{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,30]],"date-time":"2026-06-30T15:57:12Z","timestamp":1782835032349,"version":"3.54.5"},"reference-count":35,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2021,6,16]],"date-time":"2021-06-16T00:00:00Z","timestamp":1623801600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52005265"],"award-info":[{"award-number":["52005265"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Fund for Colleges and Universities in Jiangsu Province","award":["20KJB460002"],"award-info":[{"award-number":["20KJB460002"]}]},{"name":"Scientific Research Foundation of Nanjing Forestry University","award":["163040095 and 163040117"],"award-info":[{"award-number":["163040095 and 163040117"]}]},{"DOI":"10.13039\/501100013058","name":"Jiangsu Provincial Key Research and Development Program","doi-asserted-by":"publisher","award":["BE2019030637"],"award-info":[{"award-number":["BE2019030637"]}],"id":[{"id":"10.13039\/501100013058","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The goal of the paper is to present a solution to improve the fault detection accuracy of rolling bearings. The method is based on variational mode decomposition (VMD), multiscale permutation entropy (MPE) and the particle swarm optimization-based support vector machine (PSO-SVM). Firstly, the original bearing vibration signal is decomposed into several intrinsic mode functions (IMF) by using the VMD method, and the feature energy ratio (FER) criterion is introduced to reconstruct the bearing vibration signal. Secondly, the multiscale permutation entropy of the reconstructed signal is calculated to construct multidimensional feature vectors. Finally, the constructed multidimensional feature vector is fed into the PSO-SVM classification model for automatic identification of different fault patterns of the rolling bearing. Two experimental cases are adopted to validate the effectiveness of the proposed method. Experimental results show that the proposed method can achieve a higher identification accuracy compared with some similar available methods (e.g., variational mode decomposition-based multiscale sample entropy (VMD-MSE), variational mode decomposition-based multiscale fuzzy entropy (VMD-MFE), empirical mode decomposition-based multiscale permutation entropy (EMD-MPE) and wavelet transform-based multiscale permutation entropy (WT-MPE)).<\/jats:p>","DOI":"10.3390\/e23060762","type":"journal-article","created":{"date-parts":[[2021,6,16]],"date-time":"2021-06-16T21:58:32Z","timestamp":1623880712000},"page":"762","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":88,"title":["Rolling Bearing Fault Diagnosis Based on VMD-MPE and PSO-SVM"],"prefix":"10.3390","volume":"23","author":[{"given":"Maoyou","family":"Ye","sequence":"first","affiliation":[{"name":"School of Mechatronics Engineering, Nanjing Forestry University, Nanjing 210037, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaoan","family":"Yan","sequence":"additional","affiliation":[{"name":"School of Mechatronics Engineering, Nanjing Forestry University, Nanjing 210037, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Minping","family":"Jia","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Southeast University, Nanjing 211189, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"105849","DOI":"10.1016\/j.triboint.2019.105849","article-title":"Further understanding of rolling contact fatigue in rolling element bearings\u2014A review","volume":"140","author":"Wang","year":"2019","journal-title":"Tribol. 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