Bayesian CNN-LSTM for Battery State of Health (SoH) Estimation under Randomized Usage Conditions
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Published
Jul 17, 2026
Saurabh Jaywant Desai
Muralikrishan Ramanujam
Venkataramana Runkana
Abstract
The accurate assessment of State of Health (SoH) of battery plays pivotal role in enabling the safe and dependable operation of lithium-ion battery systems. In this work, we propose a hybrid deep learning architecture integrating Convolutional Neural Networks (CNN) and Long Short-Term Memory (LSTM) networks within a Bayesian learning paradigm to improve SoH prediction accuracy considering complex charge-discharge patterns. The CNN module automatically extracts temporal and local degradation features from sequential charge-discharge profiles, while the LSTM component captures long-term dependencies in the cycling behavior. Bayesian inference is incorporated to quantify predictive uncertainty; posterior sampling yields 90% prediction intervals (S = 100; μ ± 1.64σ), which support uncertainty-informed assessment under irregular and noisy inputs. The model is trained and evaluated on the NASA randomized battery usage dataset; labels are computed from capacities at consecutive reference discharge cycles as the incremental change in SoH (dSoH), with absolute SoH reconstructed by accumulation at inference. Experimental results demonstrate that the proposed Bayesian CNN-LSTM architecture achieves high prediction accuracy, with an R² score of 0.932 and an RMSE of 0.022, while providing uncertainty estimates with reasonable empirical coverage under diverse operational conditions. These findings indicate potential applicability in battery management workflows.
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Keywords
Battery, CNN, Bayesian, LSTM, State of Health
References
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Chan, B. K., Johnson, O. V., Chew, X., Khaw, K. W., Lee, M. H., & Alnoor, A. (2024). Proposed bayesian optimization based lstm-cnn model for stock trend prediction. Computing and Informatics, 43(1), 38–63. doi: 10.31577/cai2024138
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Dong, G., Chen, Z., Wei, J., & Ling, Q. (2018). Battery health prognosis using brownian motion modelling and particle filtering. IEEE Transactions on Industrial Electronics, 65(11).
Dubarry, M., Svoboda, V., Hwu, R., & Liaw, B. Y. (2008). Incremental capacity analysis and close-to-equilibrium ocv measurements to quantify capacity fade in commercial rechargeable lithium batteries. Electrochimica Acta, 53(26), 9678–9684.
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Li, W., Sengupta, N., Dechent, P., Howey, D., Annaswamy, A., & Sauer, D. U. (2021). One-shot battery degradation trajectory prediction with deep learning. Journal of Power Sources, 506, 230024.
Ma, Y., Shan, C., Gao, J., & Chen, H. (2022). A novel method for state of health estimation of lithium-ion batteries based on improved lstm and health indicators extraction. Energy, 251, 123973.
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Venugopal, P., & Vigneswaran, T. (2019). State-of-health estimation of li-ion batteries in electric vehicle using indrnn under variable load condition. Energies, 12, 4338.
Wang, D., Miao, Q., & Pecht, M. (2013). Prognostics of lithium-ion batteries based on relevance vectors and a conditional three-parameter capacity degradation model. Journal of Power Sources, 239, 253–264.
Wei, J., Dong, G., & Chen, Z. (2018). Remaining useful life prediction and state of health diagnosis for lithium-ion batteries using particle filter and support vector regression. IEEE Transactions on Industrial Electronics, 65(7).
Xu, H., Wu, L., Xiong, S., Li, W., Garg, A., & Gao, L. (2023). An improved cnn-lstm model-based state-of-health estimation approach for lithium-ion batteries. Energy, 276, 127585.
Zhang, Y., Xiong, R., He, H., & Pecht, M. G. (2018). Long short-term memory recurrent neural network for remaining useful life prediction of lithium-ion batteries. IEEE Transactions on Vehicular Technology, 67(7), 5695–5705.
Bole, B., Kulkarni, C., & Daigle, M. (2014b). Randomized battery usage data set. NASA Prognostics Data Repository, NASA Ames Research Center, Moffett Field, CA.
Bole, B., Kulkarni, C. S., & Daigle, M. (2014a). Adaptation of an electrochemistry-based li-ion battery model to account for deterioration observed under randomized use. In Annual conference of the prognostics and health management society.
Chan, B. K., Johnson, O. V., Chew, X., Khaw, K. W., Lee, M. H., & Alnoor, A. (2024). Proposed bayesian optimization based lstm-cnn model for stock trend prediction. Computing and Informatics, 43(1), 38–63. doi: 10.31577/cai2024138
Cribari-Neto, F., & Zeileis, A. (n.d.). Beta regression in r.
Dai, Z., Li, A., Sun, W., Zhou, H., Rao, R., & Luo, Q. (2024). Estimation and prediction method of lithium battery state of health based on ridge regression and gated recurrent unit. IET Energy Systems Integration.
Dong, G., Chen, Z., Wei, J., & Ling, Q. (2018). Battery health prognosis using brownian motion modelling and particle filtering. IEEE Transactions on Industrial Electronics, 65(11).
Dubarry, M., Svoboda, V., Hwu, R., & Liaw, B. Y. (2008). Incremental capacity analysis and close-to-equilibrium ocv measurements to quantify capacity fade in commercial rechargeable lithium batteries. Electrochimica Acta, 53(26), 9678–9684.
Ebden, M. (2015). Gaussian processes: A quick introduction.
Ferrari, S. L. P. (2013, February). Beta regression modelling: recent advances in theory and applications.
Ferrari, S. L. P., & Cribari-Neto, F. (2004). Beta regression for modelling rates and proportions. Journal of Applied Statistics, 31(7).
Goebel, K., Saha, B., Saxena, A., Celaya, J. R., & Christophersen, J. P. (2008). Prognostics in battery health management. IEEE Instrumentation and Measurement Magazine, 11(4).
Jaguemont, J., Boulon, L., & Dube, Y. (2016). A comprehensive review of lithium-ion batteries used in hybrid and electric vehicles at cold temperatures. Applied Energy, 164, 99–114.
Joel, A. D. (2023). Predicting implicit patterns and optimizing market entry and exit decisions in stock prices using integrated bayesian cnn-lstm with deep q-learning as a meta-labeller. [GitHub Repository]. (Available at: https://github.com/adrikodebo/bayesian-CNNLSTM-Q-learning)
Ke, Y., Long, M., Yang, F., & Peng, W. (2024). A bayesian deep learning pipeline for lithium-ion battery soh estimation with uncertainty quantification. Quality and Reliability Engineering International, 40, 406–427.
Kendall, A., & Gal, Y. (2017). What uncertainties do we need in bayesian deep learning for computer vision? In Proceedings of neurips (pp. 5574–5584).
Li, W., Sengupta, N., Dechent, P., Howey, D., Annaswamy, A., & Sauer, D. U. (2021). One-shot battery degradation trajectory prediction with deep learning. Journal of Power Sources, 506, 230024.
Ma, Y., Shan, C., Gao, J., & Chen, H. (2022). A novel method for state of health estimation of lithium-ion batteries based on improved lstm and health indicators extraction. Energy, 251, 123973.
Mrhar, K., Benhiba, L., Bourekkache, S., & Abik, M. (2021). A bayesian cnn-lstm model for sentiment analysis in massive open online courses moocs. International Journal of Emerging Technologies in Learning (iJET), 16(23), 4–18.
Nagulapati, V. M., Lee, H., Jung, D., Sargunan, S., Paramanantham, S., Brigljevic, B., . . . Lim, H. (2021). A novel combined multi-battery dataset-based approach for enhanced prediction accuracy of data-driven prognostic models in capacity estimation of lithium-ion batteries. Energy and AI, 5, 100089.
Ramadass, P., Haran, B., White, R., & Popov, B. N. (2003). Mathematical modeling of the capacity fade of li-ion cells. Journal of Power Sources, 123(2), 230–240.
Rasmussen, C. E. (2006). Gaussian processes for machine learning. CiteSeer.
Reitz, R. D., Ogawa, H., Payri, R., Fansler, T., Kokjohn, S., Moriyoshi, Y., . . . Zhao, H. (2019). The future of the internal combustion engine. International Journal of Engine Research.
Richardson, R. R., Osborne, M. A., & Howey, D. A. (2017). Gaussian process regression for forecasting battery state of health. Journal of Power Sources, 357, 209–219.
Richardson, R. R., Osborne, M. A., & Howey, D. A. (2019). Battery health prediction under generalized condition using a gaussian process transition model. Journal of Energy Storage, 23, 320–328.
Saha, B., & Goebel, K. (n.d.). Battery data set. NASA Ames Prognostics Data Repository.
Saha, B., Goebel, K., Poll, S., & Christophersen, J. (2009). Prognostics methods for battery health monitoring using a bayesian framework. IEEE Transactions on Instrumentation and Measurement, 58(2), 291–296.
Saxena, A., Celaya, J., Balaban, E., Goebel, K., Saha, B., Saha, S., & Schwabacher, M. (2008). Metrics for evaluating performance of prognostic techniques. In Ieee xplore. Denver, CO, USA.
Venugopal, P., & Vigneswaran, T. (2019). State-of-health estimation of li-ion batteries in electric vehicle using indrnn under variable load condition. Energies, 12, 4338.
Wang, D., Miao, Q., & Pecht, M. (2013). Prognostics of lithium-ion batteries based on relevance vectors and a conditional three-parameter capacity degradation model. Journal of Power Sources, 239, 253–264.
Wei, J., Dong, G., & Chen, Z. (2018). Remaining useful life prediction and state of health diagnosis for lithium-ion batteries using particle filter and support vector regression. IEEE Transactions on Industrial Electronics, 65(7).
Xu, H., Wu, L., Xiong, S., Li, W., Garg, A., & Gao, L. (2023). An improved cnn-lstm model-based state-of-health estimation approach for lithium-ion batteries. Energy, 276, 127585.
Zhang, Y., Xiong, R., He, H., & Pecht, M. G. (2018). Long short-term memory recurrent neural network for remaining useful life prediction of lithium-ion batteries. IEEE Transactions on Vehicular Technology, 67(7), 5695–5705.
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Technical Papers