基于核自构建-高斯过程回归的锂离子电池剩余使用寿命预测

doi:10.12305/j.issn.1001-506X.2023.08.38

摘要/Abstract

摘要：

高斯过程回归是锂离子电池剩余使用寿命的有效预测方法之一，其中核函数的选择对预测结果有着重要影响。对此，提出了一种自回归核自构建高斯过程回归的锂离子电池剩余寿命预测框架，可结合同型号电池的历史容量退化规律，自动构建出合适的组合核函数。通过与不同的机器学习方法及不同核函数比较，所提方法可在电池退化早期做出长期且准确的电池健康状态退化趋势预测，预测寿命均方根误差小于1%，相对误差小于6%，置信区间也更为集中，证明了所提方法能够有效提高电池剩余使用寿命的长期预测精度。

关键词: 高斯过程回归, 组合核函数, 剩余使用寿命, 锂离子电池

Abstract:

Gaussian process regression(GPR) is one of the effective methods to predict the remaining useful life(RUL) of lithium-ion batteries. At the same time, the choice of kernel function in GPR model has an important influence on the prediction result. In this regard, a GPR with self-constructed kernel method is proposed. Using the historical capacity data of the same type of batteries, the appropriate combination kernel function is automatically constructed to describe degradation trends. Compared with different machine learning methods and different kernel functions, the proposed method can make long-term and accurate prediction of battery health degradation trend in the early stage of battery degradation. The root mean square error is less than 1% of prediction results, meanwhile the relative error is less than 6%. The confidence intervals for the predicted results are more concentrated. It shows that the proposed method can effectively improve the long-term prediction accuracy of battery RUL.

Key words: Gaussian process regression, combinational kernel function, remaining useful life (RUL), lithium-ion battery

中图分类号:

TP206

张然, 刘天宇, 金光. 基于核自构建-高斯过程回归的锂离子电池剩余使用寿命预测[J]. 系统工程与电子技术, 2023, 45(8): 2623-2633.

Ran ZHANG, Tianyu LIU, Guang JIN. Remaining useful life prediction of lithium-ion batteries based on Gaussian process regression with self-constructed kernel[J]. Systems Engineering and Electronics, 2023, 45(8): 2623-2633.

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类别	名称	核函数形式
全局核	常数核	$ C\left(x, x^{\prime}\right)=\sigma_f^2$
	白噪声核	$ \mathrm{WN}\left(x, x^{\prime}\right)=\sigma_f^2 \delta_{x, x^{\prime}}$
	线性核	$ \operatorname{Lin}\left(x, x^{\prime}\right)=\sigma_f^2(x-c)\left(x^{\prime}-c\right)$
	多项式核	$ \operatorname{PL}\left(x, x^{\prime}\right)=\sigma_f^2\left(\alpha x \cdot x^{\prime}+c\right)^d$
局部核	高斯核	$ \mathrm{SE}\left(x, x^{\prime}\right)=\sigma_f^2 \exp \left(-\frac{\left(x-x^{\prime}\right)^2}{2 l^2}\right)$
	有理二次核	$ \mathrm{RQ}\left(x, x^{\prime}\right)=\sigma_f^2\left(1+\frac{\left(x-x^{\prime}\right)^2}{2 \alpha l^2}\right)^{-\alpha}$
	周期核	$ \operatorname{Per}\left(x, x^{\prime}\right)=\sigma_f^2 \exp \left(-\frac{2}{l^2} \sin ^2\left(\pi \frac{x-x^{\prime}}{p}\right)\right)$

	核函数构建过程	NLL	BIC
K₀	$ \mathrm{WN}\left(x, x^{\prime}\right)$	-	-
K₁	$ \mathrm{WN}\left(x, x^{\prime}\right)+\mathrm{SE}\left(x(3), x^{\prime}(3)\right)$	-1 665.837 7	-3 316.959 6
K₂	$ \mathrm{WN}\left(x, x^{\prime}\right)+\mathrm{SE}\left(x(3), x^{\prime}(3)\right) \cdot \operatorname{LIN}\left(x(5), x^{\prime}(5)\right)$	-1 787.786 8	-3 551.047 2
K₃	$ \mathrm{WN}\left(x, x^{\prime}\right)+\mathrm{SE}\left(x(3), x^{\prime}(3)\right) \cdot \operatorname{LIN}\left(x(5), x^{\prime}(5)\right) \cdot \operatorname{LIN}\left(x(1), x^{\prime}(1)\right)$	-1 801.619 3	-3 568.901 7
K₄	$ \mathrm{WN}\left(x, x^{\prime}\right)+\mathrm{SE}\left(x(3), x^{\prime}(3)\right) \cdot \operatorname{LIN}\left(x(5), x^{\prime}(5)\right) \cdot \operatorname{LIN}\left(x(1), x^{\prime}(1)\right)+\operatorname{LIN}\left(x(1), x^{\prime}(1)\right)$	-1 806.524 3	-3 568.901 1

电池序号	SP	LIN(x(1), x′(1))		LIN(x(5), x′(5))		SE(x(3), x′(3))		WN(x, x′)
电池序号	SP	c₁^*	σ_f1^*	c₂^*	σ_f1^*	l^*	σ_f3^*	σ_f4^*
Batt#1	3 000	-11.903 4	-0.884 8	-0.086 7	-0.904 8	14.806 8	-0.894 8	-7.993 8
	4 000	-6.242 4	-1.160 0	-3.919 2	-1.180 0	0.799 4	-1.170 0	-7.687 5
	5 000	-2.580 6	-0.883 0	-2.271 6	-0.903 0	0.694 4	-0.893 0	-7.568 8
Batt#3	3 000	-19.962 7	-0.996 8	-0.046 2	-1.016 8	6.273 5	-1.006 8	-7.839 7
	4 000	-16.998 2	-0.970 5	-0.056 0	-0.990 5	9.140 4	-0.980 5	-7.634 5
	5 000	-14.827 2	-0.148 2	-0.063 8	-0.168 2	8.791 6	-0.158 2	-7.694 7
Batt#7	3 000	-68.812 8	-1.134 2	-0.017 5	-1.154 2	25.611 8	-1.144 2	-8.102 0
	4 000	-188.949 9	-2.070 3	-1.228 2	-2.090 3	0.451 1	-2.080 3	-8.485 4
	5 000	-79.739 9	-1.687 3	-0.654 3	-1.707 3	0.753 6	-1.697 3	-7.510 1

电池序号	SP	RUL	MAE	RMSE	AE
Batt#1	3 000	3 300	0.002 2	0.002 8	0
	4 000	2 500	0.003 3	0.004 4	200
	5 000	1 700	0.007 3	0.008 4	400 AE
Batt#3	3 000	3 600	0.004 7	0.005 6	400
	4 000	3 000	0.000 8	0.001 0	0
	5 000	2 100	0.001 7	0.001 9	100
Batt#7	3 000	-	0.002 3	0.002 7	-
	4 000	-	0.006 5	0.007 4	-
	5 000	-	0.002 2	0.002 8	-

方法	MAE	RMSE
SVR	0.030 4	0.033 8
RVR	0.023 7	0.027 7
LSTM	0.008 9	0.013 0
GRU	0.055 7	0.022 0
SCK-GPR	0.003 0	0.003 9