WILEY STRUCTURAL HEALTH MONITORING A MACHINE LEARNING PERSPECTIVE. Charles R. Farrar. University of Sheffield, UK. Keith Worden

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1 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

2 Preface Acknowledgements xvii xix 1 Introduction How Engineers and Scientists Study Damage Motivation for Developing SHM Technology Definition of Damage A Statistical Pattern Recognition Paradigm for SHM Operational Evaluation Data Acquisition Data Normalisation Data Cleansing Data Compression Data Fusion Feature Extraction Statistical Modellingfor Feature Discrimination Local versus Global Damage Detection Fundamental Axioms of Structural Health Monitoring The Approach Taken in This Book 15 References 15 2 Historical Overview Rotating Machinery Applications Operational Evaluation for Rotating Machinery Data Acquisition for Rotating Machinery Feature Extraction for Rotating Machinery Statistical Modellingfor Damage Detection in Rotating Machinery Concluding Comments about Condition Monitoring of Rotating Machinery Offshore Oil Platforms Operational Evaluation for Offshore Platforms Data Acquisition for Offshore Platforms Feature Extraction for Offshore Platforms Statistical Modellingfor Offshore Platforms Lessons Learned from Offshore Oil Platform Structural Health Monitoring Studies 25

3 2.3 Aerospace Structures Operational Evaluation for Aerospace Structures Data Acquisition for Aerospace Structures Feature Extraction and Statistical Modelling for Aerospace Structures Statistical Models Used for Aerospace SHM Applications Concluding Comments about Aerospace SHM Applications Civil Engineering Infrastructure Operational Evaluation for Bridge Structures Data Acquisition for Bridge Structures Features Based on Modal Properties Statistical Classification of Features for Civil Engineering Infrastructure Applications to Bridge Structures Summary 37 References 38 3 Operational Evaluation Economic and Life-Safety Justifications for Structural Health Monitoring Defining the Damage to Be Detected The Operational and Environmental Conditions Data Acquisition Limitations Operational Evaluation Example: Bridge Monitoring Operational Evaluation Example: Wind Turbines Concluding Comment on Operational Evaluation 52 References 52 4 Sensing and Data Acquisition Introduction Sensing and Data Acquisition Strategies for SHM Strategy Strategy Conceptual Challenges for Sensing and Data Acquisition Systems What Types of Data Should Be Acquired? Dynamic Input and Response Quantities Other Damage-Sensitive Physical Quantities Environmental Quantities Operational Quantities Current SHM Sensing Systems Wired Systems Wireless Systems Sensor Network Paradigms Sensor Arrays Directly Connected to Central Processing Hardware Decentralised Processing with Hopping Connection Decentralised Processing with Hybrid Connection Future Sensing Network Paradigms Defining the Sensor System Properties Required Sensitivity and Range Required Bandwidth and Frequency Resolution Sensor Number and Locations Sensor Calibration, Stability and Reliability Define the Data Sampling Parameters 73

4 4.10 Define the Data Acquisition System Active versus Passive Sensing Multiscale Sensing Powering the Sensing System Signal Conditioning Sensor and Actuator Optimisation Sensor Fusion Summary of Sensing and Data Acquisition Issues for Structural Health Monitoring 82 References 83 5 Case Studies The 1-40 Bridge Preliminary Testing and Data Acquisition Undamaged Ambient Vibration Tests Forced Vibration Tests The Concrete Column Quasi-Static Loading Dynamic Excitation Data Acquisition The 8-DOF System Physical Parameters Data Acquisition Simulated Building Structure Experimental Procedure and Data Acquisition Measured Data The Alamosa Canyon Bridge Experimental Procedures and Data Acquisition Environmental Measurements Vibration Tests Performed to Study Variability of Modal Properties The Gnat Aircraft Simulating Damage with a Modified Inspection Panel Simulating Damage by Panel Removal 112 References Introduction to Probability and Statistics Introduction Probability: Basic Definitions Random Variables and Distributions Expected Values The Gaussian Distribution (and Others) Multivariate Statistics The Multivariate Gaussian Distribution Conditional Probability and the Bayes Theorem Confidence Limits and Cumulative Distribution Functions Outlier Analysis Outliers in Univariate Data Outliers in Multivariate Data Calculation of Critical Values of Discordancy or Thresholds Density Estimation

5 Principal X Contents 6.12 Extreme Value Statistics Introduction Basic Theory Determination oflimit Distributions Dimension - Reduction Component Analysis Simple Projection Principal Component Analysis (PCA) Conclusions 158 References Damage-Sensitive Features Common Waveforms and Spectral Functions Used in the Feature Extraction Process Waveform Comparisons Autocorrelation and Cross-Correlation Functions /.3 The Power Spectral and Cross-Spectral Density Functions The Impulse Response Function and the Frequency Response Function The Coherence Function Some Remarks Regarding Waveforms and Spectra Basic Signal Statistics 7.3 Transient Signals: Temporal Moments Transient Signals: Decay Measures Acoustic Emission Features 7.6 Features Used with Guided-Wave Approaches to SHM / Preprocessing Baseline Comparisons Damage Localisation Features Used with Impedance Measurements Basic Modal Properties Resonance Frequencies Inverse versus Forward Modelling Approaches to Feature Extraction Resonance Frequencies: The Forward Approach Resonance Frequencies: Sensitivity Issues Mode Shapes Load-Dependent Ritz Vectors Features Derived from Basic Modal Properties Mode Shape Curvature Modal Strain Energy Modal Flexibility Model Updating Approaches Objective Functions and Constraints Direct Solution for the Modal Force Error Optimal Matrix Update Methods Sensitivity-Based Update Methods Eigenstructure Assignment Method Hybrid Matrix Update Methods Concluding Comment on Model Updating Approaches Time Series Models 7.12 Feature Selection Sensitivity Analysis Information Content

6 A Outlier Contents xi Assessment of Robustness Optimisation Procedures Metrics Concluding Comments 240 References Features Based on Deviations from Linear Response Types of Damage that Can Produce a Nonlinear System Response Motivation for Exploring Nonlinear System Identification Methods for SHM Coherence Function Linearity and Reciprocity Checks Harmonic Distortion Frequency Response Function Distortions Probability Density Function Correlation Tests The Holder Exponent Linear Time Series Prediction Errors Nonlinear Time Series Models Hilbert Transform Nonlinear Acoustics Methods Applications of Nonlinear Dynamical Systems Theory Modelling a Cracked Beam as a Bilinear System Chaotic Interrogation of a Damaged Beam Local Attractor Variance Detection ofdamage Using the Local Attractor Variance Nonlinear System Identification Approaches Restoring Force Surface Model Concluding Comments Regarding Feature Extraction Based on Nonlinear System Response 291 References Machine Learning and Statistical Pattern Recognition Introduction Intelligent Damage Detection Data Processing and Fusion for Damage Identification Statistical Pattern Recognition: Hypothesis Testing Statistical Pattern Recognition: General Frameworks Discriminant Functions and Decision Boundaries Decision Trees Training - Maximum Likelihood Nearest Neighbour Classification Case Study: An Acoustic Emission Experiment Analysis and Classification of the AE Data Summary 320 References Unsupervised Learning Introduction Novelty Detection 10.2 A Gaussian-Distributed Normal Condition - Analysis A Non-Gaussian Normal Condition Neural Network Approach

7 Classification A xj; Contents 10.4 Nonparametric Density Estimation - Case Study The Experimental Structure and Data Capture Preprocessing ofdata and Features Novelty Detection Statistical Process Control Feature Extraction Based on Autoregressive Modelling The X-Bar Control Chart: An Experimental Case Study Other Control Charts and Multivariate SPC / The S Control Chart The CUSUM Chart The EWMA Chart The Hotelling or Shewhart T2 Chart The Multivariate CUSUM Chart The Multivariate EWMA Chart Thresholds for Novelty Detection Extreme Value Statistics Type 1 and Type II Errors: The ROC Curve Summary 359 References Supervised Learning and Regression Introduction Artificial Neural Networks Biological Motivation The Parallel Processing Paradigm The Artificial Neuron The Perceptron The Multilayer Perceptron A Neural Network Case Study: A Classification Problem Other Neural Network Structures Feedforward Networks Recurrent Networks 375 /1.4.3 Cellular Networks Statistical Learning Theory and Kernel Methods Structural Risk Minimisation Support Vector Machines Kernels Case Study II: Support Vector Classification Support Vector Regression Case Study III: Support Vector Regression Feature Selection for Classification Using Genetic Algorithms Feature Selection Using Engineering Judgement Genetic Feature Selection Issues of Network Generalisation Discussion and Conclusions Discussion and Conclusions References Data Normalisation 12.1 Introduction 12.2 An Example Where Data Normalisation Was Neglected

8 xiii 12.3 Sources ofenvironmental and Operational Variability Sensor System Design Modelling Operational and Environmental Variability Look-Up Tables Machine Learning Approaches to Data Normalisation Auto-Associative Neural Networks Factor Analysis Mahalanobis Squared-Distance (MSD) Singular Value Decomposition Application to the Simulated Building Structure Data Intelligent Feature Selection: A Projection Method Cointegration Theory Illustration Summary 436 References Fundamental Axioms of Structural Health Monitoring Introduction Axiom I. All Materials Have Inherent Flaws or Defects Axiom II. Damage Assessment Requires a Comparison between Two System States 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 Axiom IVa. Sensors Cannot Measure Damage. Feature Extraction through Signal Processing and Statistical Classification Are Necessary to Convert Sensor Data into Damage Information 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 Axiom V. The Length and Time Scales Associated with Damage Initiation and Evolution Dictate the Required Properties of the SHM Sensing System Axiom VI. There is a Trade-off between the Sensitivity to Damage of an Algorithm and Its Noise Rejection Capability Axiom VII. The Size of Damage that Can Be Detected from Changes in System Dynamics is Inversely Proportional to the Frequency Range of Excitation Axiom VIII. Damage Increases the Complexity of a Structure Summary 458 References Damage Prognosis Introduction Motivation for Damage Prognosis The Current State of Damage Prognosis Defining the Damage Prognosis Problem The Damage Prognosis Process Emerging Technologies Impacting the Damage Prognosis Process Damage Sensing Systems Prediction Modellingfor Future Loading Estimates Model Verification and Validation Reliability Analysisfor Damage Prognosis Decision Making 467

9 14.7 A Prognosis Case Study: Crack Propagation in a Titanium Plate The Computational Model Monte Carlo Simulation Issues Damage Prognosis of UAV Structural Components Concluding Comments on Damage Prognosis 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 A.9 Wavelets 540 A.9.1 Introduction and Continuous Wavelets 540 A.9.2 Discrete and Orthogonal Wavelets 549

10 xv A.10 Filters 564 A 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 Filter Design 571 A 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 Discrete-Time Models in the Frequency Domain 586 A.11.3 Least-Squares Parameter Estimation 587 A.11.4 Parameter Uncertainty 589 A 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