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ContentsPrefaceChapter 1 Development of entropy theories 11.1¡¡From thermodynamic to information entropy 11.2¡¡R¨¦nyi entropy 31.3¡¡Kolmogorov-Sinai entropy 31.4¡¡Eckmann-Ruelle entropy 41.5¡¡Approximate entropy 51.6¡¡Sample entropy 61.7¡¡Fuzzy entropy 81.8¡¡Permutation entropy 91.9¡¡Conclusions 101.10¡¡References 11Chapter 2 Comparative analysis of entropy methods on health conditionb monitoring of machines 132.1¡¡Comparisons of various entropy measures 132.2¡¡Quantitative comparison of entropy measures 152.3¡¡Effect of noise on entropy calculation 162.3.1¡¡Research on the effect of noise using a simulated model 162.3.2¡¡Performance comparison under strong noise 182.4¡¡Calculation efficiency 212.4.1¡¡Research on the calculation efficiency using simulation model 212.4.2¡¡Discussion on the calculation efficiency 222.5¡¡Effect of data length 232.6¡¡Classification performance 242.6.1¡¡Simulation model regarding classification performance 242.6.2¡¡Classification performances for different types of entropy algorithms 262.7¡¡Conclusions 292.8¡¡References 29Chapter 3 Intelligent fault diagnosis based on entropy theories 303.1¡¡General procedure of the intelligent fault diagnosis 303.1.1¡¡Data collection 303.1.2¡¡Feature extraction 343.1.3¡¡Feature selection 373.1.4¡¡Pattern recognition 383.2¡¡Case study: intelligent fault diagnosis method based on modified multiscale symbolic dynamic entropy and mRMR 453.2.1¡¡MMSDE-mRMR-LSSVM method 453.2.2¡¡Experiment 503.3¡¡Conclusions 533.4¡¡References 53Chapter 4 Diversity entropy 554.1¡¡Introduction: consistency problem of the entropy methods 554.2¡¡Methodology of diversity entropy 564.3¡¡Properties and simulation evaluation 604.3.1¡¡Consistency 604.3.2¡¡Robustness 624.3.3¡¡Calculation efficiency 644.4¡¡Case study: fault diagnosis of the dual-rotor system 654.4.1¡¡Fault diagnosis frame based on MDE and ELM 654.4.2¡¡Experiment setup 654.4.3¡¡Results and analysis 674.5¡¡Conclusions 714.6¡¡References 71Chapter 5 Symbolic dynamic filtering based entropy methods 735.1¡¡Introduction 735.2¡¡Methods 745.2.1¡¡Symbolic dynamic filtering 745.2.2¡¡Symbolic dynamic entropy 775.2.3¡¡Symbolic fuzzy entropy 795.2.4¡¡Symbolic diversity entropy 815.3¡¡Numerical validation for symbolic fuzzy entropy 845.3.1¡¡Complexity measure 845.3.2¡¡Robustness to noise 865.3.3¡¡Computational complexity 885.4¡¡Case study: fault diagnosis of bearing system 885.4.1¡¡MSFE-based fault diagnosis method 895.4.2¡¡Test rig 905.4.3¡¡Results and analysis 915.5¡¡Conclusions 925.6¡¡References 93Chapter 6 Multiscale based entropy methods 956.1¡¡Multiscale methods 976.1.1¡¡Multiscale entropy 986.1.2¡¡Composite multiscale entropy 996.1.3¡¡Modified multiscale entropy 1006.1.4¡¡Refined composite multiscale entropy 1016.2¡¡Generalized multiscale methods 1026.2.1¡¡Generalized multiscale entropy 1036.2.2¡¡Generalized composite multiscale entropy 1036.2.3¡¡Generalized refined composite multiscale entropy 1046.3¡¡Hierarchical multiscale methods 1056.3.1¡¡Hierarchical entropy 1056.3.2¡¡Modified hierarchical entropy 1076.3.3¡¡Modified hierarchical generalized composite entropy 1086.4¡¡Case study: multiscale entropy performance analysis 1096.4.1¡¡Dataset 1096.4.2¡¡Experiment setup 1106.4.3¡¡Results and analysis 1116.5¡¡Conclusions 1146.6¡¡References 114Chapter 7 Application of entropy methods in extracting weak fault characteristics by adaptive decomposition 1157.1¡¡Introduction 1157.1.1¡¡LMD 1167.1.2¡¡The optimum PF component selection 1187.1.3¡¡Improved multiscale fuzzy entropy 1207.1.4¡¡Feature selection using Laplacian score algorithm 1217.1.5¡¡Improved SVM-BT 1227.2¡¡Fault diagnosis based on LMD and IMFE 1247.3¡¡Case study: fault diagnosis of rolling bearing 1247.3.1¡¡Experiment setup 1247.3.2¡¡Results and analysis 1267.4¡¡Conclusions 1307.5¡¡References 130Chapter 8 Intelligent fault diagnosis based on entropy theories and transfer learning 1328.1¡¡Preliminary knowledge 1328.1.1¡¡Concepts 1338.1.2¡¡Single domain VS multisource domain 1338.1.3¡¡The domain invariant properties of the entropy 1348.2¡¡Transfer diagnosis from single source domain 1368.2.1 The application of entropy in single source domain transfer problems 1368.2.2¡¡Multiscale transfer symbolic dynamic entropy method 1368.2.3¡¡Case study 1388.3¡¡Transfer diagnosis knowledge from multisource domain 1458.3.1¡¡The application of entropy in multiple source domain transfer problems 1458.3.2¡¡Multisource domain generalization based on dispersion entropy 1468.3.3¡¡Case study 1488.4¡¡Conclusions 1548.5¡¡References 154Chapter 9¡¡Entropy-based fault diagnosis under variable rotational speed 1559.1 Introduction