融合多尺度混合核的锂电池SOE稀疏高斯过程回归及不确定性量化

杨康; 陈少卿; 石涛; 朱军

doi:10.19799/j.cnki.2095-4239.2026.0707

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融合多尺度混合核的锂电池SOE稀疏高斯过程回归及不确定性量化

XXXX | 更新时间：2026-10-16

- 融合多尺度混合核的锂电池SOE稀疏高斯过程回归及不确定性量化
- “Sparse Gaussian Process Regression and Uncertainty Quantification for Lithium-Ion Battery SOE Using Multi-Scale Mixed Kernels”
- 储能科学与技术 2026年页码：1-14
- 作者机构：
  
  1.四川蜀能电科能源技术有限公司，四川成都 610000
  2.国网四川省电力公司电力科学研究院，四川成都 610000
- 作者简介：
  
  杨康（1988—），男，本科，副高级工程师，主要研究方向为电力工程技术，E-mail：479853080@qq.com；
- 基金信息：
  
  国网四川省电力公司科技项目“基于多维等效建模的固态电池安全性测评机制研究”(521999250002)
- DOI：10.19799/j.cnki.2095-4239.2026.0707
  中图分类号： TM 912
- 收稿：2026-08-12，
  
  修回：2026-10-13，
  
  网络首发：2026-10-16，
- 稿件说明：
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杨康, 陈少卿, 石涛, 等. 融合多尺度混合核的锂电池SOE稀疏高斯过程回归及不确定性量化[J]. 储能科学与技术, XXXX, XX(XX): 1-14.

YANG Kang, CHEN Shaoqing, SHI Tao, et al. "Sparse Gaussian Process Regression and Uncertainty Quantification for Lithium-Ion Battery SOE Using Multi-Scale Mixed Kernels"[J]. Energy Storage Science and Technology, XXXX, XX(XX): 1-14.
杨康, 陈少卿, 石涛, 等. 融合多尺度混合核的锂电池SOE稀疏高斯过程回归及不确定性量化[J]. 储能科学与技术, XXXX, XX(XX): 1-14. DOI： 10.19799/j.cnki.2095-4239.2026.0707.

YANG Kang, CHEN Shaoqing, SHI Tao, et al. "Sparse Gaussian Process Regression and Uncertainty Quantification for Lithium-Ion Battery SOE Using Multi-Scale Mixed Kernels"[J]. Energy Storage Science and Technology, XXXX, XX(XX): 1-14. DOI： 10.19799/j.cnki.2095-4239.2026.0707.

摘要

准确估算锂离子电池的能量状态（State of Energy，SOE）并量化其预测不确定性，对于提升电池管理系统的能量管理、安全控制及运行可靠性具有重要意义。针对传统高斯过程回归在处理大规模时序工况数据时面临单一核函数难以兼容电池复杂物理退化行为，本研究提出了一种基于混合核稀疏高斯过程回归估计（Hybrid Composite Sparse Gaussian Process Regression，HCSGPR）的锂离子电池SOE预测框架。首先，HCSGPR构建了一种多尺度混合核函数，基于数据驱动统计特征实现了对电池全局能量演化趋势与微观局部非线性波动的特征分离与协同拟合。在此基础上，引入基于虚拟样本的诱导点稀疏近似机制，保持了模型特征的表征能力。此外，框架采用极大化边际对数似然方法实现超参数的闭环自适应寻优。在动态应力测试与北京公交车辆动态试验典型工况下的验证结果表明，所提HCSGPR模型展现出了较好的追踪精度与自适应能力，其平均决定系数R

最高可达99.74%，平均均方根误差RMSE低至1.18%，相较于标准SGPR和CNN-LSTM基准模型表现出较好的预测优势。在不确定性量化方面，对于标称覆盖率为90%的预测区间，实际预测区间覆盖率为92.46%至96.36%，预测区间归一化平均宽度为2.55%至4.77%，表明所构建的预测区间能够达到标称覆盖要求，同时保持较窄的归一化区间宽度。最后，引入核密度估计对后验估算误差进行非参数概率密度拟合，结果定量证实了残差序列在BBDST和DST的三个温度下具有较好的收敛性与鲁棒性，为大规模工业级电池大数据时序估算提供了一种可参考的评估方案。

Abstract

Accurately estimating the State of Energy (SOE) of lithium-ion batteries and quantifying the uncertainty in these predictions is crucial for improving the energy management

safety control

and operational reliability of battery management systems. Addressing the challenge faced by traditional Gaussian process regression—namely

the inability of a single kernel function to account for the complex physical degradation behavior of batteries when processing large-scale time-series operational data—this study proposes a lithium-ion battery SOE prediction framework based on Hybrid Composite Sparse Gaussian Process Regression (HCSGPR). First

HCSGPR employs a multiscale hybrid kernel function to achieve the statistical feature separation and simultaneous fitting of the global energy evolution trend and the microscopic local nonlinear fluctuations under transient operating conditions. Building on this foundation

we introduce a virtual-sample-based induced point-sparse approximation mechanism

which ensures real-time high-precision feature capture in engineering online applications. In addition

the framework employs the marginal maximum log-likelihood method to achieve closed-loop adaptive optimization of hyperparameters. Validation results for DST and BBDST under typical operating conditions indicate that the proposed HCSGPR model exhibits good tracking accuracy and adaptability: its average coefficient of determination (R²) reaches as high as 99.74%

and its average root mean square error (RMSE) is as low as 1.18%. This demonstrates that the model outperforms the standard SGPR and CNN-LSTM benchmark models in terms of prediction accuracy. In terms of uncertainty quantification

for a prediction interval with a nominal coverage of 90%

the actual prediction interval coverage ranged from 92.46% to 96.36%

and the normalized average width of the prediction interval ranged from 2.55% to 4.77%. This indicates that the constructed prediction intervals meet the nominal coverage requirements while maintaining a narrow normalized interval width. Finally

by introducing kernel density estimation to perform nonparametric probability density fitting for posterior estimation errors

the results quantitatively confirmed that the residual sequences exhibit good convergence and robustness at the three temperatures of BBDST and DST

providing a reference evaluation scheme for large-scale

industrial-grade battery big data time-series estimation.

关键词

Keywords

references

钟智栋, 倪明, 彭继宇, 等. 基于深度学习的锂电池热失控预警技术研究进展[J/OL]. 储能科学与技术, 1-12[2026-06-26].

ZHONG Z D, NI M, PENG J Y, et al. Research progress on deep learning-based early warning technology for lithium-ion battery thermal runaway[J/OL]. Energy Storage Science and Technology, 1-12[2026-06-26].

李允中, 张群, 文昊楠, 等. 锂电池产业全生命周期环境影响与应对策略[J]. 分析测试学报, 2025, 44(8): 1469-1477.

LI Y Z, ZHANG Q, WEN H N, et al. Environmental impacts and mitigation strategies across the full life cycle of the lithium-ion battery industry[J]. Journal of Instrumental Analysis, 2025, 44(8): 1469-1477.

王方, 吴泽昊, 苗秀娟, 等. 老化锂离子电池机械滥用安全性研究综述[J]. 中国科学:技术科学, 2025, 55(7): 1077-1104.

WANG F, WU Z H, MIAO X J, et al. A review of safety studies on mechanical abuse of aged lithium-ion batteries[J]. Science in China: Technological Sciences, 2025, 55(7): 1077-1104.

宋贺雁, 侯恩广, 王建纲, 等. 基于Bi-LSTM网络改进ACKF的梯次锂电池能量状态估算[J]. 电池工业, 2026, 30(2): 182-191.

SONG H Y, HOU E G, WANG J G, et al. Energy state estimation for gradient lithium-ion batteries using an ACKF model enhanced by a Bi-LSTM network[J]. Battery Industry, 2026, 30(2): 182-191.

叶思逸, 王雨杰, 庞腾威, 等. 面向安全的锂离子电池智能管理方法研究综述[J]. 传动技术, 2025, 39(2): 3-14+22.

YE S Y, WANG Y J, PANG T W, et al. A review of research on safety-oriented smart management methods for lithium-ion batteries[J]. Drive Technology, 2025, 39(2): 3-14+22.

计巧珍, 周仲康, 顾先涛, 等. 基于改进分数阶模型的锂离子电池荷电状态和能量状态联合估计[J/OL]. 电源学报, 1-12[2026-09-10]. https://link.cnki.net/urlid/12.1420.tm.20260422.1535.004.

JI Q Z, ZHOU Z K, GU X T, et al. Joint estimation of state of charge and state of energy for lithium-ion batteries based on improved fractional-order model[J/OL]. Journal of Power Supply, 1-12[2026-09-10]. https://link.cnki.net/urlid/12.1420.tm.20260422. 1535.004.

YUN X, ZHANG X, WANG C, et al. A review on state of charge estimation methods for lithium-ion batteries based on data-driven and model fusion[J]. Journal of Energy Storage, 2025, 129: 117389.

张艳辉, 赵天任. 基于双平方根无迹卡尔曼滤波的储能电池SOC与SOH联合估计方法[J]. 广东电力, 2026, 39(8): 36-44.

ZHANG Y H, ZHAO T R. Joint estimation method of SOC and SOH for energy storage batteries based on dual square-root unscented Kalman filter[J]. Guangdong Electric Power, 2026, 39(8): 36-44.

柳明贤, 李继标, 唐炳南, 等. 基于AUKF的可穿戴式设备用锂离子电池SOE在线估计方法[J]. 储能科学与技术, 2024, 13(5): 1688-1698.

LIU M X, LI J B, TANG B N, et al. An online estimation method for the SOE of lithium-ion batteries in wearable devices based on AUKF[J]. Energy Storage Science and Technology, 2024, 13(5): 1688-1698.

LI Z, NI H, ZHU W, et al. Adaptive SOC-OCV mapping-based joint estimation of SOC and SOH in aging lithium-ion batteries using extended Kalman filtering[J]. Journal of Power Electronics, 2026, 26(1): 126-138.

ZHANG J, CHEN J, LIU D, et al. Multi-state joint prediction algorithm for lithium battery packs based on data-driven and physical models[J]. Energy, 2025, 322: 135641.

余妍. 基于深度学习和卡尔曼滤波融合的环境温度状态估计[D]. 银川: 北方民族大学, 2026.

YU Y. Estimation of ambient temperature state based on fusion of deep learning and Kalman filter[D]. Yinchuan: North Minzu University, 2026.

HOU J, SU T, GAO T, et al. Early prediction of battery lifetime for lithium-ion batteries based on a hybrid clustered CNN model[J]. Energy, 2025, 319: 134992.

苏宝定, 李波, 李永利, 等. 基于数据驱动与组合模型的锂离子电池SOH估计[J]. 电池, 2024, 54(5): 696-699.

SU B D, LI B, LI Y L, et al. SOH estimation of lithium-ion battery based on data-driven and combined model[J]. Battery Bimonthly, 2024, 54(5): 696-699.

李骁龙. 数据—机理融合驱动的锂离子电池早期安全预警研究[D]. 哈尔滨: 哈尔滨工业大学, 2025.

LI X L. Study on early safety warning of lithium-ion battery driven by data-mechanism fusion[D]. Harbin: Harbin Institute of Technology, 2025.

罗明艳, 浦东玲, 秦柯云, 等. 基于高斯过程回归的锂电池寿命预测[J]. 电子制作, 2026, 34(2): 60-65.

LUO M Y, PU D L, QIN K Y, et al. Lithium-ion battery life prediction based on Gaussian process regression[J]. Electronics Projects, 2026, 34(2): 60-65.

邓鸿枥, 吴松荣, 刘齐, 等. 基于改进高斯过程回归的锂离子电池健康状态估计[J]. 电源学报, 2026, 24(4): 205-214.

DENG H L, WU S R, LIU Q, et al. Estimation of lithium-ion battery health status based on improved Gaussian process regression[J]. Journal of Power Supply Engineering, 2026, 24(4): 205-214.

MOU J, ZHOU W, YU C, et al. A data-driven SOE estimation framework for lithium-ion batteries under drive cycle conditions over wide temperature range[J]. Energy, 2025, 318: 134658.

刘贯科, 刘洋, 尹照新, 等. 基于二阶AEKF算法的LiFePO4电池能量状态估计[J]. 电源技术, 2026, 50(7): 1301-1308.

LIU G K, LIU Y, YIN Z X, et al. State of energy estimation of LiFePO4 battery based on second-order AEKF algorithm[J]. Chinese Journal of Power Sources, 2026, 50(7): 1301-1308.

ZOU Y, SHI H, CAO W, et al. A high-speed recurrent state network with noise reduction for multi-temperature state of energy estimation of electric vehicles lithium-ion batteries[J]. Energy, 2025, 322: 135639.

PENG T, MO Z, CHEN J, et al. A novel MIC-BOA-TiDE fusion framework with kernel density estimation for point and probabilistic remaining useful life prediction of lithium-ion batteries[J]. Applied Energy, 2026, 410: 127570.

HE Y, BAI W, WANG L, et al. SOH estimation for lithium-ion batteries: An improved GPR optimization method based on the developed feature extraction[J]. Journal of Energy Storage, 2024, 83: 110678.

JI X, LIAO Y, TU J, et al. PSO-GPR model for state estimation of lithium-ion battery using ultrasonic guided waves with multi-feature fusion technique[J]. Journal of Energy Storage, 2025, 112: 115580.

姜玥, 郭凤祥, 陈俐. 基于异方差高斯过程回归的电池组容量衰减不确定性建模[J/OL]. 上海交通大学学报, 1-19[2026-06-26]. https://doi.org/10.16183/j.cnki.jsjtu.2025.171.

JIANG Y, GUO F X, CHEN L. Uncertainty modeling of battery pack capacity degradation based on heteroscedastic Gaussian process regression[J/OL]. Journal of Shanghai Jiao Tong University, 1-19[2026-06-26]. https://doi.org/10.16183/j.cnki.jsjtu.2025.171.

CHEN X, CHEN X, CHEN X. A novel framework for lithium-ion battery state of charge estimation based on Kalman filter Gaussian process regression[J]. International Journal of Energy Research, 2021, 45(9): 13238-13249.

LI J, LI T, QIAO Y, et al. Internal temperature estimation method for lithium-ion battery based on multi-frequency imaginary part impedance and GPR model[J]. Journal of Energy Storage, 2025, 118: 116287.

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 L J, LI Z W. Remaining useful life prediction of lithium battery based on grey wolf optimization algorithm and combined kernel function GPR model[J]. Integrated Intelligent Energy, 2025, 47(12): 25-33.

廖大鹏, 孙其振, 王毓琦, 等. 采用关键样本自适应高斯过程回归算法的锂电池温度在线估计[J/OL]. 西安交通大学学报, 1-10[2026-09-10]. https://link.cnki.net/urlid/61.1069.t.20260907.1500.004.

LIAO D P, SUN Q Z, WANG Y Q, et al. Online temperature estimation of lithium battery using critical sample adaptive Gaussian process regression algorithm[J/OL]. Journal of Xi'an Jiaotong University, 1-10[2026-09-10]. https://link.cnki.net/urlid/61.1069.t.20260907.1500.004.

阳俊杰. 基于智能优化滤波的锂电池SOC与SOE估计研究[D]. 绵阳: 西南科技大学, 2025.

YANG J J. Research on SOC and SOE estimation of lithium battery based on intelligent optimization filtering[D]. Mianyang: Southwest University of Science and Technology, 2025.

李臣, 张会林, 张建平. 基于核函数和超参数优化的退役锂电池健康状态估计[J]. 储能科学与技术, 2024, 13(6): 2010-2021.

LI C, ZHANG H L, ZHANG J P. State of health estimation of retired lithium batteries based on kernel function and hyperparameter optimization[J]. Energy Storage Science and Technology, 2024, 13(6): 2010-2021.

XIAO C, SHI H, CHEN L, et al. Uncertainty-aware state of energy estimation for lithium-ion batteries via hybrid kernel sparse Gaussian process[J]. Batteries, 2026, 12(8): 312.

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