Abstract：Accurate state of health (SOH) estimation is crucial for the safe and efficient operation of lithium-ion battery energy storage systems. Machine learning is one of the most promising methods for battery SOH estimation by extracting features from historical cycling data and aging batteries. The charging and discharging voltages of the battery, which are easily measurable parameters, are influenced by both the thermodynamic and kinetic characteristics of the battery. Thus, many studies focused on extracting battery aging features from constant current or constant voltage charge curves. Because of the uncertain need of battery output, the change of discharge voltage value is uncertain, which makes feature extraction become difficult. Besides, there are several pathways for battery aging, and models only based on the charging process may not capture all aging features. Additionally, the randomness of the battery working start points for charging and discharging further challenges for feature extraction in practical applications. To address these issues, this study proposed a novel feature extraction and sparse Gaussian process regression (GPR) method based on random segments of the charging and discharging data. This approach extracted aging features from intermittent charge and discharge data segments, which reduced the need for historical data and enhanced the generalization capability for practical applications. In this study, five different kernel functions were applied to improve the accuracy of SOH estimation for various segments of charging or discharging data in three steps. Firstly, segment of data is built. A data processing algorithm was proposed to segment the intermittent charging and discharging data under different loads. And this data processing algorithm segment data based on the range of the state of charge (SOC). Then, features of SOH estimation are extracted. A method of feature engineering was proposed to extract aging features from the data segments, which applied various algorithms of digital signal processing, audio processing, and image processing technologies. Because battery aging contains different pathways, various features are extracted, including statistical features, evolutional features, and frequency domain-related features of voltage and current curves. Statistical features include skewness, kurtosis, root mean square, root sum square, and standard deviation of the voltage and current curves. Evolutional features include dynamic time warping, correlation coefficients, and gradients of the voltage curves. Frequency domain features include mid-reference level crossings, band power, frequency bands, mean frequency, and occupied bandwidth of the voltage curves. Finally, SOH estimation is set. The sparse Gaussian process regression models with various kernels were trained to estimate battery SOH based on charging and discharging data segments. In this study, 58 cells cycling data was used for testing and validation. The test results revealed that the GPR model trained on discharge data within the SOC range from 60% to 70% was the best model for SOH estimation, which achieved an average root mean square error (RMSE) of 0.09%. While the GPR model within the SOC range from 0% to 10% was the best model of the charging data, which achieved an average RMSE of 3.95%. Among the five kernels, the best kernel for the GPR models based on charging data was the Matern 5/2 kernel, whereas the rational quadratic kernel was the best kernel for the GPR models based on discharging data. Compared to traditional machine learning methods, such as linear regression, regularized linear regression (RLR), support vector machine regression, and multilayer perceptron, GPR achieved the lowest average RMSE and mean absolute percentage error. The test results demonstrated that the proposed method can accurately estimate SOH from charge and discharge data segments.
江银锋, 宋文祥, 施语. 基于随机充放电片段和稀疏高斯过程回归的电池健康状态估计[J]. 电工技术学报, 2025, 40(19): 6359-6377.
Jiang Yinfeng, Song Wenxiang, Shi Yu. Battery State of Health Estimation Using Sparse Gaussian Process Regression Based on Random Partial Charge and Discharge Data. Transactions of China Electrotechnical Society, 2025, 40(19): 6359-6377.
[1] 金建新, 虞儒新, 刘刚, 等. 锂离子电池健康状态估算方法研究进展[J]. 电气工程学报, 2024, 19(1): 33-48. Jin Jianxin, Yu Ruxin, Liu Gang, et al.Research progress on state-of-health estimating method for lithium-ion batteries[J]. Journal of Electrical Engineering, 2024, 19(1): 33-48. [2] 赵珈卉, 田立亭, 程林. 锂离子电池状态估计与剩余寿命预测方法综述[J]. 发电技术, 2023, 44(1): 1-17. Zhao Jiahui, Tian Liting, Cheng Lin.Review on state estimation and remaining useful life prediction methods for lithium-ion battery[J]. Power Generation Technology, 2023, 44(1): 1-17. [3] Chen Minzhi, Ma Guijun, Liu Weibo, et al.An overview of data-driven battery health estimation technology for battery management system[J]. Neuro-computing, 2023, 532: 152-169. [4] 赵靖英, 胡劲, 张雪辉, 等. 基于锂电池模型和分数阶理论的SOC-SOH联合估计[J]. 电工技术学报, 2023, 38(17): 4551-4563. Zhao Jingying, Hu Jin, Zhang Xuehui, et al.Joint estima-tion of the SOC-SOH based on lithium battery model and fractional order theory[J]. Transactions of China Electrotechnical Society, 2023, 38(17): 4551-4563. [5] Shi Yu, Ahmad S, Tong Qing, et al.The optimization of state of charge and state of health estimation for lithium-ions battery using combined deep learning and Kalman filter methods[J]. International Journal of Energy Research, 2021, 45(7): 11206-11230. [6] 刘旖琦, 雷万钧, 刘茜, 等. 基于双自适应扩展粒子滤波器的锂离子电池状态联合估计[J]. 电工技术学报, 2024, 39(2): 607-616. Liu Yiqi, Lei Wanjun, Liu Qian, et al.Joint state estimation of lithium-ion battery based on dual adaptive extended particle filter[J]. Transactions of China Electrotechnical Society, 2024, 39(2): 607-616. [7] Wang Zhuo, Gladwin D T, Smith M J, et al.Practical state estimation using Kalman filter methods for large-scale battery systems[J]. Applied Energy, 2021, 294: 117022. [8] 彭纪昌, 刘凯龙, 孟锦豪, 等. 基于变参数结构的锂离子电池建模方法[J]. 机械工程学报, 2024, 60(14): 298-305. Peng Jichang, Liu Kailong, Meng Jinhao, et al.Dynamically parameterized structure for lithium-ion battery method[J]. Journal of Mechanical Engineering, 2024, 60(14): 298-305. [9] 蒋帅, 陈铖, 段砚州, 等. 温度和老化影响下的锂离子电池荷电状态和健康状态联合估计方法研究[J]. 机械工程学报, 2024, 60(18): 266-275. Jiang Shuai, Chen Cheng, Duan Yanzhou, et al.Joint estimation of state-of-charge and state-of-health for lithium-ion batteries under the influence of tempera-ture and aging[J]. Journal of Mechanical Engineering, 2024, 60(18): 266-275. [10] 李乐卿, 王鹏, 孙万洲, 等. 基于锂离子电池容量增量曲线半峰面积的容量在线估计方法[J]. 电工技术学报, 2024, 39(17): 5354-5364. Li Leqing, Wang Peng, Sun Wanzhou, et al.Online capacity estimation method based on half peak area of lithium-ion battery capacity increment curve[J]. Transactions of China Electrotechnical Society, 2024, 39(17): 5354-5364. [11] Sun Xiaodong, Chen Qi, Zheng Linfeng, et al.Joint estimation of state-of-health and state-of-charge for lithium-ion battery based on electrochemical model optimized by neural network[J]. IEEE Journal of Emerging and Selected Topics in Industrial Electronics, 2023, 4(1): 168-177. [12] Gao Yizhao, Liu Kailong, Zhu Chong, et al.Co-estimation of state-of-charge and state-of-health for lithium-ion batteries using an enhanced electroche-mical model[J]. IEEE Transactions on Industrial Electronics, 2022, 69(3): 2684-2696. [13] 史宏思, 孙新伟, 王凯. 基于电化学阻抗谱的锂离子电池健康状态估计[J/OL]. 发电技术, 2024: 1-15[2024-09-30]. https://kns.cnki.net/KCMS/detail/detail.aspx?filename=SLJX20240716004&dbname=CJFD&dbcode=CJFQ. Shi Hongsi, Sun Xinwei, Wang Kai. Health state estimation of lithium-ion batteries based on electroche-mical impedance spectroscopy[J/OL]. Power Generation Technology, 2024: 1-15[2024-09-30]. https://kns.cnki.net/KCMS/detail/detail.aspx?filename=SLJX20240716004&dbname=CJFD&dbcode=CJFQ. [14] Pang Hui, Chen Kaiqiang, Geng Yuanfei, et al.Accurate capacity and remaining useful life prediction of lithium-ion batteries based on improved particle swarm optimization and particle filter[J]. Energy, 2024, 293: 130555. [15] 陆楠, 孙越, 彭鹏, 等. 数据驱动的钠离子电池健康状态评估方法研究[J]. 电源学报, 2024, 22(1): 1-10. Lu Nan, Sun Yue, Peng Peng, et al.Data-driven state of health estimation for sodium-ion batteries[J]. Journal of Power Supply, 2024, 22(1): 1-10. [16] Roman D, Saxena S, Robu V, et al.Machine learning pipeline for battery state-of-health estimation[J]. Nature Machine Intelligence, 2021, 3(5): 447-456. [17] 李雨佳, 欧阳权, 刘灏仪, 等. 基于支持向量机与改进高斯过程混合模型的车用电池容量预测方法[J]. 电气工程学报, 2024, 19(1): 87-96. Li Yujia, Ouyang Quan, Liu Haoyi, et al.Vehicle battery capacity prediction based on hybrid model of support vector machine and improved Gaussian process[J]. Journal of Electrical Engineering, 2024, 19(1): 87-96. [18] 李成, 陈球, 于莹莹, 等. 基于IWOA-LSSVM的锂离子电池RUL预测[J]. 电气工程学报, 2024, 19(3): 399-411. Li Cheng, Chen Qiu, Yu Yingying, et al.Remaining useful life prediction for lithium-ion batteries based on IWOA-LSSVM[J]. Journal of Electrical Engineering, 2024, 19(3): 399-411. [19] 衣思彤, 刘雅浓, 马耀浥, 等. 基于贝叶斯优化-卷积神经网络-双向长短期记忆神经网络的锂电池健康状态评估[J]. 电气技术, 2024, 25(5): 1-10, 21. Yi Sitong, Liu Yanong, Ma Yaoyi, et al.State of health assessment of lithium battery based on Bayesian optimization-convolution neural network-bi-directional long short term memory neural network[J]. Electrical Engineering, 2024, 25(5): 1-10, 21. [20] 蔡雨思, 李泽文, 刘萍, 等. 基于间接健康特征优化与多模型融合的锂电池SOH-RUL联合预测[J]. 电工技术学报, 2024, 39(18): 5883-5898. Cai Yusi, Li Zewen, Liu Ping, et al.Joint prediction of lithium battery state of health and remaining useful life based on indirect health features optimization and multi-model fusion[J]. Transactions of China Electro-technical Society, 2024, 39(18): 5883-5898. [21] 宋显华, 姚全正. 基于片段充电数据和DEKF-WNN-WLSTM的锂电池健康状态实时估计[J]. 电工技术学报, 2024, 39(5): 1565-1576. Song Xianhua, Yao Quanzheng.Real-time state of health estimation for lithium-ion batteries based on daily segment charging data and dual extended Kalman FiltersWavelet neural network-wavelet long short-term memory neural network[J]. Transactions of China Electrotechnical Society, 2024, 39(5): 1565-1576. [22] 尹杰, 刘博, 孙国兵, 等. 基于迁移学习和降噪自编码器-长短时间记忆的锂离子电池剩余寿命预测[J]. 电工技术学报, 2024, 39(1): 289-302. Yin Jie, Liu Bo, Sun Guobing, et al.Transfer learning denoising autoencoder-long short term memory for remaining useful life prediction of Li-ion batteries[J]. Transactions of China Electrotechnical Society, 2024, 39(1): 289-302. [23] Gu Xinyu, See K W, Li Penghua, et al.A novel state-of-health estimation for the lithium-ion battery using a convolutional neural network and transformer model[J]. Energy, 2023, 262: 125501. [24] Zhao Bo, Zhang Weige, Zhang Yanru, et al.Research on the remaining useful life prediction method for lithium-ion batteries by fusion of feature engineering and deep learning[J]. Applied Energy, 2024, 358: 122325. [25] Seeger M.Gaussian processes for machine learning[J]. International Journal of Neural Systems, 2004, 14(2): 69-106. [26] Gong Dongliang, Gao Ying, Kou Yalin, et al.State of health estimation for lithium-ion battery based on energy features[J]. Energy, 2022, 257: 124812. [27] Zhou Yong, Dong Guangzhong, Tan Qianqian, et al.State of health estimation for lithium-ion batteries using geometric impedance spectrum features and recurrent Gaussian process regression[J]. Energy, 2023, 262: 125514. [28] Zhu Jiangong, Wang Yixiu, Huang Yuan, et al.Data-driven capacity estimation of commercial lithium-ion batteries from voltage relaxation[J]. Nature Communications, 2022, 13(1): 2261. [29] Lu Jiahuan, Xiong Rui, Tian Jinpeng, et al.Deep learning to estimate lithium-ion battery state of health without additional degradation experiments[J]. Nature Communications, 2023, 14(1): 2760. [30] Che Yunhong, Hu Xiaosong, Lin Xianke, et al.Health prognostics for lithium-ion batteries: mechanisms, methods, and prospects[J]. Energy & Environmental Science, 2023, 16(2): 338-371. [31] 李英顺, 阚宏达, 郭占男, 等. 基于数据预处理和VMD-LSTM-GPR的锂离子电池剩余寿命预测[J]. 电工技术学报, 2024, 39(10): 3244-3258. Li Yingshun, Kan Hongda, Guo Zhannan, et al.Prediction of remaining useful life of lithium-ion battery based on data preprocessing and VMD-LSTM-GPR[J]. Transactions of China Electrotechnical Society, 2024, 39(10): 3244-3258. [32] Sheng Hanmin, Ray B, Kayamboo S, et al.Battery health estimation based on multidomain transfer learning[J]. IEEE Transactions on Power Electronics, 2024, 39(4): 4758-4770. [33] Deng Zhongwei, Hu Xiaosong, Li Penghua, et al.Data-driven battery state of health estimation based on random partial charging data[J]. IEEE Transactions on Power Electronics, 2022, 37(5): 5021-5031. [34] Jin Haiyan, Cui Ningmin, Cai Lei, et al.State-of-health estimation for lithium-ion batteries with hiera-rchical feature construction and auto-configurable Gaussian process regression[J]. Energy, 2023, 262: 125503. [35] Liu Wei, Zhao Jinbao.An online estimation method of state of health for lithium-ion batteries based on constant current charging curve[J]. Journal of the Electrochemical Society, 2022, 169(5): 050514. [36] Yang Yalong, Chen Siyuan, Chen Tao, et al.State of health assessment of lithium-ion batteries based on deep Gaussian process regression considering heteroge-neous features[J]. Journal of Energy Storage, 2023, 61: 106797. [37] 王震坡, 王秋诗, 刘鹏, 等. 大数据驱动的动力电池健康状态估计方法综述[J]. 机械工程学报, 2023, 59(2): 151-168. Wang Zhenpo, Wang Qiushi, Liu Peng, et al.Review on techniques for power battery state of health estimation driven by big data methods[J]. Journal of Mechanical Engineering, 2023, 59(2): 151-168. [38] Yang Niankai, Song Ziyou, Hofmann H, et al.Robust state of health estimation of lithium-ion batteries using convolutional neural network and random forest[J]. Journal of Energy Storage, 2022, 48: 103857. [39] Lu Jiahuan, Xiong Rui, Tian Jinpeng, et al.Battery degradation prediction against uncertain future conditions with recurrent neural network enabled deep learning[J]. Energy Storage Materials, 2022, 50: 139-151. [40] Severson K A, Attia P M, Jin N, et al.Data-driven prediction of battery cycle life before capacity degradation[J]. Nature Energy, 2019, 4(5): 383-391. [41] Keogh E, Ratanamahatana C A.Exact indexing of dynamic time warping[J]. Knowledge and Information Systems, 2005, 7(3): 358-386. [42] ten Have B, Azpurua M A, Hartman T, et al. Waveform model to characterize time-domain pulses resulting in EMI on static energy meters[J]. IEEE Transactions on Electromagnetic Compatibility, 2021, 63(5): 1542-1549. [43] Gruber M H J, Hayes M H. Statistical digital signal processing and modeling[J]. Technometrics, 1997, 39(3): 335. [44] Stoica P, Moses R L.Spectral Analysis of Signals[M]. Upper Saddle River, N.J: Pearson/Prentice Hall, 2005. [45] Al-Fahoum A S, Al-Fraihat A A. Methods of EEG signal features extraction using linear analysis in fre-quency and time-frequency domains[J]. International Scholarly Research Notices, 2014, 2014(1): 730218. [46] Fulop S A, Fitz K.Algorithms for computing the time-corrected instantaneous frequency (reassigned) spectrogram, with applications[J]. The Journal of the Acoustical Society of America, 2006, 119(1): 360-371. [47] Balestrino A, Caiti A, Crisostomi E.Generalised entropy of curves for the analysis and classification of dynamical systems[J]. Entropy, 2009, 11(2): 249-270. [48] Sundararajan M, Najmi A.The many shapley values for model explanation[J]. Papers, 2019: 9268-9278. [49] Kumar V.Feature selection: a literature review[J]. The Smart Computing Review, 2014, 4(3): 211-229.
2025, Vol. 40 
