{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T18:04:08Z","timestamp":1777658648839,"version":"3.51.4"},"reference-count":22,"publisher":"European Society of Computational Methods in Sciences and Engineering","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["JCM"],"published-print":{"date-parts":[[2022,7,8]]},"abstract":"<jats:p>The power battery is a key component of the electric vehicle, and its State of health (SOH) parameters directly affect the safety and reliability of the electric vehicle. Considering the problem of the reduced SOH estimation accuracy of Li-ion battery, this paper proposes a joint algorithm of the firefly algorithm-back propagation neural network K-means (FA-BPNN-K-means) for SOH estimation to alleviate the wide voltage platform and severe polarization. In particular, the BPNN model of the battery is first established. The ohmic resistance, polarization resistance, and polarization capacitance of the battery are used as the input parameters of the model, and SOH was used as the output parameters. Secondly, the firefly algorithm (FA) is used to optimize BPNN for SOH estimation of Li-ion battery, solving the problem that BPNN is easy to fall into the local minimum and the convergence rate is slow. Finally, the predicted output of the FA-BPNN model is substituted into the K-means algorithm for clustering, and the data points for evaluation are obtained to reduce the cumulative error caused by the battery model. Compared with the BPNN algorithm, FA-BPNN-K-means joint optimization algorithm, obtaining lower error in SOH estimation, and it has good convergence. Besides, it is accompanied by higher prediction accuracy, which can guarantee the stable operation of the battery management system.<\/jats:p>","DOI":"10.3233\/jcm226028","type":"journal-article","created":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T14:07:37Z","timestamp":1648562857000},"page":"1209-1222","source":"Crossref","is-referenced-by-count":3,"title":["SOH estimation of Li-ion battery based on FA-BPNN-K-means optimization algorithm"],"prefix":"10.66113","volume":"22","author":[{"given":"Fujian","family":"Zhang","sequence":"first","affiliation":[{"name":"College of International Vocational Education, Shanghai Polytechnic University, Shanghai, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weidong","family":"Ye","sequence":"additional","affiliation":[{"name":"College of International Vocational Education, Shanghai Polytechnic University, Shanghai, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guoping","family":"Lei","sequence":"additional","affiliation":[{"name":"School of Electronics and Information Engineering, Chongqing Three Gorges University, Chongqing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yingying","family":"Liu","sequence":"additional","affiliation":[{"name":"College of International Vocational Education, Shanghai Polytechnic University, Shanghai, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xian","family":"Wang","sequence":"additional","affiliation":[{"name":"College of International Vocational Education, Shanghai Polytechnic University, Shanghai, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"55691","reference":[{"issue":"1","key":"10.3233\/JCM226028_ref1","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1109\/TVT.2017.2751613","article-title":"The co-estimation of state of charge, state of health, and state of function for lithium-ion batteries in electric vehicles","volume":"67","author":"Shen","year":"2018","journal-title":"IEEE Trans Veh Technol."},{"issue":"11","key":"10.3233\/JCM226028_ref2","doi-asserted-by":"crossref","first-page":"2937","DOI":"10.1109\/TIM.2015.2444237","article-title":"State-of-health monitoring and prediction of lithium-ion battery using probabilistic indication and state-space model","volume":"64","author":"Yu","year":"2015","journal-title":"IEEE Trans Instrum Meas."},{"key":"10.3233\/JCM226028_ref3","doi-asserted-by":"crossref","first-page":"678","DOI":"10.1016\/j.energy.2015.05.148","article-title":"Performance analysis and SOH (state of health) evaluation of lithium polymer batteries through electrochemical impedance spectroscopy","volume":"89","author":"Galeotti","year":"2015","journal-title":"Energy."},{"key":"10.3233\/JCM226028_ref4","doi-asserted-by":"crossref","first-page":"1178","DOI":"10.1016\/j.apenergy.2018.01.011","article-title":"A single particle model with chemical\/mechanical degradation physics for lithium-ion battery state of health (SOH) estimation","volume":"212","author":"Li","year":"2018","journal-title":"Appl Energy."},{"key":"10.3233\/JCM226028_ref5","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1016\/j.jpowsour.2013.03.129","article-title":"Prognostics of lithium-ion batteries based on relevance vectors and a conditional three-parameter capacity degradation model","volume":"239","author":"Wang","year":"2013","journal-title":"J Power Sources."},{"issue":"1-2","key":"10.3233\/JCM226028_ref6","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/S0378-7753(99)00079-8","article-title":"Determination of state-of-charge and state-of-health of batteries by fuzzy logic methodology","volume":"80","author":"Salkind","year":"1999","journal-title":"J Power Sources."},{"key":"10.3233\/JCM226028_ref7","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1016\/j.est.2019.03.022","article-title":"Battery health prediction under generalized conditions using a Gaussian process transition model","volume":"23","author":"Richardson","year":"2019","journal-title":"J Energy Storage."},{"issue":"10","key":"10.3233\/JCM226028_ref8","doi-asserted-by":"crossref","first-page":"8773","DOI":"10.1109\/TVT.2017.2715333","article-title":"State of charge and state of health estimation for lithium batteries using recurrent neural networks","volume":"66","author":"Chaoui","year":"2017","journal-title":"IEEE Trans Veh Technol."},{"issue":"1","key":"10.3233\/JCM226028_ref9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2478\/amns.2020.1.00001","article-title":"Improvement of the fast clustering algorithm improved by K-Means in the big data","volume":"5","author":"Xie","year":"2020","journal-title":"Appl Math Nonlinear Sci."},{"key":"10.3233\/JCM226028_ref10","doi-asserted-by":"crossref","unstructured":"Yang D, Wang Y, Pan R, Chen RY, Chen ZH. 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