基于自适应最优组合核函数高斯过程回归的锂电池健康状态区间估计

doi:10.19799/j.cnki.2095-4239.2024.0473

储能科学与技术 ›› 2025, Vol. 14 ›› Issue (1): 346-357.doi: 10.19799/j.cnki.2095-4239.2024.0473

基于自适应最优组合核函数高斯过程回归的锂电池健康状态区间估计

刘迎迎¹(), 张孝远¹(), 刘梦楠¹, 孙俊章², 张艳³

^1.河南工业大学电气工程学院
^2.河南联合化工能源集团有限公司
^3.河南中创高科新能源科技有限公司，河南郑州 450001

收稿日期:2024-05-18 修回日期:2024-09-28 出版日期:2025-01-28 发布日期:2025-02-25
通讯作者: 张孝远 E-mail:3326845918@qq.com;freedon@haut.edu.cn
作者简介:刘迎迎（2000—），女，硕士研究生，研究方向为深度学习以及锂电池的健康状态估计，E-mail：3326845918@qq.com；
基金资助:
河南省自然科学基金项目(232300421207);河南工业大学自科创新基金计划项目(2022ZKCJ04)

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

Yingying LIU¹(), Xiaoyuan ZHANG¹(), Mengnan LIU¹, junzhang SUN², Yan ZHANG³

^1.College of Electrical Engineering, Henan University of Technology
^2.Henan United Chemical Energy Group Co. Ltd
^3.Henan Zhongchuang Hi Tech New Energy Technology Co. Ltd, Zhengzhou 450001, Henan, China

Received:2024-05-18 Revised:2024-09-28 Online:2025-01-28 Published:2025-02-25
Contact: Xiaoyuan ZHANG E-mail:3326845918@qq.com;freedon@haut.edu.cn

摘要/Abstract

摘要：

锂电池健康状态(state of health, SOH)的退化过程在一定程度上是一个非平稳随机过程，使得当前多数点估计机器学习方法在实际应用中受到限制。基于贝叶斯理论的高斯过程回归(Gaussian process regression, GPR)，因可输出估计结果的不确定性，近年来在锂电池SOH区间估计中得到广泛应用。然而，GPR的性能很大程度上取决于其核函数的选择，当前研究多凭借经验选用固定单一核函数，无法适应不同的数据集。为此，本文提出一种基于自适应最优组合核函数GPR的锂电池SOH区间估计方法。该方法首先从电池充放电数据中提取出多个健康因子(health factor, HF)，并采用皮尔森相关系数法优选出6个与SOH高度相关的健康因子作为模型的输入。然后，在当前常用的7个核函数集合上，通过两两随机组合构造新的组合核函数，并利用交叉验证自适应优选出最优组合核函数。采用3个不同数据集对所提方法进行了验证，结果表明：本文方法具有出色的SOH区间估计性能。在3个公开数据集上，平均区间宽度指标在0.0509以内，平均区间分数大于-0.0004，均方根误差小于0.0181。

关键词: 锂电池, 健康状态, 高斯过程回归, 区间估计, 组合核函数

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

中图分类号:

TM 912

刘迎迎, 张孝远, 刘梦楠, 孙俊章, 张艳. 基于自适应最优组合核函数高斯过程回归的锂电池健康状态区间估计[J]. 储能科学与技术, 2025, 14(1): 346-357.

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.

图/表 13

图1

图2

图3

图4

表1

GPR常用核函数"

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)	$K x, y = σ f 2 2 e x p - 2 I 22 s i n 2 π \| x - y \| p$

表1

图5

表2

图6

表3

图7

图8

图9

图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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基于自适应最优组合核函数高斯过程回归的锂电池健康状态区间估计

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

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