STRUCTURAL HEALTH MONITORING A MACHINE LEARNING PERSPECTIVE Charles R. Farrar Los Alamos National Laboratory, USA Keith Worden University of Sheffield, UK WILEY A John Wiley & Sons, Ltd., Publication
Preface Acknowledgements xvii 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 Modellingfor 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 Modellingfor 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 Modellingfor 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 1 54 4.2.2 Strategy 11 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 1-40 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 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 142 140
Principal X Contents 6.12 Extreme Value Statistics 148 6.12.1 Introduction 148 6.12.2 Basic Theory 148 6.12.3 Determination oflimit Distributions 151 6.13 Dimension - Reduction 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. /.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 7.3 Transient Signals: Temporal Moments 178 7.4 Transient Signals: Decay Measures 181 7.5 Acoustic Emission Features 7.6 Features Used with Guided-Wave Approaches to SHM 185 7.6. / 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 7.70.2 Direct Solution for the Modal Force Error 221 7.10.3 Optimal Matrix Update Methods 7.10.4 Sensitivity-Based Update Methods 226 7.10.5 Eigenstructure Assignment Method 7.10.6 Hybrid Matrix Update Methods 231 7.10.7 Concluding Comment on Model Updating Approaches 231 7.11 Time Series Models 7.12 Feature Selection 7.12.1 Sensitivity Analysis 234 7.12.2 Information Content 171 183 222 230 232 234 238
A Outlier Contents xi 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 ofdamage 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 - 10.1 Introduction Novelty Detection 10.2 A Gaussian-Distributed Normal Condition - Analysis 10.3 - A Non-Gaussian Normal Condition Neural Network Approach
Classification A xj; Contents 10.4 Nonparametric Density Estimation - Case Study 329 10.4.1 The Experimental Structure and Data Capture 331 10.4.2 Preprocessing ofdata 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 70.6./ 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 1 and Type II Errors: The ROC Curve 354 10.8 Summary 359 References 359 11 - Supervised Learning 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 /1.4.3 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 111 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 11.9.3 Issues of Network Generalisation 395 390 11.9.4 Discussion and Conclusions 11.10 Discussion and Conclusions References 397 398 400 12 Data Normalisation 12.1 Introduction 12.2 An Example Where Data Normalisation Was Neglected 405 403 403
xiii 12.3 Sources ofenvironmental 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 Modellingfor Future Loading Estimates 467 14.6.3 Model Verification and Validation 467 14.6.4 Reliability Analysisfor 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.l Deterministic and Random Signals 479 A.1.1 Basic Definitions 479 A.l.2 Transducers, Sensors and Calibration 480 A.l.3 Classification of Deterministic Signals 481 A. 1.4 Classification ofrandom 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 ofa Periodic Function 501 A.3.4 The Fourier Transform of a Pulse/Impulse 502 A.3 J The Convolution Theorem 504 A.3.6 Parseval's Theorem 506 A.3.7 The Effect of a Finite Time Window 506 A3.8 The Effect of Differentia/ion 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.S.I FRF Estimation I 535 A.8.2 The Coherence Function 536 A.8.3 FRF Estimators 11 538 A.9 Wavelets 540 A.9.1 Introduction and Continuous Wavelets 540 A.9.2 Discrete and Orthogonal Wavelets 549
xv A.10 Filters 564 A. 10.1 Introduction to Fillers 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.ll.l 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 Essential Linear Structural Dynamics 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