{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T16:20:28Z","timestamp":1778948428771,"version":"3.51.4"},"reference-count":52,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2017,5,18]],"date-time":"2017-05-18T00:00:00Z","timestamp":1495065600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"China Scholarship Council with a Scholarship","award":["201606160048"],"award-info":[{"award-number":["201606160048"]}]},{"name":"National Science and Technology Supporting Plan","award":["2015BAF01B04"],"award-info":[{"award-number":["2015BAF01B04"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51175208"],"award-info":[{"award-number":["51175208"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51565015"],"award-info":[{"award-number":["51565015"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"State Key Basic Research Program of China","award":["2011CB706803"],"award-info":[{"award-number":["2011CB706803"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The operating condition of rolling bearings affects productivity and quality in the rotating machine process. Developing an effective rolling bearing condition monitoring approach is critical to accurately identify the operating condition. In this paper, a hybrid generalized hidden Markov model-based condition monitoring approach for rolling bearings is proposed, where interval valued features are used to efficiently recognize and classify machine states in the machine process. In the proposed method, vibration signals are decomposed into multiple modes with variational mode decomposition (VMD). Parameters of the VMD, in the form of generalized intervals, provide a concise representation for aleatory and epistemic uncertainty and improve the robustness of identification. The multi-scale permutation entropy method is applied to extract state features from the decomposed signals in different operating conditions. Traditional principal component analysis is adopted to reduce feature size and computational cost. With the extracted features\u2019 information, the generalized hidden Markov model, based on generalized interval probability, is used to recognize and classify the fault types and fault severity levels. Finally, the experiment results show that the proposed method is effective at recognizing and classifying the fault types and fault severity levels of rolling bearings. This monitoring method is also efficient enough to quantify the two uncertainty components.<\/jats:p>","DOI":"10.3390\/s17051143","type":"journal-article","created":{"date-parts":[[2017,5,23]],"date-time":"2017-05-23T01:47:33Z","timestamp":1495504053000},"page":"1143","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["A Hybrid Generalized Hidden Markov Model-Based Condition Monitoring Approach for Rolling Bearings"],"prefix":"10.3390","volume":"17","author":[{"given":"Jie","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Youmin","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bo","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yan","family":"Wang","sequence":"additional","affiliation":[{"name":"Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fengyun","family":"Xie","sequence":"additional","affiliation":[{"name":"School of Mechatronics and Vehicle Engineering, East China Jiaotong University, Nanchang 330013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,5,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1016\/j.jsv.2007.02.029","article-title":"Cyclic spectral analysis of rolling-element bearing signals: Facts and fictions","volume":"304","author":"Antoni","year":"2007","journal-title":"J. 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