State of health interval estimation for lithium battery via Gaussian process regression with adaptive optimal combination Kernel function

doi:10.19799/j.cnki.2095-4239.2024.0473

Abstract

Abstract:

The degradation of lithium battery state of health (SOH) is to some extent a nonsmooth stochastic process, which makes most of the current point estimation machine learning approaches limited in practical applications. In recent years, Gaussian process regression (GPR), which is based on the Bayesian theory, has been widely used in lithium battery SOH interval estimation due to its ability to quantify uncertainty in the estimation results; however, the performance of GPR significantly depends on the selection of its kernel function. Current studies typically rely on empirically selecting a fixed single kernel function, which may not be suitable for diverse datasets. To address this limitation, this study introduces an SOH interval estimation method for lithium batteries based on an adaptive optimal combination of kernel functions in GPR. The proposed method first extracts multiple health factors from the battery's charge/discharge data and uses the Pearson correlation coefficient method to optimize six health factors that are strongly correlated with SOH as inputs to the model. Subsequently, with a set of seven commonly used kernel functions, new kernel function combinations were created by two-by-two random combinations. Cross-validation was then used to adaptively optimize the optimal kernel function combinations. The proposed approach was validated using three different datasets, and the results indicate its excellent performance in SOH interval estimation. For the three publicly available datasets, the average interval width index is within 0.0530, the average interval score is greater than -0.0004, and the root mean square error is less than 0.0181.

Key words: lithium-ion battery, state of health, Gaussian process regression, interval estimation, combined kernel function

CLC Number:

TM 912

Yingying LIU, Xiaoyuan ZHANG, Mengnan LIU, junzhang SUN, Yan ZHANG. State of health interval estimation for lithium battery via Gaussian process regression with adaptive optimal combination Kernel function[J]. Energy Storage Science and Technology, 2025, 14(1): 346-357.

Figures/Tables 13

Fig.1

Fig.2

Fig.3

Fig.4

Table 1

Common used kernel functions for GPR"

核函数种类	表达式
径向基核函数(radial basis function, RBF)	$K x, y = e x p - \| \| x - y \| \| 2 2 σ 2$
有理二次核函数(rational quadratic kernel function, RQ)	$K x, y = 1 - \| \| x - y \| \| 2 \| \| x - y \| \| 2 + c$
线性核函数(linear kernel function, LIN)	$K x, y = x ⊺ y$
马顿核函数(Matern kernel function, Matern)	$K x, y = e x p - α × \| \| x - y \| \| p$
点积核函数(dot product kernel function, Dot Product)	$K x, y = x × y$
神经网络核函数(neural network kernel function, NNKF)	$K x . y = σ f 1 2 s i n - 1 x T y I 12 + x T x I 12 + y T y$
周期核函数(periodic kernel function, PER)	$K x, y = σ f 2 2 e x p - 2 I 22 s i n 2 π \| x - y \| p$

Table 1

Fig.5

Table 2

Fig.6

Table 3

Fig.7

Fig.8

Fig.9

Fig.10

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基本信息	CALCE	Oxford	TRI
充电协议	CC-CV	CC	2-step
标称电压	4.2 V	3.7 V	3.3 V
标称容量	1100 mAh	740 mAh	1100 mAh

数据集	数据训练时间	在线估计时间
CALCE	36 min	1.43 s
Oxford	2 min	1.39 s
TRI	6 min	1.41 s

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