Estimated state of health for retired lithium batteries using kernel function and hyperparameter optimization

doi:10.19799/j.cnki.2095-4239.2023.0918

Abstract

Abstract:

Given the uncertainty surrounding preretirement battery conditions, this study aims to advance the data-driven approach for accurately estimating retired lithium batteries' state of health (SOH). To achieve this, an enhanced SOH estimation method based on the Gaussian process regression (GPR) model is proposed. Initially, cyclic charge and discharge data from retired lithium batteries are gathered, and statistical health characteristics are derived to depict the aging properties. Methods such as capacity increment analysis (ICA) and electrochemical impedance spectroscopy (EIS) are employed to consider temperature effects. The Pearson correlation coefficient was used to assess the correlation between selected statistical features and health characteristics, identifying those highly correlated with SOH to eliminate the feature redundancy. Subsequently, acknowledging the limitations of individual kernel functions and conventional hyperparameter optimization techniques, a hybrid approach combining linear and diagonal square exponential kernel functions is introduced to better accommodate the diverse nature of battery SOH estimation tasks. The whale optimization algorithm (WOA) is then applied to optimize the hyperparameters of the estimation model, ensuring optimal fitting. This leads to the establishment of an improved GPR estimation model to enhance estimation accuracy. Finally, the effectiveness of the proposed method was validated using four different cells with varied initial health conditions from the NASA battery dataset. Results demonstrate the method's capability to provide accurate SOH estimation, with a mean absolute error below 1.75% and a root mean square error below 2.42%.

Key words: retired lithium-ion batteries, state of health, whale optimization algorithm, kernel functions, Gaussian process regression

CLC Number:

TM 912

Chen LI, Huilin ZHANG, Jianping ZHANG. Estimated state of health for retired lithium batteries using kernel function and hyperparameter optimization[J]. Energy Storage Science and Technology, 2024, 13(6): 2010-2021.

Figures/Tables 16

Table 1

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Table 2

Fig. 11

Table 3

The statistical errors of SOH estimation for four different kernel functions"

序号	核函数	估计误差/%
		NO.5		NO.6		NO.7		NO.18
		MAE	RMSE	MAE	RMSE	MAE	RMSE	MAE	RMSE
1	$k L I N i s o (x, x')$	1.6	1.9	0.51	0.68	1.67	2.04	0.52	0.64
2	$k S E i s o (x, x')$	7.32	10.24	3.69	4.75	10.95	15.09	0.93	1.32
3	$k S E i s o_S E i s o (x, x')$	7.32	10.24	3.69	4.75	10.95	15.09	0.93	1.32
4	$k L I N i s o_S E i s o (x, x')$	2.82	3.79	0.33	0.48	1.53	1.96	0.3	0.42

Table 3

Fig. 12

Fig. 13

References 29

1	李建林, 李雅欣, 陈光, 等. 退役动力电池健康状态特征提取及评估方法综述[J]. 中国电机工程学报, 2022, 42(4): 1332-1347.
	LI J L, LI Y X, CHEN G, et al. Research on feature extraction and SOH evaluation methods for retired power battery[J]. Proceedings of the CSEE, 2022, 42(4): 1332-1347.
2	CHENG M, ZHANG X, RAN A H, et al. Optimal dispatch approach for second-life batteries considering degradation with online SoH estimation[J]. Renewable and Sustainable Energy Reviews, 2023; 173: 113053.
3	CHEN J M, ZHANG W, GONG B G, et al. Optimal policy for the recycling of electric vehicle retired power batteries[J]. Technological Forecasting and Social Change, 2022, 183: 121930.
4	WANG J W, DENG Z W, TAO Y, et al. State of health estimation based on modified Gaussian process regression for lithium-ion batteries[J]. Journal of Energy Storage, 2022, 51: 104512.
5	CHOU J H, WANG F K, LO S C. Predicting future capacity of lithium-ion batteries using transfer learning method[J]. Journal of Energy Storage, 2023, 71: 108120.
6	WU J, LIU Z L, ZHANG Y, et al. Data-driven state of health estimation for lithium-ion battery based on voltage variation curves[J]. Journal of Energy Storage, 2023, 73: 109191.
7	LIU J Z, LIU X T. An improved method of state of health prediction for lithium batteries considering different temperature[J]. Journal of Energy Storage, 2023, 63: 107028.
8	ZHAO J, LI X B, YU D W, et al. Lithium-ion battery state of health estimation using meta-heuristic optimization and Gaussian process regression[J]. Journal of Energy Storage, 2023, 58: 106319.
9	XIONG X, WANG Y J, LI K Q, et al. State of health estimation for lithium-ion batteries using Gaussian process regression-based data reconstruction method during random charging process[J]. Journal of Energy Storage, 2023, 72: 108390.
10	LI Q L, LI D Z, ZHAO K, et al. State of health estimation of lithium-ion battery based on improved ant lion optimization and support vector regression[J]. Journal of Energy Storage, 2022, 50: 104215.
11	ZHANG Z P, MIN H T, GUO H G, et al. State of health estimation method for lithium-ion batteries using incremental capacity and long short-term memory network[J]. Journal of Energy Storage, 2023, 64: 107063.
12	LIU S Z, CHEN Z Q, YUAN L H, et al. State of health estimation of lithium-ion batteries based on multi-feature extraction and temporal convolutional network[J]. Journal of Energy Storage, 2024, 75: 109658.
13	FENG H L, LI N J. A multi-feature fusion model based on differential thermal capacity for prediction of the health status of lithium-ion batteries[J]. Journal of Energy Storage, 2023, 72: 108419.
14	DAI H D, WANG J X, HUANG Y Y, et al. Lightweight state-of-health estimation of lithium-ion batteries based on statistical feature optimization[J]. Renewable Energy, 2023, 119907.
15	FU S Y, TAO S Y, FAN H T, et al. Data-driven capacity estimation for lithium-ion batteries with feature matching based transfer learning method[J]. Applied Energy, 2024, 353: 121991.
16	BUCHICCHIO E, DE ANGELIS A, SANTONI F, et al. Battery SOC estimation from EIS data based on machine learning and equivalent circuit model[J]. Energy, 2023, 283: 128461.
17	ZHANG W C, LI T T, WU W X, et al. Data-driven state of health estimation in retired battery based on low and medium-frequency electrochemical impedance spectroscopy[J]. Measurement, 2023, 211: 112597.
18	ZHOU Z K, DUAN B, KANG Y Z, et al. Practical state of health estimation for LiFePO₄ batteries based on Gaussian mixture regression and incremental capacity analysis[J]. IEEE Transactions on Industrial Electronics, 2023, 70(3): 2576-2585.
19	ZUO H Y, LIANG J W, ZHANG B, et al. Intelligent estimation on state of health of lithium-ion power batteries based on failure feature extraction[J]. Energy, 2023, 282: 128794.
20	GUO Y F, YU X Y, WANG Y S, et al. Health prognostics of lithium-ion batteries based on universal voltage range features mining and adaptive multi-Gaussian process regression with Harris Hawks Optimization algorithm[J]. Reliability Engineering & System Safety, 2023, 109913.
21	王琛, 闵永军. 基于容量增量曲线与GWO-GPR的锂离子电池SOH估计[J]. 储能科学与技术, 2023, 12(11): 3508-3518.
	WANG C, MIN Y J. SOH estimation of lithium-ion batteries based on capacity increment curve and GWO-GPR[J]. Energy Storage Science and Technology, 2023, 12(11): 3508-3518.
22	陈锐, 丁凯, 祖连兴, 等. 基于AED-CEEMD-Transformer的锂离子电池健康状态估计[J]. 储能科学与技术, 2023, 12(10): 3242-3253.
	CHEN R, DING K, ZU L X, et al. Prediction of state of health of lithium-ion batteries based on the AED-CEEMD-Transformer network[J]. Energy Storage Science and Technology, 2023, 12(10): 3242-3253.
23	LU Z F, FEI Z C, WANG B F, et al. A feature fusion-based convolutional neural network for battery state-of-health estimation with mining of partial voltage curve[J]. Energy, 2024, 288: 129690.
24	ZHOU Y, DONG G Z, TAN Q Q, 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.
25	LIU S Z, NIE Y W, TANG A H, et al. Online health prognosis for lithium-ion batteries under dynamic discharge conditions over wide temperature range[J]. eTransportation, 2023, 18: 100296.
26	BAI J Q, HUANG J Y, LUO K, et al. A feature reuse based multi-model fusion method for state of health estimation of lithium-ion batteries[J]. Journal of Energy Storage, 2023, 70: 107965.
27	ZHOU Y F, WANG S L, XIE Y X, et al. Remaining useful life prediction and state of health diagnosis for lithium-ion batteries based on improved grey wolf optimization algorithm-deep extreme learning machine algorithm[J]. Energy, 2023, 285: 128761.
28	LI Y, WANG S L, CHEN L, et al. Multiple layer kernel extreme learning machine modeling and eugenics genetic sparrow search algorithm for the state of health estimation of lithium-ion batteries[J]. Energy, 2023, 282: 128776.
29	DONG H, MAO L, QU K Q, et al. State of health estimation and remaining useful life estimation for Li-ion batteries based on a hybrid kernel function relevance vector machine[J]. International Journal of Electrochemical Science, 2022, 17(11): 221135.

实验参数	B0005	B0006	B0007	B0018
额定容量/Ah	2	2	2	2
额定电压/V	3.7	3.7	3.7	3.7
电压上/下限/V	4.2/2.7	4.2/2.5	4.2/2.2	4.2/2.5
充/放电电流/A	1.5/2	1.5/2	1.5/2	1.5/2
温度/℃	24	24	24	24

电池编号	训练样本数	选取区间 (循环次数)	测试样本数	选取区间 (循环次数)
B0005	50	75～124	37	125～161
B0006	46	63～108	31	109～139
B0007	40	86～125	43	126～168
B0018	52	45～96	36	97～132

[1]	Ping DING, Taotao LI, Linfeng ZHENG, Weixiong WU. SOH estimation of real-world power batteries based on Soft-DTW algorithm and multisource reature fusion [J]. Energy Storage Science and Technology, 2025, 14(5): 2081-2097.
[2]	Jiangwei SHEN, Yixin SHE, Xing SHU, Yonggang LIU, Fuxing WEI, Xuelei XIA, Zheng CHEN. State of health estimation for lithium batteries based on short-term random charging data and optimized convolutional neural network [J]. Energy Storage Science and Technology, 2025, 14(4): 1585-1595.
[3]	Xuzhi WU, Jian GUO. An approach for remaining useful life prediction of power battery with improved grey wolf optimized GPR model [J]. Energy Storage Science and Technology, 2025, 14(2): 728-736.
[4]	Ziheng ZHANG, Mengmeng GENG, Maosong FAN, Yuhong JIN, Jingbing LIU, Kai YANG, Hao WANG. SOH estimation based on distribution of relaxation times for the retired power lithium-ion battery [J]. Energy Storage Science and Technology, 2025, 14(2): 770-778.
[5]	Zheng CHEN, Yue PENG, Jingyuan HU, Jiangwei SHEN, Renxin XIAO, Xuelei XIA. Lithium battery capacity prediction based on short-term charging data and an enhanced whale optimization algorithm [J]. Energy Storage Science and Technology, 2025, 14(1): 319-330.
[6]	Yingying LIU, Xiaoyuan ZHANG, Mengnan LIU, junzhang SUN, Yan ZHANG. State of health interval estimation for lithium battery via Gaussian process regression with adaptive optimal combination Kernel function [J]. Energy Storage Science and Technology, 2025, 14(1): 346-357.
[7]	Jizhong LU, Simin PENG, Xiaoyu LI. State-of-health estimation of lithium-ion batteries based on multifeature analysis and LSTM-XGBoost model [J]. Energy Storage Science and Technology, 2024, 13(9): 2972-2982.
[8]	Yuan CHEN, Siyuan ZHANG, Yujing CAI, Xiaohe HUANG, Yanzhong LIU. State-of-health estimation of lithium batteries based on polynomial feature extension of the CNN-transformer model [J]. Energy Storage Science and Technology, 2024, 13(9): 2995-3005.
[9]	Xue KE, Huawei HONG, Peng ZHENG, Zhicheng LI, Peixiao FAN, Jun YANG, Yuzheng GUO, Chunguang KUAI. Estimating lithium-ion battery health using automatic feature extraction and channel attention mechanisms for multi-timescale modeling [J]. Energy Storage Science and Technology, 2024, 13(9): 3059-3071.
[10]	Yufeng HUANG, Huanchao LIANG, Lei XU. Kalman filter optimize Transformer method for state of health prediction on lithium-ion battery [J]. Energy Storage Science and Technology, 2024, 13(8): 2791-2802.
[11]	Nana FENG, Ming YANG, Zhouli HUI, Ruijie WANG, Hongyang NING. Prediction of the remaining useful life of lithium batteries based on Antlion optimization Gaussian process regression [J]. Energy Storage Science and Technology, 2024, 13(5): 1643-1652.
[12]	Hangting JIANG, Qianqian ZHANG, Songtong ZHANG, Xiayu ZHU, Wenjie MENG, Jingyi QIU, Hai MING. Internal resistance measurement and condition monitoring strategy for chemical power systems [J]. Energy Storage Science and Technology, 2024, 13(10): 3400-3422.
[13]	Fang LI, Yongjun MIN, Yong ZHANG. Review of key technology research on the reliability of power lithium batteries based on big data [J]. Energy Storage Science and Technology, 2023, 12(6): 1981-1994.
[14]	Linze LI, Xiangwen ZHANG. SOH estimation for lithium-ion batteries based on combination of frequency impedance characteristics [J]. Energy Storage Science and Technology, 2023, 12(5): 1705-1712.
[15]	Yuanchang DONG, Xiaoqiong PANG, Jianfang JIA, Yuanhao SHI, Jie WEN, Xiao LI, Xin ZHANG. Remaining useful life prediction of lithium-ion batteries based on SVD-SAE-GPR [J]. Energy Storage Science and Technology, 2023, 12(4): 1257-1267.