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    Condition Monitoring with Vibration Signals: Compressive Sampling and Learning Algorithms for Rotating Machines

    Asoke K. Nandi,Hosameldin Ahmed|2020.01.07

    Preface xvii

    About the Authors xxi

    List of Abbreviations xxiii

    Part I Introduction 1

    1 Introduction to Machine Condition Monitoring 3

    1.1 Background 3

    1.2 Maintenance Approaches for Rotating Machines Failures 4

    1.2.1 Corrective Maintenance 4

    1.2.2 Preventive Maintenance 5

    1.2.2.1 Time-Based Maintenance (TBM) 5

    1.2.2.2 Condition-Based Maintenance (CBM) 5

    1.3 Applications of MCM 5

    1.3.1 Wind Turbines 5

    1.3.2 Oil and Gas 6

    1.3.3 Aerospace and Defence Industry 6

    1.3.4 Automotive 7

    1.3.5 Marine Engines 7

    1.3.6 Locomotives 7

    1.4 Condition Monitoring Techniques 7

    1.4.1 Vibration Monitoring 7

    1.4.2 Acoustic Emission 8

    1.4.3 Fusion of Vibration and Acoustic 8

    1.4.4 Motor Current Monitoring 8

    1.4.5 Oil Analysis and Lubrication Monitoring 8

    1.4.6 Thermography 9

    1.4.7 Visual Inspection 9

    1.4.8 Performance Monitoring 9

    1.4.9 Trend Monitoring 10

    1.5 Topic Overview and Scope of the Book 10

    1.6 Summary 11

    References 11

    2 Principles of Rotating Machine Vibration Signals 17

    2.1 Introduction 17

    2.2 Machine Vibration Principles 17

    2.3 Sources of Rotating Machines Vibration Signals 20

    2.3.1 Rotor Mass Unbalance 21

    2.3.2 Misalignment 21

    2.3.3 Cracked Shafts 21

    2.3.4 Rolling Element Bearings 23

    2.3.5 Gears 25

    2.4 Types of Vibration Signals 25

    2.4.1 Stationary 26

    2.4.2 Nonstationary 26

    2.5 Vibration Signal Acquisition 26

    2.5.1 Displacement Transducers 26

    2.5.2 Velocity Transducers 26

    2.5.3 Accelerometers 27

    2.6 Advantages and Limitations of Vibration Signal Monitoring 27

    2.7 Summary 28

    References 28

    Part II Vibration Signal Analysis Techniques 31

    3 Time Domain Analysis 33

    3.1 Introduction 33

    3.1.1 Visual Inspection 33

    3.1.2 Features-Based Inspection 35

    3.2 Statistical Functions 35

    3.2.1 Peak Amplitude 36

    3.2.2 Mean Amplitude 36

    3.2.3 Root Mean Square Amplitude 36

    3.2.4 Peak-to-Peak Amplitude 36

    3.2.5 Crest Factor (CF) 36

    3.2.6 Variance and Standard Deviation 37

    3.2.7 Standard Error 37

    3.2.8 Zero Crossing 38

    3.2.9 Wavelength 39

    3.2.10 Willison Amplitude 39

    3.2.11 Slope Sign Change 39

    3.2.12 Impulse Factor 39

    3.2.13 Margin Factor 40

    3.2.14 Shape Factor 40

    3.2.15 Clearance Factor 40

    3.2.16 Skewness 40

    3.2.17 Kurtosis 40

    3.2.18 Higher-Order Cumulants (HOCs) 41

    3.2.19 Histograms 42

    3.2.20 Normal/Weibull Negative Log-Likelihood Value 42

    3.2.21 Entropy 42

    3.3 Time Synchronous Averaging 44

    3.3.1 TSA Signals 44

    3.3.2 Residual Signal (RES) 44

    3.3.2.1 NA4 44

    3.3.2.2 NA4* 45

    3.3.3 Difference Signal (DIFS) 45

    3.3.3.1 FM4 46

    3.3.3.2 M6A 46

    3.3.3.3 M8A 46

    3.4 Time Series Regressive Models 46

    3.4.1 AR Model 47

    3.4.2 MA Model 48

    3.4.3 ARMA Model 48

    3.4.4 ARIMA Model 48

    3.5 Filter-Based Methods 49

    3.5.1 Demodulation 49

    3.5.2 Prony Model 52

    3.5.3 Adaptive Noise Cancellation (ANC) 53

    3.6 Stochastic Parameter Techniques 54

    3.7 Blind Source Separation (BSS) 54

    3.8 Summary 55

    References 56

    4 Frequency Domain Analysis 63

    4.1 Introduction 63

    4.2 Fourier Analysis 64

    4.2.1 Fourier Series 64

    4.2.2 Discrete Fourier Transform 66

    4.2.3 Fast Fourier Transform (FFT) 67

    4.3 Envelope Analysis 71

    4.4 Frequency Spectrum Statistical Features 73

    4.4.1 Arithmetic Mean 73

    4.4.2 Geometric Mean 73

    4.4.3 Matched Filter RMS 73

    4.4.4 The RMS of Spectral Difference 74

    4.4.5 The Sum of Squares Spectral Difference 74

    4.4.6 High-Order Spectra Techniques 74

    4.5 Summary 75

    References 76

    5 Time-Frequency Domain Analysis 79

    5.1 Introduction 79

    5.2 Short-Time Fourier Transform (STFT) 79

    5.3 Wavelet Analysis 82

    5.3.1 Wavelet Transform (WT) 82

    5.3.1.1 Continuous Wavelet Transform (CWT) 83

    5.3.1.2 Discrete Wavelet Transform (DWT) 85

    5.3.2 Wavelet Packet Transform (WPT) 89

    5.4 Empirical Mode Decomposition (EMD) 91

    5.5 Hilbert-Huang Transform (HHT) 94

    5.6 Wigner-Ville Distribution 96

    5.7 Local Mean Decomposition (LMD) 98

    5.8 Kurtosis and Kurtograms 100

    5.9 Summary 105

    References 106

    Part III Rotating Machine Condition Monitoring Using Machine Learning 115

    6 Vibration-Based Condition Monitoring Using Machine Learning 117

    6.1 Introduction 117

    6.2 Overview of the Vibration-Based MCM Process 118

    6.2.1 Fault-Detection and -Diagnosis Problem Framework 118

    6.3 Learning from Vibration Data 122

    6.3.1 Types of Learning 123

    6.3.1.1 Batch vs. Online Learning 123

    6.3.1.2 Instance-Based vs. Model-Based Learning 123

    6.3.1.3 Supervised Learning vs. Unsupervised Learning 123

    6.3.1.4 Semi-Supervised Learning 123

    6.3.1.5 Reinforcement Learning 124

    6.3.1.6 Transfer Learning 124

    6.3.2 Main Challenges of Learning from Vibration Data 125

    6.3.2.1 The Curse of Dimensionality 125

    6.3.2.2 Irrelevant Features 126

    6.3.2.3 Environment and Operating Conditions of a Rotating Machine 126

    6.3.3 Preparing Vibration Data for Analysis 126

    6.3.3.1 Normalisation 126

    6.3.3.2 Dimensionality Reduction 127

    6.4 Summary 128

    References 128

    7 Linear Subspace Learning 131

    7.1 Introduction 131

    7.2 Principal Component Analysis (PCA) 132

    7.2.1 PCA Using Eigenvector Decomposition 132

    7.2.2 PCA Using SVD 133

    7.2.3 Application of PCA in Machine Fault Diagnosis 134

    7.3 Independent Component Analysis (ICA) 137

    7.3.1 Minimisation of Mutual Information 138

    7.3.2 Maximisation of the Likelihood 138

    7.3.3 Application of ICA in Machine Fault Diagnosis 139

    7.4 Linear Discriminant Analysis (LDA) 141

    7.4.1 Application of LDA in Machine Fault Diagnosis 142

    7.5 Canonical Correlation Analysis (CCA) 143

    7.6 Partial Least Squares (PLS) 145

    7.7 Summary 146

    References 147

    8 Nonlinear Subspace Learning 153

    8.1 Introduction 153

    8.2 Kernel Principal Component Analysis (KPCA) 153

    8.2.1 Application of KPCA in Machine Fault Diagnosis 156

    8.3 Isometric Feature Mapping (ISOMAP) 156

    8.3.1 Application of ISOMAP in Machine Fault Diagnosis 158

    8.4 Diffusion Maps (DMs) and Diffusion Distances 159

    8.4.1 Application of DMs in Machine Fault Diagnosis 160

    8.5 Laplacian Eigenmap (LE) 161

    8.5.1 Application of the LE in Machine Fault Diagnosis 161

    8.6 Local Linear Embedding (LLE) 162

    8.6.1 Application of LLE in Machine Fault Diagnosis 163

    8.7 Hessian-Based LLE 163

    8.7.1 Application of HLLE in Machine Fault Diagnosis 164

    8.8 Local Tangent Space Alignment Analysis (LTSA) 165

    8.8.1 Application of LTSA in Machine Fault Diagnosis 165

    8.9 Maximum Variance Unfolding (MVU) 166

    8.9.1 Application of MVU in Machine Fault Diagnosis 167

    8.10 Stochastic Proximity Embedding (SPE) 168

    8.10.1 Application of SPE in Machine Fault Diagnosis 168

    8.11 Summary 169

    References 170

    9 Feature Selection 173

    9.1 Introduction 173

    9.2 Filter Model-Based Feature Selection 175

    9.2.1 Fisher Score (FS) 176

    9.2.2 Laplacian Score (LS) 177

    9.2.3 Relief and Relief-F Algorithms 178

    9.2.3.1 Relief Algorithm 178

    9.2.3.2 Relief-F Algorithm 179

    9.2.4 Pearson Correlation Coefficient (PCC) 180

    9.2.5 Information Gain (IG) and Gain Ratio (GR) 180

    9.2.6 Mutual Information (MI) 181

    9.2.7 Chi-Squared (Chi-2) 181

    9.2.8 Wilcoxon Ranking 181

    9.2.9 Application of Feature Ranking in Machine Fault Diagnosis 182

    9.3 Wrapper Model–Based Feature Subset Selection 185

    9.3.1 Sequential Selection Algorithms 185

    9.3.2 Heuristic-Based Selection Algorithms 185

    9.3.2.1 Ant Colony Optimisation (ACO) 185

    9.3.2.2 Genetic Algorithms (GAs) and Genetic Programming 187

    9.3.2.3 Particle Swarm Optimisation (PSO) 188

    9.3.3 Application of Wrapper Model–Based Feature Subset Selection in Machine Fault Diagnosis 189

    9.4 Embedded Model–Based Feature Selection 192

    9.5 Summary 193

    References 194

    Part IV Classification Algorithms 199

    10 Decision Trees and Random Forests 201

    10.1 Introduction 201

    10.2 Decision Trees 202

    10.2.1 Univariate Splitting Criteria 204

    10.2.1.1 Gini Index 205

    10.2.1.2 Information Gain 206

    10.2.1.3 Distance Measure 207

    10.2.1.4 Orthogonal Criterion (ORT) 207

    10.2.2 Multivariate Splitting Criteria 207

    10.2.3 Tree-Pruning Methods 208

    10.2.3.1 Error-Complexity Pruning 208

    10.2.3.2 Minimum-Error Pruning 209

    10.2.3.3 Reduced-Error Pruning 209

    10.2.3.4 Critical-Value Pruning 210

    10.2.3.5 Pessimistic Pruning 210

    10.2.3.6 Minimum Description Length (MDL) Pruning 210

    10.2.4 Decision Tree Inducers 211

    10.2.4.1 CART 211

    10.2.4.2 ID3 211

    10.2.4.3 C4.5 211

    10.2.4.4 CHAID 212

    10.3 Decision Forests 212

    10.4 Application of Decision Trees/Forests in Machine Fault Diagnosis 213

    10.5 Summary 217

    References 217

    11 Probabilistic Classification Methods 225

    11.1 Introduction 225

    11.2 Hidden Markov Model 225

    11.2.1 Application of Hidden Markov Models in Machine Fault Diagnosis 228

    11.3 Logistic Regression Model 230

    11.3.1 Logistic Regression Regularisation 232

    11.3.2 Multinomial Logistic Regression Model (MLR) 232

    11.3.3 Application of Logistic Regression in Machine Fault Diagnosis 233

    11.4 Summary 234

    References 235

    12 Artificial Neural Networks (ANNs) 239

    12.1 Introduction 239

    12.2 Neural Network Basic Principles 240

    12.2.1 The Multilayer Perceptron 241

    12.2.2 The Radial Basis Function Network 243

    12.2.3 The Kohonen Network 244

    12.3 Application of Artificial Neural Networks in Machine Fault Diagnosis 245

    12.4 Summary 253

    References 254

    13 Support Vector Machines (SVMs) 259

    13.1 Introduction 259

    13.2 Multiclass SVMs 262

    13.3 Selection of Kernel Parameters 263

    13.4 Application of SVMs in Machine Fault Diagnosis 263

    13.5 Summary 274

    References 274

    14 Deep Learning 279

    14.1 Introduction 279

    14.2 Autoencoders 280

    14.3 Convolutional Neural Networks (CNNs) 283

    14.4 Deep Belief Networks (DBNs) 284

    14.5 Recurrent Neural Networks (RNNs) 285

    14.6 Overview of Deep Learning in MCM 286

    14.6.1 Application of AE-based DNNs in Machine Fault Diagnosis 286

    14.6.2 Application of CNNs in Machine Fault Diagnosis 292

    14.6.3 Application of DBNs in Machine Fault Diagnosis 296

    14.6.4 Application of RNNs in Machine Fault Diagnosis 298

    14.7 Summary 299

    References 301

    15 Classification Algorithm Validation 307

    15.1 Introduction 307

    15.2 The Hold-Out Technique 308

    15.2.1 Three-Way Data Split 309

    15.3 Random Subsampling 309

    15.4 K-Fold Cross-Validation 310

    15.5 Leave-One-Out Cross-Validation 311

    15.6 Bootstrapping 311

    15.7 Overall Classification Accuracy 312

    15.8 Confusion Matrix 313

    15.9 Recall and Precision 314

    15.10 ROC Graphs 315

    15.11 Summary 317

    References 318

    Part V New Fault Diagnosis Frameworks Designed for MCM 321

    16 Compressive Sampling and Subspace Learning (CS-SL) 323

    16.1 Introduction 323

    16.2 Compressive Sampling for Vibration-Based MCM 325

    16.2.1 Compressive Sampling Basics 325

    16.2.2 CS for Sparse Frequency Representation 328

    16.2.3 CS for Sparse Time-Frequency Representation 329

    16.3 Overview of CS in Machine Condition Monitoring 330

    16.3.1 Compressed Sensed Data Followed by Complete Data Construction 330

    16.3.2 Compressed Sensed Data Followed by Incomplete Data Construction 331

    16.3.3 Compressed Sensed Data as the Input of a Classifier 332

    16.3.4 Compressed Sensed Data Followed by Feature Learning 333

    16.4 Compressive Sampling and Feature Ranking (CS-FR) 333

    16.4.1 Implementations 334

    16.4.1.1 CS-LS 336

    16.4.1.2 CS-FS 336

    16.4.1.3 CS-Relief-F 337

    16.4.1.4 CS-PCC 338

    16.4.1.5 CS-Chi-2 338

    16.5 CS and Linear Subspace Learning-Based Framework for Fault Diagnosis 339

    16.5.1 Implementations 339

    16.5.1.1 CS-PCA 339

    16.5.1.2 CS-LDA 340

    16.5.1.3 CS-CPDC 341

    16.6 CS and Nonlinear Subspace Learning-Based Framework for Fault Diagnosis 343

    16.6.1 Implementations 344

    16.6.1.1 CS-KPCA 344

    16.6.1.2 CS-KLDA 345

    16.6.1.3 CS-CMDS 346

    16.6.1.4 CS-SPE 346

    16.7 Applications 348

    16.7.1 Case Study 1 348

    16.7.1.1 The Combination of MMV-CS and Several Feature-Ranking Techniques 350

    16.7.1.2 The Combination of MMV-CS and Several Linear and Nonlinear Subspace Learning Techniques 352

    16.7.2 Case Study 2 354

    16.7.2.1 The Combination of MMV-CS and Several Feature-Ranking Techniques 354

    16.7.2.2 The Combination of MMV-CS and Several Linear and Nonlinear Subspace Learning Techniques 355

    16.8 Discussion 355

    References 357

    17 Compressive Sampling and Deep Neural Network (CS-DNN) 361

    17.1 Introduction 361

    17.2 Related Work 361

    17.3 CS-SAE-DNN 362

    17.3.1 Compressed Measurements Generation 362

    17.3.2 CS Model Testing Using the Flip Test 363

    17.3.3 DNN-Based Unsupervised Sparse Overcomplete Feature Learning 363

    17.3.4 Supervised Fine Tuning 367

    17.4 Applications 367

    17.4.1 Case Study 1 367

    17.4.2 Case Study 2 372

    17.5 Discussion 375

    References 375

    18 Conclusion 379

    18.1 Introduction 379

    18.2 Summary and Conclusion 380

    Appendix Machinery Vibration Data Resources and Analysis Algorithms 389

    References 394

    Index 395

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