Contents
Preface
Chapter 1 Development of entropy theories 1
1.1　From thermodynamic to information entropy 1
1.2　Rényi entropy 3
1.3　Kolmogorov-Sinai entropy 3
1.4　Eckmann-Ruelle entropy 4
1.5　Approximate entropy 5
1.6　Sample entropy 6
1.7　Fuzzy entropy 8
1.8　Permutation entropy 9
1.9　Conclusions 10
1.10　References 11
Chapter 2 Comparative analysis of entropy methods on health conditionb monitoring of machines 13
2.1　Comparisons of various entropy measures 13
2.2　Quantitative comparison of entropy measures 15
2.3　Effect of noise on entropy calculation 16
2.3.1　Research on the effect of noise using a simulated model 16
2.3.2　Performance comparison under strong noise 18
2.4　Calculation efficiency 21
2.4.1　Research on the calculation efficiency using simulation model 21
2.4.2　Discussion on the calculation efficiency 22
2.5　Effect of data length 23
2.6　Classification performance 24
2.6.1　Simulation model regarding classification performance 24
2.6.2　Classification performances for different types of entropy algorithms 26
2.7　Conclusions 29
2.8　References 29
Chapter 3 Intelligent fault diagnosis based on entropy theories 30
3.1　General procedure of the intelligent fault diagnosis 30
3.1.1　Data collection 30
3.1.2　Feature extraction 34
3.1.3　Feature selection 37
3.1.4　Pattern recognition 38
3.2　Case study: intelligent fault diagnosis method based on modified multiscale symbolic dynamic entropy and mRMR 45
3.2.1　MMSDE-mRMR-LSSVM method 45
3.2.2　Experiment 50
3.3　Conclusions 53
3.4　References 53
Chapter 4 Diversity entropy 55
4.1　Introduction: consistency problem of the entropy methods 55
4.2　Methodology of diversity entropy 56
4.3　Properties and simulation evaluation 60
4.3.1　Consistency 60
4.3.2　Robustness 62
4.3.3　Calculation efficiency 64
4.4　Case study: fault diagnosis of the dual-rotor system 65
4.4.1　Fault diagnosis frame based on MDE and ELM 65
4.4.2　Experiment setup 65
4.4.3　Results and analysis 67
4.5　Conclusions 71
4.6　References 71
Chapter 5 Symbolic dynamic filtering based entropy methods 73
5.1　Introduction 73
5.2　Methods 74
5.2.1　Symbolic dynamic filtering 74
5.2.2　Symbolic dynamic entropy 77
5.2.3　Symbolic fuzzy entropy 79
5.2.4　Symbolic diversity entropy 81
5.3　Numerical validation for symbolic fuzzy entropy 84
5.3.1　Complexity measure 84
5.3.2　Robustness to noise 86
5.3.3　Computational complexity 88
5.4　Case study: fault diagnosis of bearing system 88
5.4.1　MSFE-based fault diagnosis method 89
5.4.2　Test rig 90
5.4.3　Results and analysis 91
5.5　Conclusions 92
5.6　References 93
Chapter 6 Multiscale based entropy methods 95
6.1　Multiscale methods 97
6.1.1　Multiscale entropy 98
6.1.2　Composite multiscale entropy 99
6.1.3　Modified multiscale entropy 100
6.1.4　Refined composite multiscale entropy 101
6.2　Generalized multiscale methods 102
6.2.1　Generalized multiscale entropy 103
6.2.2　Generalized composite multiscale entropy 103
6.2.3　Generalized refined composite multiscale entropy 104
6.3　Hierarchical multiscale methods 105
6.3.1　Hierarchical entropy 105
6.3.2　Modified hierarchical entropy 107
6.3.3　Modified hierarchical generalized composite entropy 108
6.4　Case study: multiscale entropy performance analysis 109
6.4.1　Dataset 109
6.4.2　Experiment setup 110
6.4.3　Results and analysis 111
6.5　Conclusions 114
6.6　References 114
Chapter 7 Application of entropy methods in extracting weak fault characteristics by adaptive decomposition 115
7.1　Introduction 115
7.1.1　LMD 116
7.1.2　The optimum PF component selection 118
7.1.3　Improved multiscale fuzzy entropy 120
7.1.4　Feature selection using Laplacian score algorithm 121
7.1.5　Improved SVM-BT 122
7.2　Fault diagnosis based on LMD and IMFE 124
7.3　Case study: fault diagnosis of rolling bearing 124
7.3.1　Experiment setup 124
7.3.2　Results and analysis 126
7.4　Conclusions 130
7.5　References 130
Chapter 8 Intelligent fault diagnosis based on entropy theories and transfer learning 132
8.1　Preliminary knowledge 132
8.1.1　Concepts 133
8.1.2　Single domain VS multisource domain 133
8.1.3　The domain invariant properties of the entropy 134
8.2　Transfer diagnosis from single source domain 136
8.2.1 The application of entropy in single source domain transfer problems 136
8.2.2　Multiscale transfer symbolic dynamic entropy method 136
8.2.3　Case study 138
8.3　Transfer diagnosis knowledge from multisource domain 145
8.3.1　The application of entropy in multiple source domain transfer problems 145
8.3.2　Multisource domain generalization based on dispersion entropy 146
8.3.3　Case study 148
8.4　Conclusions 154
8.5　References 154
Chapter 9　Entropy-based fault diagnosis under variable rotational speed 155
9.1 Introduction 155
9.2 The bandwidth selection criterion for Vold-Kalman filter 156
9.3 Fault diagnosis frame based on IVKF, MSE, LS and LSSVM 159
9.4 Case study: fault diagnosis of planetary gearbox 160
9.4.1 Experiment setup 160
9.4.2 Results and analysis 164
9.5 Conclusions 169
9.6 References 169
Chapter 10　Multivariate entropy methods and fault diagnosis of large-scale machinery 171
10.1 Introduction: multivariate entropy and large-scale machinery 171
10.2 Multivariate entropy 172
10.2.1 Multivariate multiscale sample entropy 173
10.2.2 Multivariate multiscale fuzzy entropy 174
10.2.3 Multivariate multiscale permutation entropy 175
10.3 Variational embedding multiscale diversity entropy 177
10.4 Simulation validation: the limitations of the multivariate entropy 180
10.4.1 Simulation setting 180
10.4.2 Results and analysis 182
10.5 Case study: fault diagnosis of bearing-rotor system 185
10.6 Conclusions 189
10.7 References 189
Chapter 11　Oscillation-based permutation entropy calculation as dynamic
nonlinear feature for health monitoring of rolling element bearing 190
11.1 Introduction 190
11.2 Weaknesses of PE in dynamic health monitoring 192
11.2.1 Simulation model 192
11.2.2 Two key weaknesses 193
11.3 Oscillation-based permutation entropy 196
11.3.1 Effect of bearing FSC on PE calculation 197
11.3.2 Theory of oscillation based FSC separation scheme 198
11.3.3 OBPE calculation for dynamic bearing health monitoring 201
11.4 Parameter selection for OBPE 202
11.4.1 Selection of parameters related to TQWT 202
11.4.2 Selection of data length 204
11.4.3 Selection of embedding dimension and time delay 205
11.5 Case study 206
11.6 Conclusions 210
11.7 References 210
Chapter 12　
Summary 212