{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,26]],"date-time":"2026-08-26T07:13:50Z","timestamp":1787728430835,"version":"build-2784847793"},"reference-count":43,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2018,12,8]],"date-time":"2018-12-08T00:00:00Z","timestamp":1544227200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No.71601022"],"award-info":[{"award-number":["No.71601022"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Bearing plays an important role in mechanical equipment, and its remaining useful life (RUL) prediction is an important research topic of mechanical equipment. To accurately predict the RUL of bearing, this paper proposes a data-driven RUL prediction method. First, the statistical method is used to extract the features of the signal, and the root mean square (RMS) is regarded as the main performance degradation index. Second, the correlation coefficient is used to select the statistical characteristics that have high correlation with the RMS. Then, In order to avoid the fluctuation of the statistical feature, the improved Weibull distributions (WD) algorithm is used to fit the fluctuation feature of bearing at different recession stages, which is used as input of Naive Bayes (NB) training stage. During the testing stage, the true fluctuation feature of the bearings are used as the input of NB. After the NB testing, five classes are obtained: health states and four states for bearing degradation. Finally, the exponential smoothing algorithm is used to smooth the five classes, and to predict the RUL of bearing. The experimental results show that the proposed method is effective for RUL prediction of bearing.<\/jats:p>","DOI":"10.3390\/e20120944","type":"journal-article","created":{"date-parts":[[2018,12,10]],"date-time":"2018-12-10T03:36:41Z","timestamp":1544413001000},"page":"944","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":34,"title":["Bearing Remaining Useful Life Prediction Based on Naive Bayes and Weibull Distributions"],"prefix":"10.3390","volume":"20","author":[{"given":"Nannan","family":"Zhang","sequence":"first","affiliation":[{"name":"College of Information Engineering, Capital Normal University, Beijing 100048, China"},{"name":"Beijing Key Laboratory of Electronic System Reliability Technology, Capital Normal University, Beijing 100048, China"},{"name":"Beijing Key Laboratory of Light Industrial Robot and Safety Verification, Capital Normal University, Beijing 100048, China"},{"name":"Beijing Advanced Innovation Center for Imaging Technology, Capital Normal University, Beijing 100048, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5238-8823","authenticated-orcid":false,"given":"Lifeng","family":"Wu","sequence":"additional","affiliation":[{"name":"College of Information Engineering, Capital Normal University, Beijing 100048, China"},{"name":"Beijing Key Laboratory of Electronic System Reliability Technology, Capital Normal University, Beijing 100048, China"},{"name":"Beijing Key Laboratory of Light Industrial Robot and Safety Verification, Capital Normal University, Beijing 100048, China"},{"name":"Beijing Advanced Innovation Center for Imaging Technology, Capital Normal University, Beijing 100048, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhonghua","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Information Engineering, Capital Normal University, Beijing 100048, China"},{"name":"Beijing Key Laboratory of Electronic System Reliability Technology, Capital Normal University, Beijing 100048, China"},{"name":"Beijing Key Laboratory of Light Industrial Robot and Safety Verification, Capital Normal University, Beijing 100048, China"},{"name":"Beijing Advanced Innovation Center for Imaging Technology, Capital Normal University, Beijing 100048, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2373-2779","authenticated-orcid":false,"given":"Yong","family":"Guan","sequence":"additional","affiliation":[{"name":"College of Information Engineering, Capital Normal University, Beijing 100048, China"},{"name":"Beijing Key Laboratory of Electronic System Reliability Technology, Capital Normal University, Beijing 100048, China"},{"name":"Beijing Key Laboratory of Light Industrial Robot and Safety Verification, Capital Normal University, Beijing 100048, China"},{"name":"Beijing Advanced Innovation Center for Imaging Technology, Capital Normal University, Beijing 100048, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2018,12,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"719","DOI":"10.1109\/TEC.2005.847955","article-title":"Condition monitoring and fault diagnosis of electrical motors\u2014A review","volume":"20","author":"Nandi","year":"2005","journal-title":"IEEE Trans. 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