Condition Monitoring with Vibration Signals
Description
Clear and concise throughout, this accessible book is the first to be wholly devoted to the field of condition monitoring for rotating machines using vibration signals. It covers various feature extraction, feature selection, and classification methods as well as their applications to machine vibration datasets. It also presents new methods including machine learning and compressive sampling, which help to improve safety, reliability, and performance.
Condition Monitoring with Vibration Signals: Compressive Sampling and Learning Algorithms for Rotating Machines starts by introducing readers to Vibration Analysis Techniques and Machine Condition Monitoring (MCM). It then offers readers sections covering: Rotating Machine Condition Monitoring using Learning Algorithms; Classification Algorithms; and New Fault Diagnosis Frameworks designed for MCM. Readers will learn signal processing in the time-frequency domain, methods for linear subspace learning, and the basic principles of the learning method Artificial Neural Network (ANN). They will also discover recent trends of deep learning in the field of machine condition monitoring, new feature learning frameworks based on compressive sampling, subspace learning techniques for machine condition monitoring, and much more.
* Covers the fundamental as well as the state-of-the-art approaches to machine condition monitoring guiding readers from the basics of rotating machines to the generation of knowledge using vibration signals
* Provides new methods, including machine learning and compressive sampling, which offer significant improvements in accuracy with reduced computational costs
* Features learning algorithms that can be used for fault diagnosis and prognosis
* Includes previously and recently developed dimensionality reduction techniques and classification algorithms
Condition Monitoring with Vibration Signals: Compressive Sampling and Learning Algorithms for Rotating Machines is an excellent book for research students, postgraduate students, industrial practitioners, and researchers.
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HOSAMELDIN AHMED, Ph.D., has recently completed his Ph.D. degree in Electronic and Computer Engineering under the supervision of Professor Nandi at Brunel University London, UK. His research interests lie in the areas of signal processing, compressive sampling, and machine learning with applications to vibration-based machine condition monitoring.
ASOKE K. NANDI, Ph.D., is the Chair and Head of Electronic and Computer Engineering at Brunel University London, UK. He has held academic positions at Oxford, Imperial College London, Strathclyde, and Liverpool, as well as a Finland Distinguished Professorship in Jyvaskyla (Finland). Professor Nandi co-discovered the three particles known as W+, W- and Z0 which verified the unification of the electromagnetic force and the nuclear weak force and led to the award of the 1984 Nobel Prize for Physics to his two team leaders. He has authored over 600 technical publications, including 240 journal papers as well as five books. Professor Nandi is a Fellow of The Royal Academy of Engineering (UK).
Content
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
