基于容量增量分析与VMD-GWO-KELM的锂电池健康状态估计

doi:10.19799/j.cnki.2095-4239.2024.1253

摘要/Abstract

摘要：

为克服传统健康状态估计方法中的特征提取质量不足、非线性特性复杂及模型参数优化困难等问题，本工作提出一种基于容量增量分析与VMD-GWO-KELM的健康状态估计方法。首先，本工作通过改进的基于洛伦兹函数的电压容量模型，对电池恒流充电过程中的电压-容量数据进行拟合，提取峰电压、峰值和峰面积等健康特征，并利用灰狼优化算法完成模型参数识别，从而有效提升了特征提取质量和鲁棒性。其次，采用变分模态分解技术对健康状态信号进行多尺度分解，将模态分量作为独立子模型的输入，捕捉不同频域的关键特性，降低了信号混叠和噪声影响。然后，结合灰狼优化算法对核极限学习机模型的关键参数进行优化，显著提高了非线性拟合能力和估计精度。最后，通过不同训练量、不同估计模型对比和多电池数据的验证，全面评估模型性能。实验结果表明，本工作提出的算法在仅使用100次循环数据的情况下，即可实现高精度健康状态估计，平均绝对误差为0.9751%，最大误差为1.9340%，同时表现出良好的鲁棒性和泛化能力。

关键词: 锂离子电池, 健康状态, 容量增量分析, 变分模态分解, 灰狼优化, 核极限学习机

Abstract:

To overcome the limitations of traditional state of health (SOH) estimation methods—such as inadequate feature extraction, nonlinear complexity, and difficulty in model parameter optimization—this study proposes a novel SOH estimation approach based on incremental capacity analysis combined with variational mode decomposition (VMD), grey wolf optimization (GWO), and kernel extreme learning machine (KELM). First, an improved voltage-capacity model based on the Lorentz function is employed to fit voltage-capacity data during the constant-current charging process, enabling the extraction of health indicators such as peak voltage, peak value, and peak area. Model parameters are optimized using the GWO algorithm, thereby improving feature extraction accuracy and robustness. Next, VMD is applied to decompose SOH-related signals into multiple intrinsic mode functions. These components serve as inputs to individual sub-models, effectively capturing signal characteristics across distinct frequency domains while mitigating noise and mode mixing. Subsequently, the GWO algorithm is used to optimize the key parameters of the KELM model, significantly enhancing its nonlinear regression capability and estimation accuracy. The proposed method is evaluated through comparative analyses across different training data sizes, estimation models, and datasets from multiple batteries. Experimental results demonstrate that the proposed method achieves high-accuracy SOH estimation using only 100 cycles of data, with a mean absolute error of 0.9751% and a maximum error of 1.9340%. The model also exhibits strong robustness and generalization performance.

Key words: lithium-ion batteries, state of health, incremental capacity analysis, variational mode decomposition, grey wolf optimization, kernel extreme learning machine

中图分类号:

TM 912

陈峥, 多功东, 申江卫, 沈世全, 刘昱, 魏福星. 基于容量增量分析与VMD-GWO-KELM的锂电池健康状态估计[J]. 储能科学与技术, 2025, 14(6): 2476-2487.

Zheng CHEN, Gongdong DUO, Jiangwei SHEN, Shiquan SHEN, Yu LIU, Fuxing WEI. State of health estimation for lithium battery based on incremental capacity analysis and VMD-GWO-KELM[J]. Energy Storage Science and Technology, 2025, 14(6): 2476-2487.

图/表 12

图1

图2

图3

表1

表2

VMD参数设置"

参数	设定值
$α$	5000
$t a u$	0
$k$	6
$t o l$	1e-7
$i n i t$	1

表2

表3

不同 k 值下电池1的中心频率"

$k$	中心频率/Hz
2	2e-4	0.2811	—	—	—	—	—
3	2e-4	0.0895	0.3044	—	—	—	—
4	2e-4	0.0895	0.2809	0.3943	—	—	—
5	2e-4	0.0893	0.1833	0.3042	0.3999	—	—
6	2e-4	0.0891	0.1619	0.2564	0.3270	0.4286	—
7	2e-4	0.0122	0.0915	0.1838	0.2821	0.3599	0.4361

表3

图4

图5

表4

不同训练量的性能指标"

数据长度	$R 2$	MAE/%	MAPE/%	RMSE/%	最大误差/%
75	0.9871	1.5791	0.7573	1.2804	3.0192
100	0.9897	0.9751	0.5780	0.8941	1.9340
125	0.9854	1.0830	0.6952	0.8563	1.9552
150	0.9914	0.8336	0.5094	0.6398	1.9033

表4

图6

图7

图8

参考文献 25

1	彭鹏, 杨瑞鑫, 孙万洲, 等. 基于容量增量分析的锂离子电池容量估计方法[J/OL]. 机械工程学报, 2024: 1-10. (2024-12-13). https://kns.cnki.net/KCMS/detail/detail.aspx?filename=JXXB20241212014&dbname=CJFD&dbcode=CJFQ.
	PENG P, YANG R X, SUN W Z, et al. Capacity estimation method of lithium-ion battery based on capacity increment analysis[J/OL]. Journal of Mechanical Engineering, 2024: 1-10. (2024-12-13). https://kns.cnki.net/KCMS/detail/detail.aspx?filename=JXXB20241212014&dbname=CJFD&dbcode=CJFQ.
2	XU Y H, ZHANG H G, YANG Y F, et al. Optimization of energy management strategy for extended range electric vehicles using multi-island genetic algorithm[J]. Journal of Energy Storage, 2023, 61: 106802. DOI: 10.1016/j.est.2023.106802.
3	XIA F, TANG C, CHEN J J. Online two-dimensional filter for anti-interference aging features extraction to accurately predict the battery health[J]. Measurement, 2024, 234: 114758. DOI: 10.1016/j.measurement.2024.114758.
4	许培德, 刘康, 康龙云, 等. 基于弛豫电压和BO-DNN的锂离子电池健康状态估计[J/OL]. 电源学报, 2024: 1-14. (2024-12-04). https://kns.cnki.net/KCMS/detail/detail.aspx?filename=DYXB20241203001&dbname=CJFD&dbcode=CJFQ.
	XU P D, LIU K, KANG L Y, et al. State of health estimation of lithium-ion battery based on relaxation voltage and BO-DNN[J/OL]. Journal of Power Supply, 2024: 1-14. (2024-12-04). https://kns.cnki.net/KCMS/detail/detail.aspx?filename=DYXB20241203001&dbname=CJFD&dbcode=CJFQ.
5	CHAE S G, BAE S J, OH K Y. State-of-health estimation and remaining useful life prediction of lithium-ion batteries using DnCNN-CNN[J]. Journal of Energy Storage, 2025, 106: 114826. DOI: 10.1016/j.est.2024.114826.
6	SUN J, FAN C Q, YAN H Y. SOH estimation of lithium-ion batteries based on multi-feature deep fusion and XGBoost[J]. Energy, 2024, 306: 132429. DOI: 10.1016/j.energy.2024.132429.
7	陈峥, 陈洋, 申江卫, 等. 基于优化支持向量回归算法的锂离子电池可用容量估计[J]. 储能科学与技术, 2023, 12(10): 3203-3213. DOI: 10.19799/j.cnki.2095-4239.2023.0387.
	CHEN Z, CHEN Y, SHEN J W, et al. Available capacity estimation of lithium-ion batteriesbased on the optimized support vector regression algorithm[J]. Energy Storage Science and Technology, 2023, 12(10): 3203-3213. DOI: 10.19799/j.cnki.2095-4239.2023. 0387.
8	SUN H L, SUN J R, ZHAO K, et al. Data-driven ICA-Bi-LSTM-combined lithium battery SOH estimation[J]. Mathematical Problems in Engineering, 2022, 2022(1): 9645892. DOI: 10.1155/2022/9645892.
9	LI X Y, YUAN C G, LI X H, et al. State of health estimation for Li-Ion battery using incremental capacity analysis and Gaussian process regression[J]. Energy, 2020, 190: 116467. DOI: 10.1016/j.energy.2019.116467.
10	LI X, JIANG J C, WANG L Y, et al. A capacity model based on charging process for state of health estimation of lithium ion batteries[J]. Applied Energy, 2016, 177: 537-543. DOI: 10.1016/j.apenergy.2016.05.109.
11	BIAN X L, LIU L C, YAN J Y. A model for state-of-health estimation of lithium ion batteries based on charging profiles[J]. Energy, 2019, 177: 57-65. DOI: 10.1016/j.energy.2019.04.070.
12	HE J T, WEI Z B, BIAN X L, et al. State-of-health estimation of lithium-ion batteries using incremental capacity analysis based on voltage-capacity model[J]. IEEE Transactions on Transportation Electrification, 2020, 6(2): 417-426. DOI: 10.1109/TTE.2020.299 4543.
13	HE J T, MENG S J, LI X Y, et al. Partial charging-based health feature extraction and state of health estimation of lithium-ion batteries[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2023, 11(1): 166-174. DOI: 10.1109/JESTPE. 2022.3143831.
14	WU C L, FU J C, HUANG X R, et al. Lithium-ion battery health state prediction based on VMD and DBO-SVR[J]. Energies, 2023, 16(10): 3993. DOI: 10.3390/en16103993.
15	FU J C, WU C L, WANG J W, 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. DOI: 10.1016/j.est.2024.111392.
16	YUAN Z F, TIAN T, HAO F C, et al. A hybrid neural network based on variational mode decomposition denoising for predicting state-of-health of lithium-ion batteries[J]. Journal of Power Sources, 2024, 609: 234697. DOI: 10.1016/j.jpowsour. 2024.234697.
17	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. DOI: 10.1016/j.energy. 2023.128776.
18	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. DOI: 10. 19799/j.cnki.2095-4239.2023.0458.
	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. DOI: 10. 19799/j.cnki.2095-4239.2023.0458.
19	陈峥, 李磊磊, 舒星, 等. 基于改进容量增量分析法的锂电池可用容量估计[J]. 中国公路学报, 2022, 35(8): 20-30. DOI: 10.19721/j.cnki.1001-7372.2022.08.003.
	CHEN Z, LI L L, SHU X, et al. Estimation of available capacity for lithium-ion battery based on improved increment capacity analysis[J]. China Journal of Highway and Transport, 2022, 35(8): 20-30. DOI: 10.19721/j.cnki.1001-7372.2022.08.003.
20	HE J T, BIAN X L, LIU L C, et al. Comparative study of curve determination methods for incremental capacity analysis and state of health estimation of lithium-ion battery[J]. Journal of Energy Storage, 2020, 29: 101400. DOI: 10.1016/j.est.2020. 101400.
21	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: 125234. DOI: 10.1016/j.energy.2022.125234.
22	陈峥, 彭月, 胡竞元, 等. 基于短期充电数据和增强鲸鱼优化算法的锂离子电池容量预测[J]. 储能科学与技术, 2025, 14(1): 319-330. DOI: 10.19799/j.cnki.2095-4239.2024.0686.
	CHEN Z, PENG Y, HU J Y, et al. 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. DOI: 10.19799/j.cnki.2095-4239.2024.0686.
23	LI Z H, BAI F, ZUO H F, et al. Remaining useful life prediction for lithium-ion batteries based on iterative transfer learning and mogrifier LSTM[J]. Batteries, 2023, 9(9): 448. DOI: 10.3390/batteries9090448.
24	ZHU T, WANG S L, FAN Y C, et al. An improved dung beetle optimizer- hybrid kernel least square support vector regression algorithm for state of health estimation of lithium-ion batteries based on variational model decomposition[J]. Energy, 2024, 306: 132464. DOI: 10.1016/j.energy.2024.132464.
25	LI X B, FAN D Q, LIU X T, et al. State of health estimation for lithium-ion batteries based on improved bat algorithm optimization kernel extreme learning machine[J]. Journal of Energy Storage, 2024, 101: 113756. DOI: 10.1016/j.est.2024. 113756.

型号	峰电压	峰值	峰面积
电池1	-0.9680	0.9862	0.9334
电池2	-0.9587	0.9785	0.9476
电池3	-0.9808	0.9928	0.9429
B0005	-0.9766	0.9931	0.9886
B0006	-0.9800	0.9898	0.9867
B0007	-0.9638	0.9884	0.9791
B0018	-0.9745	0.9697	0.9700

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