Abstract：Capacity or internal resistance is an important indicator to measure the health status of lithium-ion batteries. But in the actual operation of lithium-ion batteries, the battery capacity and internal resistance are difficult to obtain in real time. So, a method to obtain new health indicators based on the discharge process information is proposed and the remaining useful life of lithium-ion batteries is predicted. The law of voltage change during the discharging process of lithium-ion batteries is studied. On the above basis, two new health indicators which can be measured online are proposed. The accuracy of the new health indicators is corrected by Box-Cox transformation. The results show that there is a strong correlation between the extracted health indicators and the capacity, which can solve the problem that the battery capacity is difficult to measure online to some extent. In addition, the battery degradation process model based on new health indicators is established, and the remaining useful life of lithium-ion batteries is predicted by the relevance vector machine. The experimental results show that the relevance vector machine algorithm is better than other algorithms in life prediction performance. And the later the prediction time, the more accurate the prediction results. The extracted health indicators can describe the degradation process of lithium-ion batteries well and predict the remaining useful life accurately.
［1］Cadini F, Sbarufatti C, Cancelliere F, et al. State-of-life prognosis and diagnosis of lithium-ion batteries by data-driven particle filters［J］. Applied Energy, 2019, 235:661-672.
［2］程树英, 林鹏程, 林培杰. 一种新型锂电池充电剩余时间预测方法［J］. 电源技术, 2019, 43(1):99-102+135.
Cheng S Y, Lin P C, Lin P J. New method of predict remaining charging time for lithium-ion batteries［J］. Chinese Journal of Power Sources, 2019, 43(1):99-102+135.
［3］Saha B, Goebel K, Poll S, et al. Prognostics methods for battery health monitoring using a Bayesian framework［J］. IEEE Transactions on Instrumentation & Measurement, 2009, 58(2):291-296.
［4］彭宇, 刘大同, 彭喜元. 故障预测与健康管理技术综述［J］. 电子测量与仪器学报, 2010, 24(1):1-9.
Peng Y, Liu D T, Peng X Y. A review:Prognostics and health management［J］. Journal of Electronic Measurement and Instrument, 2010, 24(1) 1-9.
［5］Liu J, Wang W, Golnaraghi F. A multi-step predictor with a variable input pattern for system state forecasting［J］. Mechanical Systems & Signal Processing, 2009, 23(5):1586-1599.
［6］Lei Y G, Li N P, Guo L, et al. Machinery health prognostics:A systematic review from data acquisition to RUL prediction［J］. Mechanical Systems and Signal Processing, 2018, 104:799-834.
［7］Wang D, Zhao Y, Yang F F, et al. Nonlinear-drifted Brownian motion with multiple hidden states for remaining useful life prediction of rechargeable batteries［J］. Mechanical Systems and Signal Processing, 2017, 93:531-544.
［8］陈则王, 杨丽文, 赵晓兵, 等. 基于改进无迹卡尔曼滤波的锂电池SOC在线估计［J］. 计量学报, 2019, 40(1):40-48.
Chen Z W, Yang L W, Zhao X B, et al. Online estimation of SOC for lion battery based on an improved unscented Kalman filters approach［J］. Acta Metrologica Sinica, 2019, 40(1):40-48.
［9］陈则王, 李福胜,林娅, 等. 基于GA-ELM的锂离子电池RUL间接预测方法［J］. 计量学报, 2020, 41(6):735-742.
Chen Z W, Li F S, Lin Y, et al. Indirect Prediction Method of RUL for Lithium-ion Battery Based on GA-ELM［J］. Acta Metrologica Sinica, 2020, 41(6):735-742.
［10］Long B, Xian W M, Jiang L, et al. An improved autoregressive model by particle swarm optimization for prognostics of lithium-ion batteries［J］. Microelectronics & Reliability, 2013, 53(6):821-831.
［11］Lee S, Kim J, Lee J, et al. State-of-charge and capacity estimation of lithium-ion battery using a new open-circuit voltage versus state-of-charge［J］. Journal of power sources, 2008, 185(2):1367-1373.
［12］Dong G Z, Chen Z H, Wei J W, et al. Battery health prognosis using brownian motion modeling and particle filtering［J］. IEEE Transactions on Industrial Electronics, 2018, 65(11):8646-8655.
［13］刘月峰, 赵光权, 彭喜元. 多核相关向量机优化模型的锂电池剩余寿命预测方法［J］. 电子学报, 2019, 47(6):1285-1292.
Liu Y F, Zhao G Q, Peng X Y. A Lithium-ion battery remaining using life prediction method based on multi-kernel relevance vector machine optimized model［J］. ACTA Electronica Sinica, 2019, 47(6):1285-1292.
［14］Deng Y W, Ying H J, E J Q, et al. Feature parameter extraction and intelligent estimation of the State-of-Health of lithium-ion batteries［J］. Energy, 2019, 176:91-102.
［15］吴忠强, 尚梦瑶, 申丹丹, 等. 基于BSA-RELM的纯电动汽车锂离子电池SOC估计［J］. 计量学报, 2019, 40(4):693-699.
Wu Z Q, Shang M Y, Shen D D, et al. Estimation of SOC of li-ion battery in pure electric vehicle by BSA-RELM［J］. Acta Metrologica Sinica, 2019, 40(4):693-699.
［16］吴忠强, 王国勇,谢宗奎, 等. 基于WOA-UKF算法的锂电池容量与SOC联合估计［J］. 计量学报, 2022, 43(5):649-656.
Wu Z Q, Wang G Y, Xie Z K, et al. Joint Estimation of the Capacity and SOC of Lithium Battery Based on WOA-UKF Algorithm［J］. Acta Metrologica Sinica, 2022, 43(5):649-656.
［17］Qin W, Lv H C, Liu C L, et al. Remaining useful life prediction for lithium-ion batteries using particle filter and artificial neural network［J］. Industrial Management & Data Systems, 2019, 120(2):312-328
［18］Song Y C, Liu D T, Hou Y D, et al. Satellite lithium-ion battery remaining useful life estimation with an iterative updated RVM fused with the KF algorithm［J］. Chinese Journal of Aeronautics, 2018, 31(1):31-40.
［19］Yang W A, Xiao M H, Zhou W, et al. A hybrid prognostic approach for remaining useful life prediction of Lithium-Ion batteries［J］. Shock and Vibration, 2016, 2016:1-15
［20］Wei J W, Dong G Z, Chen Z H. Remaining Useful Life Prediction and State of Health Diagnosis for Lithium-Ion Batteries Using Particle filter and Support Vector Regression［J］. IEEE Transactions on Industrial Electronics, 2018, 65(7):5634-5643.
［21］Gomez J, Nelson R, Kalu E E, et al. Equivalent circuit model parameters of a high-power Li-ion battery:thermal and state of charge effects［J］. Journal of Power Sources, 2011, 196(10):4826-4831.
［22］Liu D T, Zhou J B, Liao H T, et al. A health indicator extraction and optimization framework for lithium-ion battery degradation modeling and prognostics［J］. IEEE Transactions on Systems Man & Cybernetics Systems, 2015, 45(6):915-928.
［23］Widodo A, Shim M C, Caesarendra W, et al. Intelligent prognostics for battery health monitoring based on sample entropy［J］. Expert Systems with Application, 2011, 38(9)11763-11769.
［24］Liu D T, Wang H, Peng Y, et al. Satellite lithium-ion battery remaining cycle life prediction with novel indirect health indicator extraction［J］. Energies, 2013, 6(8):3654-2668.
［25］Zhao Q, Qin X L, Zhao H B, et al. A novel prediction method based on the support vector regression for the remaining useful life of lithium-ion batteries［J］. Microelectronics Reliability, 2018, 85:99-108.
［26］Zhou Y P, Huang M H, Chen Y P, et al. A novel health indicator for on-line lithium-ion batteries remaining useful life prediction［J］. Journal of power sources, 2016, 321(30):1-10.
［27］Jia J F, Liang J Y, Shi Y H, et al. SOH and RUL prediction of lithium-ion batteries based on Gaussian process regression with indirect health indicators［J］. Energies, 2020, 13(2):375-395.
［28］Saha B, Goebel K. Battery Data Set:NASA ames prognostics data repository［EB/OL］.NASA Ames Research Center［2020-10-22］. https://ti. arc. nasa. gov/tech/dash/groups/pcoe/prognostic-data-repository/#battery.
［29］Zhang Y Z, Xiong R, He H W, et al. Lithium-ion battery remaining useful life prediction with Box-Cox transformation and Monte Carlo simulation［J］. IEEE Transactions on Industrial Electronics, 2019, 66(2):1585-1597.
［30］Sakia R. The Box-Cox transformation technique:a review［J］. The Statistician, 1992, 41(2):169-178.
［31］Li H, Pan D H, Chen C L P. Intelligent prognostics for battery health monitoring using the mean entropy and relevance vector machine［J］. IEEE Transactions on Systems Man & Cybernetics Systems, 2014, 44(7):851-862.
［32］Liu K L, Li Y, Hu X S, et al. Gaussian process regression with automatic relevance determination kernel for calendar aging prediction of lithium-ion batteries［J］. IEEE Transactions on Industrial Informatics, 2020, 16(6):3767-3777.
2022, Vol. 43 
