{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T10:44:40Z","timestamp":1772189080775,"version":"3.50.1"},"reference-count":32,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2022,12,8]],"date-time":"2022-12-08T00:00:00Z","timestamp":1670457600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Joint Funds of the National Natural Science Foundation of China","award":["U1933202"],"award-info":[{"award-number":["U1933202"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>As a single feature parameter cannot comprehensively evaluate the health status of a battery, a multi-source information fusion method based on the Gaussian mixture model and Bayesian inference distance is proposed for the health assessment of vehicle batteries. The missing and abnormal data from real-life vehicle operations are preprocessed to extract the sensitive characteristic parameters which determine the battery performance. The normal state Gaussian mixture model is established using the fault-free state data, whereas the Bayesian inference distance is constructed as an index to quantitatively evaluate the battery performance state. In order to solve the problem that abnormal data may exist in the measured data and introduce errors into evaluation results, the determination rules of abnormal data are formulated. The verification of real-life vehicle operation data reveals that the proposed method can accurately evaluate the onboard battery state and reduce safety hazards of electric vehicles during the normal operation process.<\/jats:p>","DOI":"10.3390\/s22249637","type":"journal-article","created":{"date-parts":[[2022,12,9]],"date-time":"2022-12-09T03:59:46Z","timestamp":1670558386000},"page":"9637","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Health State Estimation of On-Board Lithium-Ion Batteries Based on GMM-BID Model"],"prefix":"10.3390","volume":"22","author":[{"given":"Shirui","family":"Feng","sequence":"first","affiliation":[{"name":"College of Automobile and Traffic Engineering, Nanjing Forestry University, Nanjing 210037, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anchen","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Automobile and Traffic Engineering, Nanjing Forestry University, Nanjing 210037, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jing","family":"Cai","sequence":"additional","affiliation":[{"name":"School of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongfu","family":"Zuo","sequence":"additional","affiliation":[{"name":"School of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ying","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Automobile and Traffic Engineering, Nanjing Forestry University, Nanjing 210037, China"},{"name":"School of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Koch, D., and Schweiger, H.G. (2022). Possibilities for a Quick Onsite Safety-State Assessment of Stand-Alone Lithium-Ion Batteries. Batteries, 8.","DOI":"10.3390\/batteries8110213"},{"key":"ref_2","first-page":"123006","article-title":"Life cycle assessment of lithium nickel cobalt manganese oxide batteries and lithium iron phosphate batteries for electric vehicles in China","volume":"273","author":"Sun","year":"2020","journal-title":"J. Energy Storage"},{"key":"ref_3","first-page":"1002","article-title":"Vehicle energy system active defense: A health assessment of lithium-ion batteries","volume":"10","author":"Hong","year":"2020","journal-title":"Int. J. Intell. Syst."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Luciani, S., Feraco, S., Bonfitto, A., and Tonoli, A. (2021). Hardware-in-the-Loop Assessment of a Data-Driven State of Charge Estimation Method for Lithium-Ion Batteries in Hybrid Vehicles. Electronics, 10.","DOI":"10.3390\/electronics10222828"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1016\/j.jpowsour.2013.03.158","article-title":"Online battery state of health estimation based on Genetic Algorithm for electric and hybrid vehicle applications","volume":"240","author":"Chen","year":"2013","journal-title":"J. Power Sources"},{"key":"ref_6","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_7","doi-asserted-by":"crossref","unstructured":"Krupp, A., Ferg, E., Schuldt, F., Derendorf, K., and Agert, C. (2020). Incremental Capacity Analysis as a State of Health Estimation Method for Lithium-Ion Battery Modules with Series-Connected Cells. Batteries, 7.","DOI":"10.3390\/batteries7010002"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"104520","DOI":"10.1016\/j.est.2022.104520","article-title":"State of health estimation and remaining useful life assessment of lithium-ion batteries: A comparative study","volume":"51","author":"Toughzaoui","year":"2022","journal-title":"J. Energy Storage"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1016\/j.apenergy.2016.07.126","article-title":"State-of-health monitoring of lithium-ion battery modules and packs via incremental capacity peak tracking","volume":"180","author":"Weng","year":"2016","journal-title":"Appl. Energy"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1016\/j.apenergy.2016.01.125","article-title":"On-board state of health estimation of LiFePO4 battery pack through differential voltage analysis","volume":"168","author":"Wang","year":"2016","journal-title":"Appl. Energy"},{"key":"ref_11","first-page":"145","article-title":"LPV Estimation of SOC Based on Electricity Conversion and Hysteresis Characteristic","volume":"6","author":"Chang","year":"2019","journal-title":"J. Energy Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1832","DOI":"10.1109\/ACCESS.2017.2780258","article-title":"Critical review on the battery state of charge estimation methods for electric vehicles","volume":"6","author":"Xiong","year":"2018","journal-title":"IEEE Access."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Gao, D., Zhou, Y., Wang, T., and Wang, Y. (2020). A Method for Predicting the Remaining Useful Life of Lithium-Ion Batteries Based on Particle Filter Using Kendall Rank Correlation Coefficient. Energies, 13.","DOI":"10.3390\/en13164183"},{"key":"ref_14","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_15","doi-asserted-by":"crossref","first-page":"42760","DOI":"10.1109\/ACCESS.2020.2977429","article-title":"Prediction of the Remaining Useful Life of Lithium-Ion Batteries Based on Empirical Mode Decomposition and Deep Neural Networks","volume":"8","author":"Qiao","year":"2020","journal-title":"IEEE Access"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1089\/big.2018.0130","article-title":"An improved particle filtering algorithm using different correlation coefficients for nonlinear system state estimation","volume":"7","author":"Meng","year":"2019","journal-title":"Big Data"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"200016","DOI":"10.20517\/energymater.2022.14","article-title":"Accelerating perovskite materials discovery and correlated energy applications through artificial intelligence","volume":"2","author":"Liang","year":"2022","journal-title":"Energy Mater."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"100006","DOI":"10.20517\/energymater.2021.10","article-title":"Automated machine learning structure-composition-property relationships of perovskite materials for energy conversion and storage","volume":"1","author":"Deng","year":"2021","journal-title":"Energy Mater."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"104428","DOI":"10.1016\/j.est.2022.104428","article-title":"State of health assessment for echelon utilization batteries based on deep neural network learning with error correction","volume":"51","author":"Wei","year":"2022","journal-title":"J. Energy Storage"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"558","DOI":"10.1016\/j.apenergy.2016.08.138","article-title":"State-of-health estimation of lithium-ion battery packs in electric vehicles based on genetic resampling particle filter","volume":"182","author":"Bi","year":"2016","journal-title":"Appl. Energy"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1109\/TTE.2017.2776558","article-title":"State of Health Estimation of Lithium-Ion Batteries Using Capacity Fade and Internal Resistance Growth Models","volume":"4","author":"Guha","year":"2017","journal-title":"IEEE Trans. Transp. Electrif."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"105186","DOI":"10.1109\/ACCESS.2019.2923095","article-title":"State-of-Health Estimation for Lithium-ion Batteries Based on Wiener Process with Modeling the Relaxation Effect","volume":"7","author":"Xu","year":"2019","journal-title":"IEEE Access"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1134\/S1063771010020193","article-title":"Increasing the frequency resolution in the processing of acoustic signals by sliding complex weighted averaging","volume":"56","author":"Isaev","year":"2010","journal-title":"Acoust. Phys."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1093\/jac\/31.4.607","article-title":"The box-plot method for illustrating MIC data","volume":"31","year":"1993","journal-title":"J. Antimicrob. Chemother."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1518","DOI":"10.1126\/science.1205438","article-title":"Detecting Novel Associations in Large Data Sets","volume":"334","author":"Reshef","year":"2011","journal-title":"Science"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"834","DOI":"10.1016\/j.rser.2017.05.001","article-title":"A review of lithium-ion battery state of charge estimation and management system in electric vehicle applications: Challenges and recommendations","volume":"78","author":"Hannan","year":"2017","journal-title":"Renew. Sustain. Energ. Rev."},{"key":"ref_27","first-page":"36","article-title":"Battery Fault Diagnosis for Electric Vehicles Based on Voltage Abnormality by Combining the Long Short-Term Memory Neural Network and the Equivalent Circuit Model","volume":"2","author":"Li","year":"2021","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1007\/s11222-008-9056-0","article-title":"Parsimonious Gaussian mixture models","volume":"18","author":"McNicholas","year":"2008","journal-title":"Stat. Comput."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1811","DOI":"10.1002\/aic.11515","article-title":"Multimode process monitoring with Bayesian inference-based finite Gaussian mixture models","volume":"54","author":"Yu","year":"2008","journal-title":"AICHE J."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1023\/B:MACH.0000008084.60811.49","article-title":"Support Vector Data Description","volume":"54","author":"Tax","year":"2004","journal-title":"Mach. Learn."},{"key":"ref_31","first-page":"345","article-title":"Prediction of lithium-ion batteries remaining useful life based on particle filtering method","volume":"44","author":"Wang","year":"2020","journal-title":"Chin. J. Power Sources"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1016\/j.ymssp.2008.05.011","article-title":"Robust bearing performance degradation assessment method based on improved wavelet packet\u2013support vector data description","volume":"23","author":"Pan","year":"2009","journal-title":"Mech. Syst. Signal Process."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/24\/9637\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:36:46Z","timestamp":1760146606000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/24\/9637"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,8]]},"references-count":32,"journal-issue":{"issue":"24","published-online":{"date-parts":[[2022,12]]}},"alternative-id":["s22249637"],"URL":"https:\/\/doi.org\/10.3390\/s22249637","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,8]]}}}