{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T03:06:40Z","timestamp":1778123200168,"version":"3.51.4"},"reference-count":40,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2024,4,5]],"date-time":"2024-04-05T00:00:00Z","timestamp":1712275200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Union\u2019s Horizon Europe research and innovation programme","award":["101102278"],"award-info":[{"award-number":["101102278"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Li-ion batteries are integral to various applications, ranging from electric vehicles to mobile devices, because of their high energy density and user friendliness. The assessment of the Li-ion state of heath stands as a crucial research domain, aiming to innovate safer and more effective battery management systems that can predict and promptly report any operational discrepancies. To achieve this, an array of machine learning (ML) and artificial intelligence (AI) methodologies have been employed to analyze data from Li-ion batteries, facilitating the estimation of critical parameters like state of charge (SoC) and state of health (SoH). The continuous enhancement of ML and AI algorithm efficiency remains a pivotal focus of scholarly inquiry. Our study distinguishes itself by separately evaluating traditional machine learning frameworks and advanced deep learning paradigms to determine their respective efficacy in predictive modeling. We dissected the performances of an assortment of models, spanning from conventional ML techniques to sophisticated, hybrid deep learning constructs. Our investigation provides a granular analysis of each model\u2019s utility, promoting an informed and strategic integration of ML and AI in Li-ion battery state of health prognostics. Specifically, a utilization of machine learning algorithms such as Random Forests (RFs) and eXtreme Gradient Boosting (XGBoost), alongside regression models like Elastic Net and foundational neural network approaches including Multilayer Perceptron (MLP) were studied. Furthermore, our research investigated the enhancement of time series analysis using intricate models like Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs) and their outcomes with those of hybrid models, including a RNN-long short-term memory (LSTM), CNN-LSTM, CNN-Gated Recurrent Unit (GRU) and RNN-GRU. Comparative evaluations reveal that the RNN-LSTM configuration achieved a Mean Squared Error (MSE) of 0.043, R-Squared of 0.758, Root Mean Square Error (RMSE) of 0.208, and Mean Absolute Error (MAE) of 0.124, whereas the CNN-LSTM framework reported an MSE of 0.039, R-Squared of 0.782, RMSE of 0.197, and MAE of 0.122, underscoring the potential of deep learning-based hybrid models in advancing the accuracy of battery state of health assessments.<\/jats:p>","DOI":"10.3390\/sym16040436","type":"journal-article","created":{"date-parts":[[2024,4,5]],"date-time":"2024-04-05T08:27:52Z","timestamp":1712305672000},"page":"436","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["Discharge Capacity Estimation for Li-Ion Batteries: A Comparative Study"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3880-3039","authenticated-orcid":false,"given":"Saadin","family":"Oyucu","sequence":"first","affiliation":[{"name":"Department of Computer Engineering, Faculty of Engineering, Ad\u0131yaman University, 02040 Ad\u0131yaman, T\u00fcrkiye"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5752-2860","authenticated-orcid":false,"given":"Sezer","family":"D\u00fcmen","sequence":"additional","affiliation":[{"name":"Battery Research Laboratory, Faculty of Engineering and Natural Sciences, Sivas University of Science and Technology, 58010 Sivas, T\u00fcrkiye"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5492-803X","authenticated-orcid":false,"given":"\u0130remnur","family":"Duru","sequence":"additional","affiliation":[{"name":"Battery Research Laboratory, Faculty of Engineering and Natural Sciences, Sivas University of Science and Technology, 58010 Sivas, T\u00fcrkiye"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2563-1218","authenticated-orcid":false,"given":"Ahmet","family":"Aks\u00f6z","sequence":"additional","affiliation":[{"name":"MOBILERS Team, Sivas Cumhuriyet University, 58380 Sivas, T\u00fcrkiye"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9871-4102","authenticated-orcid":false,"given":"Emre","family":"Bi\u00e7er","sequence":"additional","affiliation":[{"name":"Battery Research Laboratory, Faculty of Engineering and Natural Sciences, Sivas University of Science and Technology, 58010 Sivas, T\u00fcrkiye"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1050","DOI":"10.1016\/j.jclepro.2018.06.182","article-title":"On-line life cycle health assessment for lithium-ion battery in electric vehicles","volume":"199","author":"Liu","year":"2018","journal-title":"J. Clean. Prod."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"012133","DOI":"10.1088\/1755-1315\/94\/1\/012133","article-title":"Lithium-ion battery state of function estimation based on fuzzy logic algorithm with associated variables","volume":"94","author":"Gan","year":"2017","journal-title":"IOP Conf. Ser. Earth Environ. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"95333","DOI":"10.1109\/ACCESS.2020.2995899","article-title":"Novel Lithium-Ion Battery State-of-Health Estimation Method Using a Genetic Programming Model","volume":"8","author":"Yao","year":"2020","journal-title":"IEEE Access"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"114408","DOI":"10.1016\/j.apenergy.2019.114408","article-title":"A hybrid statistical data-driven method for on-line joint state estimation of lithium-ion batteries","volume":"261","author":"Song","year":"2020","journal-title":"Appl. Energy"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2911","DOI":"10.1109\/TII.2017.2684821","article-title":"RUL Prediction of Deteriorating Products Using an Adaptive Wiener Process Model","volume":"13","author":"Zhai","year":"2017","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"11855","DOI":"10.1109\/TPEL.2020.2987383","article-title":"Multiobjective Optimization of Data-Driven Model for Lithium-Ion Battery SOH Estimation with Short-Term Feature","volume":"35","author":"Cai","year":"2020","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/j.neucom.2019.09.074","article-title":"Remaining useful life prediction of lithium-ion batteries with adaptive unscented kalman filter and optimized support vector regression","volume":"376","author":"Xue","year":"2019","journal-title":"Neurocomputing"},{"key":"ref_8","first-page":"213","article-title":"Prediction and modelling of energy consumption on temperature control for greenhouses","volume":"22","author":"Dursun","year":"2018","journal-title":"J. Polytech."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"155130","DOI":"10.1109\/ACCESS.2019.2937798","article-title":"Deep learning prognostics for lithium-ion battery based on ensembled long short-term memory networks","volume":"7","author":"Liu","year":"2019","journal-title":"IEEE Access"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3170","DOI":"10.1109\/TIE.2020.2973876","article-title":"A Data-Driven Approach with Uncertainty Quantification for Predicting Future Capacities and Remaining Useful Life of Lithium-ion Battery","volume":"68","author":"Liu","year":"2021","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Alhamayani, A. (2023). CNN-LSTM to Predict and Investigate the Performance of a Thermal\/Photovoltaic System Cooled by Nanofluid (Al2O3) in a Hot-Climate Location. Processes, 11.","DOI":"10.3390\/pr11092731"},{"key":"ref_12","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_13","doi-asserted-by":"crossref","unstructured":"Oyucu, S., Do\u011fan, F., Aks\u00f6z, A., and Bi\u00e7er, E. (2024). Comparative Analysis of Commonly Used Machine Learning Approaches for Li-Ion Battery Performance Prediction and Management in Electric Vehicles. Appl. Sci., 14.","DOI":"10.3390\/app14062306"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Sekuli\u0107, A., Kilibarda, M., Heuvelink, G.B., Nikoli\u0107, M., and Bajat, B. (2020). Random Forest spatial interpolation. Remote. Sens., 12.","DOI":"10.3390\/rs12101687"},{"key":"ref_15","unstructured":"Chen, T., He, T., and Benesty, M. XGBoost: eXtreme Gradient Boosting. R Packag. 2018, Comprehensive r archive network. version 0.71-2, 1\u20134."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/j.jco.2009.01.002","article-title":"Elastic-net regularization in learning theory","volume":"25","author":"Rosasco","year":"2009","journal-title":"J. Complex."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Khalid, A., Sundararajan, A., Acharya, I., and Sarwat, A.I. (2019, January 19\u201321). Prediction of Li-Ion Battery State of Charge Using Multilayer Perceptron and Long Short-Term Memory Models. Proceedings of the 2019 IEEE Transportation Electrification Conference and Expo (ITEC), Detroit, MI, USA.","DOI":"10.1109\/ITEC.2019.8790533"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Song, Y., Li, L., Peng, Y., and Liu, D. (2018, January 17\u201319). Lithium-Ion Battery Remaining Useful Life Prediction Based on GRU-RNN. Proceedings of the 2018 12th International Conference on Reliability, Maintainability, and Safety (ICRMS), Shanghai, China.","DOI":"10.1109\/ICRMS.2018.00067"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"e623","DOI":"10.7717\/peerj-cs.623","article-title":"The coefficient of determination R-squared is more informative than SMAPE, MAE, MAPE, MSE and RMSE in regression analysis evaluation","volume":"7","author":"Chicco","year":"2021","journal-title":"PeerJ Comput. Sci."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"226830","DOI":"10.1016\/j.jpowsour.2019.226830","article-title":"Accelerated cycle life testing and capacity degradation modeling of LiCoO2-graphite cells","volume":"435","author":"Diao","year":"2019","journal-title":"J. Power Sources"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Radivojevi\u0107, D.S., Lazovi\u0107, I.M., Mirkov, N.S., Ramadani, U.R., and Nikezi\u0107, D.P. (2023). A Comparative Evaluation of Self-Attention Mechanism with ConvLSTM Model for Global Aerosol Time Series Forecasting. Mathematics, 11.","DOI":"10.3390\/math11071744"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1007\/978-3-030-62008-0_35","article-title":"RFRSF: Employee Turnover Prediction Based on Random Forests and Survival Analysis","volume":"12343","author":"Jin","year":"2020","journal-title":"Lect. Notes Comput. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/j.egyr.2022.09.126","article-title":"Online battery health diagnosis for electric vehicles based on DTW-XGBoost","volume":"8","author":"Yan","year":"2022","journal-title":"Energy Rep."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1007\/s10114-021-8193-7","article-title":"Strong Approximation for a Toric Variety","volume":"37","author":"Wei","year":"2021","journal-title":"Acta Math. Sin. Engl. Ser."},{"key":"ref_25","unstructured":"Noriega, L. (2024, March 27). Multilayer Perceptron Tutorial. Available online: https:\/\/api.semanticscholar.org\/CorpusID:61645526."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Han, Y., Li, C., Zheng, L., Lei, G., and Li, L. (2023). Remaining Useful Life Prediction of Lithium-Ion Batteries by Using a Denoising Transformer-Based Neural Network. Energies, 16.","DOI":"10.3390\/en16176328"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"104833","DOI":"10.1016\/j.arabjc.2023.104833","article-title":"Development of advanced machine learning models for optimization of methyl ester biofuel production from papaya oil: Gaussian process regression (GPR), multilayer perceptron (MLP), and K-nearest neighbor (KNN) regression models","volume":"16","author":"Sumayli","year":"2023","journal-title":"Arab. J. Chem."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"i412","DOI":"10.1093\/bioinformatics\/bty239","article-title":"Discriminating early- and late-stage cancers using multiple kernel learning on gene sets","volume":"34","author":"Rahimi","year":"2018","journal-title":"Bioinformatics"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Camacho Olmedo, M.T., Paegelow, M., Mas, J.F., and Escobar, F. (2018). Geomatic Approaches for Modeling Land Change Scenarios, Springer International Publishing. Part of the Lecture Notes in Geoinformation and Cartography Book Series (LNGC).","DOI":"10.1007\/978-3-319-60801-3"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"183914","DOI":"10.1109\/ACCESS.2019.2960654","article-title":"Anomaly Detection in Videos Using Optical Flow and Convolutional Autoencoder","volume":"7","author":"Duman","year":"2019","journal-title":"IEEE Access"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"He, K., Yang, Q., Ji, L., Pan, J., and Zou, Y. (2023). Financial Time Series Forecasting with the Deep Learning Ensemble Model. Mathematics, 11.","DOI":"10.3390\/math11041054"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Rinc\u00f3n-Maya, C., Guevara-Carazas, F., Hern\u00e1ndez-Barajas, F., Patino-Rodriguez, C., and Usuga-Manco, O. (2023). Remaining Useful Life Prediction of Lithium-Ion Battery Using ICC-CNN-LSTM Methodology. Energies, 16.","DOI":"10.3390\/en16207081"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"7166","DOI":"10.1109\/TITS.2023.3263358","article-title":"Beyond RMSE: Do Machine-Learned Models of Road User Interaction Produce Human-Like Behavior?","volume":"24","author":"Srinivasan","year":"2023","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"012002","DOI":"10.1088\/1742-6596\/930\/1\/012002","article-title":"Forecasting Error Calculation with Mean Absolute Deviation and Mean Absolute Percentage Error","volume":"930","author":"Khair","year":"2017","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Cocianu, C.L., Uscatu, C.R., and Avramescu, M. (2022). Improvement of LSTM-Based Forecasting with NARX Model through Use of an Evolutionary Algorithm. Electronics, 11.","DOI":"10.3390\/electronics11182935"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"123829","DOI":"10.1016\/j.energy.2022.123829","article-title":"Lithium-ion batteries health prognosis via differential thermal capacity with simulated annealing and support vector regression","volume":"250","author":"Lin","year":"2022","journal-title":"Energy"},{"key":"ref_37","first-page":"787","article-title":"Cyclic Degradation Prediction of Lithium-Ion Batteries using Data-Driven Machine Learning","volume":"94","author":"Lim","year":"2022","journal-title":"Chem. Eng. Trans."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"108821","DOI":"10.1016\/j.ress.2022.108821","article-title":"Remaining capacity estimation for lithium-ion batteries via co-operation of multi-machine learning algorithms","volume":"228","author":"Shu","year":"2022","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1551","DOI":"10.1021\/acscentsci.1c00611","article-title":"Machine-Learning Approach for Predicting the Discharging Capacities of Doped Lithium Nickel\u2013Cobalt\u2013Manganese Cathode Materials in Li-Ion Batteries","volume":"7","author":"Wang","year":"2021","journal-title":"ACS Central Sci."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"19541","DOI":"10.1038\/s41598-021-98915-8","article-title":"Deep learning approach towards accurate state of charge estimation for lithium-ion batteries using self-supervised transformer model","volume":"11","author":"Hannan","year":"2021","journal-title":"Sci. Rep."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/4\/436\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:23:46Z","timestamp":1760106226000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/4\/436"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,5]]},"references-count":40,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2024,4]]}},"alternative-id":["sym16040436"],"URL":"https:\/\/doi.org\/10.3390\/sym16040436","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,4,5]]}}}