{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T13:56:03Z","timestamp":1783086963853,"version":"3.54.6"},"reference-count":52,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,4,12]],"date-time":"2023-04-12T00:00:00Z","timestamp":1681257600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Bashkir State Medical University","award":["PRIORITY-2030"],"award-info":[{"award-number":["PRIORITY-2030"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, an adaptive remaining useful life prediction model is proposed for electric vehicle lithium batteries. Capacity degradation of the electric car lithium batteries is modeled by the multi-fractal Weibull motion. The varying degree of long-range dependence and the 1\/f characteristics in the frequency domain are also analyzed. The age and state-dependent degradation model is derived, with the associated adaptive drift and diffusion coefficients. The adaptive mechanism considers the quantitative relations between the drift and diffusion coefficients. The unit-to-unit variability is considered a random variable. To facilitate the application, the convergence of the RUL prediction model is proved. Replacement of the lithium battery in the electric car is recommended according to the remaining useful life prediction results. The effectiveness of the proposed model is shown in the case study.<\/jats:p>","DOI":"10.3390\/e25040646","type":"journal-article","created":{"date-parts":[[2023,4,13]],"date-time":"2023-04-13T02:29:15Z","timestamp":1681352955000},"page":"646","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Multi-Fractal Weibull Adaptive Model for the Remaining Useful Life Prediction of Electric Vehicle Lithium Batteries"],"prefix":"10.3390","volume":"25","author":[{"given":"Wujin","family":"Deng","sequence":"first","affiliation":[{"name":"School of Electronic & Electrical Engineering, Shanghai University of Engineering Science, Shanghai 201620, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0076-8901","authenticated-orcid":false,"given":"Yan","family":"Gao","sequence":"additional","affiliation":[{"name":"School of Electronic & Electrical Engineering, Shanghai University of Engineering Science, Shanghai 201620, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianxue","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Electronic & Electrical Engineering, Shanghai University of Engineering Science, Shanghai 201620, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7211-0741","authenticated-orcid":false,"given":"Aleksey","family":"Kudreyko","sequence":"additional","affiliation":[{"name":"Department of Medical Physics and Informatics, Bashkir State Medical University, Lenina St. 3, 450008 Ufa, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7504-0424","authenticated-orcid":false,"given":"Carlo","family":"Cattani","sequence":"additional","affiliation":[{"name":"Engineering School, DEIM, University of Tuscia, 01100 Viterbo, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Enrico","family":"Zio","sequence":"additional","affiliation":[{"name":"The Centre for Research on Risk and Crises (CRC) of Ecole de Mines, Paris Sciences & Lettres (PSL) University, 06904 Paris, France"},{"name":"Energy Department, Politecnico di Milano, Via La Masa 34\/3, 20156 Milan, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0561-3258","authenticated-orcid":false,"given":"Wanqing","family":"Song","sequence":"additional","affiliation":[{"name":"School of Electronic & Electrical Engineering, Shanghai University of Engineering Science, Shanghai 201620, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"113091","DOI":"10.1016\/j.jenvman.2021.113091","article-title":"Electric car battery: An overview on global demand, recycling and future approaches towards sustainability","volume":"295","author":"Martins","year":"2021","journal-title":"J. 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