Preface Chapter 1 Development of entropy theories 1.1 From thermodynamic to information entropy 1.2 Renyi entropy 1.3 Kolmogorov-Sinai entropy 1.4 Eckmann-Ruelle entropy 1.5 Approximate entropy 1.6 Sample entropy 1.7 Fuzzy entropy 1.8 Permutation entropy 1.9 Conclusions 1.10 References Chapter 2 Comparative analysis of entropy methods on health condition monitoring of machines 2.1 Comparisons of various entropy measures 2.2 Quantitative comparison of entropy measures 2.3 Effect of noise on entropy calculation 2.3.1 Research on the effect of noise using a simulated model 2.3.2 Performance comparison under strong noise 2.4 Calculation efficiency 2.4.1 Research on the calculation efficiency using simulation model 2.4.2 Discussion on the calculation efficiency 2.5 Effect of data length 2.6 Classification performance 2.6.1 Simulation model regarding classification performance 2.6.2 Classification performances for different types of entropy algorithms 2.7 Conclusions 2.8 References Chapter 3 Intelligent fault diagnosis based on entropy theories 3.1 General procedure of the intelligent fault diagnosis 3.1.1 Data collection 3.1.2 Feature extraction 3.1.3 Feature selection 3.1.4 Pattern recognition 3.2 Case study: intelligent fault diagnosis method based on modified multiscale symbolic dynamic entropy and mRMR 3.2.1 MMSDE-mRMR-LSSVM method 3.2.2 Experiment 3.3 Conclusions 3.4 References Chapter 4 Diversity entropy 4.1 Introduction: consistency problem of the entropy methods 4.2 Methodology of diversity entropy 4.3 Properties and simulation evaluation 4.3.1 Consistency 4.3.2 Robustness 4.3.3 Calculation efficiency 4.4 Case study: fault diagnosis of the dual-rotor system 4.4.1 Fault diagnosis frame based on MDE and ELM 4.4.2 Experiment setup 4.4.3 Results and analysis 4.5 Conclusions
4.6 References Chapter 5 Symbolic dynamic filtering based entropy methods 5.1 Introduction 5.2 Methods 5.2.1 Symbolic dynamic filtering 5.2.2 Symbolic dynamic entropy 5.2.3 Symbolic fuzzy entropy 5.2.4 Symbolic diversity entropy 5.3 Numerical validation for symbolic fuzzy entropy 5.3.1 Complexity measure 5.3.2 Robustness to noise 5.3.3 Computational complexity 5.4 Case study: fault diagnosis of bearing system 5.4.1 MSFE-based fault diagnosis method 5.4.2 Test rig 5.4.3 Results and analysis 5.5 Conclusions 5.6 References Chapter 6 Multiscale based entropy methods 6.1 Multiscale methods 6.1.1 Multiscale entropy 6.1.2 Composite multiscale entropy 6.1.3 Modified multiscale entropy 6.1.4 Refined composite multiscale entropy 6.2 Generalized multiscale methods 6.2.1 Generalized multiscale entropy 6.2.2 Generalized composite multiscale entropy 6.2.3 Generalized refined composite multiscale entropy 6.3 Hierarchical multiscale methods 6.3.1 Hierarchical entropy 6.3.2 Modified hierarchical entropy 6.3.3 Modified hierarchical generalized composite entropy 6.4 Case study: multiscale entropy performance analysis 6.4.1 Dataset 6.4.2 Experiment setup 6.4.3 Results and analysis 6.5 Conclusions 6.6 References Chapter 7 Application of entropy methods in extracting weak fault characteristics by adaptive decomposition 7.1 Introduction 7.1.1 LMD 7.1.2 The optimum PF component selection 7.1.3 Improved mulfiscale fuzzy entropy 7.1.4 Feature selection using Laplacian score algorithm 7.1.5 Improved SVM-BT 7.2 Fault diagnosis based on LMD and IMFE 7.3 Case study: fault diagnosis of rolling bearing 7.3.1 Experiment setup 7.3.2 Results and analysis 7.4 Conclusions
7.5 References Chapter 8 Intelligent fault diagnosis based on entropy theories and transfer learning 8.1 Preliminary knowledge 8.1.1 Concepts 8.1.2 Single domain VS multisource domain 8.1.3 The domain invariant properties of the entropy 8.2 Transfer diagnosis from single source domain 8.2.1 The application of entropy in single source domain transfer problems 8.2.2 Multiscale transfer symbolic dynamic entropy method 8.2.3 Case study 8.3 Transfer diagnosis knowledge from multisource domain 8.3.1 The application of entropy in multiple source domain transfer problems 8.3.2 Multisource domain generalization based on dispersion entropy 8.3.3 Case study 8.4 Conclusions 8.5 References Chapter 9 Entropy-based fault diagnosis under variable rotational speed 9.1 Introduction 9.2 The bandwidth selection criterion for Vold-Kalman filter 9.3 Fault diagnosis frame based on IVKF, MSE, LS and LSSVM 9.4 Case study: fault diagnosis of planetary gearbox 9.4.1 Experiment setup 9.4.2 Results and analysis 9.5 Conclusions 9.6 References Chapter 10 Multivariate entropy methods and fault diagnosis of large-scale machinery 10.1 Introduction: multivariate entropy and large-scale machinery 10.2 Multivariate entropy 10.2.1 Multivariate multiscate sample entropy 10.2.2 Multivariate multiscale fuzzy entropy 10.2.3 Multivariate multiscale permutation entropy 10.3 Variational embedding multiscale diversity entropy 10.4 Simulation validation: the limitations of the multivariate entropy 10.4.1 Simulation setting 10.4.2 Results and analysis 10.5 Case study: fault diagnosis of bearing-rotor system 10.6 Conclusions 10.7 References Chapter 11 Oscillation-based permutation entropy calculation as dynamic nonlinear feature for health monitoring of rolling element bearing 11.1 Introduction 11.2 Weaknesses of PE in dynamic health monitoring 11.2.1 Simulation model 11.2.2 Two key weaknesses 11.3 Oscillation-based permutation entropy 11.3.1 Effect of bearing FSC on PE calculation 11.3.2 Theory of oscillation based FSC separation scheme 11.3.3 OBPE calculation for dynamic beating health monitoring 11.4 Parameter selection for OBPE 11.4.1 Selection of parameters related to TQWT 11.4.2 Selection of data length
11.4.3 Selection of embedding dimension and time delay 11.5 Case study 11.6 Conclusions 11.7 References Chapter 12 Summary
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