{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T05:37:03Z","timestamp":1774935423898,"version":"3.50.1"},"reference-count":38,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2021,6,23]],"date-time":"2021-06-23T00:00:00Z","timestamp":1624406400000},"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>The working environment of wind turbine gearboxes is complex, complicating the effective monitoring of their running state. In this paper, a new gearbox fault diagnosis method based on improved variational mode decomposition (IVMD), combined with time-shift multi-scale sample entropy (TSMSE) and a sparrow search algorithm-based support vector machine (SSA-SVM), is proposed. Firstly, a novel algorithm, IVMD, is presented for solving the problem where VMD parameters (K and \u03b1) need to be selected in advance, which mainly contains two steps: the maximum kurtosis index is employed to preliminarily determine a series of local optimal decomposition parameters (K and \u03b1), then from the local parameters, the global optimum parameters are selected based on the minimum energy loss coefficient (ELC). After decomposition by IVMD, the raw signal is divided into K intrinsic mode functions (IMFs), the optimal IMF(s) with abundant fault information is (are) chosen based on the minimum envelopment entropy criterion. Secondly, the time-shift technique is introduced to information entropy, the time-shift multi-scale sample entropy algorithm is applied for the analysis of the complexity of the chosen optimal IMF and extract fault feature vectors. Finally, the sparrow search algorithm, which takes the classification error rate of SVM as the fitness function, is used to adaptively optimize the SVM parameters. Next, the extracted TSMSEs are input into the SSA-SVM model as the feature vector to identify the gear signal types under different conditions. The simulation and experimental results confirm that the proposed method is feasible and superior in gearbox fault diagnosis when compared with other methods.<\/jats:p>","DOI":"10.3390\/e23070794","type":"journal-article","created":{"date-parts":[[2021,6,23]],"date-time":"2021-06-23T03:22:00Z","timestamp":1624418520000},"page":"794","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":29,"title":["Fault Diagnosis of a Wind Turbine Gearbox Based on Improved Variational Mode Algorithm and Information Entropy"],"prefix":"10.3390","volume":"23","author":[{"given":"Fan","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Xinjiang University, Urumqi 830047, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenlei","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Xinjiang University, Urumqi 830047, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongwei","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Xinjiang University, Urumqi 830047, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tiantian","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Xinjiang University, Urumqi 830047, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Teng, W., Ding, X., Tang, S., Xu, J., Shi, B., and Liu, Y. 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