{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,6]],"date-time":"2026-07-06T15:38:06Z","timestamp":1783352286884,"version":"3.54.6"},"reference-count":25,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,12,21]],"date-time":"2023-12-21T00:00:00Z","timestamp":1703116800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Research Grants Council of the National Nature Science Foundation of China","award":["52105115"],"award-info":[{"award-number":["52105115"]}]},{"name":"Research Grants Council of the National Nature Science Foundation of China","award":["62120106011"],"award-info":[{"award-number":["62120106011"]}]},{"name":"Research Grants Council of the National Nature Science Foundation of China","award":["2023YFSY0003"],"award-info":[{"award-number":["2023YFSY0003"]}]},{"name":"Research Grants Council of the National Nature Science Foundation of China","award":["2023NSFSC0862"],"award-info":[{"award-number":["2023NSFSC0862"]}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities, Sichuan Science and Technology Program","doi-asserted-by":"publisher","award":["52105115"],"award-info":[{"award-number":["52105115"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities, Sichuan Science and Technology Program","doi-asserted-by":"publisher","award":["62120106011"],"award-info":[{"award-number":["62120106011"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities, Sichuan Science and Technology Program","doi-asserted-by":"publisher","award":["2023YFSY0003"],"award-info":[{"award-number":["2023YFSY0003"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities, Sichuan Science and Technology Program","doi-asserted-by":"publisher","award":["2023NSFSC0862"],"award-info":[{"award-number":["2023NSFSC0862"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Bearing faults are one kind of primary failure in rotatory machines. To avoid economic loss and casualties, it is important to diagnose bearing faults accurately. Vibration-based monitoring technology is widely used to detect bearing faults. Graph signal processing methods promising for the extraction of the fault features of bearings. In this work, graph multi-scale permutation entropy (MPEG) is proposed for bearing fault diagnosis. In the proposed method, the vibration signal is first transformed into a visibility graph. Secondly, a graph coarsening method is used to generate coarse graphs with different reduced sizes. Thirdly, the graph\u2019s permutation entropy is calculated to obtain bearing fault features. Finally, a support vector machine (SVM) is applied for fault feature classification. To verify the effectiveness of the proposed method, open-source and laboratory data are used to compare conventional entropies and other graph entropies. Experimental results show that the proposed method has higher accuracy and better robustness and de-noising ability.<\/jats:p>","DOI":"10.3390\/s24010056","type":"journal-article","created":{"date-parts":[[2023,12,21]],"date-time":"2023-12-21T08:16:02Z","timestamp":1703146562000},"page":"56","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Graph Multi-Scale Permutation Entropy for Bearing Fault Diagnosis"],"prefix":"10.3390","volume":"24","author":[{"given":"Qingwen","family":"Fan","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Sichuan University, Chengdu 610017, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuqi","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Sichuan University, Chengdu 610017, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jingyuan","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Engineering, University of Birmingham, Birmingham B152TT, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5843-9428","authenticated-orcid":false,"given":"Dingcheng","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Sichuan University, Chengdu 610017, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1016\/j.triboint.2015.12.037","article-title":"A review on signal processing techniques utilized in the fault diagnosis of rolling element bearings","volume":"96","author":"Rai","year":"2016","journal-title":"Tribol. 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