{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T01:33:15Z","timestamp":1772674395126,"version":"3.50.1"},"reference-count":46,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2019,4,15]],"date-time":"2019-04-15T00:00:00Z","timestamp":1555286400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In recent years, a new method of fault diagnosis, named variational mode decomposition (VMD), has been widely used in industrial production, but the decomposition accuracy of VMD is determined by two parameters, which are respectively the decomposition layer number k and the penalty factor \u03b1, if the parameters are not properly selected, there will be over-decomposition or under-decomposition. In order to find an approach to determine the parameters adaptively, a method to optimize VMD by using the immune fruit fly optimization algorithm (IFOA) is proposed in this paper. In this method, permutation entropy is used as the fitness function, firstly, the immune fruit fly optimization algorithm is used to search the combined parameters of k and \u03b1 in VMD, searching for the best combination parameters of k and \u03b1 by iteration, and then uses the combined parameters to perform VMD, finally, the center frequency is determined through frequency spectrum analysis. The method mentioned is applied to the fault extraction of a simulated signal and a measured signal of a wind turbine gearbox, and the fault frequency is successfully extracted. Using ensemble empirical mode decomposition (EEMD) and singular spectrum decomposition (SSD) to compare with the proposed method, which validated feasibility of the proposed method.<\/jats:p>","DOI":"10.3390\/e21040400","type":"journal-article","created":{"date-parts":[[2019,4,15]],"date-time":"2019-04-15T11:15:58Z","timestamp":1555326958000},"page":"400","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Research on Fault Extraction Method of Variational Mode Decomposition Based on Immunized Fruit Fly Optimization Algorithm"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9335-9597","authenticated-orcid":false,"given":"Jie","family":"Zhou","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoming","family":"Guo","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhijian","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenhua","family":"Du","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junyuan","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaofeng","family":"Han","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jingtai","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gaofeng","family":"He","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huihui","family":"He","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huiling","family":"Xue","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanfei","family":"Kou","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,4,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"336","DOI":"10.1016\/j.mechmachtheory.2018.10.007","article-title":"A statistical feature investigation of the spalling propagation assessment for a ball bearing","volume":"131","author":"Liu","year":"2019","journal-title":"Mech. 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