{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T13:54:19Z","timestamp":1780408459902,"version":"3.54.1"},"reference-count":35,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2024,5,8]],"date-time":"2024-05-08T00:00:00Z","timestamp":1715126400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key Research and Development Project of China","award":["2022YFB3404705"],"award-info":[{"award-number":["2022YFB3404705"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>As one of the most vital energy conversation systems, the safe operation of wind turbines is very important; however, weak fault and time-varying speed may challenge the conventional monitoring strategies. Thus, an entropy-aided meshing-order modulation method is proposed for detecting the optimal frequency band, which contains the weak fault-related information. Specifically, the variable rotational frequency trend is first identified and extracted based on the time\u2013frequency representation of the raw signal by constructing a novel scaling-basis local reassigning chirplet transform (SLRCT). A new entropy-aided meshing-order modulation (EMOM) indicator is then constructed to locate the most sensitive modulation frequency area according to the extracted fine speed trend with the help of order tracking technique. Finally, the raw vibration signal is bandpass filtered via the corresponding optimal frequency band with the highest EMOM indicator. The order components resulting from the weak fault can be highlighted to accomplish weak fault detection. The effectiveness of the proposed EMOM analysis-based method has been tested using the experimental data of three different gear fault types of different fault levels from a planetary test rig.<\/jats:p>","DOI":"10.3390\/e26050409","type":"journal-article","created":{"date-parts":[[2024,5,8]],"date-time":"2024-05-08T12:27:11Z","timestamp":1715171231000},"page":"409","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":38,"title":["Entropy-Aided Meshing-Order Modulation Analysis for Wind Turbine Planetary Gear Weak Fault Detection under Variable Rotational Speed"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5898-3992","authenticated-orcid":false,"given":"Shaodan","family":"Zhi","sequence":"first","affiliation":[{"name":"Electronic and Control Engineering, School of Mechanical, Beijing Jiaotong University, Beijing 100091, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-8456-9830","authenticated-orcid":false,"given":"Hengshan","family":"Wu","sequence":"additional","affiliation":[{"name":"Electronic and Control Engineering, School of Mechanical, Beijing Jiaotong University, Beijing 100091, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1849-7927","authenticated-orcid":false,"given":"Haikuo","family":"Shen","sequence":"additional","affiliation":[{"name":"Electronic and Control Engineering, School of Mechanical, Beijing Jiaotong University, Beijing 100091, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7256-883X","authenticated-orcid":false,"given":"Tianyang","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hongfei","family":"Fu","sequence":"additional","affiliation":[{"name":"Electronic and Control Engineering, School of Mechanical, Beijing Jiaotong University, Beijing 100091, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,5,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4919","DOI":"10.1016\/j.jsv.2012.05.039","article-title":"Vibration Signal Models for Fault Diagnosis of Planetary Gearboxes","volume":"331","author":"Feng","year":"2012","journal-title":"J. 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