{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,15]],"date-time":"2025-11-15T17:13:20Z","timestamp":1763226800103,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,1,24]],"date-time":"2020-01-24T00:00:00Z","timestamp":1579824000000},"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":["51675001, 51875001"],"award-info":[{"award-number":["51675001, 51875001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"State Key Program of National Natural Science of China","award":["51637001"],"award-info":[{"award-number":["51637001"]}]},{"name":"Key Research and Development Plan of Anhui Province","award":["201904A05020034"],"award-info":[{"award-number":["201904A05020034"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In real industrial applications, bearings in pairs or even more are often mounted on the same shaft. So the collected vibration signal is actually a mixed signal from multiple bearings. In this study, a method based on Hybrid Kernel Function-Support Vector Regression (HKF\u2013SVR) whose parameters are optimized by Krill Herd (KH) algorithm was introduced for bearing performance degradation prediction in this situation. First, multi-domain statistical features are extracted from the bearing vibration signals and then fused into sensitive features using Kernel Joint Approximate Diagonalization of Eigen-matrices (KJADE) algorithm which is developed recently by our group. Due to the nonlinear mapping capability of the kernel method and the blind source separation ability of the JADE algorithm, the KJADE could extract latent source features that accurately reflecting the performance degradation from the mixed vibration signal. Then, the between-class and within-class scatters (SS) of the health-stage data sample and the current monitored data sample is calculated as the performance degradation index. Second, the parameters of the HKF\u2013SVR are optimized by the KH (Krill Herd) algorithm to obtain the optimal performance degradation prediction model. Finally, the performance degradation trend of the bearing is predicted using the optimized HKF\u2013SVR. Compared with the traditional methods of Back Propagation Neural Network (BPNN), Extreme Learning Machine (ELM) and traditional SVR, the results show that the proposed method has a better performance. The proposed method has a good application prospect in life prediction of coaxial bearings.<\/jats:p>","DOI":"10.3390\/s20030660","type":"journal-article","created":{"date-parts":[[2020,1,24]],"date-time":"2020-01-24T11:01:00Z","timestamp":1579863660000},"page":"660","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["HKF-SVR Optimized by Krill Herd Algorithm for Coaxial Bearings Performance Degradation Prediction"],"prefix":"10.3390","volume":"20","author":[{"given":"Fang","family":"Liu","sequence":"first","affiliation":[{"name":"College of Electrical Engineering and Automation, Anhui University, Hefei 230601, China"},{"name":"National Engineering Laboratory of Energy-Saving Motor and Control Technology, Anhui University, Hefei 230601, China"}]},{"given":"Liubin","family":"Li","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering and Automation, Anhui University, Hefei 230601, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3420-3784","authenticated-orcid":false,"given":"Yongbin","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering and Automation, Anhui University, Hefei 230601, China"},{"name":"National Engineering Laboratory of Energy-Saving Motor and Control Technology, Anhui University, Hefei 230601, China"}]},{"given":"Zheng","family":"Cao","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering and Automation, Anhui University, Hefei 230601, China"}]},{"given":"Hui","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering and Automation, Anhui University, Hefei 230601, China"}]},{"given":"Siliang","family":"Lu","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering and Automation, Anhui University, Hefei 230601, China"},{"name":"National Engineering Laboratory of Energy-Saving Motor and Control Technology, Anhui University, Hefei 230601, China"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"144","DOI":"10.2174\/2212797609666160408154213","article-title":"Study on a Novel Fault Diagnosis Method of Rolling Bearing in Motor","volume":"9","author":"Zheng","year":"2016","journal-title":"Recent Pat. 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