Lithium-ion batteries SOH estimation based on gaussian processed regression optimized by egret swarm optimization

doi:10.19799/j.cnki.2095-4239.2025.0021

Abstract

Abstract:

The estimation of the State of Health (SOH) of lithium-ion batteries directly impacts the safety and reliability of battery systems and is a crucial function of battery management systems. Addressing the issues in existing data-driven SOH estimation methods, such as the lack of uncertainty representation and incomplete decoupling of training and testing data, this paper proposes an SOH estimation method based on the Egret Swarm Optimization Algorithm (ESOA) and Gaussian Process Regression (GPR). First, health features related to battery aging are extracted from the charging voltage, current, and relaxation voltage data of similar batteries, and features with high correlation to battery capacity are selected through Pearson correlation analysis. Subsequently, a Gaussian Process Regression model with a squared exponential kernel function is employed for SOH estimation, with the hyperparameters of the GPR model optimized using the Egret Swarm Optimization Algorithm. Finally, the proposed model is validated using NCA and NCM battery datasets from Tongji University to assess its accuracy and robustness. Experimental results demonstrate that the proposed method effectively improves the precision and reliability of SOH estimation. For the tested battery types, the maximum RMSE and MAE of SOH estimation errors are 0.0028 and 0.22%, respectively, representing improvements of 58.82% and 57.69% compared to conventional GPR models. Furthermore, the method enables SOH interval estimation, thereby avoiding safety risks caused by overestimating battery SOH.

Key words: Lithium-ion battery, State of health, Egret swarm optimization algorithm, Gaussian process regression, Interval Estimation

CLC Number:

TM 912

Chunling WU, Liding WANG, Yong Lu, Yao MA, Hao Chen, Jinhao Meng. Lithium-ion batteries SOH estimation based on gaussian processed regression optimized by egret swarm optimization[J]. Energy Storage Science and Technology, doi: 10.19799/j.cnki.2095-4239.2025.0021.

Figures/Tables 13

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References 26

1	杨夯, 黄小庆, 于慎仟, 等. 电化学储能电站主动安全研究[J]. 电力自动化设备, 2023, 43(08):78-87.
	YANG H, HUANG X, YU S, et al. Research on active safety of electrochemical energy storage station[J].Dianli Zidonghua Shebei/Electric Power Automation Equipment, 2023, 43(8):78-87.
2	ZHENG Y, HU J, CHEN J, et al. State of health estimation for lithium battery random charging process based on CNN-GRU method[J]. Energy Reports, 2023, 9:1-10.
3	DINI P, COLICELLI A, SAPONARA S. Review on Modeling and SOC/SOH Estimation of Batteries for Automotive Applications[J]. Batteries-Basel, 2024, 10(1).
4	LI X, ZHANG L, LIU Y, et al. A fast classification method of retired electric vehicle battery modules and their energy storage application in photovoltaic generation[J]. International Journal of Energy Research, 2019, 44(3):2337-2344.
5	赵鹤, 韩策, 程小露, 等. 采用阳极预锂化技术的锂离子电池高倍率老化容量衰减机理研究[J]. 储能科学与技术, 2021, 10(02):454-461.
	ZHAO He, HAN Ce, CHENG Xiaolu, et al. Research on the capacity fading mechanism of high rate aged lithium-ion batteries with anode prelithiation treatment[J]. Energy Storage Science and Technology, 2021, 10(02):454-461.
6	BASIA A, SIMEU-ABAZI Z, GASCARD E, et al. Review on State of Health estimation methodologies for lithium-ion batteries in the context of circular economy[J]. Cirp Journal of Manufacturing Science and Technology, 2021, 32:517-528.
7	CHANG C, WANG Q, JIANG J, et al. Lithium-ion battery state of health estimation using the incremental capacity and wavelet neural networks with genetic algorithm[J]. Journal of Energy Storage, 2021, 38:102570.
8	STROE D-I, SCHALTZ E. Lithium-ion battery state-of-health estimation using the incremental capacity analysis technique[J]. IEEE Transactions on Industry Applications, 2019, 56(1):678-685.
9	CHEN Y, HUANG M. A Method of Battery State of Health Prediction Based on AR-Particle Filter[R]. SAE Technical Paper, 2016.
10	FU J, WU C, WANG J, et al. Lithium-ion battery SOH prediction based on VMD-PE and improved DBO optimized temporal convolutional network model[J]. Journal of Energy Storage, 2024, 87:111392.
11	FENG X, WENG C, HE X, et al. Online State-of-Health Estimation for Li-Ion Battery Using Partial Charging Segment Based on Support Vector Machine[J]. IEEE Transactions on Vehicular Technology, 2019, 68(9):8583-8592.
12	巫春玲,吕晶晶,相里康,等.基于变分模态分解和核极限学习机集成模型的电动汽车锂电池健康状态预测[J/OL].电源学报:1-14,2023-09-21.
	Chunling WU, Jingjing LÜ, XIANGLI Kang, et al. Health State Prediction of Electric Vehicle Lithium Battery based on Integrated Model of Variation Modal Decomposition and Kernel Limit Learning Machine [J/OL]. Journal of Power Supply:1-14, 2023-09-21.
13	Chunling Wu, Juncheng Fu, Xinrong Huang, Xianfeng Xu, Jinhao Meng. Lithium-Ion Battery Health State Prediction Based on VMD and DBO-SVR [J]. Energies, 2023, 16(10), 3993.
14	RAUF H, KHALID M, ARSHAD N. Machine learning in state of health and remaining useful life estimation: Theoretical and technological development in battery degradation modelling[J]. Renewable and Sustainable Energy Reviews, 2022, 156:111903.
15	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 J, JIANG L, ZHANG X, et al. Estimation and Influencing Factor Analysis of Lithium-Ion Batteries State of Health Based on Features Extraction[J]. Diangong Jishu Xuebao /Transactions of China Electrotechnical Society, 2023, 38(19):5330-5342.
16	ZHU J, WANG Y, HUANG Y, et al. Data-driven capacity estimation of commercial lithium-ion batteries from voltage relaxation[J]. Nature Communications, 2022, 13(1).
17	李放, 闵永军, 王琛, et al. 基于充电过程的锂电池 SOH 估计和 RUL 预测[J]. 储能科学与技术, 2022, 11(10): 3316-3327.
	LI F, MIN Y J, WANG C, et al. State of health estimation and remaining useful life predication of lithium batteries using charging process[J]. Energy Storage Science and Technology, 2022, 11(10): 3316-3327.
18	张朝龙, 陈阳, 刘梦玲, 等.一种基于ICA-T特征和CNN-LA-BiLSTM 的锂离子电池健康状态估计方法[J]. 储能科学与技术.
	ZHANG ChaoLong, CHEN Yang, LIU MengLing, et al. A state of health estimation method for lithium-ion batteries based on ICA-T
	features and CNN-LA-BiLSTM[J]. Energy Storage Science and Technology.
19	WEN J P, CHEN X, LI X H, et al. SOH prediction of lithium battery based on IC curve feature and BP neural network[J]. Energy, 2022, 261:8.
20	ZHAO Y-P, WANG J-J, LI X-Y, et al. Extended least squares support vector machine with applications to fault diagnosis of aircraft engine[J]. ISA Transactions, 2020, 97:189-201.
21	REEVES B. Noise Modulated GPR: Second Generation Technology[C]. 15th International Conference on Ground Penetrating Radar (GPR), 2014:708-713.
22	李晓燕,李弢,马尽文.高斯过程混合模型在含噪输入预测策略下的煤矿瓦斯浓度柔性预测[J].信号处理,2021,37(11):2031-2040.
	LI Xiaoyan, LI Tao, MA Jinwen. Gaussian process mixture model for flexible prediction of coal mine gas concentration under noisy input prediction strategy[J]. Signal Processing,2021,37(11):2031-2040.
23	徐厚宝, 杨承莲, 张永康. 卡尔曼滤波优化的高斯过程回归模型[J]. 北京理工大学学报:1-8,2024-03-29.
	XU Houbao, YANG Chenglian, ZHANG Yongkang. Optimization Model of Gaussian Process Regression Based on Kalman Filtering. Transactions of BeijingInstitute of Technology:1-8,2024-03-29.
24	SHAMI T M, EL-SALEH A A, ALSWAITTI M, et al. Particle Swarm Optimization: A Comprehensive Survey[J]. IEEE Access, 2022, 10:10031-10061.
25	LI Chaoran,XIAO Fei,FAN Yaxiang, et al. An Approach to Lithium-ion Battery SOH Estimation Based on Convolutional Neural Network[J] Transactions of China Electrotechnical Society,2020,35(19): 4106-4119.
26	Chen Z, Francis A, Li S, et al. Egret swarm optimization algorithm: an evolutionary computation approach for model free optimization[J]. Biomimetics, 2022, 7(4): 144.

电池类型	NCA电池	NCM电池
电池类型	18650	18650
阳极材料	Graphite/Si	Graphite
阴极材料	Li_0.86(Ni_0.86Co_0.11Al_0.03)O₂ (NCA)	Li_0.84(Ni_0.83Co_0.11Mn_0.07)O₂ (NCM)
电解液	-	非水溶剂与LiPF₆
额定电压	-	3.60V
截止电压	2.65V~4.20V	2.50V~4.20V
额定容量	3.5Ah	3.5Ah
电池质量	-	45.0g

电池编号	特征参数
电池编号	HF1 (DCEVI)	HF2 (DCECI)	HF3 (Voltage Max)	HF4 (Voltage Drop)
NCA1	0.9982	0.9985	0.9680	0.9834
NCA2	0.9987	0.9996	0.9803	0.9904
NCA3	0.9968	0.9973	0.9862	0.9880
NCA4	0.9959	0.9990	0.9804	0.9909
NCM1	0.9956	0.9998	0.9932	0.9942
NCM2	0.9962	0.9982	0.9978	0.9978
NCM3	0.9928	0.9980	0.9934	0.9936
NCM4	0.9951	0.9991	0.9942	0.9941

电池编号	计算耗时/s
电池编号	GRU	LSTM	BP	PSO-BP	ESOA-BP	GPR	PSO-GPR	ESOA-GPR
NCA1	0.00999	0.01157	0.17290	0.00984	0.00994	0.01642	0.01437	0.01621
NCA2	0.01382	0.01072	0.10458	0.00705	0.00818	0.01977	0.01682	0.01388
NCA3	0.01272	0.01246	0.01999	0.00950	0.00726	0.00625	0.00639	0.00651
NCA4	0.01597	0.01735	0.01006	0.00804	0.009289	0.01873	0.02061	0.01897

电池编号	计算耗时/s
电池编号	GRU	LSTM	BP	PSO-BP	ESOA-BP	GPR	PSO-GPR	ESOA-GPR
NCM1	0.01371	0.01103	0.00963	0.00920	0.00890	0.00620	0.00810	0.00636
NCM2	0.01471	0.01500	0.00813	0.00684	0.00694	0.01364	0.01161	0.02107
NCM3	0.01046	0.01362	0.00867	0.00761	0.00737	0.01305	0.01221	0.01565
NCM4	0.01847	0.01233	0.00737	000732	0.00690	0.02433	0.02319	0.02668

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