{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:32:16Z","timestamp":1760239936619,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,1,27]],"date-time":"2019-01-27T00:00:00Z","timestamp":1548547200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51675001, 51707001, 51605002, and 51705001"],"award-info":[{"award-number":["51675001, 51707001, 51605002, and 51705001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the State Key Program of National Natural Science of China","award":["51637001"],"award-info":[{"award-number":["51637001"]}]},{"name":"the Natural Science Foundation of Anhui Province","award":["1808085QE121 and 1808085QF212"],"award-info":[{"award-number":["1808085QE121 and 1808085QF212"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this study, a nonlinear analysis method called improved information entropy (IIE) is proposed on the basis of constructing a special probability mass function for the normalized analysis of Shannon entropy for a time series. The definition is directly applied to several typical time series, and the characteristic of IIE is analyzed. This method can distinguish different kinds of signals and reflects the complexity of one-dimensional time series of high sensitivity to the changes in signal. Thus, the method is applied to the fault diagnosis of a rolling bearing. Experimental results show that the method can effectively extract the sensitive characteristics of the bearing running state and has fast operation time and minimal parameter requirements.<\/jats:p>","DOI":"10.3390\/e21020115","type":"journal-article","created":{"date-parts":[[2019,1,29]],"date-time":"2019-01-29T11:27:52Z","timestamp":1548761272000},"page":"115","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Method for Detecting Dynamic Mutation of Complex Systems Using Improved Information Entropy"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2834-9744","authenticated-orcid":false,"given":"Bin","family":"Ju","sequence":"first","affiliation":[{"name":"College of Electrical Engineering and Automation, Anhui University, Hefei 230601, China"},{"name":"National Engineering Laboratory of Energy-Saving Motor &amp; Control Technology, Anhui University, Hefei 230601, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haijiao","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering and Automation, Anhui University, Hefei 230601, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3420-3784","authenticated-orcid":false,"given":"Yongbin","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering and Automation, Anhui University, Hefei 230601, China"},{"name":"National Engineering Laboratory of Energy-Saving Motor &amp; Control Technology, Anhui University, Hefei 230601, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Donghui","family":"Pan","sequence":"additional","affiliation":[{"name":"College of Mathematical Sciences, Anhui University, Hefei 230601, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ping","family":"Zheng","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering and Automation, Anhui University, Hefei 230601, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lanbing","family":"Xu","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering and Automation, Anhui University, Hefei 230601, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guoli","family":"Li","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering and Automation, Anhui University, Hefei 230601, China"},{"name":"National Engineering Laboratory of Energy-Saving Motor &amp; Control Technology, Anhui University, Hefei 230601, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,1,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1109\/MIE.2013.2287651","article-title":"Trends in fault diagnosis for electrical machines: A review of diagnostic techniques","volume":"8","author":"Henao","year":"2014","journal-title":"IEEE Ind. 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