基于灰狼优化算法和组合核函数GPR模型的锂电池剩余使用寿命预测

doi:10.3969/j.issn.2097-0706.2025.12.003

摘要/Abstract

摘要：

准确地预测锂离子电池剩余使用寿命（RUL）可以帮助用户制定合理的维护策略。高斯过程回归（GPR）算法作为一种数据驱动方法能够很好地捕捉特征和变量之间的非线性关系，被广泛应用于锂电池RUL估计。传统的单核GPR对特征捕捉能力不足，为此提出一种基于灰狼优化算法（GWO）的组合核GPR模型。通过组合核函数来增强模型对非线性特征的捕捉能力，同时利用GWO解决组合核函数超参数优化中的困难。采用美国国家航空航天局（NASA）锂电池循环老化数据集进行对该模型进行验证，并将其与基于粒子群优化（PSO）的单核GPR模型进行对比。试验结果显示：GWO优化的组合核GPR模型较PSO优化的单核GPR模型的均方根误差（RMSE）下降了37.89%，平均绝对误差（MAE）下降了70.42%，对容量衰减的捕捉能力更强。结果表明相比于传统GPR模型，灰狼优化的组合核GPR模型对锂电池RUL预测的准确性更高。

关键词: 锂离子电池, 剩余使用寿命, 高斯过程回归, 灰狼优化算法, 电池老化, 容量衰减, 预测误差, 粒子群优化算法

Abstract:

Accurately predicting the remaining useful life （RUL） of lithium-ion batteries can help users formulate reasonable maintenance strategies. As a data-driven method， Gaussian process regression （GPR） algorithm can effectively capture the nonlinear relationship between features and variables， and thus is widely used in the RUL estimation of lithium batteries. To address the deficiency of traditional single-kernel GPR in feature capture， a combined kernel GPR model based on the grey wolf optimization （GWO） algorithm was proposed. By combining kernel functions， the model's ability to capture nonlinear features was enhanced， and the GWO algorithm was utilized to overcome the difficulty in optimizing the hyperparameters of the combined kernel function. The NASA lithium battery cycle aging dataset was adopted to verify this model， and the single-kernel GPR model based on particle swarm（PSO） optimization was selected for comparison. The experimental results showed that the GWO-optimized combined kernel GPR model achieved a 37.89% reduction in root mean square error （RMSE） and a 70.42% reduction in mean absolute error （MAE） compared with the PSO-optimized single-kernel GPR model， demonstrating a stronger ability to capture capacity degradation. The results indicate that compared with the traditional GPR model， the GWO-optimized combined kernel GPR model has higher accuracy for the RUL prediction of lithium batteries.

Key words: lithium-ion battery, remaining useful life, Gaussian process regression, grey wolf optimization algorithm, battery aging, capacity degradation, prediction error, particle swarm optimization

中图分类号:

TM912

胡林静, 李在伟. 基于灰狼优化算法和组合核函数GPR模型的锂电池剩余使用寿命预测[J]. 综合智慧能源, 2025, 47(12): 25-33.

HU Linjing, LI Zaiwei. Prediction of remaining useful life of lithium batteries based on grey wolf optimization and combined kernel function GPR model[J]. Integrated Intelligent Energy, 2025, 47(12): 25-33.

图/表 15

图1

图2

图3

图4

表1

特征与容量的Pearson相关性

电池编号	与容量的Pearson相关性
电池编号	$H 1$	$H 2$	$H 3$	$H 4$
B0005	0.908	0.982	0.988	-0.972
B0006	0.918	0.971	0.983	-0.970
B0007	0.785	0.978	0.979	-0.959

表1

表2

图5

表3

常见单一核函数

函数	数学表达式
高斯核	$k (x, x') = σ 2 e x p (- x - x' 2 2 l 2)$
马顿核	$k (x, x') = σ 2 (1 + 3 x - x' l) e x p (- 3 x - x' l)$
线性核	$k (x, x') = σ 02 + x x'$
周期核	$k (x, x') = σ 2 e x p (- 2 s i n 2 (π x - x' / p) l 2)$
指数核	$k (x, x') = σ 2 e x p (- x - x' l)$
拉普拉斯核	$k (x, x') = e x p (- x - x' l)$

表3

图6

图7

图8

图9

表4

图10

表5

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电池编号	主成分1	主成分2	主成分3	主成分4
B0005	0.804 1	0.169 0	0.014 4	0.012 5
B0006	0.900 0	0.090 1	0.007 9	0.002 1
B0007	0.692 3	0.246 2	0.033 2	0.028 2

项目		RMSE			MAE
项目		以80为起点	以100为起点	以120为起点	以80为起点	以100为起点	以120为起点
LIN+RBF 核模型	B0005	0.006 1	0.005 1	0.005 9	0.003 7	0.001 8	0.002 1
	B0006	0.005 9	0.004 3	0.004 1	0.004 6	0.003 2	0.002 8
	B0007	0.027 3	0.016 2	0.012 4	0.023 2	0.014 0	0.011 1
LIN核模型	B0005	0.070 9	0.039 6	0.025 0	0.058 4	0.031 9	0.019 6
	B0006	0.059 5	0.022 8	0.052 6	0.051 4	0.018 7	0.051 0
	B0007	0.052 6	0.035 2	0.028 6	0.041 9	0.028 9	0.024 6
RBF核模型	B0005	0.019 4	0.013 2	0.015 0	0.017 5	0.011 0	0.012 6
	B0006	0.011 6	0.008 0	0.010 2	0.008 2	0.005 9	0.008 1
	B0007	0.028 6	0.018 9	0.017 0	0.025 4	0.016 7	0.015 5
Matern核模型	B0005	0.058 7	0.029 9	0.009 1	0.048 6	0.026 3	0.008 0
	B0006	0.053 5	0.035 4	0.021 4	0.046 6	0.030 7	0.018 6
	B0007	0.026 5	0.016 2	0.008 3	0.020 0	0.013 1	0.007 2

起始循环次数	RMSE			MAE
起始循环次数	GWO	无优化	PSO	GWO	无优化	PSO
80	0.006 1	0.062 6	0.016 7	0.003 7	0.052 3	0.013 9
100	0.005 1	0.028 0	0.010 9	0.001 8	0.012 5	0.008 6
120	0.005 9	0.018 0	0.009 5	0.002 1	0.013 0	0.007 1