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NSREF. 2020011"],"award-info":[{"award-number":["HIT. NSREF. 2020011"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Rotating machinery plays an important role in various kinds of industrial engineering. How to assess their conditions is a key problem for operating safety and condition-based maintenance. The potential anomaly, fault and failure information can be obtained by analyzing the collected condition monitoring data of the previously deployed sensors in rotating machinery. Among the available methods of analyzing sensors data, entropy and its variants can provide quantitative information contained in these sensing data. For implementing fault detection, diagnosis, and prognostics, this information can be utilized for feature extraction and selecting appropriate training data for machine learning methods. This article aims to review the related entropy theories which have been applied for condition monitoring of rotating machinery. This review consists of typical entropy theories presentation, application, summary, and discussion.<\/jats:p>","DOI":"10.3390\/e21111061","type":"journal-article","created":{"date-parts":[[2019,10,31]],"date-time":"2019-10-31T05:18:26Z","timestamp":1572499106000},"page":"1061","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":29,"title":["Related Entropy Theories Application in Condition Monitoring of Rotating Machineries"],"prefix":"10.3390","volume":"21","author":[{"given":"Liansheng","family":"Liu","sequence":"first","affiliation":[{"name":"School of Electronics and Information Engineering, Harbin Institute of Technology, Harbin 150080, China"}]},{"given":"Zhuo","family":"Zhi","sequence":"additional","affiliation":[{"name":"School of Electronics and Information Engineering, Harbin Institute of Technology, Harbin 150080, China"}]},{"given":"Hanxing","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Electronics and Information Engineering, Harbin Institute of Technology, Harbin 150080, China"}]},{"given":"Qing","family":"Guo","sequence":"additional","affiliation":[{"name":"School of Electronics and Information Engineering, Harbin Institute of Technology, Harbin 150080, China"}]},{"given":"Yu","family":"Peng","sequence":"additional","affiliation":[{"name":"School of Electronics and Information Engineering, Harbin Institute of Technology, Harbin 150080, China"}]},{"given":"Datong","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Electronics and Information Engineering, Harbin Institute of Technology, Harbin 150080, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,10,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"66723","DOI":"10.1109\/ACCESS.2018.2873782","article-title":"The entropy algorithm and its variants in the fault diagnosis of rotating machinery: A review","volume":"6","author":"Li","year":"2018","journal-title":"IEEE Access"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1016\/j.ymssp.2018.06.032","article-title":"A review of stochastic resonance in rotating machine fault detection","volume":"116","author":"Lu","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1362","DOI":"10.1109\/TFUZZ.2018.2878200","article-title":"A systematic review of fuzzy formalisms for bearing fault diagnosis","volume":"27","author":"Li","year":"2019","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1016\/j.measurement.2017.02.031","article-title":"Atomic decomposition and sparse representation for complex signal analysis in machinery fault diagnosis: A review with examples","volume":"103","author":"Feng","year":"2017","journal-title":"Measurement"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Mo, Z., Wang, J., Zhang, H., and Miao, Q. (2019). Weighted cyclic harmonic-to-noise ratio for rolling element bearing fault diagnosis. IEEE Trans. Instrum. Meas.","DOI":"10.1109\/TIM.2019.2903615"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"55631","DOI":"10.1109\/ACCESS.2019.2912716","article-title":"Flexible Kurtogram for Extracting Repetitive Transients for Prognostics and Health Management of Rotating Components","volume":"7","author":"Zhong","year":"2019","journal-title":"IEEE Access"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1539","DOI":"10.1109\/TIE.2017.2733438","article-title":"Machine health monitoring using local feature-based gated recurrent unit networks","volume":"65","author":"Zhao","year":"2017","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"410","DOI":"10.1016\/j.measurement.2018.06.051","article-title":"Quantitative trend fault diagnosis of a rolling bearing based on Sparsogram and Lempel-Ziv","volume":"128","author":"Cui","year":"2018","journal-title":"Measurement"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"125104","DOI":"10.1088\/1361-6501\/aa9460","article-title":"A hybrid approach to fault diagnosis of roller bearings under variable speed conditions","volume":"28","author":"Wang","year":"2017","journal-title":"Meas. Sci. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1638","DOI":"10.1109\/TFUZZ.2017.2738607","article-title":"A random fuzzy accelerated degradation model and statistical analysis","volume":"26","author":"Li","year":"2017","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Sun, F., Liu, L., Li, X., and Liao, H. (2016). Stochastic Modeling and Analysis of Multiple Nonlinear Accelerated Degradation Processes through Information Fusion. Sensors, 16.","DOI":"10.3390\/s16081242"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"8695","DOI":"10.1109\/TIE.2017.2698359","article-title":"Quantitative and localization diagnosis of a defective ball bearing based on vertical\u2013horizontal synchronization signal analysis","volume":"64","author":"Cui","year":"2017","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1331","DOI":"10.1109\/TR.2017.2739126","article-title":"Statistical modeling of bearing degradation signals","volume":"66","author":"Wang","year":"2017","journal-title":"IEEE Trans. Reliab."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1016\/j.jsv.2018.01.001","article-title":"Multi-scale stochastic resonance spectrogram for fault diagnosis of rolling element bearings","volume":"420","author":"He","year":"2018","journal-title":"J. Sound Vib."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"250","DOI":"10.1016\/j.jsv.2015.01.052","article-title":"Smoothness index-guided Bayesian inference for determining joint posterior probability distributions of anti-symmetric real Laplace wavelet parameters for identification of different bearing faults","volume":"345","author":"Wang","year":"2015","journal-title":"J. Sound Vib."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.jsv.2018.07.039","article-title":"Initial center frequency-guided VMD for fault diagnosis of rotating machines","volume":"435","author":"Jiang","year":"2018","journal-title":"J. Sound Vib."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2716","DOI":"10.1109\/TIE.2017.2736510","article-title":"A new family of model-based impulsive wavelets and their sparse representation for rolling bearing fault diagnosis","volume":"65","author":"Qin","year":"2017","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"16277","DOI":"10.1109\/ACCESS.2017.2735966","article-title":"Remaining useful life prediction for a machine with multiple dependent features based on Bayesian dynamic linear model and copulas","volume":"5","author":"Sun","year":"2017","journal-title":"IEEE Access"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3671","DOI":"10.3233\/JIFS-169542","article-title":"Regrouping particle swarm optimization based variable neural network for gearbox fault diagnosis","volume":"34","author":"Liao","year":"2018","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3467","DOI":"10.1109\/TFUZZ.2018.2833820","article-title":"Step-by-step fuzzy diagnosis method for equipment based on symptom extraction and trivalent logic fuzzy diagnosis theory","volume":"26","author":"Song","year":"2018","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1109\/TII.2018.2810226","article-title":"Feature trend extraction and adaptive density peaks search for intelligent fault diagnosis of machines","volume":"15","author":"Wang","year":"2018","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1887","DOI":"10.1109\/TIM.2018.2806984","article-title":"Vibration-based intelligent fault diagnosis for roller bearings in low-speed rotating machinery","volume":"67","author":"Song","year":"2018","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1115\/1.4028833","article-title":"An intelligent prognostic system for gear performance degradation assessment and remaining useful life estimation","volume":"137","author":"Wang","year":"2015","journal-title":"J. Vib. Acoust."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/j.ymssp.2018.05.050","article-title":"Deep learning and its applications to machine health monitoring","volume":"115","author":"Zhao","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"3814","DOI":"10.1109\/TIE.2018.2856205","article-title":"The optimized deep belief networks with improved logistic Sigmoid units and their application in fault diagnosis for planetary gearboxes of wind turbines","volume":"66","author":"Qin","year":"2018","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2446","DOI":"10.1109\/TII.2018.2864759","article-title":"Highly-accurate machine fault diagnosis using deep transfer learning","volume":"15","author":"Shao","year":"2019","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/j.knosys.2017.12.027","article-title":"Convolutional neural network-based hidden Markov models for rolling element bearing fault identification","volume":"144","author":"Wang","year":"2018","journal-title":"Knowl. Based Syst."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.neucom.2018.04.048","article-title":"Adaptive deep feature learning network with Nesterov momentum and its application to rotating machinery fault diagnosis","volume":"305","author":"Tang","year":"2018","journal-title":"Neurocomputing"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1693","DOI":"10.1109\/TIM.2017.2669947","article-title":"Multisensor feature fusion for bearing fault diagnosis using sparse autoencoder and deep belief network","volume":"66","author":"Chen","year":"2017","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Wei, Y., Li, Y., Xu, M., and Huang, W. (2019). A review of early fault diagnosis approaches and their applications in rotating machinery. Entropy, 21.","DOI":"10.3390\/e21040409"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2092","DOI":"10.1016\/j.microrel.2015.06.076","article-title":"Entropy-based sensor selection for condition monitoring and prognostics of aircraft engine","volume":"55","author":"Liu","year":"2015","journal-title":"Microelectron. Reliab."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1016\/j.isatra.2018.06.001","article-title":"Health condition identification of planetary gearboxes based on variational mode decomposition and generalized composite multi-scale symbolic dynamic entropy","volume":"81","author":"Li","year":"2018","journal-title":"ISA Trans."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1016\/j.microrel.2017.03.008","article-title":"Quantitative selection of sensor data based on improved permutation entropy for system remaining useful life prediction","volume":"75","author":"Liu","year":"2017","journal-title":"Microelectron. Reliab."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"3110","DOI":"10.3390\/e17053110","article-title":"The multiscale entropy algorithm and its variants: A review","volume":"17","year":"2015","journal-title":"Entropy"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1553","DOI":"10.3390\/e14081553","article-title":"Permutation entropy and its main biomedical and econophysics applications: A review","volume":"14","author":"Zanin","year":"2012","journal-title":"Entropy"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Liu, L., Wang, S., Liu, D., and Peng, Y. (2016, January 19\u201321). Quantitative description of sensor data monotonic trend for system degradation condition monitoring. Proceedings of the Prognostics and System Health Management Conference (PHM-Chengdu), Chengdu, China.","DOI":"10.1109\/PHM.2016.7819924"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J."},{"key":"ref_38","first-page":"1","article-title":"The fault diagnosis of rolling bearing based on ensemble empirical mode decomposition and random forest","volume":"2017","author":"Qin","year":"2017","journal-title":"Shock Vib."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"174102","DOI":"10.1103\/PhysRevLett.88.174102","article-title":"Permutation entropy: A natural complexity measure for time series","volume":"88","author":"Bandt","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"022911","DOI":"10.1103\/PhysRevE.87.022911","article-title":"Weighted-permutation entropy: A complexity measure for time series incorporating amplitude information","volume":"87","author":"Fadlallah","year":"2013","journal-title":"Phys. Rev. E"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/j.ymssp.2017.06.011","article-title":"Generalized composite multiscale permutation entropy and Laplacian score based rolling bearing fault diagnosis","volume":"99","author":"Zheng","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_42","first-page":"547","article-title":"On measures of entropy and information","volume":"Volume 1","year":"1961","journal-title":"Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability"},{"key":"ref_43","unstructured":"Cachin, C. (1997, January 11\u201315). Smooth entropy and R\u00e9nyi entropy. Proceedings of the International Conference on Theory & Application of Cryptographic Techniques, Konstanz, Germany."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"2039","DOI":"10.1152\/ajpheart.2000.278.6.H2039","article-title":"Physiological time-series analysis using approximate entropy and sample entropy","volume":"278","author":"Richman","year":"2000","journal-title":"Am. J. Physiol. Heart Circ. Physiol."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"R789","DOI":"10.1152\/ajpregu.00069.2002","article-title":"Sample entropy analysis of neonatal heart rate variability","volume":"283","author":"Lake","year":"2002","journal-title":"Am. J. Physiol. Regul. Integr. Comp. Physiol."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"6077","DOI":"10.1016\/j.eswa.2010.02.118","article-title":"Bearing fault diagnosis using multi-scale entropy and adaptive neuro-fuzzy inference","volume":"37","author":"Zhang","year":"2010","journal-title":"Expert Syst. Appl."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"2297","DOI":"10.1073\/pnas.88.6.2297","article-title":"Approximate entropy as a measure of system complexity","volume":"88","author":"Pincus","year":"1991","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/j.medengphy.2008.04.005","article-title":"Measuring complexity using FuzzyEn, ApEn, and SampEn","volume":"31","author":"Chen","year":"2009","journal-title":"Med. Eng. Phys."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/j.mechmachtheory.2014.03.014","article-title":"A rolling bearing fault diagnosis method based on multi-scale fuzzy entropy and variable predictive model-based class discrimination","volume":"78","author":"Zheng","year":"2014","journal-title":"Mech. Mach. Theory"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"125002","DOI":"10.1088\/0957-0233\/24\/12\/125002","article-title":"Rolling bearing fault detection using an adaptive lifting multiwavelet packet with a dimension spectrum","volume":"24","author":"Jiang","year":"2013","journal-title":"Meas. Sci. Technol."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"2081","DOI":"10.1177\/1077546310395970","article-title":"Rolling element bearing fault diagnosis using autocorrelation and continuous wavelet transform","volume":"17","author":"Kankar","year":"2011","journal-title":"J. Vib. Control"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/j.apacoust.2015.11.003","article-title":"Roller bearing acoustic signature extraction by wavelet packet transform, applications in fault detection and size estimation","volume":"104","author":"Hemmati","year":"2016","journal-title":"Appl. Acoust."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"11460","DOI":"10.1016\/j.matpr.2018.02.114","article-title":"Bearing fault diagnosis using empirical mode decomposition, entropy based features and data mining techniques","volume":"5","author":"Reddy","year":"2018","journal-title":"Mater. Today Proc."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"458","DOI":"10.1016\/j.physa.2018.09.052","article-title":"Entropy measures for early detection of bearing faults","volume":"514","author":"Leite","year":"2019","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1016\/j.neucom.2015.01.016","article-title":"Multi-fault diagnosis for rotating machinery based on orthogonal supervised linear local tangent space alignment and least square support vector machine","volume":"157","author":"Su","year":"2015","journal-title":"Neurocomputing"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"384","DOI":"10.1016\/j.ymssp.2017.03.005","article-title":"Weak fault detection and health degradation monitoring using customized standard multiwavelets","volume":"94","author":"Jing","year":"2017","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Wan, S., and Xiong, Z. (2018). Teager energy entropy ratio of wavelet packet transform and its application in bearing fault diagnosis. Entropy, 20.","DOI":"10.3390\/e20050388"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/s00170-019-03551-2","article-title":"Real-time chatter detection and automatic suppression for intelligent spindles based on wavelet packet energy entropy and local outlier factor algorithm","volume":"103","author":"Yao","year":"2019","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_59","first-page":"211","article-title":"Mechanical fault diagnosis method based on lmd shannon entropy and improved fuzzy c-means clustering","volume":"22","author":"Luo","year":"2017","journal-title":"Int. J. Acoust. Vib."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2014\/825825","article-title":"A roller bearing fault diagnosis method based on LCD energy entropy and ACROA-SVM","volume":"2014","author":"Ao","year":"2014","journal-title":"Shock Vib."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/j.neucom.2012.11.012","article-title":"Fault diagnosis of rolling element bearing using cyclic autocorrelation and wavelet transform","volume":"110","author":"Kankar","year":"2013","journal-title":"Neurocomputing"},{"key":"ref_62","doi-asserted-by":"crossref","unstructured":"Pang, B., Tang, G., Zhou, C., and Tian, T. (2018). Rotor fault diagnosis based on characteristic frequency band energy entropy and support vector machine. Entropy, 20.","DOI":"10.3390\/e20120932"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/j.isatra.2018.11.044","article-title":"A multi-step progressive fault diagnosis method for rolling element bearing based on energy entropy theory and hybrid ensemble auto-encoder","volume":"87","author":"Jiang","year":"2019","journal-title":"ISA Trans."},{"key":"ref_64","first-page":"200","article-title":"Bearing fault diagnosis of a wind turbine based on variational mode decomposition and permutation entropy","volume":"231","author":"An","year":"2017","journal-title":"Proc. Inst. Mech. Eng. Part O J. Risk Reliab."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1016\/j.jsv.2015.09.016","article-title":"A fault diagnosis scheme for rolling bearing based on local mean decomposition and improved multiscale fuzzy entropy","volume":"360","author":"Li","year":"2016","journal-title":"J. Sound Vib."},{"key":"ref_66","doi-asserted-by":"crossref","unstructured":"Liu, J., Hu, Y., Wu, B., Wang, Y., and Xie, F. (2017). A hybrid generalized hidden Markov model-based condition monitoring approach for rolling bearings. Sensors, 17.","DOI":"10.3390\/s17051143"},{"key":"ref_67","doi-asserted-by":"crossref","unstructured":"Shi, Z., Song, W., and Taheri, S. (2016). Improved LMD, permutation entropy and optimized K-means to fault diagnosis for roller bearings. Entropy, 18.","DOI":"10.3390\/e18030070"},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1016\/j.isatra.2016.10.014","article-title":"A hybrid fault diagnosis approach based on mixed-domain state features for rotating machinery","volume":"66","author":"Xue","year":"2017","journal-title":"ISA Trans."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1177\/1687814016676157","article-title":"Railway rolling bearing fault diagnosis based on multi-scale intrinsic mode function permutation entropy and extreme learning machine classifier","volume":"8","author":"Yao","year":"2016","journal-title":"Adv. Mech. Eng."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"1887","DOI":"10.1177\/0954406214550014","article-title":"Feature extraction for rolling bearing fault diagnosis by electrostatic monitoring sensors","volume":"229","author":"Zhang","year":"2015","journal-title":"Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/j.ymssp.2014.09.002","article-title":"Detection of weak transient signals based on wavelet packet transform and manifold learning for rolling element bearing fault diagnosis","volume":"54\u201355","author":"Wang","year":"2015","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"6447","DOI":"10.3390\/e17096447","article-title":"Rolling bearing fault diagnosis based on wavelet packet decomposition and multi-scale permutation entropy","volume":"17","author":"Zhao","year":"2015","journal-title":"Entropy"},{"key":"ref_73","doi-asserted-by":"crossref","unstructured":"Fu, L., Zhu, T., Zhu, K., and Yang, Y. (2019). Condition monitoring for the roller bearings of wind turbines under variable working conditions based on the fisher score and permutation entropy. Energies, 12.","DOI":"10.3390\/en12163085"},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1016\/j.measurement.2018.08.038","article-title":"A novel intelligent detection method for rolling bearing based on IVMD and instantaneous energy distribution-permutation entropy","volume":"130","author":"Yan","year":"2018","journal-title":"Measurement"},{"key":"ref_75","doi-asserted-by":"crossref","unstructured":"Yasir, M.N., and Koh, B.-H. (2018). Data decomposition techniques with multi-scale permutation entropy calculations for bearing fault diagnosis. Sensors, 18.","DOI":"10.3390\/s18041278"},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"658","DOI":"10.1016\/j.ymssp.2016.04.028","article-title":"Self-adaptive bearing fault diagnosis based on permutation entropy and manifold-based dynamic time warping","volume":"114","author":"Tian","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_77","doi-asserted-by":"crossref","unstructured":"Lv, Y., Zhang, Y., and Yi, C. (2018). Optimized adaptive local iterative filtering algorithm based on permutation entropy for rolling bearing fault diagnosis. Entropy, 20.","DOI":"10.3390\/e20120920"},{"key":"ref_78","first-page":"1","article-title":"Multiscale permutation entropy based rolling bearing fault diagnosis","volume":"2014","author":"Zheng","year":"2014","journal-title":"Shock Vib."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1177\/1350650118788929","article-title":"A fault diagnosis method combined with compound multiscale permutation entropy and particle swarm optimization\u2013support vector machine for roller bearings diagnosis","volume":"233","author":"Xu","year":"2018","journal-title":"Proc. Inst. Mech. Eng. Part J J. Eng. Tribol."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"2711","DOI":"10.1007\/s12206-017-0514-5","article-title":"A rolling bearing fault diagnosis strategy based on improved multiscale permutation entropy and least squares SVM","volume":"31","author":"Li","year":"2017","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"17050","DOI":"10.1109\/ACCESS.2019.2893497","article-title":"A new bearing fault diagnosis method based on fine-to-coarse multiscale permutation entropy, laplacian score and SVM","volume":"7","author":"Huo","year":"2019","journal-title":"IEEE Access"},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.measurement.2015.08.034","article-title":"A new rolling bearing fault diagnosis method based on multiscale permutation entropy and improved support vector machine based binary tree","volume":"77","author":"Li","year":"2016","journal-title":"Measurement"},{"key":"ref_83","doi-asserted-by":"crossref","unstructured":"Dong, Z., Zheng, J., Huang, S., Pan, H., and Liu, Q. (2019). Time-shift multi-scale weighted permutation entropy and GWO-SVM based fault diagnosis approach for rolling bearing. Entropy, 21.","DOI":"10.3390\/e21060621"},{"key":"ref_84","doi-asserted-by":"crossref","unstructured":"Zhou, S., Qian, S., Chang, W., Xiao, Y., and Cheng, Y. (2018). A novel bearing multi-fault diagnosis approach based on weighted permutation entropy and an improved SVM ensemble classifier. Sensors, 18.","DOI":"10.3390\/s18061934"},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1177\/1077546313490778","article-title":"Bearing fault diagnosis based on multi-scale permutation entropy and adaptive neuro fuzzy classifier","volume":"21","author":"Tiwari","year":"2015","journal-title":"J. Vib. Control"},{"key":"ref_86","doi-asserted-by":"crossref","unstructured":"Yi, C., Lv, Y., Ge, M., Xiao, H., and Yu, X. (2017). Tensor singular spectrum decomposition algorithm based on permutation entropy for rolling bearing fault diagnosis. Entropy, 19.","DOI":"10.3390\/e19040139"},{"key":"ref_87","doi-asserted-by":"crossref","unstructured":"Zhang, W., and Zhou, J. (2019). Fault diagnosis for rolling element bearings based on feature space reconstruction and multiscale permutation entropy. Entropy, 21.","DOI":"10.3390\/e21050519"},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.measurement.2019.05.002","article-title":"Composite multi-scale weighted permutation entropy and extreme learning machine based intelligent fault diagnosis for rolling bearing","volume":"143","author":"Zheng","year":"2019","journal-title":"Measurement"},{"key":"ref_89","doi-asserted-by":"crossref","unstructured":"Xue, X., Li, C., Cao, S., Sun, J., and Liu, L. (2019). Fault diagnosis of rolling element bearings with a two-step scheme based on permutation entropy and random forests. Entropy, 21.","DOI":"10.3390\/e21010096"},{"key":"ref_90","first-page":"327","article-title":"Bearing fault prognostics using R\u00e9nyi entropy based features and Gaussian process models","volume":"52\u201353","author":"Petelin","year":"2015","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1243\/954406JMES291","article-title":"R\u00e9nyi entropy-based generalized statistical moments for early fatigue defect detection of rolling-element bearing","volume":"221","author":"Tao","year":"2007","journal-title":"Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci."},{"key":"ref_92","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1016\/j.ymssp.2016.10.028","article-title":"Bearing damage assessment using Jensen-R\u00e9nyi Divergence based on EEMD","volume":"87","author":"Singh","year":"2016","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_93","doi-asserted-by":"crossref","unstructured":"Liang, J., Zhong, J.-H., and Yang, Z.-X. (2017). Correlated EEMD and effective feature extraction for both periodic and irregular faults diagnosis in rotating machinery. Energies, 10.","DOI":"10.3390\/en10101652"},{"key":"ref_94","first-page":"557","article-title":"Fault diagnosis based on optimized node entropy using lifting wavelet packet transform and genetic algorithms","volume":"224","author":"Zhang","year":"2010","journal-title":"Proc. Inst. Mech. Eng. Part I J. Syst. Control Eng."},{"key":"ref_95","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1016\/j.asoc.2017.04.034","article-title":"Classification of ball bearing faults using a hybrid intelligent model","volume":"57","author":"Seera","year":"2017","journal-title":"Appl. Soft Comput."},{"key":"ref_96","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/j.measurement.2015.08.019","article-title":"A fault diagnosis method combined with LMD, sample entropy and energy ratio for roller bearings","volume":"76","author":"Han","year":"2015","journal-title":"Measurement"},{"key":"ref_97","doi-asserted-by":"crossref","unstructured":"Yang, F., Kou, Z., Wu, J., and Li, T. (2018). Application of mutual information-sample entropy based MED-ICEEMDAN De-noising scheme for weak fault diagnosis of hoist bearing. Entropy, 20.","DOI":"10.3390\/e20090667"},{"key":"ref_98","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/j.csefa.2017.10.002","article-title":"A case study of sample entropy analysis to the fault detection of bearing in wind turbine","volume":"9","author":"Ni","year":"2017","journal-title":"Case Stud. Eng. Fail. Anal."},{"key":"ref_99","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1016\/j.ymssp.2016.12.040","article-title":"A fault diagnosis scheme for planetary gearboxes using modified multi-scale symbolic dynamic entropy and mRMR feature selection","volume":"91","author":"Li","year":"2017","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_100","doi-asserted-by":"crossref","first-page":"45603","DOI":"10.1088\/0957-0233\/23\/4\/045603","article-title":"Approximate entropy as a nonlinear feature parameter for fault diagnosis in rotating machinery","volume":"23","author":"He","year":"2012","journal-title":"Meas. Sci. Technol."},{"key":"ref_101","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.ymssp.2016.05.009","article-title":"A frequency-weighted energy operator and complementary ensemble empirical mode decomposition for bearing fault detection","volume":"82","author":"Imaouchen","year":"2017","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_102","doi-asserted-by":"crossref","first-page":"3228","DOI":"10.1177\/0954406216642478","article-title":"Wind turbine bearing fault diagnosis based on adaptive local iterative filtering and approximate entropy","volume":"231","author":"An","year":"2017","journal-title":"Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci."},{"key":"ref_103","doi-asserted-by":"crossref","first-page":"286","DOI":"10.1016\/j.ymssp.2015.10.026","article-title":"Detection of cracks in shafts with the approximated entropy algorithm","volume":"72\u201373","author":"Sampaio","year":"2016","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_104","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1016\/j.mechmachtheory.2013.08.014","article-title":"A rolling bearing fault diagnosis approach based on LCD and fuzzy entropy","volume":"70","author":"Zheng","year":"2013","journal-title":"Mech. Mach. Theory"},{"key":"ref_105","doi-asserted-by":"crossref","first-page":"784","DOI":"10.1016\/j.acme.2016.05.003","article-title":"Rolling bearing fault diagnosis based on partially ensemble empirical mode decomposition and variable predictive model-based class discrimination","volume":"16","author":"Zheng","year":"2016","journal-title":"Arch. Civ. Mech. Eng."},{"key":"ref_106","doi-asserted-by":"crossref","first-page":"1431","DOI":"10.1177\/1077546314534870","article-title":"A fault diagnosis approach for roller bearing based on improved intrinsic timescale decomposition de-noising and kriging-variable predictive model-based class discriminate","volume":"22","author":"Yang","year":"2016","journal-title":"J. Vib. Control"},{"key":"ref_107","doi-asserted-by":"crossref","unstructured":"Zhao, H., Sun, M., Deng, W., and Yang, X. (2016). A new feature extraction method based on EEMD and multi-scale fuzzy entropy for motor bearing. Entropy, 19.","DOI":"10.3390\/e19010014"},{"key":"ref_108","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1007\/s12206-018-1211-8","article-title":"Refined composite multiscale fuzzy entropy: Localized defect detection of rolling element bearing","volume":"33","author":"Li","year":"2019","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_109","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1177\/0954408917691072","article-title":"Cross-fuzzy entropy-based approach for performance degradation assessment of rolling element bearings","volume":"232","author":"Zhu","year":"2018","journal-title":"Proc. Inst. Mech. Eng. Part E J. Process Mech. Eng."},{"key":"ref_110","doi-asserted-by":"crossref","first-page":"3317","DOI":"10.1177\/0954406218805510","article-title":"Multi-fault diagnosis of rolling bearing using fuzzy entropy of empirical mode decomposition, principal component analysis, and SOM neural network","volume":"233","author":"Zair","year":"2019","journal-title":"Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci."},{"key":"ref_111","doi-asserted-by":"crossref","first-page":"35042","DOI":"10.1109\/ACCESS.2018.2834540","article-title":"A novel fault diagnosis method based on integrating empirical wavelet transform and fuzzy entropy for motor bearing","volume":"6","author":"Deng","year":"2018","journal-title":"IEEE Access"},{"key":"ref_112","doi-asserted-by":"crossref","unstructured":"Zhu, K., Chen, L., and Hu, X. (2018). Rolling element bearing fault diagnosis by combining adaptive local iterative filtering, modified fuzzy entropy and support vector machine. Entropy, 20.","DOI":"10.3390\/e20120926"},{"key":"ref_113","doi-asserted-by":"crossref","unstructured":"Liu, Q., Pan, H., Zheng, J., Tong, J., and Bao, J. (2019). Composite interpolation-based multiscale fuzzy entropy and its application to fault diagnosis of rolling bearing. Entropy, 21.","DOI":"10.3390\/e21030292"},{"key":"ref_114","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1016\/j.measurement.2018.07.045","article-title":"Sigmoid-based refined composite multiscale fuzzy entropy and t-SNE based fault diagnosis approach for rolling bearing","volume":"129","author":"Zheng","year":"2018","journal-title":"Measurement"},{"key":"ref_115","doi-asserted-by":"crossref","unstructured":"Zhu, X., Zheng, J., Pan, H., Bao, J., and Zhang, Y. (2018). Time-shift multiscale fuzzy entropy and laplacian support vector machine based rolling bearing fault diagnosis. Entropy, 20.","DOI":"10.3390\/e20080602"},{"key":"ref_116","doi-asserted-by":"crossref","first-page":"3194","DOI":"10.1177\/1077546317702030","article-title":"Performance degradation assessment of rolling element bearings based on hierarchical entropy and general distance","volume":"24","author":"Zhu","year":"2018","journal-title":"J. Vib. Control"},{"key":"ref_117","doi-asserted-by":"crossref","first-page":"1223","DOI":"10.1243\/09544062JMES1224","article-title":"Spectral entropy: A complementary index for rolling element bearing performance degradation assessment","volume":"223","author":"Pan","year":"2009","journal-title":"Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci."},{"key":"ref_118","doi-asserted-by":"crossref","unstructured":"An, D., Kim, N.H., and Choi, J. (2016, January 4\u20138). Bearing prognostics method based on entropy decrease at specific frequency. Proceedings of the 18th AIAA Non-deterministic Approaches Conference, San Diego, CA, USA.","DOI":"10.2514\/6.2016-1678"},{"key":"ref_119","doi-asserted-by":"crossref","unstructured":"Song, W., Li, M., and Liang, J.K. (2016). Prediction of bearing fault using fractional Brownian motion and minimum entropy Deconvolution. Entropy, 18.","DOI":"10.3390\/e18110418"},{"key":"ref_120","doi-asserted-by":"crossref","first-page":"6683","DOI":"10.3390\/e17106683","article-title":"Feature extraction method of rolling bearing fault signal based on EEMD and cloud model characteristic entropy","volume":"17","author":"Han","year":"2015","journal-title":"Entropy"},{"key":"ref_121","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1016\/j.isatra.2018.12.002","article-title":"Application of EEMD and improved frequency band entropy in bearing fault feature extraction","volume":"88","author":"Li","year":"2019","journal-title":"ISA Trans."},{"key":"ref_122","doi-asserted-by":"crossref","first-page":"616","DOI":"10.1007\/s12204-019-2108-0","article-title":"Low speed bearing fault diagnosis based on EMD-CIIT histogram entropy and KFCM clustering","volume":"24","author":"Zhang","year":"2019","journal-title":"J. Shanghai Jiaotong Univ. (Sci.)"},{"key":"ref_123","doi-asserted-by":"crossref","unstructured":"Fu, W., Tan, J., Xu, Y., Wang, K., and Chen, T. (2019). Fault diagnosis for rolling bearings based on fine-sorted dispersion entropy and SVM optimized with mutation SCA-PSO. Entropy, 21.","DOI":"10.3390\/e21040404"},{"key":"ref_124","doi-asserted-by":"crossref","unstructured":"Rodriguez, N., Cabrera, G., Lagos, C., and Cabrera, E. (2017). Stationary wavelet singular entropy and kernel extreme learning for bearing multi-fault diagnosis. Entropy, 19.","DOI":"10.3390\/e19100541"},{"key":"ref_125","doi-asserted-by":"crossref","first-page":"742","DOI":"10.1016\/j.ymssp.2016.02.061","article-title":"Multifractal entropy based adaptive multiwavelet construction and its application for mechanical compound-fault diagnosis","volume":"76\u201377","author":"He","year":"2016","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_126","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1016\/j.neucom.2013.12.018","article-title":"Application of wavelet energy and Shannon entropy for feature extraction in gearbox fault detection under varying speed conditions","volume":"133","author":"Bafroui","year":"2014","journal-title":"Neurocomputing"},{"key":"ref_127","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.ymssp.2016.08.005","article-title":"Diagnosis of combined faults in rotary machinery by non-naive bayesian approach","volume":"85","author":"Asr","year":"2017","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_128","doi-asserted-by":"crossref","unstructured":"Xiao, Y., Na, K., Yi, H., and Zhang, G. (2017). Misalignment fault diagnosis of DFWT based on IEMD energy entropy and PSO-SVM. Entropy, 19.","DOI":"10.3390\/e19010006"},{"key":"ref_129","doi-asserted-by":"crossref","first-page":"823","DOI":"10.1016\/j.measurement.2007.03.004","article-title":"Application of time\u2013frequency entropy method based on Hilbert\u2013Huang transform to gear fault diagnosis","volume":"40","author":"Yu","year":"2007","journal-title":"Measurement"},{"key":"ref_130","doi-asserted-by":"crossref","first-page":"161","DOI":"10.3390\/e20030161","article-title":"A joint fault diagnosis scheme based on tensor nuclear norm canonical polyadic decomposition and multi-scale permutation entropy for gears","volume":"20","author":"Mao","year":"2018","journal-title":"Entropy"},{"key":"ref_131","doi-asserted-by":"crossref","unstructured":"Kuai, M., Cheng, G., Pang, Y., and Li, Y. (2018). Research of planetary gear fault diagnosis based on permutation entropy of CEEMDAN and ANFIS. Sensors, 18.","DOI":"10.20944\/preprints201801.0102.v1"},{"key":"ref_132","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1016\/j.ymssp.2012.04.016","article-title":"Fault detection of mechanical drives under variable operating conditions based on wavelet packet R\u00e9nyi entropy signatures","volume":"31","year":"2012","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_133","first-page":"5044","article-title":"Fault diagnosis of planetary gear based on entropy feature fusion of DTCWT and OKFDA","volume":"24","author":"Chen","year":"2017","journal-title":"J. Vib. Control"},{"key":"ref_134","doi-asserted-by":"crossref","unstructured":"Zhang, Z., Zhang, X., Zhang, P., Wu, F., and Li, X. (2018). Gearbox composite fault diagnosis method based on minimum entropy deconvolution and improved dual-tree complex wavelet transform. Entropy, 21.","DOI":"10.3390\/e21010018"},{"key":"ref_135","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1016\/j.measurement.2016.05.059","article-title":"Study on planetary gear fault diagnosis based on entropy feature fusion of ensemble empirical mode decomposition","volume":"91","author":"Gang","year":"2016","journal-title":"Measurement"},{"key":"ref_136","doi-asserted-by":"crossref","first-page":"2453","DOI":"10.1007\/s12206-016-0505-y","article-title":"Diagnosing planetary gear faults using the fuzzy entropy of LMD and ANFIS","volume":"30","author":"Chen","year":"2016","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_137","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1016\/j.measurement.2019.04.049","article-title":"Fault diagnosis of sun gear based on continuous vibration separation and minimum entropy deconvolution","volume":"141","author":"Zhang","year":"2019","journal-title":"Measurement"},{"key":"ref_138","doi-asserted-by":"crossref","unstructured":"Tang, G., Pang, B., He, Y., and Tian, T. (2019). Gearbox fault diagnosis based on hierarchical instantaneous energy density dispersion entropy and dynamic time warping. Entropy, 21.","DOI":"10.3390\/e21060593"},{"key":"ref_139","doi-asserted-by":"crossref","unstructured":"Cai, W., and Wang, Z. (2018). Application of an improved multipoint optimal minimum entropy deconvolution adjusted for gearbox composite fault diagnosis. Sensors, 18.","DOI":"10.3390\/s18092861"},{"key":"ref_140","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/j.jsv.2018.08.025","article-title":"Application of dispersion entropy to status characterization of rotary machines","volume":"438","author":"Rostaghi","year":"2019","journal-title":"J. Sound Vib."},{"key":"ref_141","doi-asserted-by":"crossref","unstructured":"Zhou, X., and Tang, Y. (2018). Modeling and fusing the uncertainty of FMEA experts using an entropy-like measure with an application in fault evaluation of aircraft turbine rotor blades. Entropy, 20.","DOI":"10.3390\/e20110864"},{"key":"ref_142","doi-asserted-by":"crossref","unstructured":"Wu, Z., Zhang, Q., Wang, L., Cheng, L., and Zhou, J. (2018). Early fault detection method for rotating machinery based on harmonic-assisted multivariate empirical mode decomposition and transfer entropy. Entropy, 20.","DOI":"10.3390\/e20110873"},{"key":"ref_143","doi-asserted-by":"crossref","unstructured":"Li, Q., Ji, X., and Liang, S.Y. (2017). Incipient fault feature extraction for rotating machinery based on improved AR-minimum entropy deconvolution combined with variational mode decomposition approach. Entropy, 19.","DOI":"10.3390\/e19070317"},{"key":"ref_144","first-page":"1","article-title":"Fault detection and diagnosis for gas turbines based on a kernelized information entropy model","volume":"2014","author":"Wang","year":"2014","journal-title":"Sci. World J."},{"key":"ref_145","doi-asserted-by":"crossref","first-page":"1100","DOI":"10.1016\/j.energy.2019.03.057","article-title":"Vibration fault diagnosis of wind turbines based on variational mode decomposition and energy entropy","volume":"174","author":"Chen","year":"2019","journal-title":"Energy"},{"key":"ref_146","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.renene.2013.06.025","article-title":"Fault diagnosis for a wind turbine transmission system based on manifold learning and Shannon wavelet support vector machine","volume":"62","author":"Tang","year":"2014","journal-title":"Renew. Energy"},{"key":"ref_147","doi-asserted-by":"crossref","unstructured":"Xiao, Y., Yi, H., Chen, X., and Chen, W. (2017). The application of Dual-Tree Complex Wavelet Transform (DTCWT) energy entropy in misalignment fault diagnosis of Doubly-Fed Wind Turbine (DFWT). Entropy, 19.","DOI":"10.3390\/e19110587"},{"key":"ref_148","doi-asserted-by":"crossref","first-page":"1287","DOI":"10.1631\/FITEE.1601365","article-title":"Finite-sensor fault-diagnosis simulation study of gas turbine engine using information entropy and deep belief networks","volume":"17","author":"Feng","year":"2016","journal-title":"Front. Inf. Technol. Electron. Eng."},{"key":"ref_149","doi-asserted-by":"crossref","unstructured":"Yin, B., Zhang, M., Lin, X., Fang, J., and Su, S. (2019). A fault diagnosis approach for autonomous underwater vehicle thrusters using time-frequency entropy enhancement and boundary constraint\u2013assisted relative gray relational grade. Proc. Inst. Mech. Eng. Part I J. Syst. Control Eng., 1\u201315.","DOI":"10.1177\/0959651819862177"},{"key":"ref_150","doi-asserted-by":"crossref","first-page":"26997","DOI":"10.3390\/s151026997","article-title":"Fault diagnosis of demountable disk-drum aero-engine rotor using customized multiwavelet method","volume":"15","author":"Chen","year":"2015","journal-title":"Sensors"},{"key":"ref_151","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2014\/957531","article-title":"Quantitative diagnosis of rotor vibration fault using process power spectrum entropy and support vector machine method","volume":"2014","author":"Fei","year":"2014","journal-title":"Shock Vib."},{"key":"ref_152","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1155\/2013\/403920","article-title":"Wavelet correlation feature scale entropy and fuzzy support vector machine approach for aeroengine whole-body vibration fault diagnosis","volume":"20","author":"Fei","year":"2013","journal-title":"Shock Vib."},{"key":"ref_153","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1631\/FITEE.1500337","article-title":"Application of complete ensemble intrinsic time-scale decomposition and least-square SVM optimized using hybrid DE and PSO to fault diagnosis of diesel engines","volume":"18","author":"Zhang","year":"2017","journal-title":"Front. Inf. Technol. Electron. Eng."},{"key":"ref_154","doi-asserted-by":"crossref","first-page":"8103","DOI":"10.1016\/j.eswa.2008.10.017","article-title":"Fault diagnosis of turbine based on fuzzy cross entropy of vague sets","volume":"36","author":"Ye","year":"2009","journal-title":"Expert Syst. Appl."},{"key":"ref_155","doi-asserted-by":"crossref","unstructured":"Xiao, L., Lv, Y., and Fu, G. (2019). Fault classification of rotary machinery based on smooth local subspace projection method and permutation entropy. Appl. Sci., 9.","DOI":"10.3390\/app9102102"},{"key":"ref_156","doi-asserted-by":"crossref","unstructured":"Wang, X., Si, S., Wei, Y., and Li, Y. (2019). The optimized multi-scale permutation entropy and its application in compound fault diagnosis of rotating machinery. Entropy, 21.","DOI":"10.3390\/e21020170"},{"key":"ref_157","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1016\/j.neucom.2018.07.021","article-title":"A method based on refined composite multi-scale symbolic dynamic entropy and ISVM-BT for rotating machinery fault diagnosis","volume":"315","author":"Li","year":"2018","journal-title":"Neurocomputing"},{"key":"ref_158","doi-asserted-by":"crossref","unstructured":"Fu, W., Tan, J., Li, C., Zou, Z., Li, Q., and Chen, T. (2018). A hybrid fault diagnosis approach for rotating machinery with the fusion of entropy-based feature extraction and SVM optimized by a chaos quantum sine cosine algorithm. Entropy, 20.","DOI":"10.3390\/e20090626"},{"key":"ref_159","doi-asserted-by":"crossref","unstructured":"Jiang, Q., Shen, Y., Li, H., and Xu, F. (2018). New fault recognition method for rotary machinery based on information entropy and a probabilistic neural network. Sensors, 18.","DOI":"10.3390\/s18020337"},{"key":"ref_160","doi-asserted-by":"crossref","unstructured":"Liu, L., Liu, D., Zhang, Y., and Peng, Y. (2016). Effective sensor selection and data anomaly detection for condition monitoring of aircraft engines. Sensors, 16.","DOI":"10.3390\/s16050623"},{"key":"ref_161","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1016\/j.microrel.2016.07.113","article-title":"FESeR: A data-driven framework to enhance sensor reliability for the system condition monitoring","volume":"64","author":"Liu","year":"2016","journal-title":"Microelectron. Reliab."},{"key":"ref_162","doi-asserted-by":"crossref","unstructured":"Liu, L., Peng, Y., Wang, L., Dong, Y., Liu, D., and Guo, Q. (2019). Improving EGT sensing data anomaly detection of aircraft auxiliary power unit. Chin. J. Aeronaut.","DOI":"10.1016\/j.cja.2019.10.001"},{"key":"ref_163","unstructured":"Liu, L., Liu, D., Guo, Q., Peng, Y., and Liang, J. (2008, January 14\u201317). SDR: Sensor data recovery for system condition monitoring. Proceedings of the IEEE International Instrumentation and Measurement Technology Conference, Houston, TX, USA."},{"key":"ref_164","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/j.microrel.2016.07.101","article-title":"DRES: Data recovery for condition monitoring to enhance system reliability","volume":"64","author":"Liu","year":"2016","journal-title":"Microelectron. Reliab."},{"key":"ref_165","doi-asserted-by":"crossref","first-page":"58336","DOI":"10.1109\/ACCESS.2019.2914236","article-title":"Data-driven remaining useful life prediction considering sensor anomaly detection and data recovery","volume":"7","author":"Liu","year":"2019","journal-title":"IEEE Access"},{"key":"ref_166","doi-asserted-by":"crossref","unstructured":"Saxena, A., Kai, G., Simon, D., and Eklund, N. (2008, January 6\u20139). Damage propagation modeling for aircraft engine run-to-failure simulation. Proceedings of the International Conference on Prognostics & Health Management, Denver, CO, USA.","DOI":"10.1109\/PHM.2008.4711414"},{"key":"ref_167","doi-asserted-by":"crossref","first-page":"1124","DOI":"10.1109\/JSEN.2013.2293517","article-title":"PHM-oriented integrated fusion prognostics for aircraft engines based on sensor data","volume":"14","author":"Xu","year":"2014","journal-title":"IEEE Sens. J."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/11\/1061\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:30:17Z","timestamp":1760189417000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/11\/1061"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,29]]},"references-count":167,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2019,11]]}},"alternative-id":["e21111061"],"URL":"https:\/\/doi.org\/10.3390\/e21111061","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,10,29]]}}}