{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,26]],"date-time":"2026-04-26T15:32:18Z","timestamp":1777217538607,"version":"3.51.4"},"reference-count":28,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,1,19]],"date-time":"2021-01-19T00:00:00Z","timestamp":1611014400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2018YFB0105300"],"award-info":[{"award-number":["2018YFB0105300"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["No. 2017YFD07006"],"award-info":[{"award-number":["No. 2017YFD07006"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In the fault monitoring of rotating machinery, the vibration signal of the bearing and gear in a complex operating environment has poor stationarity and high noise. How to accurately and efficiently identify various fault categories is a major challenge in rotary fault diagnosis. Most of the existing methods only analyze the single channel vibration signal and do not comprehensively consider the multi-channel vibration signal. Therefore, this paper presents Refined Composite Multivariate Multiscale Fluctuation Dispersion Entropy (RCMMFDE), a method which extracts the recognition information of multi-channel signals with different scale factors, and the refined composite analysis ensures the recognition stability. The simulation results show that this method has the characteristics of low sensitivity to signal length and strong anti-noise ability. At the same time, combined with Joint Mutual Information Maximisation (JMIM) and support vector machine (SVM), RCMMFDE-JMIM-SVM fault diagnosis method has been proposed. This method uses RCMMFDE to extract the state characteristics of the multiple vibration signals of the rotary machine, and then uses the JMIM method to extract the sensitive characteristics. Finally, different states of the rotary machine are classified by SVM. The validity of the method is verified by the composite gear fault data set and bearing fault data set. The diagnostic accuracy of the method is 99.25% and 100.00%. The experimental results show that RCMMFDE-JMIM-SVM can effectively recognize multiple signals.<\/jats:p>","DOI":"10.3390\/e23010128","type":"journal-article","created":{"date-parts":[[2021,1,19]],"date-time":"2021-01-19T11:39:55Z","timestamp":1611056395000},"page":"128","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["A Refined Composite Multivariate Multiscale Fluctuation Dispersion Entropy and Its Application to Multivariate Signal of Rotating Machinery"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3722-8725","authenticated-orcid":false,"given":"Chenbo","family":"Xi","sequence":"first","affiliation":[{"name":"Institute of Agricultural Machinery, Hubei University of Technology, Wuhan 430068, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guangyou","family":"Yang","sequence":"additional","affiliation":[{"name":"Institute of Agricultural Machinery, Hubei University of Technology, Wuhan 430068, China"},{"name":"Hubei Engineering Research Center for Intellectualization of Agricultural Equipment, Wuhan 430068, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lang","family":"Liu","sequence":"additional","affiliation":[{"name":"Institute of Agricultural Machinery, Hubei University of Technology, Wuhan 430068, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongyuan","family":"Jiang","sequence":"additional","affiliation":[{"name":"Institute of Agricultural Machinery, Hubei University of Technology, Wuhan 430068, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xuehai","family":"Chen","sequence":"additional","affiliation":[{"name":"Institute of Agricultural Machinery, Hubei University of Technology, Wuhan 430068, China"},{"name":"Hubei Engineering Research Center for Intellectualization of Agricultural Equipment, Wuhan 430068, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"88","DOI":"10.3901\/JME.2007.04.088","article-title":"Rolling-bearings fault diagnosis based-on empirical mode decomposition and least square support vector machine","volume":"43","author":"Wang","year":"2007","journal-title":"J. Mech. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"803","DOI":"10.1007\/s00170-017-1474-8","article-title":"Development and trend of condition monitoring and fault diagnosis of multi-sensors information fusion for rolling bearings: A review","volume":"96","author":"Duan","year":"2018","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1016\/j.rser.2015.11.032","article-title":"A review of wind turbine bearing condition monitoring: State of the art and challenges","volume":"56","author":"Bouchonneau","year":"2016","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"168732","DOI":"10.1109\/ACCESS.2019.2940627","article-title":"An improved empirical wavelet transform and refined composite multiscale dispersion entropy based fault diagnosis method for rolling bearing","volume":"8","author":"Zheng","year":"2019","journal-title":"IEEE Access"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1109\/18.119732","article-title":"Entropy-based algorithms for best basis selection","volume":"38","author":"Coifman","year":"2002","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1109\/TBME.2018.2852713","article-title":"On the Relevance of Computing a Local Version of Sample Entropy in Cardiovascular Control Analysis","volume":"3","author":"Porta","year":"2019","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"824","DOI":"10.1016\/j.ymssp.2006.02.009","article-title":"Approximate Entropy as a diagnostic tool for machine health monitoring","volume":"21","author":"Yan","year":"2007","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_8","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_9","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1016\/S0076-6879(04)84011-4","article-title":"Sample Entropy","volume":"384","author":"Richman","year":"2004","journal-title":"Method Enzym."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"610","DOI":"10.1109\/LSP.2016.2542881","article-title":"Dispersion Entropy: A Measure for Time-Series Analysis","volume":"23","author":"Rostaghi","year":"2016","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_11","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_12","doi-asserted-by":"crossref","unstructured":"Azami, H., and Escudero, J. (2018). Amplitude- and Fluctuation-Based Dispersion Entropy. Entropy, 20.","DOI":"10.3390\/e20030210"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"68718","DOI":"10.1109\/ACCESS.2019.2918560","article-title":"Multiscale Fluctuation-based Dispersion Entropy and its Applications to Neurological Diseases","volume":"7","author":"Azami","year":"2019","journal-title":"IEEE Access"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Gan, X., Lu, H., and Yang, G. (2019). Fault Diagnosis Method for Rolling Bearings Based on Composite Multiscale Fluctuation Dispersion Entropy. Entropy, 21.","DOI":"10.3390\/e21030290"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2020\/2375947","article-title":"Fault Diagnosis of Hydraulic Pumps Using PSO-VMD and Refined Composite Multiscale Fluctuation Dispersion Entropy","volume":"2020","author":"Zhou","year":"2020","journal-title":"Shock Vib."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Azami, H., Fernandez, A., and Escudero, J. (2017). Multivariate Multiscale Dispersion Entropy of Biomedical Times Series. Entropy, 21.","DOI":"10.3390\/e21090913"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"107233","DOI":"10.1016\/j.measurement.2019.107233","article-title":"Refined composite multivariate multiscale symbolic dynamic entropy and its application to fault diagnosis of rotating machine","volume":"151","author":"Yang","year":"2020","journal-title":"Measurement"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1109\/LSP.2011.2180713","article-title":"Multivariate Multiscale Entropy Analysis","volume":"19","author":"Ahmed","year":"2012","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Zheng, J., Tu, D., Pan, H., Hu, X., Liu, T., and Liu, Q. (2017). A Refined Composite Multivariate Multiscale Fuzzy Entropy and Laplacian Score-Based Fault Diagnosis Method for Rolling Bearings. Entropy, 19.","DOI":"10.3390\/e19110585"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Azami, H., Escudero, J., and Fern\u00e1ndez, A. (2016, January 20\u201321). Refined composite multivariate multiscale entropy based on variance for analysis of resting-state magnetoencephalograms in Alzheimer\u2019s disease. Proceedings of the 2016 International Conference for Students on Applied Engineering (ICSAE), Newcastle upon Tyne, UK.","DOI":"10.1109\/ICSAE.2016.7810227"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"8520","DOI":"10.1016\/j.eswa.2015.07.007","article-title":"Feature selection using Joint Mutual Information Maximisation","volume":"42","author":"Bennasar","year":"2015","journal-title":"Expert Syst. Appl."},{"key":"ref_22","first-page":"734","article-title":"Feature selection based on maximum conditional and joint mutual information","volume":"39","author":"Mao","year":"2019","journal-title":"J. Comput. Appl."},{"key":"ref_23","first-page":"8887","article-title":"JMIM: A Feature Selection Technique using Joint Mutual Information Maximization Approach","volume":"975","author":"Rajlakshmi","year":"2017","journal-title":"Int. J. Comput. Appl."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"61070","DOI":"10.1109\/ACCESS.2020.2983219","article-title":"Identification Failure Data for Cluster Heads Aggregation in WSN based on Improving Classification of SVM","volume":"8","author":"Dao","year":"2020","journal-title":"IEEE Access"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"9767","DOI":"10.1109\/ACCESS.2018.2794346","article-title":"ECG Signal Preprocessing and SVM Classifier-Based Abnormality Detection in Remote Healthcare Applications","volume":"6","author":"Venkatesan","year":"2018","journal-title":"IEEE Access"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Mao, X., Wang, L., and Li, C. (2008, January 20\u201322). SVM Classifier for Analog Fault Diagnosis Using Fractal Features. Proceedings of the Second International Symposium on Intelligent Information Technology Application (IITA\u201908), Shanghai, China.","DOI":"10.1109\/IITA.2008.249"},{"key":"ref_27","unstructured":"Azami, H., Rostaghi, M., and Escudero, J. (2016). Refined Composite Multiscale Dispersion Entropy: A Fast Measure of Complexity. arXiv."},{"key":"ref_28","first-page":"2579","article-title":"Visualizing Data using t-SNE","volume":"9","author":"Laurens","year":"2008","journal-title":"J. Mach. Learn. Res."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/1\/128\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:13:01Z","timestamp":1760159581000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/1\/128"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,19]]},"references-count":28,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,1]]}},"alternative-id":["e23010128"],"URL":"https:\/\/doi.org\/10.3390\/e23010128","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,19]]}}}