An Interpretable Remaining Life Prediction Method for Lithium-Ion Batteries Considering Capacity Regeneration
Wu Shengli1, Guo Qi1, Xing Wenting2
1. School of Traffic and Transportation Chongqing Jiaotong University Chongqing 400074 China; 2. School of Management Science and Engineering Chongqing Technology and Business University Chongqing 400067 China
Abstract：As lithium-ion batteries undergo repeated charge-discharge cycles, their performance gradually deteriorates, resulting in aging phenomena. To address the failure of conventional remaining useful life (RUL) prediction models caused by the coupling between nonlinear degradation behavior and capacity regeneration effects, this study considers the influence of capacity regeneration while incorporating model interpretability, and innovatively constructs a hybrid prediction framework (VGL) that integrates variational mode decomposition (VMD), Gaussian process regression (GPR), and linear optimization resampling particle filtering (LOPF). Specifically, VMD is employed to adaptively decompose battery health indicator sequences into a high-frequency capacity regeneration component and a low-frequency global degradation component, thereby reducing signal non-stationarity and coupling complexity while preserving clear physical interpretability. The capacity regeneration component is modeled using GPR to capture its nonlinear and stochastic dynamics, enabling accurate short-term regeneration prediction. Meanwhile, the global degradation trend is characterized by an LOPF-based approach, which combines a bi-exponential degradation assumption with a linear optimization resampling strategy to maintain particle diversity and robustly track long-term degradation behavior. Finally, the outputs of GPR and LOPF are probabilistically fused to construct a joint failure probability density function, achieving multi-scale decision fusion. The proposed framework significantly improves RUL prediction accuracy while providing enhanced interpretability for lithium-ion battery aging mechanisms. The proposed model is validated and analyzed using the NASA battery degradation dataset and is compared with the VPG, ELM, and WOA-ELM models. From the degradation curves, it can be observed that although the ELM and WOA-ELM methods are able to reflect the general trend of capacity fading, their prediction errors increase significantly with the number of cycles. In contrast, the RUL predictions obtained by the proposed method are highly concentrated around the true values, and the corresponding capacity tracking curves exhibit a higher degree of consistency with the measured data. In particular, the proposed approach is able to maintain accurate tracking of the degradation trend in long-term prediction scenarios. Moreover, the prediction error results demonstrate that, under identical experimental conditions, the proposed method achieves significantly higher prediction accuracy than the VPG, ELM, and WOA-ELM models. To further verify the generalization capability of the proposed VMD-GPR-LOPF model across different chemical systems and operating conditions, in addition to the NASA 18650 battery dataset, the publicly available CS35 and CS36 battery datasets from the University of Maryland CALCE are also employed for validation. The experimental results indicate that, while maintaining the same model parameter settings as those used in the NASA dataset experiments, the proposed method is able to accurately predict the capacity degradation processes of both the CS35 and CS36 batteries. Specifically, the average absolute error (AE) of both battery datasets remains below 0.25%, the mean absolute percentage error (MAPE) is less than 1%, and the root mean square error (RMSE) is approximately 0.62%, demonstrating that the proposed model maintains high prediction accuracy and stability across different battery types and environmental operating conditions.
[1] 袁奥特, 蔡涛, 刘政辰, 等. 基于电化学阻抗谱的锂离子电池电滥用失效预警研究[J]. 电工技术学报, 2025, 40(7): 2306-2321. Yuan Aote, Cai Tao, Liu Zhengchen, et al.Study of electrical abuse failure early warning of lithium-ion batteries based on electrochemical impedance spectroscopy[J]. Transactions of China Electrotechnical Society, 2025, 40(7): 2306-2321. [2] 范兴明, 吴润玮, 封浩, 等. 基于变窗口自适应无迹卡尔曼滤波的锂离子电池荷电状态预测[J]. 电工技术学报, 2025, 40(6): 1974-1983. Fan Xingming, Wu Runwei, Feng Hao, et al.Lithium-ion battery state of charge estimation based on variable-window adaptive untraceable Kalman filtering algorithm[J]. Transactions of China Electrotechnical Society, 2025, 40(6): 1974-1983. [3] 顾菊平, 蒋凌, 张新松, 等. 基于特征提取的锂离子电池健康状态评估及影响因素分析[J]. 电工技术学报, 2023, 38(19): 5330-5342. Gu Juping, Jiang Ling, Zhang Xinsong, et al.Estimation and influencing factor analysis of lithium-ion batteries state of health based on features extraction[J]. Transactions of China Electrotechnical Society, 2023, 38(19): 5330-5342. [4] 陈猛, 王军, 王雯雯, 等. 应用支持向量机的锂电池不可逆析锂检测研究[J]. 电工技术学报, 2025, 40(4): 1323-1332. Chen Meng, Wang Jun, Wang Wenwen, et al.Research on irreversible lithium plating detection in lithium-ion batteries using support vector machine[J]. Transactions of China Electrotechnical Society, 2025, 40(4): 1323-1332. [5] 孔纯, 朱国荣, 魏学良, 等. 考虑固相扩散诱导应力的锂离子电池电极颗粒破裂机理研究[J]. 电工技术学报, 2025, 40(5): 1672-1684. Kong Chun, Zhu Guorong, Wei Xueliang, et al.Research on lithium-ion battery electrode particles cracking mechanism considering solid-phase dif- fusion induced stress[J]. Transactions of China Electrotechnical Society, 2025, 40(5): 1672-1684. [6] Yan Lisen, Peng Jun, Gao Dianzhu, et al.A hybrid method with cascaded structure for early-stage remaining useful life prediction of lithium-ion battery[J]. Energy, 2022, 243: 123038. [7] 吴伟丽, 卢双双. 基于PCA-CEEMDAN和改进SVR的锂电池RUL预测[J]. 电源学报, 2025, 23(6): 267-280. Wu Weili, Lu Shuangshuang.RUL prediction of lithium-ion batteries based on PCA-CEEMDAN and improved SVR[J]. Journal of Power Supply, 2025, 23(6): 267-280. [8] 张鹏新, 高明明, 解沛然, 等. 基于数据驱动的循环流化床机组深度调峰NOx预测[J]. 发电技术, 2025, 46(3): 627-636. Zhang Pengxin, Gao Mingming, Xie Peiran, et al.NOx prediction for deep peaking regulation of circulating fluidized bed units based on data-driven[J]. Power Generation Technology, 2025, 46(3): 627-636. [9] Prasad G K, Rahn C D.Model based identification of aging parameters in lithium ion batteries[J]. Journal of Power Sources, 2013, 232: 79-85. [10] Chen Minzhi, Ma Guijun, Liu Weibo, et al.An overview of data-driven battery health estimation technology for battery management system[J]. Neurocomputing, 2023, 532: 152-169. [11] Liu Yiwei, Sun Jing, Shang Yunlong, et al.A novel remaining useful life prediction method for lithium-ion battery based on long short-term memory network optimized by improved sparrow search algorithm[J]. Journal of Energy Storage, 2023, 61: 106645. [12] Zhang Yingda, Ma Hongyan, Wang Shuai, et al.Indirect prediction of remaining useful life for lithium-ion batteries based on improved multiple kernel extreme learning machine[J]. Journal of Energy Storage, 2023, 64: 107181. [13] Chen Zheng, Zhao Hongqian, Zhang Yuanjian, et al.State of health estimation for lithium-ion batteries based on temperature prediction and gated recurrent unit neural network[J]. Journal of Power Sources, 2022, 521: 230892. [14] Wang Xiaohua, Dai Ke, Hu Min, et al.Lithium-ion battery health state and remaining useful life prediction based on hybrid model MFE-GRU-TCA[J]. Journal of Energy Storage, 2024, 95: 112442. [15] Chang Yang, Fang Huajing, Zhang Yong.A new hybrid method for the prediction of the remaining useful life of a lithium-ion battery[J]. Applied Energy, 2017, 206: 1564-1578. [16] Yu Xiaofang, Ma Zhuang, Wen Jialin.Joint estimation of SOH and RUL for lithium batteries based on variable frequency and model integration[J]. International Journal of Electrochemical Science, 2024, 19(11): 100842. [17] Huang Zhelin, Ma Zhihua.Remaining useful life prediction of lithium-ion batteries based on autoregression with exogenous variables model[J]. Reliability Engineering & System Safety, 2024, 252: 110485. [18] 张周同, 盛文娟. 基于ISW和优化VMD-LSTM的锂电池剩余寿命预测[J]. 电器与能效管理技术, 2024(11): 45-57. Zhang Zhoutong, Sheng Wenjuan.Remaining useful life prediction of lithium batteries based on ISW and optimized VMD-LSTM[J]. Electrical & Energy Management Technology, 2024(11): 45-57. [19] 戴俊彦, 夏明超, 陈奇芳. 基于双重注意力机制的电池SOH估计和RUL预测编解码模型[J]. 电力系统自动化, 2023, 47(6): 168-177. Dai Junyan, Xia Mingchao, Chen Qifang.Encoding and decoding model of state of health estimation and remaining useful life prediction for batteries based on dual-stage attention mechanism[J]. Automation of Electric Power Systems, 2023, 47(6): 168-177. [20] Wang Fujin, Zhao Zhibin, Zhai Zhi, et al.Explainability-driven model improvement for SOH estimation of lithium-ion battery[J]. Reliability Engineering & System Safety, 2023, 232: 109046. [21] Elmahallawy M, Elfouly T, Alouani A, et al.A comprehensive review of lithium-ion batteries modeling, and state of health and remaining useful lifetime prediction[J]. IEEE Access, 2022, 10: 119040-119070. [22] Li Hao, Fu Lijun, Zhang Yan.A novel hybrid data-driven method based on uncertainty quantification to predict the remaining useful life of lithium battery[J]. Journal of Energy Storage, 2022, 52: 104984. [23] He Rong, He Yongling, Xie Wenlong, et al.Multi-scale analysis for accelerated degradation mechanisms of cylindrical LiFePO4/graphite batteries under distinct positions of jelly roll[J]. Electrochimica Acta, 2023, 444: 142048. [24] Li Hua, Liu Tao, Wu Xing, et al.An optimized VMD method and its applications in bearing fault diagnosis[J]. Measurement, 2020, 166: 108185. [25] Zhou Di, Zheng Wenbin, Chen Shaohui, et al.Research on state of health prediction model for lithium batteries based on actual diverse data[J]. Energy, 2021, 230: 120851. [26] Tagade P, Hariharan K S, Ramachandran S, et al.Deep Gaussian process regression for lithium-ion battery health prognosis and degradation mode diagnosis[J]. Journal of Power Sources, 2020, 445: 227281. [27] Zhou Yong, Dong Guangzhong, Tan Qianqian, et al.State of health estimation for lithium-ion batteries using geometric impedance spectrum features and recurrent Gaussian process regression[J]. Energy, 2023, 262: 125514. [28] Wang Zhenpo, Yuan Changgui, Li Xiaoyu.Lithium battery state-of-health estimation via differential thermal voltammetry with Gaussian process regression[J]. IEEE Transactions on Transportation Electrification, 2021, 7(1): 16-25. [29] Weddle P J, Kim S, Chen B R, et al.Battery state-of-health diagnostics during fast cycling using physics-informed deep-learning[J]. Journal of Power Sources, 2023, 585: 233582. [30] El-Dalahmeh M, Al-Greer M, El-Dalahmeh M, et al.Physics-based model informed smooth particle filter for remaining useful life prediction of lithium-ion battery[J]. Measurement, 2023, 214: 112838. [31] Li Penghua, Zhang Zijian, Xiong Qingyu, et al.State-of-health estimation and remaining useful life prediction for the lithium-ion battery based on a variant long short term memory neural network[J]. Journal of Power Sources, 2020, 459: 228069. [32] Kuptametee C, Aunsri N.A review of resampling techniques in particle filtering framework[J]. Measurement, 2022, 193: 110836. [33] 王小明, 何叶, 王路路, 等. 基于DWD-SVR模型的锂离子电池剩余使用寿命预测[J]. 太阳能学报, 2025, 46(2): 52-59. Wang Xiaoming, He Ye, Wang Lulu, et al.Rul prediction for lithium-ion batteries based on DWD-SVR model[J]. Acta Energiae Solaris Sinica, 2025, 46(2): 52-59.
2026, Vol. 41 
