30. The training history of the three ANNs is displayed in Figure 7.24(a) and the prediction results for through-thickness holes in SP1# ~ SP3# are integrated in a schematic diagram, Figure 7.24(b). It is interesting to observe that in Figure 7.24(a), both ANN-20/08 and ANN50/30 have relatively slow convergence when compared with ANN-36/14; in Figure 7.24(b), ANN-36/14 outperforms the other two in terms of prediction accuracy. This implies that both insufficient and superfluous neurons in the neural layers of an ANN can impair prediction accuracy. Although no cardinal doctrines are available to determine the most appropriate network architecture for a specific application and an optimal ANN configuration is often achieved only via reiterative trial and experience, an empirical approach can be referred to in choosing the number of neurons in a neural layer [44]:

i = m+n + A,

(7.11)

where i , m and n are the number of neurons, number of input elements and number of output elements, respectively. A is an empirical constant, ranging from 4 to 8 depending on the application. 7.6.4.4 Robustness In the evaluations in the previous sections, the captured Lamb wave signals, preprocessed with CWT (Section 5.3.1) and DWT (Section 5.3.2), are filtered to remove the ambient noise, and only the wave components in the active excitation frequency range (500 kHz) are selected from which DDF are extracted for ANN training. To examine the robustness of the approach with regard to noise interference, broadband white noise is added to raw Lamb wave signals captured under two damage scenarios arbitrarily selected from 80 damage cases, from which DDF are extracted directly by skipping the step of noise filtering. The extracted DDF are then mixed with the DDF extracted from noises-free signals for the other 78 damage cases for ANN training. The prediction results for throughthickness holes in SP1# ~ SP3# using an ANN (36/14 neurons in the first/second neural layers) trained by mixed DDF, labelled ANN-NOISE, and trained by DDF extracted upon removal of noise for all the signals, ANN-NOSFR, are integrated in a schematic diagram, Figure 7.25.

Network TrainingMSE Performance (MSE)

Application of Algorithms for Identifying Structural Damage 10

2

10

0

289

20/8DPD-A-2008 neurons

10

-2

10

-4

50/30 eurons DPD-A-5030

DPD-A-3614 10

-6

10

-8

36/14 neurons

0

1

2

3

4

5

Iteration X 100,000] 100,000 ) Iteration([×

a

Actual damage

Results from ANN-36/14 Results from ANN-20/8

Results from ANN-50/30

b Fig. 7.24. a. Training progress of the ANNs with different numbers of neurons; and b. integrated identification results for through-thickness holes in SP1# ~ SP3# using the ANNs with different numbers of neurons (diagram shows aggregated results for three specimens and each specimen has only one through-thickness hole)

290

Identification of Damage Using Lamb Waves

Actual damage

Results from ANN-NOSFR

Results from ANN-NOISE

Fig. 7.25. Integrated identification results for through-thickness holes in SP1# ~ SP3# using the ANN trained by DDF with/without a certain amount of noise (diagram shows aggregated results for three specimens and each specimen has only one through-thickness hole)

No substantial negative impact on the prediction accuracy is observed when using ANN-NOISE, indicating that with a small amount of noise among many training data, the robustness and tolerance to noise interference of a well-trained ANN remain. 7.6.4.5 Problematic Issues and Suggestions Damage identification, a complex inverse inferential procedure, inherently involves themes of searching, solvability and uniqueness. Despite many advantages such as elimination of the need to canvass individual signals at subjective discretion, damage identification capitalising on ANN technique presents some problematic issues. First and foremost, the performance of an ANN is predominantly subject to the quantity of training cases. Some efforts [45-50] have been directed to reducing the quantity of training cases required while maintaining reasonable prediction accuracy. It is advisable to predict different damage parameters using individual ANNs, rather than trying to predict all parameters using an ANN of large size and trained by a comprehensive database. Step by step, it is possible to predict the presence, location and then severity of damage using individual ANNs. These individual ANNs, in relatively compact architecture, can be trained by databases

Application of Algorithms for Identifying Structural Damage

291

of reduced capacity to perform more cost-effective evaluation, eschewing extensive training. In particular, an approach called novelty detection or anomaly detection has been developed for Lamb-wave-based damage identification in virtue of ANN technique [51-54]. In this approach, features are extracted from baseline signals only (i.e., signals captured from the benchmark structure without damage), and these features are duplicated but artificially corrupted with Gaussian white noise, so as to obtain a certain number of cases just using the baseline signals for ANN training (no damage cases are considered). For every single training case, the ANN targets are always the same: the structure is ‘healthy’. When features of signals captured from a structure of an unknown health status are supplied to the ANN, any deviation of the ANN outputs from the targets indicates the existence of damage. The major advantage of this approach is that the training data are baseline information only, dramatically reducing the effort required for modelling various damage cases. However, the capacity of the novelty detection is obviously limited to qualitative awareness of damage only. On the other hand, considering the fact that the presence and location of damage are of great interest in engineering practice, a hierarchical training scheme [55] and a fast training scheme [56] have been developed, with the aim of quickly and cost-effectively training an ANN with databases of reduced capacity. These two schemes hierarchically answer the key questions of damage identification: ‘Is there damage?’ and ‘Where is the damage?’ (Section 1.2), rather than predicting comprehensive damage parameters at the one time. The time consumed for the ANN training is significantly decreased from several hours to a couple of minutes, in comparison with the approaches aforementioned that attempt to predict comprehensive damage parameters in a single manipulation. Posteriorly, the applicability of a well-trained ANN is clearly limited to identifying a single instance of damage in a structure with the given material and geometric properties, for which the DPD has been specifically developed. Such an ANN is in general not extendable to multiple damage, other types of damage and other structures. This limitation considerably hampers more widespread application of the ANN technique in engineering practice, stimulating efforts to improve the versatility of a trained ANN with possibly less extra work when used for other applications. It is understood that developing a universal training database, broadly effective for multiple damage, various types of damage, different structural properties and geometric identities, and diverse working conditions, would unavoidably require burdensome work and incur expensive computational cost. Moreover, prediction accuracy may be sacrificed due to the over-training and over-fitting problems already mentioned. A feasible solution in this respect is to combine the ANN-based identification approach with other identification algorithms introduced in Chapter 6 (e.g., ToF-based triangulation or phased-array beamforming). In this way one may first classify damage type and discern the number of instances of damage in the structure under inspection, and then apply appropriate ANN-based algorithms to further quantitatively identify the remaining damage parameters of individual damage instances. Last but not least, FEM simulations have been employed in this case study to produce the Lamb wave signals from which the DDF are extracted for ANN

292

Identification of Damage Using Lamb Waves

training. Higher prediction precision is expected to be achieved by adding in a certain number of DDF extracted from experimentally captured signals for rectification.

7.7 Identifying Structural Damage in a Composite Laminate Using Bayesian Inference

0.75

This case study presents a two-level damage identification scheme using Bayesian inference (BI) (Section 6.2.8.3) [57-60]. In this approach, level-one decision fusion is based on signal features (DDF) extracted from individual Lamb wave signals provided by an active PZT sensor network, for creating perceptions as to damage and then a knowledge database. H i in Equation 6.29, the theorem of BI, is the posterior probability as to the presence of damage, and P(Ev | H i ) estimates the confidence of an individual sensor as to the perception of the presence of damage. Perceptions from individual sensors are subsequently aggregated at the second level, to provide a detailed description of the damage including the size and shape. Using the DPD developed for identifying a through-thickness hole in composite laminates described previously (Section 7.6) which hosts DDF extracted from Lamb wave signals under a total of 80 damage scenarios, the prediction results for the through-thickness hole in SP3# used in the preceding case study (Section 7.6) are displayed in Figure 7.26, where the greyscale is associated with the probability of the presence of damage. The lighter the greyscale the greater the probability of the presence of damage, similar to the probability image in a diagnostic imaging approach (Section 7.4), providing an intuitive depiction of location and shape of the damage.

Error due to boundary

Fig. 7.26. Identification results for a through-thickness hole in SP3# using BI-based identification algorithm (solid ellipse: actual damage; dotted ellipse: predicted damage (high probability); diagram shows only the zone where damage is present)

Application of Algorithms for Identifying Structural Damage

293

7.8 Summary Several representative case studies of damage identification based on Lamb waves using some identification algorithms introduced in Chapter 6 are presented in this chapter, to further explore key issues of Lamb-wave-based damage identification techniques elaborated in preceding chapters. It can be seen that during a process of damage identification, whichever algorithms are used, individual signals captured by distributed sensors in a sensor network are processed first to establish individual perceptions as to damage in the structure under inspection. The signals are then fused to deliver a comprehensive consensus as to the damage. Locating damage and evaluating its severity in a simple structure can be cost-effectively achieved using ToF-based triangulation and DI-based interpolation, respectively. Probability-based diagnostic imaging can offer an intuitive depiction of the damage, having the potential to identify multiple damage instances in the structure. Quantitative prediction of damage, including size estimation, is generally a highly complicated inverse procedure, which can be implemented using an ANN-based algorithm. However, it often comes at the cost of intensive labour effort and much time required for preparing training cases. It is noteworthy that the efficiency and accuracy of an approach capitalising on ANNs is somewhat subject to certain factors, in particular the number of training cases and the network configurations. Excessive training and complex network configuration involving a greater number of training cases and neurons do not necessarily lead to improvement in efficiency and accuracy.

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8 Systems and Engineering Applications

8.1 Introduction The practical implementation of Lamb-wave-based damage identification techniques in actual engineering structures often involves challenges and difficulties, and it may require comprehensive knowledge in system design, development and integration. As a result of intensive research and development in this area over the past few years and recent technical breakthroughs such as active sensor networks and high performance instruments, the practicability of Lambwave-based damage identification has been substantially consolidated, and some applications have attained commercial development. This chapter embraces representative deployment of such techniques in actual engineering structures, following a brief introduction to the development of systems (hardware and software) for practical implementation.

8.2 System for Implementation Identification of damage can only be fulfilled by a system comprised of a series of hardware and supporting software. At a rudimentary level, a system for implementing Lamb-wave-based damage identification and structural health monitoring (SHM) consists of (i) a computing unit such as a computer with integrated algorithms and software for controlling, signal processing, data fusion, presentation of identification results, etc.; (ii) a signal excitation unit for activating customised diagnostic Lamb wave signals; (iii) a data acquisition unit for receiving Lamb wave signals upon propagation in the structure under interrogation; (iv) a certain number of sensors and actuators, a sensor array or a network; and (v) other ancillaries such as data storage devices and cables for transmitting commands and signals. Z. Su and L. Ye: Identification of Damage Using Lamb Waves, LNACM 48, pp. 299–328. springerlink.com © Springer-Verlag Berlin Heidelberg 2009

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At an advanced level, communication devices such as a radio link, wireless agent, telemetry or the internet are often part of the system, and at this level ample consideration must be given to the robustness of system and tolerance of the algorithms to variable working conditions. Identification can be conducted offline (for the purpose of damage identification) or online (for the purpose of SHM). As an illustrative paradigm, the Lamb-wave-based damage identification system developed by the authors, which has been demonstrated in a diversity of case studies (Chapter 7), is shown in Figure 8.1. The system, built on a VXI platform†, includes a signal generation subsystem (SGS), a data acquisition subsystem (DAS), a central control/analysis unit (CCAU) and an active sensor network in conformity to the concept of ‘standard sensor unit’ (SSU) (Section 4.5.2).

Fig. 8.1. A damage identification system based on Lamb waves

†

The VXI bus architecture is an open standard platform for automated testing based on VMEbus. VXI stands for VME eXtensions for Instrumentation, defining additional bus lines for timing and triggering as well as mechanical requirements and standard protocols for configuration, message-based communication, multi-chassis extension, and other features. The basic building block of a VXI system is the mainframe or chassis, containing up to 13 slots into which various modules (instruments) can be added. It is therefore possible to configure a system to meet a particular requirement by selecting the required modules.

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8.2.1 Signal Generation Subsystem The SGS bridges the CCAU with individual piezoelectric lead zirconate titanate (PZT) elements (with PZT elements serving as active actuators) of the sensor network (formed by a series of SSUs) embedded in or surface-bonded on the structure under inspection, with its principle shown in Figure 8.2. A digital diagnostic Lamb wave signal of desired waveform and central frequency is customised in the CCAU and transmitted to an arbitrary waveform generator (Agilent®1 E1441), in which the digital signal is converted to the corresponding analog signal via a built-in digital-to-analog (D/A) converter. The analog signal of a maximum amplitude of 10 Vpeak-peak is downloaded to a PZT amplifier (Piezo Systems®2 EPA-104), and the amplified analog signal in an appropriate voltage range drives the PZT elements of the sensor network, so as to activate diagnostic Lamb waves in the structure.

Fig. 8.2. Principle of SGS

8.2.2 Data Acquisition Subsystem The DAS links the CCAU with individual PZT elements (with PZT elements serving as wave sensors) of the sensor network (formed by a series of SSUs) embedded in or surface-bonded on the structure under inspection, to receive Lamb waves after their propagation in the structure. In a closed acquisition loop, Figure 8.3, a sensor in the sensor network captures dynamic responses of the structure. Allowing for possible incompatibility between signals and hardware, the captured signal is conditioned with a signal conditioner (Agilent® E3242A). The 1

Agilent® is a registered trademark of Agilent Technologies, Inc., Palo Alto, CA, USA. http://www.home.agilent.com 2 EPA-104 is a Piezo linear amplifier, available from Piezo Systems®. Piezo Systems, Inc. 186 Massachusetts Ave. Cambridge, MA, USA. http://www.piezo.com

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conditioning operation includes signal amplification, filtering, electrical isolation and multiplexing. A signal conditioner usually generates a few micro-volts of internal noise. To minimise such internal noise, an amplifier with a bandwidth that closely matches the bandwidth of the input signal is built in the conditioner. The conditioned signal is then acquired by a digitiser (Agilent® E1437A) at sampling rates up to 20.48 MHz, transmitted through cables, converted to digital bits by a built-in analog-to-digital (A/D) converter and finally stored in a storage device for further processing by the CCAU. Shielded cables, kept as short as possible, are used to connect the DAS with the CCAU, so as to screen electrical and mechanical noise during measurement.

Fig. 8.3. Principle of DAS

8.2.3 Central Control/Analysis Unit As the core of the system, the CCAU integrates the diagnosis controller and signal processing/fusion algorithms. In-house software, developed on LabVIEW™3 (National Instrument Co.) and MATLAB®4 (the MathWorks, Inc.) is embedded in the CCAU to fulfill the designated functions of (i) controlling, (ii) interactively communicating with the SGS and DAS through Agilent® Virtual Instrument Software Architecture (VISA), (iii) processing signal (signal filtering, waveletbased spectrographic analysis, etc.), (iv) fusing processed signals, and (v) presenting final identification results to the operator. The interactive interfaces of the CCAU for controlling the SGS and DAS are shown in Figure 8.4. 8.2.4 Calibration of System Proper calibration of a system is a prerequisite to guarantee the correctness of identification results of damage. A calibration exercise basically includes zero setting and drift offsetting (e.g., gain error offsetting, AD/DA converter offsetting and voltage offsetting). The calibration setup for the current system is shown schematically in Figure 8.5(a) for the SGS (by benchmarking a standard signal

3

4

LabVIEW™ is a trademark of National Instruments. National Instruments Corporation, 11500 N Mopac Expwy, Austin, TX 78759-3504, USA. http://www.ni.com MATLAB® is a registered trademark of The MathWorks, Inc., 3 Apple Hill Drive, Natick, MA 01760-2098, USA. http://www.mathworks.com

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generator (HP™5 3310A)), and in Figure 8.5(b) for the DAS (by referencing a standard oscilloscope (Agilent® 54620A)). Both standard instruments are factory-calibrated. For calibrating the SGS, a series of excitation signals of the same waveform but in a sweep frequency range is generated by both the standard signal generator and the SGS, respectively, to drive a PZT element (as wave actuator) surface-bonded on an aluminium plate, Figure 8.5(a). Signals are then collected by another PZT element (as wave sensor) using a standard oscilloscope. The signals activated by the standard signal generator and the SGS are compared, and the difference between them is used to collimate the configuration of the SGS so as to minimise that difference.

a

b Fig. 8.4. Interfaces of in-house software for a. arbitrary signal generation by SGS; and b. dual-channel data acquisition by DAS

5

HP™ is a trademark of HP and its suppliers or licensors. http://welcome.hp.com

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a

b Fig. 8.5. Setups for calibration of a. SGS; and b. DAS

For calibrating the DAS, various signals activated by the standard signal generator are simultaneously acquired by both the standard oscilloscope and the DAS, Figure 8.5(b), and a similar procedure as for calibrating the SGS is applied for adjusting the configuration of the DAS.

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8.3 Application in Engineering Structures Lamb waves can be used to identify damage and evaluate integrity of a broad range of engineering structures, from underground petroleum pipeline through space vehicles to civil infrastructure. But Lamb-wave-based damage identification is most likely limited to plate-like or shell-like structures in light of the existence condition of Lamb waves (Lamb waves are elastic disturbances existing in thin plate or shell). Some demonstrated engineering applications of such a technique are briefly described here. 8.3.1 Detection of Corrosion in Pipelines Corrosion in a pipeline is hazardous damage of concern to the engineering community and to the oil, chemical and petro-chemical industries in particular. Since most pipelines are insulated for protection or buried underground, corrosion may be invisible, even on the external surface of the pipe, without removing the insulation layers. Excavation is often necessary for inspection of pipelines crossing urban areas, which becomes highly prohibitive and incurs high cost in terms of labour and disruption to the traffic. In this respect, damage identification using cylindrical Lamb waves (Section 2.2.4) can be of great advantage over traditional approaches [1-19]. Cylindrical Lamb waves propagate following the curvature of the pipe and can be directed along desired helical paths from circumferential to longitudinal direction of the pipe in virtue of their different modes, permitting identification of corrosion not only on the inner or outer surfaces but also within the wall of the pipe. Compared to bulk waves that are three-dimensional in nature and thus radiate energy omnidirectionally, cylindrical Lamb waves possess a low rate of attenuation with propagation distance, because cylindrical Lamb waves in pipelines are guided along the pipe, no lateral spreading occurs and the propagation is essentially one-dimensional [5]. Hence cylindrical Lamb waves can propagate over a considerably longer distance than bulk waves while retaining a reasonable signal-to-noise ratio, ideal for inspection of long pipelines. It has been demonstrated that pipelines of lengths up to 25 m and diameters ranging from 50 mm to 600 mm can be instantly inspected using cylindrical Lamb waves. A unique complexity of cylindrical Lamb waves propagating in a pipeline or tube, activated by a single actuator at one end and received by a sensor at the other end of a section of the pipe (in the pitch-catch configuration, Sections 1.2 and 6.2), is that there can be an infinite number of helical routes between this actuatorsensor pair, as illustrated in Figure 8.6, one of which takes the most direct path from the actuator to the sensor while others with steeper helicities travel further around the pipe circumferentially and can miss the sensor. Still others will travel one or more complete loops around the pipe and then arrive at the sensor. Moreover, this does not mean that the activated Lamb waves propagate only along these routes, as waves propagate omnidirectionally in both clockwise and counterclockwise directions, depending on the relative angular positions of the actuator. In the presence of damage in the pipe, this complexity is increased because the damage scatters incident waves omnidirectionally, causing mode conversion.

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However, rather than treating such complexity pessimistically, most studies and applications in this field take advantage of it since multiple propagation routes, travelling on the pipe surface from different angles, provide rich information as to damage in the pipe.

Fig. 8.6. Cylindrical Lamb wave propagation paths in a pipeline (note that the waves also travel in opposite directions to the displayed paths) [20]

Expanding the above discussion to the case in which a single actuator is placed at one end of the pipe and multiple sensors at the other end, triangular inspection coverage of the pipe surface can be achieved, as highlighted in Figure 8.7(a). Obviously such coverage is insufficient for detecting damage in the blind zones on the pipe surface (indicated in the figure), no matter how many sensors are placed at one end of the pipe, if only the first arriving Lamb wave signals (the waves that travel directly between the actuator and sensor) are used for inspection. However, it is possible to use multiple actuators (reciprocally activated at both ends of a pipe section as illustrated in Figure 8.7(b)) to provide complete coverage of the pipe [18]. During propagation in a pipe, incident diagnostic Lamb waves can be modulated to a prominent degree in the presence of damage, leading to changes in signal features (Section 5.4.3), including time-of-flight (ToF) of waves, signal reflection/transmission ratio and signal magnitude. A long pipe can accordingly be inspected in minutes by calibrating changes in the ToF (for locating damage) and deviations from the baseline signals (for evaluating damage severity) in either the pitch-catch or pulse-echo configuration (Sections 1.2 and 6.2). The demonstrated sensitivity of such an approach in terms of the severity of detectable damage is generally below 10% of the cross-sectional area of the pipe [4], which is very promising for most engineering applications. As introduced in Section 2.2.4, two fundamental cylindrical Lamb wave modes co-exist in an axisymmetric pipeline: L(0,1) propagates similarly to the A0 mode in flat plates, while properties of L(0,2) are similar to those of the S 0 mode in flat plates. The L(0,1) [18] and L(0,2) [4, 5] are both preferable to other modes for identifying damage in pipelines because they can be easily activated in an axisymmetric or anti-axisymmetric way, facilitating interpretation of wave signals.

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Inspection area

Sensor

Actuator

Blind zone

Blind zone

a

b Fig. 8.7. a. Inspection coverage and blind zones of a pipeline using one actuator at one end and multiple sensors at the other end of a section of the pipe; and b. use of multiple actuators for full inspection coverage of the pipe [18]

Two approaches, using Lamb wave tomography (Section 6.2.5) and ToF (Section 6.2.2), respectively, are briefly described here. 8.3.1.1 Lamb Wave Tomography In practical applications, crosshole projection tomography is often employed rather than parallel projection scheme (Section 6.2.5). That is because the latter requires a consistent propagation distance of all diagnostic Lamb waves, activated and collected by an actuator-sensor pair, from different incident angles for covering the entire inspection area, as shown in Figure 6.12(a) (Chapter 6), which

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is difficult to achieve in pipelines with curved surfaces and isolated by protection layers. For convenience of discussion in what follows, a pipe or tube is ‘unwrapped/unfolded’ and laid flat, and the surface is grid-meshed with crisscross rays, shown schematically in Figure 8.8. There are two means of applying crosshole Lamb wave tomography to this unfolded pipeline, distinguished by the location of transducers: helical ultrasound tomography (HUT) [1] and meridional ultrasonic tomography (MUT) [2].

a

b Fig. 8.8. Principle of pipeline inspection using cylindrical Lamb wave tomography (for illustration, the pipeline is virtually ‘unwrapped and laid flat’): a. HUT; and b. MUT

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In HUT, Figure 8.8(a), transducers are placed along two parallel (left and right) circumferential peripheries of the pipe. Changes in the propagation velocity of the first arriving Lamb wave signal (the wave that travels directly between the actuator and sensor) within each grid cell, subject to severity of damage, can be calculated for tomographic reconstruction using the algorithm described by Equation 6.7. In contrast, in MUT, Figure 8.8(b), all the transducers are placed along a surface line of the pipe which is parallel to the central axis of the pipe. When the pipe is virtually unwrapped, these transducers are allocated equally to the top and bottom edges of the pipe. Changes in the magnitude of the first arriving Lamb wave signal within each grid cell, subject to severity of damage, can be calculated for tomographic reconstruction using the algorithm defined by Equation 6.12. The output of the tomographic reconstruction is a readily interpretable image across the entire pipe, depicting changes in wave propagation velocity if HUT is adopted, or changes in signal magnitude if MUT is adopted, which are associated with damage in the pipe (e.g., corrosion-induced reduction in pipe wall thickness). It is noteworthy that the greatest barrier to successful implementation of MUT in engineering practice is that, because the transmitting and receiving transducers are in the same line, the wave components, in which we are interested for the purpose of examining amplitude attenuation, are often no longer in the first arriving wave in the captured signal, unlike in HUT. However, by gating the signal around the mode of interest and smoothing the magnitude data, tomographic images can be obtained. In practice, cylindrical Lamb waves can be launched and received by transducers in either a contact or non-contact manner. Figure 8.9(a) shows a setup for inspecting corrosion in a steel pipe using cylindrical Lamb wave tomography. In this setup a spring-loaded contact transducer moves circumferential by small increments along the periphery of the pipe, activating Lamb waves at different circumferential positions, so does the wave receiver at the other end of a section of the pipe (in the pitch-catch configuration). This method using only one pair of moveable transducers avoids the need for a large number of transducers distributed at both ends of a section of the pipe to provide sufficient rays for tomographic reconstruction. For illustration, tomographic results for a flaw in a pipe using HUT and MUT techniques, respectively, are presented in Figure 8.9(b), in which the identified flaw in the pipe is intuitive. 8.3.1.2 ToF It is observed that the reflection coefficient of axisymmetric (or antiaxisymmetric) waves (in the pulse-echo configuration) is especially sensitive to changes in the depth and circumferential severity of damage in a pipe, and at a given depth the coefficient is proportional to the circumferential dimension of the damage [4]. For example, the refection coefficient of the L(0,2) axisymmetric wave, reflected from a notch of depth equivalent to half the thickness of the pipe wall and circumferential size equivalent to 16% of the pipe circumference, is as evident as approximately -26 dB [4]. Based on this mechanism, some damage inspection techniques for pipelines have been commercialised, typified by the

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Spring-loaded contact transducer

a

Pipe axial direction

Pipe axial direction

b Fig. 8.9. a. Setup for inspection of steel pipeline using cylindrical Lamb wave tomography [1]; b. left: identification results for a square flaw (50 mm × 50 mm) in a steel pipe (inner diameter: 130 mm; outer diameter: 175 mm) using HUT; right: identification results for a circular flaw (diameter: 35 mm) in an aluminium pipe (inner diameter: 142 mm; outer diameter: 175 mm) using MUT [2] (grey circles: transducer locations)

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Belt with actuators

Fig. 8.10. Wavemaker™ Pipe Screening System and its application for inspection of pipework in soil

Wavemaker™6 Pipe Screening System (Guided Ultrasonics Ltd.), Figure 8.10, and Teletest®7 (Plant Integrity Ltd.), Figure 8.11. The key parts of these products are the circumferential transducer belts (called sensing rings), each containing a certain number of PZT elements (for example in some engineering applications 16 PZT elements are hosted on a belt around pipe with a diameter of 76 mm, and 32 PZT elements for pipe diameters ranging from 50 mm to 200 mm). These transducer belts can be clamped onto the pipe at one end of a section, to activate cylindrical Lamb waves and subsequently collect the echoed signals (in the pulse-echo configuration), by which damage (e.g., corrosion either at the inner or outer surface or in the pipe wall) along the pipeline can be located by measuring the ToFs and further be quantified by calibrating the reflection coefficient of damage-reflected waves in the echoed signals. In practical implementation more than one such belt can be applied and clamped at one end of a section of the pipeline. With the assistance of active mode selection techniques by virtue of multiple actuators (Section 3.3.1.2), these belts can activate relatively pure L(0,2) mode, axisymmetric or anti-axisymmetric (with a desired helical angle) along the pipe. The fast propagation speed of the L(0,2) mode in comparison to other cylindrical Lamb wave modes in a nondispersive frequency range of 40-100 kHz greatly facilitates signal processing [5]. 6

Wavemaker™ Pipe Screening System is a trademark of Guided Ultrasonics Ltd. http://www.guided-ultrasonics.com 7 Teletest® is a registered trademark of Plant Integrity Ltd, Granta Park, Great Abington, Cambridge, CB21 6GP, UK. http://www.plantintegrity.com

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Applications have demonstrated that damage identification techniques which take advantage of the ToF extracted from damage-reflected cylindrical Lamb wave signals can rapidly detect external or internal corrosion as well as axial and circumferential cracking in a section of pipeline of length up to 25 m in both directions, including pipes that are buried, insulated, filled with fluid or in service [4, 14, 15], although in the latter cases the detectable range normally becomes shorter since the pipe is often heavily coated with highly attenuative materials such as fresh bitumen. In engineering applications it is crucial for the system to differentiate actual damage from structural features such as welds or flanges which are part of the pipes. This problem can be circumvented by considering that a pipeline is in general axisymmetric but defects are not. If an axisymmetric wave encounters a structural feature such as a flange, axisymmetric properties are conserved and all the scattered waves are axisymmetric. In contrast, if an axisymmetric wave

a

b ®

Fig. 8.11. Teletest system and its application for inspection of pipework: a. transducer belt [19]; and b. a steel pipe clamped with a Teletest® transducer belt hosting 44 elements (each element having three transducers positioned in a line in the pipe axial direction) [17]

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encounters an asymmetric feature such as damage, both the axisymmetric and asymmetric modes are scattered [4]. By examining the axisymmetric and asymmetric properties of captured wave signals, the source of wave scattering, either structural feature or damage, can be identified [4]. 8.3.2 Identification of Damage in Aerospace Structures

Under high cyclic loads and in corrosive environments, an airframe often presents various types of damage including fatigue cracks, corrosion, and debonding or delamination if it is made of fibre-reinforced composites. In particular, cracks may initiate from the rivet holes or cut-outs (open holes, etc.) for joints, bolts, fasteners and lugs, as a consequence of stress concentrations associated with abrupt changes in geometry. These cracks often propagate across the panel, stiffeners, ribs or spars, and are observed in the wing and fuselage. According to the American Joint Air Force contract ‘Smart Structures Concept Requirements’ (SSCORE) [21], a functional damage identification or SHM system for military aircraft should be capable of reliably detecting cracks of 1.25 mm in length in geometrically complex parts, close to fastener holes, apertures and sharp edges. Aerospace structures are often formed with thin walls and are thus good waveguides for Lamb wave propagation. Hence Lamb waves have increasingly been investigated as tools for the development of damage identification and SHM techniques that could be integrated to aircraft model structures or key components including fuselage [21, 22], wing section structures [23-31], wing-box [28, 32, 33], stiffened components [34-36], ribbed aluminium aircraft skins [37], riveted fuselage joints [38], skin-to-spar parts [39-41], adhesively bonded structures of Boeing B-737®8 [42] and unmanned aerial vehicles [39], bolted thermal protection panels [43], ageing and fatigue components [23, 27, 35, 38, 44-48], rocket engines [49], GLARE composites [50], pendulum yoke [51], etc. Three approaches, using ToF (Section 6.2.2), damage index (DI, Section 6.2.1) and probability-based diagnostic imaging (Section 6.2.6), respectively, are briefly described here. 8.3.2.1 ToF Using a series of active PZT wafers affixed to aircraft parts of interest to activate and collect Lamb wave signals, damage, if any, can in principle be located by measuring the ToF of damage-reflected waves in echoed signals (in the pulse-echo configuration), and its severity can be estimated by calibrating changes in the magnitude (or energy) of transmitted signals (in the pitch-catch configuration) in relation to baseline signals. For example, to identify a crack near rivets of an ageing aircraft lap-splice joint panel [23, 27], a transducer array comprised of three PZT wafers is surfacemounted on the panel, Figure 8.12(a). When one PZT element in the array activates the diagnostic signal, the rest serve as sensors to capture Lamb waves propagating in the panel. Crack-induced extra Lamb waves can be clearly observed by collimating the captured signals with benchmark signals, Figure 8.12(b). With the ToF of the extra wave in the differentiated signal, the crack can be located using the ToF-based identification algorithm (Section 6.2.2). 8

Boeing B-737® is a registered trademark of Boeing Co. http://www.boeing.com

Identification of Damage Using Lamb Waves

Amplitude of signal [mV]

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a

b

Fig. 8.12. Identification of a crack in an ageing aircraft lap-splice joint panel: a. partial of the panel with sensor array and crack near rivet; b. difference between the present and baseline signals [27]

8.3.2.2 DI DI-based interpolation/extrapolation (Section 6.2.1) is a straightforward approach for evaluating the severity of damage. As an example, for evaluating impact delamination in a stiffener-reinforced carbon-epoxy flap of an aircraft in conjunction with use of a surface-bonded active piezoelectric sensor network, in Figure 8.13 [34], a DI in the frequency domain (defined by Equation 5.38) is established in terms of the fast Fourier transform coefficients (Section 5.2.2.1) of captured Lamb wave signals. When the DI of signals, acquired from a structure under inspection with an unknown damage state, exceeds a preset threshold, damage is suspected to exist. Similarly, to monitor crack growth in the riveted lap joint of a fuselage panel of an aircraft, a DI in the joint time-frequency domain (defined by Equation 5.40) is introduced using the short-time Fourier transform (STFT, Section 5.2.3.1) [22, 48]. Variation of the DI subject to the length of a crack in the riveted lap joint is displayed in Figure 8.14, whereby the crack growth in the fuselage panel can be monitored by interpolating into the relationship the DIs of signals captured from the panel with an unknown damage state. Using the same DI, the work is extended to evaluate growth of multiple fatigue cracks at riveted fuselage joints and cracks beneath a metallic panel repaired with a bonded composite patch, Figure 8.15 [38]. To activate diagnostic Lamb waves and capture damage-scattered signals, two strips of SMART Layer®9 (Section 4.5.3) are surface-mounted on these structures. Furthermore, through comparison of the identification results obtained using the A0 and S0 modes as the diagnostic signals, respectively, this application confirms that the A0 mode is more sensitive to debonding of composite patch than the S0 mode.

9

SMART Layer® is a registered trademark of Acellent Technologies, Inc. 835 Stewart Dr. Sunnyvale, CA 94085, USA. http://www.acellent.com

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STFT-based DI

Fig. 8.13. Stiffener-reinforced carbon/epoxy flap of an aircraft under delamination inspection [34]

Crack length [mm]

Fig. 8.14. DI based on STFT of Lamb wave signals vs. length of a crack in a fuselage panel of an aircraft [22]

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Rivet

Rivet

a

Rivets SMART layers Rivets

b Fig. 8.15. a. A fuselage lap joint with two strips of surface-bonded SMART Layer®; and b. zoomed-in part with affixed SMART layers [38]

A hybrid SHM system has been developed for a wing-box using PZT arrayactivated and fibre Bragg grating (FBG) sensor-received Lamb waves (so-called multi-agent technique) [28]. The wing-box system, Figure 8.16, measures 1000 mm × 1800 mm × 200 mm. Its top skin is made of carbon fibre-reinforced composite materials while the bottom skin is aluminium alloy, both fastened onto a steel box frame. On the skin six T-shape stiffeners are spaced 130 mm apart. Eight SMART layers, each having three PZT wafers (8 mm in diameter and 0.8 mm in thickness), are surface-bonded on the inner surface of the carbon fibre skin, and another eight SMART layers, each having four FBG sensors, are mounted on the inner surface of the aluminium skin, providing in total 68 sensing paths.

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b

FBG SMART layers

PZT SMART layers

c Fig. 8.16. An aircraft wing-box structure under damage inspection: a. aluminium wing-box skin; b. carbon fibre-reinforced composite wing-box skin; and c. skin dimension and distribution of hybrid SMART layers [28]

To estimate damage, a DI in the time domain (defined by Equation 5.32) is introduced by taking into account changes in both the magnitude and ToF of captured signals, which is then linked with damage parameters (presence and location). In addition, wireless sensors with on-board microprocessors are integrated into the system for data transmission. Wireless agents locally complete a portion of signal processing and data fusion in parallel, reducing the overall load in transmitting signals to the central computer. This initiative is an important step towards practical deployment of a SHM technique in aircraft structures.

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Pressurised vessels such as pipes in liquid rocket engines may fail due to causes such as serious corrosion, pitting, seam weld cracks and dents. Timely awareness of the damage and subsequent monitoring of its growth is of vital importance for maintaining the functionality of the rocket engines. For monitoring crack growth in a rocket engine pipe, two strips of SMART Layer® each having eight PZT elements are surface-mounted on the outer surface of the pipe, Figure 8.17 [49], and then instrumented with an active diagnostic system which is comprised of portable diagnostic hardware and data analysis software. A DI in the joint time-frequency domain (Equation 5.40) is applied and a relationship between the DI and the crack length in the pipe is established. The DIs of signals captured from a pipe with unclear damage state can be interpolated into the relationship to estimate the crack length. Using this technique, surface cracks as small as 4 mm in length and through-thickness cracks as small as 2 mm in length, both in high pressure engine pipes (152.4 mm in diameter, 1470 mm in length and 3.2 mm in thickness) are detected. This application recapitulates the observation that the A0 mode outperforms the S0 mode in terms of accuracy for detecting cracks due to its smaller wavelength.

Fig. 8.17. A rocket engine pipe with surface-bonded SMART layers for monitoring growth of crack in the pipe [49]

8.3.2.3 Probability-based Diagnostic Imaging To identify loose of rivet or defect near the wing rivet of an aircraft structure made of aluminium alloys and coated with paint, Figure 8.18, a probability-based diagnostic imaging technique in terms of signal correlation (Section 6.2.6.4) is employed [24, 25]. In this application, the S0 mode at a central frequency of 350 kHz is activated as the diagnostic signal. The field value at each pixel of the probability image is defined by Equation 6.20, based on the signal correlation coefficients and the distance from the pixel to the sensing paths. The probability image as to the presence of damage across the inspection area near the rivet hole is

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delineated and exhibited in Figure 8.19, in which the circled area, with a higher probability of damage presence at the pixels involved, highlights the damage, a 3 mm notch. In addition, wireless signal transmission technique is used in this application.

a

b

Fig. 8.18. a. An aircraft wing section under damage inspection; b. a notch near a rivet hole in the wing section [24]

Plate y-dimension [mm]

Sensor

Sensor

Sensor

Sensor Predicted damage

Sensor Sensor

Sensor

Sensor

Plate x-dimension [mm]

Fig. 8.19. Probability image across inspection area near the rivet hole of the wing section (actual damage: 3 mm notch; dotted area: the area containing pixels of higher field values, i.e., higher probability of damage presence) [24]

To identify damage in the aluminium panel of an aircraft structure (measuring 508 mm × 508 mm × 1.02 mm), a probability-based diagnostic imaging technique in terms of signal magnitude (Section 6.2.6.2) is employed [22]. To improve the efficiency of this approach the damage-scattered Lamb wave signals are preprocessed using the STFT (Section 5.2.3.1) to produce an envelope of the signal magnitude associated with energy, for establishing the field value (Equation 6.17b). Lamb wave signals are captured using four PZT wafers surface-bonded on

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Identification of Damage Using Lamb Waves

the panel. Extending this approach to a complex aircraft composite panel (measuring 762 mm × 762 mm), a SMART Layer® consisting of 30 PZT wafers is surface-mounted on the inner (bottom) side of the panel, Figure 8.20. Probability images as to the presence of disturbance to the structure (including damage) are displayed in Figure 8.21. The size of damage is further roughly estimated by drawing the smallest circle that connects the two major scattering locations highlighted in the image, assuming that the damage is circular.

762 mm

762 mm

Fig. 8.20. An aircraft composite panel with stiffeners under damage inspection, surfacebonded with a SMART Layer® consisting of 30 PZT elements [22]

During the application of Lamb-wave-based damage detection to large aircraft structures it has been found that identification relying on wave propagation beyond 1 m is not feasible, since the attenuation of the wave over the distance of 1 m is likely to be above circa 40 db/m [21]. A sensor network comprised of a certain number of sensors such as PZT elements to shorten the sensing path can be a solution, by which means identification is conducted locally and an overall estimate of the health status in the structure can subsequently be provided by aggregating individual local information. 8.3.3 Evaluation of Integrity of Civil Infrastructure

Civil infrastructure deteriorates at an alarming rate because of ageing. With recent technical breakthroughs such as sensing/actuating patch techniques, guided waves including Lamb waves have been increasingly introduced to detect damage and evaluate integrity of bulky civil infrastructure [52-59], exemplified by the identification of damage in a steel bridge [60, 61], in the welded zone of truss

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structures [62], in heat exchanger tubing [63] and in nuclear steam generator tubing [64]. Because of the large bulk of infrastructure such as a bridge deck, much greater power is usually required to activate guided waves using an in situ actuator to insure that the incident diagnostic waves carry sufficient energy to travel a reasonably broad inspection area and penetrate through the bulky structure. This is the reason why a pulse signal with intensive energy rather than windowed tonebursts is often employed in these applications.

Plate y-dimension

PZT in SMART Layer®

Plate x-dimension

Plate y-dimension

a

Plate x-dimension

b Fig. 8.21. Identification results for a. added mass (an aluminium cylinder with a diameter of 28 mm); and b. fracture damage (right: the results from C-scan), in an aircraft composite panel, obtained using a probability-based diagnostic imaging approach [22]

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In the technique for rehabilitation of ageing infrastructure using composite patches, disbonding of carbon fibre-reinforced composite repair patches from host structures continues to be a great concern. To monitor the disbonding between composite repair patches (150 mm in width and 1730 mm in length) and the lower surface of a deck slab of a steel-reinforced concrete bridge, a Lamb-wave-based integrity monitoring system has been developed [61]. This system consists of three SMART layers, diagnostic hardware and data analysis software (ACESSTM10, introduced in Section 4.5.3). Three SMART layers each having eight PZT elements (6.35 mm in diameter and 0.25 mm in thickness), 178 mm apart along the length, are surface-bonded on the composite repair patches, Figure 8.22. SMART layers

Repair patch

Deck slab

Fig. 8.22. The deck slab of a steel-reinforced concrete bridge, surface-bonded with composite repair patches and SMART layers [61]

A DI in the time domain (defined by Equation 5.34c) is applied [61]. Detection of disbonding is carried out while the bridge is in service. When a sensing path is affected in the presence of disbonding, a prominent increase in the DI can be observed. Such increases in DIs, extracted from signals sensed by individual sensing paths in the SMART layers, are then aggregated to construct a probability image, Figure 8.23, intuitively showing the location and rough size of the disbonding of patches (the size of disbonding can be estimated by highlighting pixels whose field values exceed a preset threshold).

10

ACESS™ is a trademark of Acellent Technologies, Inc. 835 Stewart Dr. Sunnyvale, CA 94085, USA. http://www.acellent.com

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Load: 400 kN

Load: 578 kN

Load: 666 kN

Load: 757 kN

Load: 846 kN

Load: 934 kN

Fig. 8.23. Identification results for disbonding of composite repair patch from bridge deck slab under different loads, obtained using a probability-based diagnostic imaging approach [61]

Similarly, for monitoring the growth of a fatigue crack in a steel bridge member (150 mm × 150 mm × 530 mm) which simulates the vertical truss member of the Seongsu Bridge, Seoul, Korea, which collapsed in 1994, two PZT patches in the pitch-catch configuration are surface-mounted on the member to activate and capture the A0 mode. The steel bridge member consists of two segments with wide flange sections of different thicknesses welded together. Fatigue cracks often develop in the welded zone, potentially causing severance of the member. A DI in the joint time-frequency domain (defined by Equation 5.42) is introduced in terms of the coefficients of continuous wavelet transform (CWT, Section 5.3.1) extracted from captured Lamb wave signals [60, 62]. The DI is then linked with the lengths of the fatigue cracks, in Figure 8.24. When a DI is extracted from signals captured from a bridge member with an unknown damage state, it is interpolated into the relationship to estimate the crack length.

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Damage index

324

Length of growing crack [mm]

Fig. 8.24. DI based on CWT coefficients of Lamb wave signals vs. length of a crack in a steel bridge member [60]

8.4 Summary Damage identification and SHM techniques using Lamb waves have been incorporated in a number of engineering applications, with the potential to play a significant role in enhancing the integrity and preventing failure of engineering structures. Because Lamb waves exist only in thin plate/shell structures, application of this emerging technique is usually confined to engineering structures featuring low thickness such as thin-walled pipes and panels in aircraft. During implementation, the identification algorithms introduced in Chapter 6 can be applied. In particular, ToF-based triangulation and DI-based interpolation/extrapolation are cost-effective means of locating damage and estimating its severity, respectively. Some integrated systems have been commercialised, represented by the Wavemaker™ Pipe Screening System and the SMART Layer® technique, demonstrating the great potential for application of Lamb-wave-based damage identification in various industrial sectors.

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References 1. Leonard, K.R., Hinders, M.K.: Guided wave helical ultrasonic tomography of pipes. Journal of the Acoustical Society of America 114(2), 767–774 (2003) 2. Leonard, K.R., Hinders, M.K.: Lamb wave tomography of pipe-like structures. Ultrasonics 43, 574–583 (2005) 3. Lowe, M.J.S., Alleyne, D.N., Cawley, P.: Defect detection in pipes using guided waves. Ultrasonics 36, 147–154 (1998) 4. Alleyne, D.N., Pavlakovic, B., Lowe, M.J.S., Cawley, P.: Rapid long-range inspection of chemical plant pipework using guided waves. Insight 43(2), 93–96 (2001) 5. Alleyne, D.N., Cawley, P.: The excitation of Lamb waves in pipes using dry-coupled piezoelectric transducers. Journal of Nondestructive Evaluation 15(1), 11–20 (1996) 6. Alleyne, D.N., Cawley, P.: Long range propagation of Lamb waves in chemical plant pipework. Materials Evaluation 55, 504–508 (1997) 7. Alleyne, D.N., Cawley, P., Lank, A.M., Mudge, P.J.: The Lamb wave inspection of chemical plant pipework. In: Thompson, D.O., Chimenti, D.E. (eds.) Review of Progress in Quantitative Nondestructive Evaluation, vol. 16, pp. 1269–1276. Plenum Press, New York (1997) 8. Lu, Y., Ye, L., Wang, D., Zhou, L.-M., Cheng, L.: Piezo-activated guided wave propagation and interaction with damage in tubular structures. Submitted to Smart Structures and Systems 9. Rose, J.L., Jiao, D., Spanner Jr., J.: Ultrasonic guided wave NDE for piping. Materials Evaluation 54(11), 1310–1313 (1996) 10. Quarry, M.J., Rose, J.L.: Multimode guided wave inspection of piping using comb transducers. Materials Evaluation 57, 1089–1090 (1999) 11. Sun, Z., Rose, J.L., Quarry, M., Chin, D.: Flexural mode tuning in pipe inspection. In: Thompson, D.O., Chimenti, D.E. (eds.) Review of Progress in Quantitative Nondestructive Evaluation, vol. 21, pp. 262–269. American Institute of Physics, New York (2002) 12. Rose, J.L.: A baseline and vision of ultrasonic guided wave inspection potential. Journal of Pressure Vessel Technology 124, 273–282 (2002) 13. Alleyne, D.N., Lowe, M.J.S., Cawley, P.: The reflection of guided waves from circumferential notches in pipes. Journal of Applied Mechanics 65, 635–641 (1998) 14. Long, R., Lowe, M., Cawley, P.: Attenuation characteristics of the fundamental modes that propagate in buried iron water pipes. Ultrasonics 41, 509–519 (2003) 15. Na, W.-B., Kundu, T.: Underwater pipeline inspection using guided waves. Journal of Pressure Vessel Technology 124, 196–200 (2002) 16. Zhang, L., Gavigan, B.J., Rose, J.L.: High frequency guided wave natural focusing pipe inspection with frequency and angle tuning. Journal of Pressure Vessel Technology 128, 433–438 (2006) 17. Sun, Z., Zhang, L., Rose, J.L.: Flexural torsional guided wave mechanics and focusing in pipe. Journal of Pressure Vessel Technology 127, 471–478 (2005) 18. Tua, P.S., Quek, S.T., Wang, Q.: Detection of cracks in cylindrical pipes and plates using piezo-actuated Lamb waves. Smart Materials and Structures 14, 1325–1342 (2005) 19. Siqueira, M.H.S., Gatts, C.E.N., da Silva, R.R., Rebello, J.M.A.: The use of ultrasonic guided waves and wavelets analysis in pipe inspection. Ultrasonics 41, 785–797 (2004)

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20. Hinders, M.: Guided wave helical ultrasound tomography of pipes and tubes, http://www.as.wm.edu/Faculty/Hinders/HUT-W&M.pdf 21. Dalton, R.P., Cawley, P., Lowe, M.S.J.: The potential of guided waves for monitoring large areas of metallic aircraft fuselage structure. Journal of Nondestructive Evaluation 20(1), 29–46 (2001) 22. Ihn, J.-B., Chang, F.-K.: Pitch-catch active sensing methods in structural health monitoring for aircraft structures. Structural Health Monitoring: An International Journal 7(1), 5–19 (2008) 23. Giurgiutiu, V., Zagrai, A., Bao, J.: Piezoelectric wafer embedded active sensors for aging aircraft structural health monitoring. Structural Health Monitoring: An International Journal 1, 41–61 (2002) 24. Zhao, X., Gao, H., Zhang, G., Ayhan, B., Yan, F., Kwan, C., Rose, J.L.: Active health monitoring of an aircraft wing with embedded piezoelectric sensor/actuator network: I. defect detection, localization and growth monitoring. Smart Materials and Structures 16, 1208–1217 (2007) 25. Zhao, X., Qian, T., Mei, G., Kwan, C., Zane, R., Walsh, C., Paing, T., Popovic, Z.: Active health monitoring of an aircraft wing with an embedded piezoelectric sensor/actuator network: II. wireless approaches. Smart Materials and Structures 16, 1218–1225 (2007) 26. Silva, M.Z., Gouyon, R., Lepoutre, F.: Hidden corrosion detection in aircraft aluminum structures using laser ultrasonics and wavelet transform signal analysis. Ultrasonics 41, 301–305 (2003) 27. Giurgiutiu, V., Zagrai, A., Bao, J.: Damage identification in aging aircraft structures with piezoelectric wafer active sensors. Journal of Intelligent Material Systems and Structures 15, 673–687 (2004) 28. Yuan, S., Liang, D., Shi, L., Zhao, X., Wu, J., Li, G., Qiu, L.: Recent progress on distributed structural health monitoring research at NUAA. Journal of Intelligent Material Systems and Structures 19, 373–386 (2008) 29. Lee, J.-R., Ryu, C.-Y., Koo, B.-Y., Kang, S.-G., Hong, C.-S., Kim, C.-G.: In-flight health monitoring of a subscale wing using a fiber Bragg grating sensor system. Smart Materials and Structures 12, 147–155 (2003) 30. Harri, K., Guillaume, P., Vanlanduit, S.: On-line damage detection on a wing panel using transmission of multisine ultrasonic waves. NDT&E International 41(4), 312– 317 (2008) 31. Wong, C.K.W., Chiu, W.K., Rajic, N., Galea, S.C.: Can stress waves be used for monitoring sub-surface defects in repaired structures? Composite Structures 76, 199– 208 (2006) 32. Chen, H.G., Yan, Y.J., Chen, W.H., Jiang, J.S., Yu, L., Wu, Z.Y.: Early damage detection in composite wingbox structures using Hilbert-Huang transform and genetic algorithm. Structural Health Monitoring: An International Journal 6(4), 281–297 (2007) 33. Grondel, S., Assaad, J., Delebarre, C., Moulin, E.: Health monitoring of a composite wingbox structure. Ultrasonics 42, 819–824 (2004) 34. Monnier, T.: Lamb waves-based impact damage monitoring of a stiffened aircraft panel using piezoelectric transducers. Journal of Intelligent Material Systems and Structures 17, 411–421 (2006) 35. Giurgiutiu, V., Zagrai, A., Bao, J.: Embedded active sensors for in-situ structural health monitoring of thin-wall structures. Journal of Pressure Vessel Technology 124, 293–302 (2002)

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36. Schwartz, W.G., Read, M.E., Kremer, M.J., Hinders, M.K., Smith, B.T.: Lamb wave tomographic imaging system for aircraft structural health assessment. In: Proceedings of the SPIE, vol. 3586, pp. 292–296 (1999) 37. Hay, T.R., Royer, R.L., Gao, H., Zhao, X., Rose, J.L.: A comparison of embedded sensor Lamb wave ultrasonic tomography approaches for material loss detection. Smart Materials and Structures 15, 946–951 (2006) 38. Ihn, J.-B., Chang, F.-K.: Detection and monitoring of hidden fatigue crack growth using a built-in piezoelectric sensor/actuator network: II. validation using riveted joints and repair patches. Smart Materials and Structures 13, 621–630 (2004) 39. di Scalea, F.L., Matt, H., Bartoli, I., Coccia, S., Park, G., Farrar, C.: Health monitoring of UAV wing skin-to-spar joints using guided waves and macro fiber composite transducers. Journal of Intelligent Material Systems and Structures 18, 373–388 (2007) 40. Matt, H., Marzani, A., Restivo, G., Oliver, J., di Scalea, F.L., Kosmatka, J., Sohn, H., Park, G., Farrar, C.: A guided-wave system for monitoring the wing skin-to-spar bond in unmanned aerial vehicles. In: Proceedings of the 23rd International Modal Analysis Conference (IMAC), Orlando, FL, USA, January 31- February 3 (2005) 41. Matt, H., Bartoli, I., di Scalea, F.L.: Ultrasonic guided wave monitoring of composite wing skin-to-spar bonded joints in aerospace structures. Journal of the Acoustical Society of America 118, 2240–2252 (2005) 42. Rose, J.L., Rajana, K.M., Hansch, K.T.: Ultrasonic guided waves for NDE of adhesively bonded structures. Journal of Adhesion 50, 71–82 (1995) 43. Yang, J., Chang, F.-K., Derriso, M.M.: Design of a built-in health monitoring system for thermal protection panels. In: Proceedings of the SPIE, vol. 5046, pp. 59–70 (2003) 44. Giurgiutiu, V., Zagrai, A.N., Bao, J., Redmond, J.M., Roach, D., Rackow, K.: Active sensors for health monitoring of aging aerospace structures. International Journal of Condition Monitoring and Diagnostic Engineering Management 6(1), 3–21 (2003) 45. Monnier, T., Jayet, Y., Guy, P., Baboux, J.C.: Aging and damage assessment of composite structures using embedded piezoelectric sensors. In: Thompson, D.O., Chimenti, D.E. (eds.) Review of Progress in Quantitative Nondestructive Evaluation, vol. 19, pp. 1269–1276. Springer, Heidelberg (2000) 46. Sealea, M.D., Smith, B.T., Prosser, W.H.: Lamb wave assessment of fatigue and thermal damage in composites. Journal of the Acoustical Society of America 103(5), 2416–2424 (1998) 47. Grondel, S., Delebarre, C., Assaad, J., Dupuis, J.-P., Reithler, L.: Fatigue crack monitoring of riveted aluminium strap joins by Lamb wave analysis and acoustic emission measurement techniques. NDT&E International 35, 137–146 (2002) 48. Ihn, J.-B., Chang, F.-K.: Detection and monitoring of hidden fatigue crack growth using a built-in piezoelectric sensor/actuator network: I. diagnostics. Smart Materials and Structures 13, 609–620 (2004) 49. Qing, X.P., Chan, H.-L., Beard, S.J., Kumar, A.: An active diagnostic system for structural health monitoring of rocket engines. Journal of Intelligent Material Systems and Structures 17, 619–628 (2006) 50. Demcenko, A., Zukauskas, E., Kazys, R., Voleisis, A.: Investigation of interaction of the Lamb wave with delamination type defect in GLARE composite using air-coupled ultrasonic technique. In: Proceedings of the Forum Acusticum, pp. 2817–2822 (2005) 51. Edmonds, J., Hickman, G.A.: Damage detection and identification in composite aircraft components. In: Proceedings of the IEEE Conference on Aerospace, Big Sky, MT, USA, March 18-25, 2000, pp. 263–269 (2000)

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52. Beard, M.D., Lowe, M., Cawley, P.: Development of a guided wave inspection technique for rock bolts. Insight 44(1), 19–24 (2002) 53. Pu, S.H., Cegla, F., Drozdz, M., Lowe, M.J.S., Cawley, P., Buenfeld, N.R.: Monitoring the setting and early hardening of concrete using an ultrasonic waveguide. Insight 46(6), 350–354 (2004) 54. Rose, J.L., Avioli, M.J., Song, W.-J.: Application and potential of guided wave rail inspection. Insight 44(6), 353–358 (2002) 55. Wilcox, P., Evans, M., Pavlakovic, B., Alleyne, D.N., Vine, K., Cawley, P., Lowe, M.: Guided wave testing of rail. Insight 45(6), 413–420 (2003) 56. Barke, D., Chiu, W.K.: Structural health monitoring in the railway industry: a review. Structural Health Monitoring: An International Journal 4, 81–93 (2005) 57. Rizzo, P., di Scalea, F.L.: Feature extraction for defect detection in strands by guided ultrasonic waves. Structural Health Monitoring: An International Journal 5(3), 297– 308 (2006) 58. Wu, F., Chang, F.-K.: Debond detection using embedded piezoelectric elements for reinforced concrete structures - part I: experiment. Structural Health Monitoring: An International Journal 5(1), 5–15 (2006) 59. Wang, W.D.: Applications of guided wave techniques in the petrochemical industry. In: Thompson, D.O., Chimenti, D.E. (eds.) Review of Progress in Quantitative Nondestructive Evaluation, vol. 18A, pp. 277–284. Plenum Press, New York (1999) 60. Park, S., Yun, C.-B., Roh, Y., Lee, J.-J.: PZT-based active damage detection techniques for steel bridge components. Smart Materials and Structures 15, 957–966 (2006) 61. Wu, Z., Qing, X.P., Ghosh, K., Karbhar, V., Chang, F.-K.: Health monitoring of bonded composite repair in bridge rehabilitation. Smart Materials and Structures (in press) 62. Park, S., Yun, C.-B., Roh, Y.: Damage diagnostics on a welded zone of a steel truss member using an active sensing network system. NDT&E International 40, 71–76 (2007) 63. Silk, M.G., Bainton, K.F.: The propagation in metal tubing of ultrasonic wave modes equivalent to Lamb waves. Ultrasonics 17, 11–19 (1979) 64. Rose, J.L., Ditri, J.J., Pilarski, A., Rajana, K., Carr, F.T.: A guided wave inspection technique for nuclear steam generator tubing. NDT&E International 27, 307–310 (1994)

9 Looking Forward

9.1 State of the Art Lamb waves are guided waves that propagate in thin plate/shell structures. Taking advantage of recent advances and technical breakthroughs in sensor technology, manufacturing, electronic packaging, signal processing, informatics, diagnostics, applied mechanics and material sciences, damage identification and structural health monitoring (SHM) techniques using Lamb waves have been the subject of intensive research and development in the past decades. Now on the verge of maturity for diverse engineering applications, this emerging technique has exciting potential to facilitate continuous and automated surveillance of the integrity of engineering structures in a cost-effective manner. In this book, key aspects concerning understanding, developing and implementing Lamb-wave-based damage identification and SHM are elaborated from theoretical fundamentals to engineering applications. Although most of the discussion refers to Lamb waves, it can be also applied to other forms of guided waves. Some important conclusions were drawn in previous chapters and are recapitulated as follows: (i) Lamb waves feature low attenuation during propagation, strong penetration capability, fast propagation speed, omnidirectional dissemination, convenience of activation and acquisition, inexpensive implementation, low energy consumption and, most importantly, high sensitivity to structural damage/inhomogeneity even when it is small in size or lies beneath the structural surface, making Lamb waves an excellent candidate to develop cost-effective damage identification and SHM techniques; (ii) major impediments towards efficient implementation of Lamb-wave-based damage identification can be attributed to the co-existence of multiple wave modes, wave dispersion, uneven propagation in anisotropic media, vulnerability to ambient noise, etc., with resulting complexity of signal appearance and difficulty in signal interpretation; (iii) signal processing plays a pivotal role in extracting the signal features associated with damage (i.e., damage index). Wavelet transform (for denoising, decomposing and deploying a signal over the time-frequency Z. Su and L. Ye: Identification of Damage Using Lamb Waves, LNACM 48, pp. 329–340. springerlink.com © Springer-Verlag Berlin Heidelberg 2009

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domain), the Hilbert transform (for pinpointing the signal energy peak), time reversal (for improving the signal-to-noise ratio (SNR)), and digital damage fingerprints (DDF) (for extracting Lamb wave signal patterns) are some demonstrated approaches that can streamline processing of a Lamb wave signal; (iv) as well as signal processing, properly selecting a Lamb mode, optimally designing a diagnostic wave signal and appropriately collocating actuators and sensors are some measures to further benefit signal interpretation and enhance detectability; (v) transducers are diverse and, among available options, the piezoelectric element is a sort of active transducer able to activate and collect Lamb wave signals cost-effectively with high precision, whereas the fibre Bragg grating (FBG) sensor is a passive transducer for easy realisation of multi-point signal acquisition. The capacity of both transducers is somewhat subject to factors such as transducer shape, attachment manner to host structure, and direction of collocation. A hybrid arrangement using piezoelectric elements as wave actuators and FBG sensors as wave receivers can reap the benefit of their individual merits, while avoiding demerits. Light and small, both can be easily integrated into engineering structures as built-in transducers for realisation of on-line SHM; (vi) sensor networks have proved to be a thriving technique to facilitate realisation of Lamb-wave-based SHM for diverse engineering structures, by providing multiple signals containing rich information to define a damage event and thereby decreasing dependence of identification on a particular sensor or signal. A sensor network can significantly enhance the tolerance of an identification approach to noise and uncertainty in varying working conditions; (vii) quantitative identification of damage is a complex inverse inferential and data fusion procedure. Time-of-flight (ToF)-based triangulation is an explicit way to locate planar position of damage in a structure, and DI-based interpolation/extrapolation is a simple approach for evaluating severity of damage. Time reversal and beamforming in virtue of a sensor array technique (e.g., piezoelectric wafer active sensors (PWASs) [1]) can enhance the SNR of captured Lamb wave signals and then locate damage. There has been increasing interest in using imaging-based approaches to intuitionally delineate damage in a structure, typified by probability-based diagnostic imaging and Lamb wave tomography. Artificial intelligence has the capacity to associate extracted signal signatures (e.g., DDF) with damage parameters, while avoiding subjective canvassing of individual signals, although it often entails the high cost required for preparing a training database of sufficient depth; and (viii) in spite of the exponential proliferation of Lamb-wave-based damage identification techniques in recent years, most efforts to date have been of a theoretical, computational or experimental nature, and demonstrated success often remains in the laboratory. Practical applications of such techniques are mainly limited to specific engineering structures such as thin-walled pipelines and aircraft skins. The principal handicaps in this connection are (i) the

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complexity of real large-scale engineering structures with diverse geometries and structural attachments/inhomogeneity (e.g., stiffeners); and (ii) working conditions that are much more unpredictable than those in a laboratory.

9.2 Prospects In comparison with conventional nondestructive evaluation (NDE) techniques such as ultrasonic scan and radiography which have been well developed over decades, damage identification and SHM using Lamb waves have been in a stage of burgeoning development. With authors’ outlook upon further development of this technique for practical applications, it is envisioned that some fundamental and tactical issues will attract attention in the coming years. Interaction Between Lamb Waves and Structural Damage The underlining principle that allows identification of damage using Lamb waves relies on the interaction mechanisms between waves and damage, a mechanism that includes wave scattering and reflection. The former occurs when the size of damage is in the same scale as the wavelength of the incident diagnostic Lamb wave, whereas the latter occurs when the size of damage is much greater than the wavelength. It is well appreciated that damage in general has little influence on elastic wave propagation if its effective size is getting much smaller than half the wavelength. When applying the algorithms presented in Chapter 6 for identifying damage in a two-dimensional structure (e.g., a panel), it has been debatable whether the algorithms relying on damage-scattered/reflected waves can characterise the size or severity of the damage. For algorithms which use signal features irrelevant to the strength of scattered/reflected waves (e.g., magnitude or energy) such as ToFs, there is no clear mechanism to support the estimation of size or severity of damage. But if the damage is much larger than the wavelength (e.g., a long crack/notch or a large hole), ToFs extracted from scattered/reflected waves may locate sources of major scattering/reflection (e.g., tips of notch/crack or edges of hole), which may facilitate estimation of the size or severity of damage. On the other hand, with algorithms which use signal features relevant to the strength of scattered/reflected waves (e.g., magnitude, energy, or correlation coefficients with regard to baseline signals), one may be able to calibrate the size or severity of damage, based on the argument that the more severe the damage, the stronger the damage-scattered/reflected wave signals. Both scenarios, however, need quantitative elaboration in further studies. Higher-order Lamb Modes The majority of current approaches employ the lowest-order symmetric ( S 0 ) or anti-symmetric ( A0 ) Lamb modes, for convenience of activation and signal processing. For characterising smaller damage with acceptable accuracy, Lamb

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waves of smaller wavelength are preferred. One possible way is to increase the excitation frequency to achieve a smaller wavelength, and another way is to use higher-order Lamb modes such as S1 and A1 since they possess greater sensitivity to damage than the lowest-order modes [2]. As demonstrated [3], higher-order Lamb modes can facilitate identification of micro-damage caused by plastic deformation such as fatigue damage. However, the complexity of using higher-order modes can be attributed to two factors: (i) higher power requirements for activating wave modes with higher frequencies (higher-order modes exist in a higher frequency band only); and (ii) lack of efficient signal processing tools to screen the higher-order modes from other modes in a captured signal (high-order modes co-exist with loworder modes normally with faster propagation than S 0 and A0 ) [2]. The attractiveness of using higher-order Lamb modes provides an impetus for developing techniques to address these two concerns. Environmental Effects Most existing approaches for activating and receiving Lamb waves were developed with the scenario that the structure to which the transducers are affixed is placed in laboratory conditions with ideal environmental temperatures (2025°C). The effects of environmental temperature and moisture on the activation and acquisition of wave signals as well as wave propagation characteristics have not been of concern. It has been demonstrated that there is no particular need to apply corrections to compensate for a small change in ambient temperature in normal applications (Section 2.6). However, an engineering structure such as an aerospace vehicle may work intermittently in diverse environments with temperature fluctuations of hundreds of Celsius or more (e.g., day vs. night, high altitude vs. ground). For most approaches that use piezoelectric materials as actuators and sensors for Lamb wave activation and acquisition, the nonlinearity of piezoelectric properties, as a consequence of such prominent temperature variation, may substantially erode identification efficiency in the absence of correction to the algorithms developed for ‘ideal’ working conditions. A similar argument applies to moisture content that may vary significantly in diverse environments, changing characteristics of actuators and sensors affixed to engineering structures. Anisotropy of Medium One of the premises adopted for developing most Lamb-wave-based damage identification approaches is that materials in structural components are isotropic in nature. However, most metal alloys after extrusion or roll forming are likely to present certain structural anisotropy in mechanical properties (e.g., discrepancy of moduli of elasticity in different directions) because of directional grain flattening/orientation and other mechanisms. For fibre-reinforced composite laminates, anisotropic (or orthotropic) and unbalanced properties are important features. Many composite structures used in airframes are sandwiched such that

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the plates are supported by the synthetic core or honeycomb, imposing complex constraints to Lamb wave propagation [4-8]. Furthermore, most studies have focused on flat plates of uniform thickness or plates of little curvature, in spite of the fact that structural components in practice either vary in thickness or display a strong curvature in shape. The effect of anisotropy of medium (in both material and geometrical properties) on propagation characteristics of Lamb waves and its impact on algorithms of damage identification have not been well addressed. Multiple Damage The effectiveness of most existing approaches has been verified by identifying single damage in a structure. However, in practice an engineering structure is likely to evidence multiple instances of damage simultaneously. Rather than being a simple expansion from the approaches developed for single damage, qualitative or quantitative identification of multiple damage is a highly challenging topic. The principal impediments are twofold: (i) in comparison with the case of single damage, much more intricate scattering phenomena are often observed in captured Lamb wave signals. The wave packets scattered by different sites of damage considerably superpose and interfere with each other. This may become much severe in structures with irregular boundaries or when multiple damage sites are sufficiently close to each other. Under such a circumstance, to isolate each wave packet scattered by individual damage instances in a signal is a formidable task, and success is often achieved in a somewhat subjective manner at the discretion of the operator; and (ii) even if the above is not a concern in some cases, in principle, being the solutions to an inverse problem, the identification results for multiple damage can be uncertain or ambiguous. Apparently, it is possible that the appearance or extracted features of a wave signal captured from a structure with multiple damage are very similar to those from a structure with single damage of different location or severity. Thus, identification based on wave signals captured from few sensors may fail to ascertain the correct number of damage instances in the structure, not to mention the location and severity of individual damage. Some approaches virtually divide the structure under inspection into sub-regions using an appropriate sensor network and prior knowledge. Each small sub-region, enclosed by a certain number of sensors or crossed by a few sensing paths, is considered to hold single damage at most. For these sub-regions, normal damage identification algorithms introduced in Chapter 6 can be employed. However, it is axiomatic that such an approach will become deficient when multiple sites of damage are within the same sub-region or so close to each other to become ‘aggregated damage’, in which the concept of sub-regions cannot be applied, although in practice a finding of aggregated damage may be sufficient to meet the general purpose of damage identification. On the other hand, probability-based diagnostic imaging in conjunction with an active sensor network comprised of a certain number of sensors (or sensing paths) can be a solution towards identification of multiple damage, as introduced in

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Section 6.2.6 and applied in a proof-of-concept demonstration in Section 7.4. The wish to cost-effectively detect multiple structure damage will entail more efforts in the coming years. Hybrid Approaches Like other NDE methods, damage identification based on Lamb waves presents some problematic issues in development and implementation. To fully capture the beneficial aspects while avoiding the inefficiencies of individual approaches, hybrid damage identification techniques promise a new vista for researchers [914]. A hybrid damage identification technique can be developed by combining two or more available methods, whereby different identification mechanisms and models can be mixed in terms of actual requirements. For example, a modal analysis can be conducted first to globally perceive the presence of damage, followed by elastic wave-based scrutiny to locally characterise the damage. Such a hybrid endeavour may enhance the resolution and efficiency of identification while meeting diverse requirements in applications [9]. In another example [10], it has been demonstrated that the electro-mechanical-impedance-based method can identify the presence of damage in a near field, and the wave-based approach can then be triggered to efficiently identify more distant damage in a pulse-echo configuration. Thus the simultaneous utilisation of two approaches is able to completely cover the inspection area. But the automated switching of different methods is a tactical issue that need to be addressed, as is the development of ways to maximise the practical efficiency of hybrid approaches. Similar interest exists in developing a sensor network, in which diverse sensing agents are expected to constitute a hybrid sensor network. The hybrid piezoelectric actuator-optic sensor unit (Section 4.4) is an example. This would benefit minimisation of power consumption, reduction in cost and enhancement of activation/acquisition efficiency. Enhanced and Automated Signal Processing/Data Fusion Signal processing and data fusion play the most substantial role in delivering efficient and accurate identification of damage based on captured wave signals. The majority of the currently existing signal processing tools were developed for laboratory tests, which may not be very effective for application in the field. For example, during practical implementation of the Lamb-wave-based damage identification technique in large-scale structures, it has been observed that identification results are not sufficiently accurate when using information extracted from wave signals propagating for more than 1 m, since the attenuation of wave over the distance of 1 m is likely to be over about 40 db/m in some engineering structures [15], as a result of beam spreading. Under such a circumstance, the damage-scattered wave packets can easily be masked by background noise (the background noise, however, would not decrease with distance). Thus signals captured in the field often present a very complex appearance as a consequence of corruption by background noise. Further developmental work is needed on signal processing tools developed for the laboratory applications, so as to enhance their

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capability of filtering background noise and extracting essential damage-scattered wave components from noise-corrupted signals. On the other hand, damage identification based on fusion of Lamb wave signals inherently involves the themes of recognising, searching, solvability and uniqueness. Such an inverse inferential procedure may be somewhat subjective in most current approaches. To reduce dependence on the subjective judgment of individuals, fragmented signal analyses and manipulation should be avoided, replaced by automated signal processing and data fusion with less involvement of the operator. Ideally, the processing and fusion exercise would be automatically triggered and accomplished when signals are available. Independence of Benchmark As pointed out in Section 5.2.1.2, damage is a structural state different from the pristine state that is supposed to be healthy. That is to say, the states of damage and health are defined relatively; a damage event is not meaningful without a reference or comparison. Although it may not be explicitly stated, most existing approaches are primarily dependent on referencing or comparing the experimentally captured signals with the baseline signals obtained theoretically or experimentally from a benchmark counterpart that is assumed to be free of damage or in a prior state. However, during this process, any changes in working conditions or measurement noise, if they are not included in the baseline signals, may lead to false identification. Furthermore, baseline signals are not always obtainable. Thus the excessive reliance of algorithms on a benchmark may narrow their applicability. It is of vital importance in further studies to minimise such reliance through appropriate algorithms. It would be interesting to explore additional features in a wave signal captured from the structure under inspection such as the reversibility of the signal (Section 6.2.3), while avoid benchmarking or comparing a baseline signal. In additional, some other properties of sensors may be explored. For example, the polarised characteristics of piezoelectric wafers attached to the structure under inspection can be used to identify damage [16], in recognition of the fact that the presence of damage can create wave mode conversion and break down the symmetrical nature of signals captured by symmetrically allocated sensors. However, these features may be modulated not only by damage but also by structural inhomogeneity such as stiffeners, leading to difficulty in signal interpretation. Attempting to reduce the dependence on baseline information poses a challenge to the technology, and is worthy of further attention. Advanced Modelling Current research and development in damage identification using Lamb waves has been focused on certain representative structures such as beams and thin plates, with relatively simple geometry on a scale of 10-1-100 m. There have been few significant advances in solving practical problems on a large scale (101-103 m) that would allow the techniques to be deployed in real-world structures, despite a great deal of effort being directed to improvement in the practicability of such

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techniques. Experimental validation has been conducted for specimens in laboratory using a limited number of sensors, in which the sensors were strategically positioned distant from the specimen boundaries to minimise wave interference and distortion due to boundary reflection. Many studies have attempted to find optimal locations for sensors or to use dense populations of sensors over small structural areas so as to improve the efficiency of identification. Some researchers [17] hold the opinion that the most significant limitations of the current damage identification methods are errors attributable to the difference between laboratory models and actual full-scale structures. For instance, Lamb wave signals in an aircraft fuselage skin, activated and collected using piezoelectric elements when the aircraft is flying, present much greater complexity in signal appearance, under the random turbulence and in a cryogenic environment, than those obtained in a laboratory. A clear understanding of the behaviour of guided waves in complex large-scale structures (e.g., aircraft fuselages with stiffeners and joints, pipelines and bridges of various geometries) is therefore essential. This may rely on advanced modelling and characterisation techniques of guided waves in these engineering structures. In addition, in most studies the models are linear and they are effective in detecting macro-discontinuities in materials such as cracks, voids or inclusions. But these linear techniques fail to account for structural behaviour in the nonlinear damage scenario†. For example, major studies have focused on the case of open cracks or delamination, where any nonlinearity due to physical crack closure was neglected; or they have assumed ‘machined notches’ as the cracks, and ‘inserts’ as debonding cracks or delamination. But it is envisaged that actual cracks normally display a perfect engagement between two separated surfaces, which can open and close depending on the loading mode [18]. The closure of cracks under load may substantially influence the characteristics of transmission, reflection, scattering and mode conversion of Lamb waves, in turn lowering identification accuracy. Another example of nonlinear damage identification is the monitoring of microdamage prior to formation of macro-crack such as fatigue cracks [3, 18]. A robust damage detection method should be able to quantitatively track damage before formation of macro-cracks, calling for efforts to develop advanced and enhanced modelling techniques to address the mechanisms involved. Novel Sensor and Sensor Network Initiatives The past two decades have witnessed an explosion of sensor technology. The majority of the today’s wave-based damage identification or SHM employs piezoelectric transducers, but their practical application may be limited due to particular features [2]: (i) being brittle, piezoelectric elements might easily lose functionality in field applications with demanding working conditions. In SHM, it is crucial that

†

A linear damage scenario is defined as the case in which an initially linear-elastic structure remains linear-elastic after damage; a nonlinear damage scenario is the case in which an initially linear-elastic structure behaves in a nonlinear manner after damage is introduced.

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the transducers should be able to survive unexpected events such as impact or collision; and (ii) piezoelectric materials clearly have a limited temperature range of operation (e.g., PZT-5A can resist temperatures as high as 175°C [19]), and their performance degrades significantly when the ambient temperature is high (over roughly half their Curie temperature) or low (in cryogenic environment). Recent advances in material science, manufacturing and bio-technology have yielded encouraging prospects for overcoming these problems of piezoelectric materials, further benefiting the development of novel sensors and sensor networks for damage identification and SHM in particular. For example, piezoelectric transducers that can resist very high working temperatures (up to 1210°C), made from lithium niobate, are being introduced in demanding applications such as SHM for aerospace vehicles. Sensors made of nanotubes have outperformed traditional piezoelectric sensors, and can be used in super-high temperature environments (up to 1000°C). Nanotube materials and piezo-nano-composites incorporate excellent structural properties with actuation-sensing capabilities, and offer extremely high strength and stiffness but low weight, together with characteristics of superelasticity, thermal stability and large strain actuation [20]. Bio-sensors are claiming an essential role in the new millennium in revolutionising SHM techniques. Modern bio-sensors with advanced microfabrication will become inexpensive and reliable, offering cost-efficient and accurate measurement. Another encouraging sensing device for damage identification is the sensor based on the micro-electro-mechanical system (MEMS) technique. MEMS sensors provide flexibility in design such that they can be optimised for a specific SHM activity. There is increasing preference for systems that can accommodate remote control and signal transmission in a wireless manner. Wireless-based research is now one of the most attractive funding areas in many countries. With wireless sensor network techniques still in their infancy, much work remains to be done on their use for deploying Lamb-wave-based damage identification and SHM in practice, such as improvement in data acquisition/transmission rate and reduction of energy consumption. Damage Prognosis A fully deployed SHM technique integrates identification of damage (diagnosis) with analysis of structural integrity (prognosis). Damage prognosis is the estimation of the remaining useful life and residual strength of an engineering structure. This estimation is based on a predictive model, which develops such estimate by aggregating information from usage surveillance, health monitoring, past, current and anticipated future operational conditions, design guidelines and criteria, failure theories, previous testing, etc. In some cases, ‘soft’ information such as the user’s ‘feeling’ about how the system is responding is also engaged in the aggregation when determining a damage prognosis solution [21]. Stated in another way, damage prognosis attempts to forecast system performance by measuring the current state of the system, estimating its future loading

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environments, and predicting through simulation and past experience the remaining useful life of the system. However, many unpredictable uncertainties in service can hinder the quantitative estimation of the impact of a damage event on the integrity of engineering structures. Relevant studies and in particular the development of sophisticated predictive models should be pursued. Integrated System and Robustness It comes to our attention that although the relevant theory for damage identification using guided waves is well developed, development of SHM techniques/systems has considerably lagged behind. At present, engineering structures are often designed to be overly conservative, to guarantee an adequate safety margin. Subsequently, damage identification or SHM is introduced if necessary. However, from a holistic viewpoint, the capacities of damage identification and in particular SHM or even structural rehabilitation (e.g., selfhealing) should be integrated into structures at the design and manufacture stages, being core ingredients of the structures from the onset rather than added appendages. For example, the new vision of National Aeronautics and Space Administration (NASA) and the European Space Agency (ESA) for the future of space activities brought to light a new space transportation system scenario, featuring an integrated vehicle health management system for ensuring vehicle safety and reliability as well as maximising crew survivability. Integrated SHM is an indispensable component in the new transportation system, rather than being added compensation. By comprehensive consideration of the functionality of an engineering structure with operational safety, a system with integrated SHM capacity can be optimally designed, fabricated and retrofitted. For example, piezoelectric materials have been used as actuation units for noise reduction in aircraft engines; by appropriate design and system integration, these piezoelectric materials can also be used as wave generators and receivers to implement wave-based damage identification or online SHM, while without the need to introduce additional transducers. As a result, an engineering system can be endowed with much resilience. One of the basic criteria of an integrated SHM technique is that it must be reliable, tolerable and robust in application. For example, nuances in the captured signals, because of measurement noise or the difference between a laboratory model and an actual structure, may be deemed by an algorithm a consequence of the presence of damage, leading to false characterisation. The long-term reliability and stability of a SHM technique/system in varying or even deteriorating working conditions is a key indicator for evaluating the capacity of the technique/system. This indicator is in particular accentuated for applications in long-life engineering systems such as bridges and offshore platforms. The desire for such reliability and stability has incurred additional requirements for damage identification and SHM techniques including tolerance to elevated temperatures or cryogenic environments, electromagnetic interference, humid and corrosive operation conditions, and human factors.

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References 1. Giurgiutiu, V.: Structural Health Monitoring with Piezoelectric Wafer Active Sensors. Elsevier Academic Press, Boston (2008) 2. Raghavan, A., Cesnik, C.E.S.: Review of guided-wave structural health monitoring. The Shock and Vibration Digest 39(2), 91–114 (2007) 3. Pruell, C., Kim, J.-Y., Qu, J., Jacobs, L.J.: Evaluation of fatigue damage using nonlinear guided waves. Smart Materials and Structures (in press) 4. Castaings, M., Hosten, B.: The propagation of guided waves in composite, sandwichlike structures and their use for NDT. In: Thompson, D.O., Chimenti, D.E. (eds.) Review of Progress in Quantitative Nondestructive Evaluation, vol. 20B, pp. 999– 1006. American Institute of Physics, New York (2001) 5. Kessler, S.S., Spearing, S.M., Soutis, C.: Structural health monitoring in composite materials using Lamb wave methods. In: Proceedings of the American Society for Composites, the 16th Technical Conference, Blacksburg, VA, USA, September 9-12 (2001) 6. Pierce, S.G., Culshaw, B., Manson, G., Worden, K., Staszewski, W.J.: The application of ultrasonic Lamb wave techniques to the evaluation of advanced composite structures. In: Claus, R.O., Spillman Jr., W.B. (eds.) Proceedings of the SPIE, vol. 3986, pp. 93–103 (2000) 7. Diamanti, K., Soutis, C., Hodgkinson, J.M.: Lamb waves for the non-destructive inspection of monolithic and sandwich composite beams. Composites: Part A 36, 189– 195 (2005) 8. Osmont, D., Barnoncel, D., Devillers, D., Dupont, M.: Health monitoring of sandwich plates based on the analysis of the interaction of Lamb waves with damages. In: Balageas, D. (ed.) Proceedings of the 1st European Workshop on Structural Health Monitoring, Paris, France, July 10-12, 2002, pp. 336–343. DEStech Publications, Inc (2002) 9. Mal, A.K., Banerjee, S., Ricci, F.: Automated structural health monitoring system using acoustic emission and modal data. In: Proceedings of the SPIE, vol. 5394, pp. 1– 10 (2004) 10. Giurgiutiu, V., Zagrai, A., Bao, J.: Damage identification in aging aircraft structures with piezoelectric wafer active sensors. Journal of Intelligent Material Systems and Structures 15, 673–687 (2004) 11. Kessler, S., Spearing, M.: Design of a piezoelectric-based structural health monitoring system for damage detection in composite materials. In: Proceedings of the SPIE, vol. 4701, pp. 86–96 (2002) 12. Osmont, D., Dupont, M., Gouyon, R., Lemistre, M., Balageas, D.: Piezoelectric transducer network for dual mode (active/passive) detection, localization and evaluation of impact damages in carbon/epoxy composite plates. In: Proceedings of the SPIE, vol. 4073, pp. 130–137 (2000) 13. Wait, J.R., Park, G., Sohn, H., Farrar, C.R.: Plate damage identification using wave propagation and impedance methods. In: Proceedings of the SPIE, vol. 5394, pp. 53– 65 (2004) 14. Monnier, T., Jayet, Y., Guy, P., Baboux, J.C.: Aging and damage assessment of composite structures using embedded piezoelectric sensors. In: Thompson, D.O., Chimenti, D.E. (eds.) Review of Progress in Quantitative Nondestructive Evaluation, vol. 19, pp. 1269–1276. Springer, Heidelberg (2000)

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15. Dalton, R.P., Cawley, P., Lowe, M.S.J.: The potential of guided waves for monitoring large areas of metallic aircraft fuselage structure. Journal of Nondestructive Evaluation 20(1), 29–46 (2001) 16. Kim, S.B., Sohn, H.: Instantaneous reference-free crack detection based on polarization characteristics of piezoelectric materials. Smart Materials and Structures 16, 2375–2387 (2007) 17. Friswell, M.I., Penny, J.E.T.: Is damage location using vibration measurements practical? - structural damage assessment using advanced signal processing procedures. In: Proceedings of the 2nd International Conference on Damage Assessment of Structures (DAMAS-1997), pp. 351–362. Sheffield Academic Press, Sheffield (1997) 18. Dutta, D., Sohn, H., Harries, K.A., Rizzo, P.: A nonlinear acoustic technique for crack detection in metallic structures. Structural Health Monitoring: An International Journal 8(3), 251–262 (2009) 19. http://www.physikinstrumente.com/ 20. Schulz, M.J., Sundaresan, M.J., McMichael, J., Clayton, D., Sadler, R., Nagel, B.: Piezoelectric materials at elevated temperature. Journal of Intelligent Material Systems and Structures 14, 693–705 (2003) 21. Inman, D.J., Farrar, C.R., Lopes Jr., V., Steffen Jr., V.: Damage Prognosis: for Aerospace, Civil and Mechanical Systems. John Wiley & Sons, Inc, Chichester (2005)

Index

ABAQUS® 35, 39, 85, 275, 279 Acellent Software Suite (ACESS™) 128, 322 ACESS™ see Acellent Software Suite acoustic emission 5 acoustic holography 1 acousto-ultrasonic 7 active fibre composites 61 analytical signal 145 ANN see artificial neural network anomaly detection see novelty detection ANSYS® 35 ART see tomography artificial intelligence 234, 330 artificial neural network (ANN) 235, 273, 277 backpropagation ANN 237, 276, 281 fast ANN training 291 feedforward backpropagation 237, 276, 281 hierarchical training 291 linear filter ANN 237 mean square error (MSE) 237, 282, 289 over-fitting 288, 291 over-training 285, 291 perception ANN 237 supervised training 237, 282 unsupervised training 237 attenuation 42, 334 attenuation coefficient 42

Bayesian inference (BI) 240, 292 likelihood function of BI 241 beam spreading 43, 334 beamforming 228, 330, also see phased-array grating lobe 233 main beam 233 main lobe 233 receiver beamforming 127, 229, 231 side lobe 233 transmitter beamforming 127, 229 transmitter focusing see transmitter beamforming wave steering 127, 229, 232 BI see Bayesian inference blind zone 306, 307 boundary element method 35 CDF see cumulative distribution function central control/analysis unit 302 characteristic function 33 Choi-Williams analysis 157 Cognitive-based model 195 Cooley-Tukey algorithm 152 creep wave 18 cumulative distribution function (CDF) 268 Curie temperature 109, 337 cut-off frequency 29, 103 CWT see wavelet transform cylindrical Lamb wave 24, 305, also see helical wave

342

Index

damage diagnostics 1, 2, 337 damage index 172, 199, 255, 314, 322, 329, 330 damage orientation influence 48 damage parameter database 183, 275, 280, 284, 287 damage prognosis 2, 337 data acquisition subsystem 301 data fusion 196, 241, 330 architecture 241 centralised architecture 241 compromised scheme 243, 272 conjunctive scheme 243, 272 decentralised architecture 241 disjunctive scheme 243 independent architecture 241 scheme 243 DDF see digital damage fingerprints degree of freedom 40, 279 diagnostic imaging see probability-based diagnostic imaging digital damage fingerprints (DDF) 181, 273, 275, 279, 330 digital signal filter 153 bandpass filter 153 band-stop filter 153 high-pass filter 153 low-pass filter 153 direct memory access 133 Disperse 34 dispersion 27 curve 29 equation 29, 31 equation for multi-layered structure 31 non-dispersion 29, 103 displacement potentials method 16 DWT see wavelet transform dye penetrant testing 1 eddy-current 1 effective elastic constant technique 34, 36, 85

effective independence algorithm 125 electro-mechanical-impedance-based damage identification 4, 334 EMAT see transducer Euler-Bernoulli beam 256 Fabry-Pérot interferometer 62 fast Fourier transform (FFT) 152 FBG see fibre Bragg grating feature vector pair 183 feature-based inference 195 FFT see fast Fourier transform fibre Bragg grating (FBG) 64, 110, 316, 330 directivity of FBG 117 embedding 116 FBG filter 64, 112 rosette technique 118 surface-bonding 116 wavelength 110 fibre-optic sensor 64, 100, 109 field value 219, 269, 271, 273 figure of merit 175 filter function 153 finite difference method 35 finite strip element method 35 Fisher information matrix 125 Fourier transform (FT) 152 discrete Fourier transform 152 inverse Fourier transform 152 frequency domain analysis 152 frequency response function 176 FT see Fourier transform GA see genetic algorithm Gauss’ theorem 84 Gaussian distribution function (GDF) 269 Gaussian pulse 150, 151 Gaussian quadrature formula 125 GDF see Gaussian distribution function genetic algorithm (GA) 125, 238 fitness function see objective function objective function 239

Index

helical wave 24, also see cylindrical Lamb wave Helmholtz decomposition 16, 22, 24 HELP Layer® 128 heterodyne interferometer 62 Hilbert transform 145, 224, 330 HUT see tomography hybrid piezoelectric actuator-optic sensor unit 119, 316, 334 hydrophone 6 IDT see transducer infrared thermography 1 inter-element distance 67 interferometric holography inscription 111 intrinsic dimension 181 inverse algorithm 195 inverse analysis see inverse problem inverse identification see inverse problem inverse problem 7, 195, 234 iterative root-finding 32 joint time-frequency domain analysis 155 Lamb wave leakage see leaky Lamb wave Lamé constant 16 large f ⋅ d problem 34 laser interferometer 100, also see laserbased ultrasonics laser interferometry 1, also see laser-based ultrasonics laser-based ultrasonics 62 leaky Lamb wave 22 longitudinal wave 17 velocity of longitudinal wave 19 Love wave 22 macro fibre composite 61, 131 magnetic resonance imagery 1 matching pursuit 158,164 matrix technique 33 global matrix method 34 transfer matrix method 33

343

MEMS see micro-electro-mechanical system micro-electro-mechanical system (MEMS) 64, 337 migration technique 209 Mindlin theory 73 minimum resolvable distance (MRD) 70 modal analysis 9, 10 modal-data-based damage identification 4 mode conversion 7, 41, 48, 86, 161, 202, 208, 275, 305, 335, 336 moisture influence 332 MRD see minimum resolvable distance MSE see artificial neural network multi-layered medium 22 multiple damage 248, 263, 268, 291, 333 MUT see tomography Navier’s displacement equation 22 nonlinear damage 336 novelty detection 291 optical coupler 113 optical fibre 9, 10, 109, also see fibre-optic sensor multimode fibre 109 single mode fibre 109 optical spectrum analyser 112 parameterised modelling technique 280 Patran® 35, 280 Patran® command language 280 pattern recognition 234 Paul Langévin experiment 6 PCA see principal component analysis PDF see probability density function phase mask inscription technique 111 phased-array 228, also see beamforming array aperture 234 array elements 228 photodetector 64, 112

344

Index

physical model 195 piezoceramic fibre 61 piezoelectric transducer/wafer 61 electro-mechanical constitutive equation of piezoelectric material 76 embedding 106 piezoelectric coefficient 102 piezoelectricity 101 polyvinylidene fluoride (PVDF) piezoelectric film 100, also see transducer strain constant 102 surface-mounting 76, 106 piezoelectric wafer active sensor (PWAS) 67, 126, 228, 330 pitch-catch 3, 7, 197, 273, 305, 306, 309, 313, 323 power-spectral-density (PSD) 71 primary damage 264 principal component 179, 181 principal component analysis (PCA) 179 probability density function (PDF) 269 probability-based diagnostic imaging 219, 268, 318, 322, 330, 333 PSD see power-spectral-density pulse-echo 3, 7, 197, 229, 259, 306, 309, 311, 313, 334 PVDF see piezoelectric transducer, also see transducer PWAS see piezoelectric wafer active sensor

radioscopy 1 Rayleigh wave 17 Rayleigh-Lamb equation 20 reflection coefficient 49, 166, 258, 306, 309 root mean square 144, 166 Sammon mapping 179 SAP see scale-averaged wavelet power scale-averaged wavelet power (SAP) 166

secondary damage 264 sensor network 121, 206, 336 large-scale sensor network 130 sensor network optimisation 123 standardised sensor network 126 SH see shear wave shear wave 17 group velocity of shear horizontal (SH) wave 26 phase velocity of shear horizontal (SH) wave 26 shear horizontal (SH) wave 22, 23, 86, 161, 275 shear vertical (SV) wave 23 velocity of shear wave 19 velocity of transverse wave see velocity of shear wave shearography 1 short-time Fourier transform (STFT) 156, 224 signal averaging asynchronous averaging 168 cyclic averaging 168 synchronous averaging 168 signal characteristic see signal feature signal compression 178 compression ratio 179 threshold-based linear compression 179 signal condensation see signal compression signal correlation 146, 175, 226, 263 auto-correlation 147 correlation coefficient 147 signal de-noising 170 signal feature 171 characteristic component 183 feature extraction 171 feature recognition see feature extraction model-based feature extraction 172, also see feature extraction non-characteristic component 183 signal-based feature extraction 172, also see feature extraction

Index

signal generation subsystem 301 signal normalisation 169 Min-Max normalisation 170 sigmoidal normalisation 170 Zscore normalisation 170 signal processing 144, 334 signal regression 144 signal smoothing 168 SIRT see tomography slowness 26, 31 slowness profile 26 SMART Layer® 128, 314, 316, 318, 320, 322 Snell’s law 33, 59 spectral element method 35 spectrogram 155 SSU see standard sensor unit standard sensor unit (SSU) 126, 300 state awareness 1 static-parameter-based damage identification 4 STFT see short-time Fourier transform Stonely wave 18 structural neural system 130 superficial dimension 181 SV see shear wave sweet spot 68 system for damage identification and structural health monitoring 299, 338

Teletest® 311 temperature compensation 48 temperature influence 47, 332 Thomson-Haskell method see matrix technique time domain analysis 144 time reversal 147, 175, 209, 330 time reversal for identifying damage 209 time reversal for improving quality of signal 147 time-of-flight (ToF) 144, 164, 171, 173, 197, 199, 209, 213, 219, 227, 229, 245, 259, 261, 263, 268, 306, 309, 313, 330, 331

345

ToF see time-of-flight tomogram 213 tomograph 213 tomography 213, 307, 330 cell velocity 214 crosshole projection 216, 307 fan beam projection see parallel beam projection helical ultrasound tomography (HUT) 308 iterative algebraic reconstruction technique (ART) 214 meridional ultrasonic tomography (MUT) 308 parallel beam projection 216, 307 simultaneous iterative reconstruction technique (SIRT) 214 transducer 100, 101 accelerometer 100 acoustic emission sensor 100 air/gas-coupled transducer 59 bio-sensor 337 comb ultrasonic probe 59 eddy-current transducer 100 electro-magnetic acoustic transducer (EMAT) 59, 100 fluid-coupled transducer 59 Hertzian contact probe 59 interdigital transducer (IDT) 62, 103 magnetic transducer 100 magnetostrictive transducer 64 piezocomposite transducer 61 polyvinylidene fluoride (PVDF) transducer 62, 100, 103, also see piezoelectric transducer shape memory alloy transducer 100 strain gauge 9, 10, 100 ultrasonic probe 59, 100 transducer shape influence 73 transmission coefficients 49, 166, 306 transverse wave see shear wave

346

Index

two-dimensional fast Fourier transform 154 two-dimensional Fourier transform 154 ultrasonic scanning 1 velocity cell velocity 214, also see tomography group velocity 25 group velocity of shear horizontal (SH) wave 26, also see shear wave phase velocity 25 phase velocity of shear horizontal (SH) wave 26, also see shear wave velocity of longitudinal wave 19, also see longitudinal wave velocity of shear wave 19, also see shear wave velocity of transverse wave see velocity of shear wave VXI platform, 300

wave mode selection 64, 65, 311, 330 wave mode tuning 65, 127, also see wave mode selection multi-sensor mode tuning technique 66 wavelet transform (WT) 158, 329 continuous wavelet transform (CWT) 159, 259, 262, 276, 281, 283, 323 discrete wavelet transform (DWT) 161, 262, 276, 283 inverse continuous wavelet transform 161 inverse discrete wavelet transform 163 wavelet function 159, 164 wavelet packet 163 Wavemaker™ Pipe Screening System 311 Wigner-Ville distribution transform 157 window function 69, 156, 223 wireless sensor 131, 317, 319, 337 WT see wavelet transform