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Firstly, the subtraction-average-based optimizer is used to optimize the parameters of the variational mode decomposition algorithm. Secondly, the vibration signals of bearings are decomposed by using the optimized results, and the feature vector of the intrinsic mode function component corresponding to the minimum envelope entropy is extracted. Finally, the grey proximity and similarity relation degree based on standard distance entropy are weighted to calculate the grey comprehensive relation degree between the feature vector of vibration signals and each standard state. By comparing the results, the diagnosis of different fault states and degrees of rolling bearings is realized. The XJTU-SY dataset was used for experimentation, and the results show that the proposed method achieves a diagnostic accuracy of 95.24% and has better diagnosis performance compared to various algorithms. It provides a reference for the fault diagnosis of rolling bearings throughout the full life cycle.<\/jats:p>","DOI":"10.3390\/e26030222","type":"journal-article","created":{"date-parts":[[2024,3,1]],"date-time":"2024-03-01T03:31:23Z","timestamp":1709263883000},"page":"222","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Fault Diagnosis Method for Rolling Bearings Based on Grey Relation Degree"],"prefix":"10.3390","volume":"26","author":[{"given":"Yulin","family":"Mao","sequence":"first","affiliation":[{"name":"School of Automotive and Rail Transit, Nanjing Institute of Technology, Nanjing 211167, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianghui","family":"Xin","sequence":"additional","affiliation":[{"name":"School of Automotive and Rail Transit, Nanjing Institute of Technology, Nanjing 211167, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6761-3165","authenticated-orcid":false,"given":"Liguo","family":"Zang","sequence":"additional","affiliation":[{"name":"School of Automotive and Rail Transit, Nanjing Institute of Technology, Nanjing 211167, China"},{"name":"State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun 130015, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jing","family":"Jiao","sequence":"additional","affiliation":[{"name":"School of Automotive and Rail Transit, Nanjing Institute of Technology, Nanjing 211167, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cheng","family":"Xue","sequence":"additional","affiliation":[{"name":"School of Automotive and Rail Transit, Nanjing Institute of Technology, Nanjing 211167, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"10792","DOI":"10.1109\/JSEN.2020.2995109","article-title":"Autocorrelation aided random forest classifier-based bearing fault detection framework","volume":"20","author":"Roy","year":"2020","journal-title":"IEEE Sens. 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