Equivalent-circuit-model-guided feature selection for interpretable battery state-of-health estimation

Abstract

Reliable state-of-health (SOH) estimation depends not only on the nonlinear mapper but also on whether its inputs are compact, informative, and physically interpretable. We develop an equivalent circuit model (ECM)-guided feature-selection strategy that uses fractional-ECM parameters offline as physical anchors for charging-response and incremental capacity analysis (ICA) features. The predictive evaluation comprises 4259 cycle samples from ten commercial nickel–cobalt–aluminum (NCA) cells tested at 25 °C, 35 °C, and 45 °C under a 0.5 C protocol. A 13-dimensional (13D) full input is compared with five equal-cardinality 8-dimensional (8D) schemes using gated recurrent unit (GRU) and temporal convolutional network (TCN) nonlinear mappers. Ten-fold leave-one-battery-out (LOBO) validation provides the primary evidence. Among the 8D schemes, the Pearson correlation coefficient (PCC-8D) gives the lowest GRU macro root-mean-square error (RMSE; $0.005272\pm 0.002064$). Physically anchored ECM-8D gives the lowest TCN macro RMSE ($0.005882\pm 0.003804$). ECM-8D is therefore competitive rather than universally most accurate. The two retained charging-time ratios are deterministically related, and 7D removal sensitivities reveal battery- and architecture-dependent effects. ECM fitting is required only during offline feature design; inference uses charging, ICA, and temperature variables. These results support a bounded route to interpretable SOH input construction within the tested NCA protocol, not cross-chemistry or wider-regime generalization.

Keywords

Electrochemical impedance spectroscopy / Equivalent circuit model / Feature selection / Leave-one-battery-out validation / Lithium-ion battery / State of health

References

[1] C.-Y. Liu, H. Li, K.-X. Li, et al., Deep learning for state of health estimation of lithium-ion batteries in electric vehicles: a systematic review, Energies 18 (6) (2025) 1463.

[2] F. von Bülow, T. Meisen, A review on methods for state of health forecasting of lithium-ion batteries applicable in real-world operational conditions, J. Energy Storage 57 (2023) 105978.

[3] L.-P. Chen, X.-Y. Bao, A.M. Lopes, et al., State of health estimation of lithium-ion batteries based on equivalent circuit model and data-driven method, J. Energy Storage 73 (2023) 109195.

[4] F.-J. Wang, Z. Zhai, Z.-B. Zhao, et al., Physics-informed neural network for lithium-ion battery degradation stable modeling and prognosis, Nat. Commun. 15 (1) (2024) 4332.

[5] Y.-J. Zhang, Y.-J. Liu, J. Wang, et al., State-of-health estimation for lithium-ion batteries by combining model-based incremental capacity analysis with support vector regression, Energy 239 (2022) 121986.

[6] A. Lanubile, P. Bosoni, G. Pozzato, et al., Domain knowledge-guided machine learning framework for state of health estimation in lithium-ion batteries, Commun. Eng. 3 (1) (2024) 168.

[7] B. Jiang, J.-G. Zhu, X.-Y. Wang, et al., A comparative study of different features extracted from electrochemical impedance spectroscopy in state of health estimation for lithium-ion batteries, Appl. Energy 322 (2022) 119502.

[8] Q.-M. Zhang, C.-G. Huang, H. Li, et al., Electrochemical impedance spectroscopy based state-of-health estimation for lithium-ion battery considering temperature and state-of-charge effect, IEEE T. Transp. Electr. 8 (4) (2022) 4633-4645.

[9] B.-H. Shao, J. Zhong, J. Tian, et al., State-of-health estimation of lithium-ion batteries based on electrochemical impedance spectroscopy features and fusion interpretable deep learning framework, Energies 18 (6) (2025) 1385.

[10] L.-P. Chen, S.-Q. Xie, A.M. Lopes, et al., A new SOH estimation method for lithium-ion batteries based on model-data-fusion, Energy 286 (2024) 129597.

[11] S. Bockrath, V. Lorentz, M. Pruckner, State of health estimation of lithium-ion batteries with a temporal convolutional neural network using partial load profiles, Appl. Energy 329 (2023) 120307.

[12] J.-S. Xue, W.-T. Ma, X.-Y. Feng, et al., Stacking integrated learning model via ELM and GRU with mixture correntropy loss for robust state of health estimation of lithium-ion batteries, Energy 284 (2023) 129279.

[13] X.-P. Li, M.-H. Zhao, S.-S. Zhong, et al., BMSFormer: an efficient deep learning model for online state-of-health estimation of lithium-ion batteries under high-frequency early SOC data with strong correlated single health indicator, Energy 313 (2024) 134030.

[14] Y. Chen, X.-H. Huang, Y.-G. He, et al., Edge–cloud collaborative estimation lithium-ion battery SOH based on MEWOA-VMD and Transformer, J. Energy Storage 99 (2024) 113388.

[15] Y. Chen, D.-Y. Li, X.-H. Huang, et al., Exploring life warning solution of lithium-ion batteries in real-world scenarios: TCN-transformer fusion model for battery pack SOH estimation, Energy 335 (2025) 138053.

[16] C.-S. Lin, L.-X. Wu, X.-G. Tuo, et al., A lightweight two-stage physics-informed neural network for SOH estimation of lithium-ion batteries with different chemistries, J. Energy Chem. 105 (2025) 261-279.

[17] J.-G. Zhu, Y.-X. Wang, Y. Huang, et al., Data-driven capacity estimation of commercial lithium-ion batteries from voltage relaxation, Nat. Commun. 13 (1) (2022) 2261.

[18] Y. Xie, K. Luo, L.-H. Zheng, et al., A state of health estimation method for lithium-ion batteries based on initial charging segment and gated recurrent unit neural network, J. Power Sources 638 (2025) 236607.

[19] G.-J. Qian, Y.-J. Zheng, X.-Y. Li, et al., State of health estimation for lithium-ion batteries using impedance-based simplified timescale information, Appl. Energy 382 (2025) 125272.

[20] Y.-L. Zhu, B. Jiang, J.-G. Zhu, et al., Adaptive state of health estimation for lithium-ion batteries using impedance-based timescale information and ensemble learning, Energy 284 (2023) 129283.

[21] L. Yao, J.-S. Wen, Y.-Q. Xiao, et al., State of health estimation approach for Li-ion batteries based on mechanism feature empowerment, J. Energy Storage 84 (2024) 110965.

[22] X.-L. Xia, Y. Chen, J.-W. Shen, et al., State of health estimation for lithium-ion batteries based on impedance feature selection and improved support vector regression, Energy 326 (2025) 136135.

[23] K. Cho, B. van Merriënboer, C. Gulcehre, et al., Learning phrase representations using RNN encoder–decoder for statistical machine translation, in: Proc. of the Conf. on Empirical Methods in Natural Language Processing (EMNLP), Doha, Qatar, 2014, pp. 1724-1734.

[24] S.-J. Bai, J.Z. Kolter, V. Koltun, An empirical evaluation of generic convolutional and recurrent networks for sequence modeling [Online]. Available,https://arxiv.org/abs/1803.01271, March 2018.

[25] T. Akiba, S. Sano, T. Yanase, et al., Optuna: a next-generation hyperparameter optimization framework, in: Proc. of the 25th ACM SIGKDD Intl. Conf. on Knowledge Discovery & Data Mining, Anchorage, USA, 2019, pp. 2623-2631.

[26] S.M. Lundberg, S.-I. Lee, A unified approach to interpreting model predictions, in: Proc. of the 31st Intl. Conf. on Neural Information Processing Systems, Long Beach, USA, 2017, pp. 4768-4777.