{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:20:39Z","timestamp":1760242839382,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2016,12,24]],"date-time":"2016-12-24T00:00:00Z","timestamp":1482537600000},"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":["NSFC: 61304218"],"award-info":[{"award-number":["NSFC: 61304218"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004543","name":"China Scholarship Council","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004543","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>State of health (SOH) prediction in Li-ion batteries plays an important role in intelligent battery management systems (BMS). However, the existence of capacity regeneration phenomena remains a great challenge for accurately predicting the battery SOH. This paper proposes a novel prognostic framework to predict the regeneration phenomena of the current battery using the data of a historical battery. The global degradation trend and regeneration phenomena (characterized by regeneration amplitude and regeneration cycle number) of the current battery are extracted from its raw SOH time series. Moreover, regeneration information of the historical battery derived from corresponding raw SOH data is utilized in this framework. The global degradation trend and regeneration phenomena of the current battery are predicted, and then the prediction results are integrated together to calculate the overall SOH prediction values. Particle swarm optimization (PSO) is employed to obtain an appropriate regeneration threshold for the historical battery. Gaussian process (GP) model is adopted to predict the global degradation trend, and linear models are utilized to predict the regeneration amplitude and the cycle number of each regeneration region. The proposed framework is validated using experimental data from the degradation tests of Li-ion batteries. The results demonstrate that both the global degradation trend and the regeneration phenomena of the testing batteries can be well predicted. Moreover, compared with the published methods, more accurate SOH prediction results can be obtained under this framework.<\/jats:p>","DOI":"10.3390\/sym9010004","type":"journal-article","created":{"date-parts":[[2016,12,28]],"date-time":"2016-12-28T11:22:14Z","timestamp":1482924134000},"page":"4","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["State of Health Estimation of Li-ion Batteries with Regeneration Phenomena: A Similar Rest Time-Based Prognostic Framework"],"prefix":"10.3390","volume":"9","author":[{"given":"Taichun","family":"Qin","sequence":"first","affiliation":[{"name":"School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China"},{"name":"IVHM Centre, Cranfield University, Cranfield MK43 0AL, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2857-4626","authenticated-orcid":false,"given":"Shengkui","family":"Zeng","sequence":"additional","affiliation":[{"name":"School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China"},{"name":"Science and Technology on Reliability and Environmental Engineering Laboratory, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianbin","family":"Guo","sequence":"additional","affiliation":[{"name":"School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China"},{"name":"Science and Technology on Reliability and Environmental Engineering Laboratory, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0366-2870","authenticated-orcid":false,"given":"Zakwan","family":"Skaf","sequence":"additional","affiliation":[{"name":"IVHM Centre, Cranfield University, Cranfield MK43 0AL, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,12,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"572","DOI":"10.1016\/j.rser.2015.11.042","article-title":"Critical review of state of health estimation methods of Li-ion batteries for real applications","volume":"56","author":"Berecibar","year":"2016","journal-title":"Renew. Sust. Energ. Rev."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"176052","DOI":"10.1155\/2014\/176052","article-title":"Tuning of Kalman Filter Parameters via Genetic Algorithm for State-of-Charge Estimation in Battery Management System","volume":"2014","author":"Ting","year":"2014","journal-title":"Sci. World J."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1016\/j.jpowsour.2015.11.070","article-title":"State-of-health estimation of LiFePO4\/graphite batteries based on a model using differential capacity","volume":"306","author":"Torai","year":"2016","journal-title":"J. Power Sources"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"5217","DOI":"10.3390\/en8065217","article-title":"Extended Kalman Filter with a Fuzzy Method for Accurate Battery Pack State of Charge Estimation","volume":"8","author":"Sepasi","year":"2015","journal-title":"Energies"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/j.jpowsour.2016.03.042","article-title":"A systematic review of lumped-parameter equivalent circuit models for real-time estimation of lithium-ion battery states","volume":"316","author":"Nejad","year":"2016","journal-title":"J. Power Sources"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"4774","DOI":"10.1109\/TPEL.2014.2361755","article-title":"State-of-Charge Estimation of Lithium-Ion Battery Using Square Root Spherical Unscented Kalman Filter (Sqrt-UKFST) in Nanosatellite","volume":"30","author":"Aung","year":"2015","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"4948","DOI":"10.1109\/TIE.2015.2403796","article-title":"Robust and Adaptive Estimation of State of Charge for Lithium-Ion Batteries","volume":"62","author":"Zhang","year":"2015","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"7854","DOI":"10.3390\/en8087854","article-title":"State-of-Charge Estimation for Lithium-Ion Batteries Using a Kalman Filter Based on Local Linearization","volume":"8","author":"Yu","year":"2015","journal-title":"Energies"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/j.jpowsour.2015.07.100","article-title":"A failure modes, mechanisms, and effects analysis (FMMEA) of lithium-ion batteries","volume":"297","author":"Hendricks","year":"2015","journal-title":"J. Power Sources"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1445","DOI":"10.1016\/j.rser.2015.05.080","article-title":"Microscale characterization of coupled degradation mechanism of graded materials in lithium batteries of electric vehicles","volume":"50","author":"Li","year":"2015","journal-title":"Renew. Sust. Energ. Rev."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"660","DOI":"10.1109\/TIM.2014.2348613","article-title":"An Integrated Probabilistic Approach to Lithium-Ion Battery Remaining Useful Life Estimation","volume":"64","author":"Liu","year":"2015","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1016\/j.microrel.2013.01.006","article-title":"An improved autoregressive model by particle swarm optimization for prognostics of lithium-ion batteries","volume":"53","author":"Long","year":"2013","journal-title":"Microelectron. Reliab."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1109\/TIM.2008.2005965","article-title":"Prognostics Methods for Battery Health Monitoring Using a Bayesian Framework","volume":"58","author":"Saha","year":"2009","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"805","DOI":"10.1016\/j.microrel.2012.12.004","article-title":"Remaining useful life prediction of lithium-ion battery with unscented particle filter technique","volume":"53","author":"Miao","year":"2013","journal-title":"Microelectron. Reliab."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"832","DOI":"10.1016\/j.microrel.2013.03.010","article-title":"Prognostics for state of health estimation of lithium-ion batteries based on combination Gaussian process functional regression","volume":"53","author":"Liu","year":"2013","journal-title":"Microelectron. Reliab."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"520","DOI":"10.3390\/en7020520","article-title":"Remaining Useful Life Prediction of Lithium-Ion Batteries Based on the Wiener Process with Measurement Error","volume":"7","author":"Tang","year":"2014","journal-title":"Energies"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"11763","DOI":"10.1016\/j.eswa.2011.03.063","article-title":"Intelligent prognostics for battery health monitoring based on sample entropy","volume":"38","author":"Widodo","year":"2011","journal-title":"Expert Syst. Appl."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/j.jpowsour.2015.01.164","article-title":"A Bayesian approach for Li-Ion battery capacity fade modeling and cycles to failure prognostics","volume":"281","author":"Guo","year":"2015","journal-title":"J. Power Sources"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1016\/j.jpowsour.2014.07.116","article-title":"A support vector machine-based state-of-health estimation method for lithium-ion batteries under electric vehicle operation","volume":"270","author":"Klass","year":"2014","journal-title":"J. Power Sources"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3654","DOI":"10.3390\/en6083654","article-title":"Satellite Lithium-Ion Battery Remaining Cycle Life Prediction with Novel Indirect Health Indicator Extraction","volume":"6","author":"Liu","year":"2013","journal-title":"Energies"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1109\/TIM.2011.2169182","article-title":"Prediction of Machine Health Condition Using Neuro-Fuzzy and Bayesian Algorithms","volume":"61","author":"Chen","year":"2012","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Wu, L.F., Fu, X.H., and Guan, Y. (2016). Review of the Remaining Useful Life Prognostics of Vehicle Lithium-Ion Batteries Using Data-Driven Methodologies. Appl. Sci., 6.","DOI":"10.3390\/app6060166"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/j.ress.2012.12.011","article-title":"A Bayesian framework for on-line degradation assessment and residual life prediction of secondary batteries in spacecraft","volume":"113","author":"Jin","year":"2013","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_24","unstructured":"Saha, B., and Goebel, K. (October, January 27). Modeling Li-ion battery capacity depletion in a particle filtering framework. Proceedings of Annual Conference of the Prognostics and Health Management Society, San Diego, CA, USA."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"750","DOI":"10.1016\/j.electacta.2013.10.101","article-title":"Lithium-ion battery performance improvement based on capacity recovery exploitation","volume":"114","author":"Eddahech","year":"2013","journal-title":"Electrochim. Acta"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1589","DOI":"10.1002\/aic.14760","article-title":"State of health estimation of lithium-ion batteries: A multiscale Gaussian process regression modeling approach","volume":"61","author":"He","year":"2015","journal-title":"AICHE J."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1109\/TIM.2012.2215142","article-title":"Particle-Filtering-Based Prognosis Framework for Energy Storage Devices With a Statistical Characterization of State-of-Health Regeneration Phenomena","volume":"62","author":"Olivares","year":"2013","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1109\/TR.2015.2394356","article-title":"Information-Theoretic Measures and Sequential Monte Carlo Methods for Detection of Regeneration Phenomena in the Degradation of Lithium-Ion Battery Cells","volume":"64","author":"Orchard","year":"2015","journal-title":"IEEE Trans. Reliab."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1280","DOI":"10.1016\/j.microrel.2015.06.133","article-title":"Robust prognostics for state of health estimation of lithium-ion batteries based on an improved PSO-SVR model","volume":"55","author":"Qin","year":"2015","journal-title":"Microelectron. Reliab."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Qin, T.C., Zeng, S.K., Guo, J.B., and Skaf, Z.W. (2016). A Rest Time-Based Prognostic Framework for State of Health Estimation of Lithium-Ion Batteries with Regeneration Phenomena. Energies, 9.","DOI":"10.3390\/en9110896"},{"key":"ref_31","unstructured":"Kennedy, J., and Eberhart, R. (December, January 27). Particle swarm optimization. Proceedings of IEEE International Conference on Neural Networks, Perth, Australia."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1016\/S0020-0190(02)00447-7","article-title":"The particle swarm optimization algorithm: convergence analysis and parameter selection","volume":"85","author":"Trelea","year":"2003","journal-title":"Inf. Process. Lett."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"705","DOI":"10.1016\/j.csda.2004.02.006","article-title":"Gaussian process for nonstationary time series prediction","volume":"47","author":"Bermak","year":"2004","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_34","unstructured":"Murphy, K.P. (2012). Machine Learning: A Probabilistic Perspective, MIT press."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"10314","DOI":"10.1016\/j.jpowsour.2011.08.040","article-title":"Prognostics of lithium-ion batteries based on Dempster-Shafer theory and the Bayesian Monte Carlo method","volume":"196","author":"He","year":"2011","journal-title":"J. Power Sources"},{"key":"ref_36","unstructured":"Saha, B., and Goebel, K. (2007). Battery Data Set."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1016\/j.jpowsour.2012.10.060","article-title":"A review on the key issues for lithium-ion battery management in electric vehicles","volume":"226","author":"Lu","year":"2013","journal-title":"J. Power Sources"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"658","DOI":"10.1016\/j.jpowsour.2014.06.111","article-title":"A comparative study of commercial lithium ion battery cycle life in electric vehicle: Capacity loss estimation","volume":"268","author":"Han","year":"2014","journal-title":"J. Power Sources"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/9\/1\/4\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:29:16Z","timestamp":1760210956000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/9\/1\/4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,12,24]]},"references-count":38,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2017,1]]}},"alternative-id":["sym9010004"],"URL":"https:\/\/doi.org\/10.3390\/sym9010004","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2016,12,24]]}}}