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

Abstract

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

CLC Number:

TP206

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.

Figures/Tables 13

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References 36

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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

Remaining useful life prediction of lithium-ion batteries based on Gaussian process regression with self-constructed kernel

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电池序号	核结构	SP
		3 000		4 000		5 000
		MAE	RMSE	MAE	RMSE	MAE	RMSE
Batt#1	K_best^*	0.002 2	0.002 8	0.003 3	0.004 4	0.007 3	0.008 4
Batt#1	SE_ARD	0.015 3	0.018 2	0.002 2	0.002 8	0.006 0	0.006 9
Batt#3	K_best^*	0.004 7	0.005 6	0.000 8	0.001 0	0.001 7	0.001 9
Batt#3	SE_ARD	0.028 3	0.036 7	0.008 6	0.011 1	0.000 9	0.001 0
Batt#7	K_best^*	0.002 3	0.002 7	0.006 5	0.007 4	0.002 2	0.002 8
Batt#7	SE_ARD	0.341 6	0.555 1	0.021 7	0.027 2	0.002 0	0.002 6

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