{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,10]],"date-time":"2026-01-10T19:03:47Z","timestamp":1768071827464,"version":"3.49.0"},"reference-count":34,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2019,8,1]],"date-time":"2019-08-01T00:00:00Z","timestamp":1564617600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Vibration signals are used to diagnosis faults of the rolling bearing which is symmetric structure. Stochastic resonance (SR) has been widely applied in weak signal feature extraction in recent years. It can utilize noise and enhance weak signals. However, the traditional SR method has poor performance, and it is difficult to determine parameters of SR. Therefore, a new second-order tristable SR method (STSR) based on a new potential combining the classical bistable potential with Woods-Saxon potential is proposed in this paper. Firstly, the envelope signal of rolling bearings is the input signal of STSR. Then, the output of signal-to-noise ratio (SNR) is used as the fitness function of the Seeker Optimization Algorithm (SOA) in order to optimize the parameters of SR. Finally, the optimal parameters are used to set the STSR system in order to enhance and extract weak signals of rolling bearings. Simulated and experimental signals are used to demonstrate the effectiveness of STSR. The diagnosis results show that the proposed STSR method can obtain higher output SNR and better filtering performance than the traditional SR methods. It provides a new idea for fault diagnosis of rotating machinery.<\/jats:p>","DOI":"10.3390\/sym11080965","type":"journal-article","created":{"date-parts":[[2019,8,1]],"date-time":"2019-08-01T11:39:37Z","timestamp":1564659577000},"page":"965","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["A New Second-Order Tristable Stochastic Resonance Method for Fault Diagnosis"],"prefix":"10.3390","volume":"11","author":[{"given":"Lu","family":"Lu","sequence":"first","affiliation":[{"name":"College of Locomotive and Rolling Stock Engineering, Dalian Jiaotong University, Dalian 116028, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yu","family":"Yuan","sequence":"additional","affiliation":[{"name":"College of Locomotive and Rolling Stock Engineering, Dalian Jiaotong University, Dalian 116028, China"},{"name":"Traction Power State Key Laboratory, Southwest Jiaotong University, Chengdu 610031, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Heng","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Locomotive and Rolling Stock Engineering, Dalian Jiaotong University, Dalian 116028, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xing","family":"Zhao","sequence":"additional","affiliation":[{"name":"College of Locomotive and Rolling Stock Engineering, Dalian Jiaotong University, Dalian 116028, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianjie","family":"Zheng","sequence":"additional","affiliation":[{"name":"College of Locomotive and Rolling Stock Engineering, Dalian Jiaotong University, Dalian 116028, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Zhao, H.M., Yao, R., Xu, L., Yuan, Y., Li, G.Y., and Deng, W. 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