{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T02:47:00Z","timestamp":1774579620673,"version":"3.50.1"},"reference-count":30,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,2,4]],"date-time":"2022-02-04T00:00:00Z","timestamp":1643932800000},"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":["61973041"],"award-info":[{"award-number":["61973041"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2019YFB1705403"],"award-info":[{"award-number":["2019YFB1705403"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Owing to the symmetry of the rolling bearing structure and the rotating operation mode, the rolling bearing works in a complex environment. It is very easy to be submerged by noise and misdiagnosis. For the non-stationary signal in variable speed state, this paper presents a condition monitoring method based on deep belief network (DBN) optimized by multi-order fractional Fourier transform (FRFT) and sparrow search algorithm (SSA). Firstly, the fractional Fourier transform based on curve feature segmentation is used to filter the fault vibration signal and extract the fault feature frequency. Then, the fault features are input into the SSA-DBN model for training, and the bearing fault features are classified, identified, and diagnosed. Finally, the rotating machinery fault simulator in the laboratory of Ottawa University is taken as the practical application object to verify the effectiveness of the method. The experimental results show that the proposed method has higher recognition accuracy and stronger stability.<\/jats:p>","DOI":"10.3390\/sym14020320","type":"journal-article","created":{"date-parts":[[2022,2,6]],"date-time":"2022-02-06T20:40:18Z","timestamp":1644180018000},"page":"320","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Condition Monitoring of Rolling Bearing Based on Multi-Order FRFT and SSA-DBN"],"prefix":"10.3390","volume":"14","author":[{"given":"Jie","family":"Ma","sequence":"first","affiliation":[{"name":"Mechanical Electrical Engineering School, Beijing Information Science and Technology University, Beijing 100192, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shule","family":"Li","sequence":"additional","affiliation":[{"name":"Publishing House of Electronics Industry, Beijing 100039, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7453-4724","authenticated-orcid":false,"given":"Xinyu","family":"Wang","sequence":"additional","affiliation":[{"name":"Mechanical Electrical Engineering School, Beijing Information Science and Technology University, Beijing 100192, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ma, J.P., Zhuo, S., Li, C.W., Zhan, L.W., and Zhang, G.Z. 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