{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T15:33:03Z","timestamp":1781019183078,"version":"3.54.1"},"reference-count":51,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,5,10]],"date-time":"2025-05-10T00:00:00Z","timestamp":1746835200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Jiangsu Engineering Research Center of Key Technology for Intelligent Manufacturing Equipment and Suqian Key laboratory of Intelligent Manufacturing","award":["M202108"],"award-info":[{"award-number":["M202108"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Efficient extraction and classification of fault features remain critical challenges in planetary gearbox fault diagnosis. A fault diagnosis framework is proposed that integrates hierarchical refined composite multiscale fuzzy entropy (HRCMFE) for feature extraction and a gray wolf optimization (GWO)-optimized least squares support vector machine (LSSVM) for classification. Firstly, the HRCMFE is developed for feature extraction, which combines the segmentation advantage of hierarchical entropy (HE) and the computational stability advantage of refined composite multiscale fuzzy entropy (RCMFE). Secondly, the hyperparameters of LSSVM are optimized by GWO using a proposed fitness function. Finally, fault diagnosis of the planetary gearbox is achieved by the optimized LSSVM using the HRCMFE-extracted features. Simulation and experimental study results indicate that the proposed method demonstrates superior effectiveness in both feature discriminability and diagnosis accuracy.<\/jats:p>","DOI":"10.3390\/e27050512","type":"journal-article","created":{"date-parts":[[2025,5,12]],"date-time":"2025-05-12T12:18:06Z","timestamp":1747052286000},"page":"512","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Fault Diagnosis of Planetary Gearbox Based on Hierarchical Refined Composite Multiscale Fuzzy Entropy and Optimized LSSVM"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2259-7982","authenticated-orcid":false,"given":"Xin","family":"Xia","sequence":"first","affiliation":[{"name":"School of Mechanical and Electrical Engineering, Suqian University, Suqian 223800, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2999-1429","authenticated-orcid":false,"given":"Xiaolu","family":"Wang","sequence":"additional","affiliation":[{"name":"Information Construction Center, Suqian University, Suqian 223800, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"645","DOI":"10.1016\/j.renene.2023.01.056","article-title":"Fault diagnosis of wind turbines under nonstationary conditions based on a novel tacho-less generalized demodulation","volume":"206","author":"Liu","year":"2023","journal-title":"Renew. 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