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### More About This Title Structural Health Monitoring

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**Written by global leaders and pioneers in the field, this book is a must-have read for researchers, practicing engineers and university faculty working in SHM.**

*Structural Health Monitoring: A Machine Learning Perspective* is the first comprehensive book on the general problem of structural health monitoring. The authors, renowned experts in the field, consider structural health monitoring in a new manner by casting the problem in the context of a machine learning/statistical pattern recognition paradigm, first explaining the paradigm in general terms then explaining the process in detail with further insight provided via numerical and experimental studies of laboratory test specimens and *in-situ* structures. This paradigm provides a comprehensive framework for developing SHM solutions.

*Structural Health Monitoring: A Machine Learning Perspective* makes extensive use of the authors’ detailed surveys of the technical literature, the experience they have gained from teaching numerous courses on this subject, and the results of performing numerous analytical and experimental structural health monitoring studies.

- Considers structural health monitoring in a new manner by casting the problem in the context of a machine learning/statistical pattern recognition paradigm
- Emphasises an integrated approach to the development of structural health monitoring solutions by coupling the measurement hardware portion of the problem directly with the data interrogation algorithms
- Benefits from extensive use of the authors’ detailed surveys of 800 papers in the technical literature and the experience they have gained from teaching numerous short courses on this subject.

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**Charles R Farrar, Los Alamos National Laboratory, New Mexico, USA**is currently the director of The Engineering Institute at LANL. His research interests focus on developing integrated hardware and software solutions to structural health monitoring problems and the development of damage prognosis technology. The results of this research have been documented in 50 refereed journal articles, 14 book chapters, more than 100 conference papers, 31 Los Alamos Reports and numerous keynote lectures at international conferences. In 2000 he founded the Los Alamos Dynamics Summer School. His has recently received the inaugural Los Alamos Fellows Prize for Technical Leadership and the inaugural Lifetime Achievement Award in Structural Health Monitoring. He is currently working with engineering faculty at University of California, San Diego to develop the Los Alamos/UCSD Engineering Institute and Education Initiative with a research focus on Damage Prognosis. He is associate editor for the

*Int. Journal of Structural Health Monitoring and Earthquake Engineering and Structural Dynamics*.

**Keith Worden, University of Sheffield, UK** is Head of the Dynamics Research Group in the Department of Mechanical Engineering at the University of Sheffield. His research interests lie in the applications of advanced signal processing and machine learning methods to structural dynamics. He has authored over 400 research publications including two co-authored books on nonlinear structural dynamics and nonlinear system identification, two book chapters and over 130 refereed journal papers. He serves on the editorial boards of 2 international journals: *Journal of Sound and Vibration* and *Mechanical Systems and Signal Processing*. He was awarded "2004 Person of the Year" (jointly with W.J. Staszewski) awarded by *Structural Health Monitoring* journal for outstanding contribution in the field.

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Preface xvii

Acknowledgements xix

**1 Introduction 1**

1.1 How Engineers and Scientists Study Damage 2

1.2 Motivation for Developing SHM Technology 3

1.3 Definition of Damage 4

1.4 A Statistical Pattern Recognition Paradigm for SHM 7

1.4.1 Operational Evaluation 10

1.4.2 Data Acquisition 10

1.4.3 Data Normalisation 10

1.4.4 Data Cleansing 11

1.4.5 Data Compression 11

1.4.6 Data Fusion 11

1.4.7 Feature Extraction 12

1.4.8 Statistical Modelling for Feature Discrimination 12

1.5 Local versus Global Damage Detection 13

1.6 Fundamental Axioms of Structural Health Monitoring 14

1.7 The Approach Taken in This Book 15

References 15

**2 Historical Overview 17**

2.1 Rotating Machinery Applications 17

2.1.1 Operational Evaluation for Rotating Machinery 18

2.1.2 Data Acquisition for Rotating Machinery 18

2.1.3 Feature Extraction for Rotating Machinery 19

2.1.4 Statistical Modelling for Damage Detection in Rotating Machinery 20

2.1.5 Concluding Comments about Condition Monitoring of Rotating Machinery 21

2.2 Offshore Oil Platforms 21

2.2.1 Operational Evaluation for Offshore Platforms 21

2.2.2 Data Acquisition for Offshore Platforms 24

2.2.3 Feature Extraction for Offshore Platforms 24

2.2.4 Statistical Modelling for Offshore Platforms 25

2.2.5 Lessons Learned from Offshore Oil Platform Structural Health Monitoring Studies 25

2.3 Aerospace Structures 25

2.3.1 Operational Evaluation for Aerospace Structures 28

2.3.2 Data Acquisition for Aerospace Structures 29

2.3.3 Feature Extraction and Statistical Modelling for Aerospace Structures 31

2.3.4 Statistical Models Used for Aerospace SHM Applications 32

2.3.5 Concluding Comments about Aerospace SHM Applications 32

2.4 Civil Engineering Infrastructure 32

2.4.1 Operational Evaluation for Bridge Structures 34

2.4.2 Data Acquisition for Bridge Structures 34

2.4.3 Features Based on Modal Properties 35

2.4.4 Statistical Classification of Features for Civil Engineering Infrastructure 36

2.4.5 Applications to Bridge Structures 36

2.5 Summary 37

References 38

**3 Operational Evaluation 45**

3.1 Economic and Life-Safety Justifications for Structural Health Monitoring 45

3.2 Defining the Damage to Be Detected 46

3.3 The Operational and Environmental Conditions 47

3.4 Data Acquisition Limitations 47

3.5 Operational Evaluation Example: Bridge Monitoring 48

3.6 Operational Evaluation Example: Wind Turbines 51

3.7 Concluding Comment on Operational Evaluation 52

References 52

**4 Sensing and Data Acquisition 53**

4.1 Introduction 53

4.2 Sensing and Data Acquisition Strategies for SHM 53

4.2.1 Strategy I 54

4.2.2 Strategy II 54

4.3 Conceptual Challenges for Sensing and Data Acquisition Systems 55

4.4 What Types of Data Should Be Acquired? 56

4.4.1 Dynamic Input and Response Quantities 57

4.4.2 Other Damage-Sensitive Physical Quantities 59

4.4.3 Environmental Quantities 59

4.4.4 Operational Quantities 60

4.5 Current SHM Sensing Systems 60

4.5.1 Wired Systems 60

4.5.2 Wireless Systems 61

4.6 Sensor Network Paradigms 63

4.6.1 Sensor Arrays Directly Connected to Central Processing Hardware 64

4.6.2 Decentralised Processing with Hopping Connection 65

4.6.3 Decentralised Processing with Hybrid Connection 66

4.7 Future Sensing Network Paradigms 67

4.8 Defining the Sensor System Properties 68

4.8.1 Required Sensitivity and Range 70

4.8.2 Required Bandwidth and Frequency Resolution 71

4.8.3 Sensor Number and Locations 71

4.8.4 Sensor Calibration, Stability and Reliability 72

4.9 Define the Data Sampling Parameters 73

4.10 Define the Data Acquisition System 74

4.11 Active versus Passive Sensing 75

4.12 Multiscale Sensing 75

4.13 Powering the Sensing System 77

4.14 Signal Conditioning 77

4.15 Sensor and Actuator Optimisation 78

4.16 Sensor Fusion 79

4.17 Summary of Sensing and Data Acquisition Issues for Structural Health Monitoring 82

References 83

**5 Case Studies 87**

5.1 The I-40 Bridge 87

5.1.1 Preliminary Testing and Data Acquisition 89

5.1.2 Undamaged Ambient Vibration Tests 90

5.1.3 Forced Vibration Tests 91

5.2 The Concrete Column 92

5.2.1 Quasi-Static Loading 95

5.2.2 Dynamic Excitation 95

5.2.3 Data Acquisition 95

5.3 The 8-DOF System 98

5.3.1 Physical Parameters 100

5.3.2 Data Acquisition 100

5.4 Simulated Building Structure 100

5.4.1 Experimental Procedure and Data Acquisition 101

5.4.2 Measured Data 102

5.5 The Alamosa Canyon Bridge 104

5.5.1 Experimental Procedures and Data Acquisition 104

5.5.2 Environmental Measurements 107

5.5.3 Vibration Tests Performed to Study Variability of Modal Properties 108

5.6 The Gnat Aircraft 108

5.6.1 Simulating Damage with a Modified Inspection Panel 109

5.6.2 Simulating Damage by Panel Removal 112

References 116

**6 Introduction to Probability and Statistics 119**

6.1 Introduction 119

6.2 Probability: Basic Definitions 120

6.3 Random Variables and Distributions 122

6.4 Expected Values 125

6.5 The Gaussian Distribution (and Others) 130

6.6 Multivariate Statistics 132

6.7 The Multivariate Gaussian Distribution 133

6.8 Conditional Probability and the Bayes Theorem 134

6.9 Confidence Limits and Cumulative Distribution Functions 137

6.10 Outlier Analysis 140

6.10.1 Outliers in Univariate Data 140

6.10.2 Outliers in Multivariate Data 141

6.10.3 Calculation of Critical Values of Discordancy or Thresholds 141

6.11 Density Estimation 142

6.12 Extreme Value Statistics 148

6.12.1 Introduction 148

6.12.2 Basic Theory 148

6.12.3 Determination of Limit Distributions 151

6.13 Dimension Reduction – Principal Component Analysis 155

6.13.1 Simple Projection 156

6.13.2 Principal Component Analysis (PCA) 156

6.14 Conclusions 158

References 159

**7 Damage-Sensitive Features 161**

7.1 Common Waveforms and Spectral Functions Used in the Feature Extraction Process 163

7.1.1 Waveform Comparisons 164

7.1.2 Autocorrelation and Cross-Correlation Functions 165

7.1.3 The Power Spectral and Cross-Spectral Density Functions 166

7.1.4 The Impulse Response Function and the Frequency Response Function 168

7.1.5 The Coherence Function 169

7.1.6 Some Remarks Regarding Waveforms and Spectra 170

7.2 Basic Signal Statistics 171

7.3 Transient Signals: Temporal Moments 178

7.4 Transient Signals: Decay Measures 181

7.5 Acoustic Emission Features 183

7.6 Features Used with Guided-Wave Approaches to SHM 185

7.6.1 Preprocessing 186

7.6.2 Baseline Comparisons 186

7.6.3 Damage Localisation 188

7.7 Features Used with Impedance Measurements 188

7.8 Basic Modal Properties 191

7.8.1 Resonance Frequencies 192

7.8.2 Inverse versus Forward Modelling Approaches to Feature Extraction 194

7.8.3 Resonance Frequencies: The Forward Approach 195

7.8.4 Resonance Frequencies: Sensitivity Issues 195

7.8.5 Mode Shapes 197

7.8.6 Load-Dependent Ritz Vectors 203

7.9 Features Derived from Basic Modal Properties 206

7.9.1 Mode Shape Curvature 207

7.9.2 Modal Strain Energy 210

7.9.3 Modal Flexibility 215

7.10 Model Updating Approaches 218

7.10.1 Objective Functions and Constraints 220

7.10.2 Direct Solution for the Modal Force Error 221

7.10.3 Optimal Matrix Update Methods 222

7.10.4 Sensitivity-Based Update Methods 226

7.10.5 Eigenstructure Assignment Method 230

7.10.6 Hybrid Matrix Update Methods 231

7.10.7 Concluding Comment on Model Updating Approaches 231

7.11 Time Series Models 232

7.12 Feature Selection 234

7.12.1 Sensitivity Analysis 234

7.12.2 Information Content 238

7.12.3 Assessment of Robustness 239

7.12.4 Optimisation Procedures 239

7.13 Metrics 239

7.14 Concluding Comments 240

References 240

**8 Features Based on Deviations from Linear Response 245**

8.1 Types of Damage that Can Produce a Nonlinear System Response 245

8.2 Motivation for Exploring Nonlinear System Identification Methods for SHM 248

8.2.1 Coherence Function 250

8.2.2 Linearity and Reciprocity Checks 251

8.2.3 Harmonic Distortion 256

8.2.4 Frequency Response Function Distortions 261

8.2.5 Probability Density Function 264

8.2.6 Correlation Tests 266

8.2.7 The Holder Exponent 266

8.2.8 Linear Time Series Prediction Errors 271

8.2.9 Nonlinear Time Series Models 273

8.2.10 Hilbert Transform 277

8.2.11 Nonlinear Acoustics Methods 279

8.3 Applications of Nonlinear Dynamical Systems Theory 280

8.3.1 Modelling a Cracked Beam as a Bilinear System 281

8.3.2 Chaotic Interrogation of a Damaged Beam 282

8.3.3 Local Attractor Variance 284

8.3.4 Detection of Damage Using the Local Attractor Variance 286

8.4 Nonlinear System Identification Approaches 288

8.4.1 Restoring Force Surface Model 288

8.5 Concluding Comments Regarding Feature Extraction Based on Nonlinear System Response 291

References 292

**9 Machine Learning and Statistical Pattern Recognition 295**

9.1 Introduction 295

9.2 Intelligent Damage Detection 295

9.3 Data Processing and Fusion for Damage Identification 298

9.4 Statistical Pattern Recognition: Hypothesis Testing 300

9.5 Statistical Pattern Recognition: General Frameworks 303

9.6 Discriminant Functions and Decision Boundaries 306

9.7 Decision Trees 308

9.8 Training – Maximum Likelihood 309

9.9 Nearest Neighbour Classification 312

9.10 Case Study: An Acoustic Emission Experiment 312

9.10.1 Analysis and Classification of the AE Data 314

9.11 Summary 320

References 320

**10 Unsupervised Learning – Novelty Detection 321**

10.1 Introduction 321

10.2 A Gaussian-Distributed Normal Condition – Outlier Analysis 322

10.3 A Non-Gaussian Normal Condition – A Neural Network Approach 325

10.4 Nonparametric Density Estimation – A Case Study 329

10.4.1 The Experimental Structure and Data Capture 331

10.4.2 Preprocessing of Data and Features 332

10.4.3 Novelty Detection 333

10.5 Statistical Process Control 338

10.5.1 Feature Extraction Based on Autoregressive Modelling 339

10.5.2 The X-Bar Control Chart: An Experimental Case Study 340

10.6 Other Control Charts and Multivariate SPC 343

10.6.1 The S Control Chart 344

10.6.2 The CUSUM Chart 344

10.6.3 The EWMA Chart 345

10.6.4 The Hotelling or Shewhart T2 Chart 346

10.6.5 The Multivariate CUSUM Chart 347

10.6.6 The Multivariate EWMA Chart 347

10.7 Thresholds for Novelty Detection 348

10.7.1 Extreme Value Statistics 348

10.7.2 Type I and Type II Errors: The ROC Curve 354

10.8 Summary 359

References 359

**11 Supervised Learning – Classification and Regression 361**

11.1 Introduction 361

11.2 Artificial Neural Networks 361

11.2.1 Biological Motivation 361

11.2.2 The Parallel Processing Paradigm 364

11.2.3 The Artificial Neuron 365

11.2.4 The Perceptron 366

11.2.5 The Multilayer Perceptron 367

11.3 A Neural Network Case Study: A Classification Problem 372

11.4 Other Neural Network Structures 374

11.4.1 Feedforward Networks 374

11.4.2 Recurrent Networks 375

11.4.3 Cellular Networks 375

11.5 Statistical Learning Theory and Kernel Methods 375

11.5.1 Structural Risk Minimisation 375

11.5.2 Support Vector Machines 377

11.5.3 Kernels 381

11.6 Case Study II: Support Vector Classification 382

11.7 Support Vector Regression 384

11.8 Case Study III: Support Vector Regression 386

11.9 Feature Selection for Classification Using Genetic Algorithms 389

11.9.1 Feature Selection Using Engineering Judgement 390

11.9.2 Genetic Feature Selection 390

11.9.3 Issues of Network Generalisation 395

11.9.4 Discussion and Conclusions 397

11.10 Discussion and Conclusions 398

References 400

**12 Data Normalisation 403**

12.1 Introduction 403

12.2 An Example Where Data Normalisation Was Neglected 405

12.3 Sources of Environmental and Operational Variability 406

12.4 Sensor System Design 409

12.5 Modelling Operational and Environmental Variability 411

12.6 Look-Up Tables 414

12.7 Machine Learning Approaches to Data Normalisation 421

12.7.1 Auto-Associative Neural Networks 422

12.7.2 Factor Analysis 423

12.7.3 Mahalanobis Squared-Distance (MSD) 424

12.7.4 Singular Value Decomposition 424

12.7.5 Application to the Simulated Building Structure Data 425

12.8 Intelligent Feature Selection: A Projection Method 429

12.9 Cointegration 431

12.9.1 Theory 432

12.9.2 Illustration 433

12.10 Summary 436

References 436

**13 Fundamental Axioms of Structural Health Monitoring 439**

13.1 Introduction 439

13.2 Axiom I. All Materials Have Inherent Flaws or Defects 440

13.3 Axiom II. Damage Assessment Requires a Comparison between Two System States 441

13.4 Axiom III. Identifying the Existence and Location of Damage Can Be Done in an Unsupervised Learning Mode, but Identifying the Type of Damage Present and the Damage Severity Can Generally Only Be Done in a Supervised Learning Mode 444

13.5 Axiom IVa. Sensors Cannot Measure Damage. Feature Extraction through Signal Processing and Statistical Classification Are Necessary to Convert Sensor Data into Damage Information 446

13.6 Axiom IVb. Without Intelligent Feature Extraction, the More Sensitive a Measurement is to Damage, the More Sensitive it is to Changing Operational and Environmental Conditions 447

13.7 Axiom V. The Length and Time Scales Associated with Damage Initiation and Evolution Dictate the Required Properties of the SHM Sensing System 448

13.8 Axiom VI. There is a Trade-off between the Sensitivity to Damage of an Algorithm and Its Noise Rejection Capability 449

13.9 Axiom VII. The Size of Damage that Can Be Detected from Changes in System Dynamics is Inversely Proportional to the Frequency Range of Excitation 451

13.10 Axiom VIII. Damage Increases the Complexity of a Structure 454

13.11 Summary 458

References 459

**14 Damage Prognosis 461**

14.1 Introduction 461

14.2 Motivation for Damage Prognosis 462

14.3 The Current State of Damage Prognosis 463

14.4 Defining the Damage Prognosis Problem 464

14.5 The Damage Prognosis Process 465

14.6 Emerging Technologies Impacting the Damage Prognosis Process 467

14.6.1 Damage Sensing Systems 467

14.6.2 Prediction Modelling for Future Loading Estimates 467

14.6.3 Model Verification and Validation 467

14.6.4 Reliability Analysis for Damage Prognosis Decision Making 467

14.7 A Prognosis Case Study: Crack Propagation in a Titanium Plate 468

14.7.1 The Computational Model 469

14.7.2 Monte Carlo Simulation 471

14.7.3 Issues 471

14.8 Damage Prognosis of UAV Structural Components 474

14.9 Concluding Comments on Damage Prognosis 475

14.10 Cradle-to-Grave System State Awareness 476

References 476

**Appendix A Signal Processing for SHM 479**

A.1 Deterministic and Random Signals 479

A.1.1 Basic Definitions 479

A.1.2 Transducers, Sensors and Calibration 480

A.1.3 Classification of Deterministic Signals 481

A.1.4 Classification of Random Signals 485

A.2 Fourier Analysis and Spectra 489

A.2.1 Fourier Series 489

A.2.2 The Square Wave Revisited 493

A.2.3 A First Look at Spectra 495

A.2.4 The Exponential Form of the Fourier Series 496

A.3 The Fourier Transform 497

A.3.1 Basic Transform Theory 497

A.3.2 An Interesting Function that is not a Function 499

A.3.3 The Fourier Transform of a Periodic Function 501

A.3.4 The Fourier Transform of a Pulse/Impulse 502

A.3.5 The Convolution Theorem 504

A.3.6 Parseval’s Theorem 506

A.3.7 The Effect of a Finite Time Window 506

A.3.8 The Effect of Differentiation and Integration 509

A.4 Frequency Response Functions and the Impulse Response 510

A.4.1 Basic Definitions 510

A.4.2 Harmonic Probing 511

A.5 The Discrete Fourier Transform 512

A.5.1 Basic Definitions 512

A.5.2 More About Sampling 516

A.5.3 The Fast Fourier Transform 519

A.5.4 The DFT of a Sinusoid 524

A.6 Practical Matters: Windows and Averaging 525

A.6.1 Windows 525

A.6.2 The Harris Test 527

A.6.3 Averaging and Power Spectral Density 528

A.7 Correlations and Spectra 532

A.8 FRF Estimation and Coherence 535

A.8.1 FRF Estimation I 535

A.8.2 The Coherence Function 536

A.8.3 FRF Estimators II 538

A.9 Wavelets 540

A.9.1 Introduction and Continuous Wavelets 540

A.9.2 Discrete and Orthogonal Wavelets 549

A.10 Filters 564

A.10.1 Introduction to Filters 564

A.10.2 A Digital Low-Pass Filter 566

A.10.3 A High-Pass Filter 569

A.10.4 A Simple Classification of Filters 570

A.10.5 Filter Design 571

A.10.6 The Bilinear Transformation 573

A.10.7 An Example of Digital Filter Design 576

A.10.8 Combining Filters 578

A.10.9 General Butterworth Filters 579

A.11 System Identification 583

A.11.1 Introduction 583

A.11.2 Discrete-Time Models in the Frequency Domain 586

A.11.3 Least-Squares Parameter Estimation 587

A.11.4 Parameter Uncertainty 589

A.11.5 A Case Study 590

A.12 Summary 591

References 592

**Appendix B EssentialLinear StructuralDynamics 593**

B.1 Continuous-Time Systems: The Time Domain 593

B.2 Continuous-Time Systems: The Frequency Domain 600

B.3 The Impulse Response 603

B.4 Discrete-Time Models: Time Domain 605

B.5 Multi-Degree-of-Freedom (MDOF) Systems 607

B.6 Modal Analysis 613

B.6.1 Free, Undamped Motion 613

B.6.2 Free, Damped Motion 617

B.6.3 Forced, Damped Motion 618

References 621

Index 623