Battery Capacity Prediction Based on Pearson Correlation and RBF Neural Network AITranslate
Abstract AITranslate
With the peak of a large number of scrap power batteries approaching，it becomes increasingly important to efficiently recycle and dispose of them. Currently，there are two ways to recycle power batteries：direct recycling and stepwise utilization before recycling. In fact，retired power batteries still retain 70%~80% of their available capacity，which can be used in applications such as electric bicycles，low-speed electric vehicles，smart grids，and energy storage. On one hand，stepwise utilization helps extend the overall lifespan of lithium-ion batteries. On the other hand，it also reflects the complete lifecycle value of the batteries. However，there are significant technical limitations in the stepwise utilization of discarded batteries. Due to the constraints of battery production processes，even within the same batch of batteries，there can be various issues and challenges from the same manufacturer. To obtain the higher voltage and capacity required for practical use，hundreds or even thousands of individual batteries may need to be connected in series and parallel to form a battery pack. Over time and in complex usage environments，the inconsistencies between individual batteries within the battery pack will be amplified. Therefore，in order to facilitate the stepwise utilization of discarded batteries，it is necessary to develop a low-energy，high-precision，and fast capacity prediction method to lay the foundation for the separation and recombination of discarded batteries. To address the issues of long testing time and high energy consumption in capacity testing of retired lithium batteries，this study proposed a retired battery capacity prediction method based on RBF （radial basis function） neural networks. First，the batteries were adequately stored. Then，three complete charge-discharge tests were performed on the batteries at 1C to obtain the discharge capacity of the batteries. Based on the results of the three discharge capacity tests，the average value was calculated to determine the remaining capacity of the retired batteries. Afterward，the batteries were subjected to 10 s of pulse discharge and pulse charge at 1C. The charge and discharge ohmic resistance as well as the charge and discharge polarization resistance of the retired batteries were calculated based on the results of the pulse testing data. Additionally，the batteries were charged at a constant current to 3.5 V under 1C conditions，and short-term constant current charging data was obtained. From this data，characteristic parameters such as the charging capacity to 3.5 V and charging time were extracted. Pearson correlation coefficient method was used to calculate the relationship between these characteristic parameters and retired battery capacity in the range of –0.8~–0.6 and 0.6~0.8. The results indicated a strong correlation between the feature parameters and the actual capacity of retired batteries. The feature parameter with the highest correlation was the polarization resistance obtained through pulse discharge. During the degradation process of retired batteries，the internal structure of the battery's active material had been damaged，affecting the migration and diffusion of lithium ions between the active materials in the electrochemical reaction process. This led to the occurrence of different forms and intensities of polarization within the battery，resulting in different internal polarization resistances. Therefore，the polarization resistance obtained through pulse testing could，to some extent，reflect the degree of deterioration of the internal structure of the battery. Finally，RBF neural network was introduced to establish the mapping relationship between multiple feature parameters and battery capacity，establishing a prediction model for the capacity of retired batteries. In the process of establishing the capacity prediction model，the proportion of training and test data could affect the prediction results of the model. In order to evaluate the effectiveness and robustness of the established capacity prediction model，50%，60%，70%，80%，and 90% of each data set were used as the training set （input to RBF neural network），and the remaining data were used as the test set （output of the model） to establish the capacity prediction model. The maximum relative error and prediction accuracy were used to analyze the effectiveness of the prediction part of the model. The results were analyzed based on different training and test ratios. Using 50%，60%，70%，80%，and 90% of the data from 93 sets for training the model，the rest were used for testing the model. It could be seen that the capacity prediction model built based on RBF neural network achieved a prediction accuracy of over 90% under different data training ratios. According to the results of the verification experiments，the retired battery capacity prediction method based on multiple feature parameter combinations and RBF neural networks was effective. Compared with the current direct measurement of retired battery capacity，this new method significantly shortened the charge-discharge process and eliminated long-standing steps. Therefore，it achieved significant time，energy，and cost savings. The model was applied to verify different types of batteries，and the maximum error in predicting capacity was within 0.6443 Ah. The verification showed that the model could efficiently and robustly predict the remaining capacity of retired lithium batteries and had great practical value in engineering.
KeyWords AITranslate
［1］Chang L，Ma C，Zhang Y L. Experimental assessment of the discharge characteristics of multi-type retired lithium-ion batteries in parallel for echelon utilization［J］.Journal of Energy Storage，2022，55：105539.
［2］（杨森，赵宁，张帅卿，董伟. 稀有金属基锂离子电池负极材料研究综述［J］.稀有金属，2024，48（5）：705.）
S Yang，N Zhao，S Q Zhang，W Dong. Review on anode materials of rare metal based lithium-ion batteries［J］.Chinese Journal of Rare Metals，2024，48（5）：705.
［3］（李恒，邱睿，郭平安，曹清林. 复合材料电池包上盖模压成形工艺参数优化［J］.锻压技术，2024，49（2）：77.）
H Li，R Qiu，P A Guo，Q L Cao. Optimization of compression molding process parameters for upper cover of composite battery pack［J］.Forging & Stamping Technology，2024，49（2）：77.
［4］（孟金岭，肖健夫，闵婕，李章溢，孙瑞. 储能用梯次利用电池组一致性检测与评价方法［J］.电源技术，2021，45（5）：585.）
J L Meng，J F Xiao，J Min，Z Y Li，R Sun. Consistency testing and evaluation method of echelon utilization battery pack for energy storage［J］.Chinese Journal of Power Sources，2021，45（5）：585.
［5］（雷超，李小龙，刘君. 基于机器学习嵌接有限元的蠕变时效成形全过程形性演变预测［J］.塑性工程学报，2024，31（1）：60.）
C Lei，X L Li，J Liu. Prediction of shape and property evolution in whole process of creep aging forming based on machine learning embedded into finite element［J］.Journal of Plasticity Engineering，2024，31（1）：60.
［6］（计雅芹，赵冬晴，梁升，王黎. 锂离子电池聚合物基复合金属氧化物固态电解质研究进展［J］.铜业工程，2024，（1）：119.）
Y Q Ji，D Q Zhao，S Liang，L Wang. Advances in polymer-based composite metal oxide solid-state electrolytes for lithium-ion batteries［J］.Copper Engineering，2024，（1）：119.
［7］（王华昕，褚启迪，罗扬帆. 基于衰退速度预测的退役电池剩余价值优化方法［J］.南方电网技术，2022，（4）：124.）
H X Wang，Q D Chu，Y F Luo. Residual value optimization method of retired batteries based on recession rate prediction［J］.Southern Power System Technology，2022，（4）：124.
［8］（刘超，邱显扬，刘勇，何晓娟，陈志强，刘牡丹. 废锂离子电池物理分选技术研究现状及展望［J］.稀有金属，2021，45（4）：493.）
C Liu，X Y Qiu，Y Liu，X J He，Z Q Chen，M D Liu. Research status and prospects of physical separation technology of spent lithium-ion batteries［J］.Chinese Journal of Rare Metals，2021，45（4）：493.
［9］（孙广明，贾新羽，陈良亮. 基于K近邻回归的锂离子电池健康状态估计［J］.电源技术，2022，46（8）：872.）
G M Sun，X Y Jia，L L Chen. State of health estimation of lithium-ion battery based on K nearest neighbour regression and IC curve［J］.Chinese Journal of Power Sources，2022，46（8）：872.
［10］Ma H Z，Deng Y L，Liu W W. State of health estimation of retired battery for echelon utilization based on charging curve［J］.Procedia CIRP，2022，105：458.
［11］Wei Z X，Han X J，Li J R. State of health assessment for echelon utilization batteries based on deep neural network learning with error correction［J］.Journal of Energy Storage，2022，51：104428.
［12］Zhao X B，Xuan D J，Zhao K Y. Elman neural network using ant colony optimization algorithm for estimating of state of charge of lithium-ion battery［J］.Journal of Energy Storage，2020，32：101789.
［13］（李苏阳，陈富安. 基于注意力机制的双向LSTM锂电池SOH估算模型［J］.电源技术，2022，46（7）：739.）
S Y Li，F A Chen. Lithium battery SOH prediction based on Bi-LSTM attention mechanism［J］.Chinese Journal of Power Sources，2022，46（7）：739.
［14］（李程，马霖睿，陈郭力，杨建新，王博. 退役磷酸铁锂电芯性能研究［J］.电气技术，2021，22（6）：74.）
C Li，L R Ma，G L Chen，J X Yang，B Wang. Study on the performance of retired lithium iron phosphate batteries［J］.Electrical Engineering，2021，22（6）：74.
［15］（陈峥，李磊磊，舒星，沈世全，刘永刚，申江卫. 基于特征处理与径向基神经网络的锂电池剩余容量估算方法［J］.储能科学与技术，2021，10（1）：262.）
Z Chen，L L Li，X Shu，S Q Shen，Y G Liu，J W Shen. Efficient remaining capacity estimation method for LIB based on feature processing and the RBF neural network［J］.Energy Storage Science and Technology，2021，10（1）：262.
［16］Yang Y，Okonkwo E G，Huang G Y，Xu S M，Sun W，He Y H. On the sustainability of lithium ion battery industry-a review and perspective［J］.Energy Storage Materials，2021，36：186.
Basic Information:
DOI：10.13373/j.cnki.cjrm.XY23070015
Chinese Library Classification Number:TM911
Citation Information:
With the peak of a large number of scrap power batteries approaching，it becomes increasingly important to efficiently recycle and dispose of them. Currently，there are two ways to recycle power batteries：direct recycling and stepwise utilization before recycling. In fact，retired power batteries still retain 70%~80% of their available capacity，which can be used in applications such as electric bicycles，low-speed electric vehicles，smart grids，and energy storage. On one hand，stepwise utilization helps extend the overall lifespan of lithium-ion batteries. On the other hand，it also reflects the complete lifecycle value of the batteries. However，there are significant technical limitations in the stepwise utilization of discarded batteries. Due to the constraints of battery production processes，even within the same batch of batteries，there can be various issues and challenges from the same manufacturer. To obtain the higher voltage and capacity required for practical use，hundreds or even thousands of individual batteries may need to be connected in series and parallel to form a battery pack. Over time and in complex usage environments，the inconsistencies between individual batteries within the battery pack will be amplified. Therefore，in order to facilitate the stepwise utilization of discarded batteries，it is necessary to develop a low-energy，high-precision，and fast capacity prediction method to lay the foundation for the separation and recombination of discarded batteries. To address the issues of long testing time and high energy consumption in capacity testing of retired lithium batteries，this study proposed a retired battery capacity prediction method based on RBF （radial basis function） neural networks. First，the batteries were adequately stored. Then，three complete charge-discharge tests were performed on the batteries at 1C to obtain the discharge capacity of the batteries. Based on the results of the three discharge capacity tests，the average value was calculated to determine the remaining capacity of the retired batteries. Afterward，the batteries were subjected to 10 s of pulse discharge and pulse charge at 1C. The charge and discharge ohmic resistance as well as the charge and discharge polarization resistance of the retired batteries were calculated based on the results of the pulse testing data. Additionally，the batteries were charged at a constant current to 3.5 V under 1C conditions，and short-term constant current charging data was obtained. From this data，characteristic parameters such as the charging capacity to 3.5 V and charging time were extracted. Pearson correlation coefficient method was used to calculate the relationship between these characteristic parameters and retired battery capacity in the range of –0.8~–0.6 and 0.6~0.8. The results indicated a strong correlation between the feature parameters and the actual capacity of retired batteries. The feature parameter with the highest correlation was the polarization resistance obtained through pulse discharge. During the degradation process of retired batteries，the internal structure of the battery's active material had been damaged，affecting the migration and diffusion of lithium ions between the active materials in the electrochemical reaction process. This led to the occurrence of different forms and intensities of polarization within the battery，resulting in different internal polarization resistances. Therefore，the polarization resistance obtained through pulse testing could，to some extent，reflect the degree of deterioration of the internal structure of the battery. Finally，RBF neural network was introduced to establish the mapping relationship between multiple feature parameters and battery capacity，establishing a prediction model for the capacity of retired batteries. In the process of establishing the capacity prediction model，the proportion of training and test data could affect the prediction results of the model. In order to evaluate the effectiveness and robustness of the established capacity prediction model，50%，60%，70%，80%，and 90% of each data set were used as the training set （input to RBF neural network），and the remaining data were used as the test set （output of the model） to establish the capacity prediction model. The maximum relative error and prediction accuracy were used to analyze the effectiveness of the prediction part of the model. The results were analyzed based on different training and test ratios. Using 50%，60%，70%，80%，and 90% of the data from 93 sets for training the model，the rest were used for testing the model. It could be seen that the capacity prediction model built based on RBF neural network achieved a prediction accuracy of over 90% under different data training ratios. According to the results of the verification experiments，the retired battery capacity prediction method based on multiple feature parameter combinations and RBF neural networks was effective. Compared with the current direct measurement of retired battery capacity，this new method significantly shortened the charge-discharge process and eliminated long-standing steps. Therefore，it achieved significant time，energy，and cost savings. The model was applied to verify different types of batteries，and the maximum error in predicting capacity was within 0.6443 Ah. The verification showed that the model could efficiently and robustly predict the remaining capacity of retired lithium batteries and had great practical value in engineering.
quote
| GB/T 7714-2015 | [1] Chuanyu Bie, Hongling Liu, Xueqing Wang, et al. Battery Capacity Prediction Based on Pearson Correlation and RBF Neural Network[J]. Chinese Journal of Rare Metals, 2025, 49(7): 1119-1126. DOI:10.13373/j.cnki.cjrm.XY23070015. |
| MLA | [1] Chuanyu Bie, et al., "Battery Capacity Prediction Based on Pearson Correlation and RBF Neural Network." Chinese Journal of Rare Metals, vol. 49, no. 7, 2025, pp. 1119-1126, https://doi.org/10.13373/j.cnki.cjrm.XY23070015. |
| APA | [1] Chuanyu Bie, Hongling Liu, Xueqing Wang, Yuping Zhang, & Biao Gao. (2025). Battery Capacity Prediction Based on Pearson Correlation and RBF Neural Network. Chinese Journal of Rare Metals, 49(7), 1119-1126. https://doi.org/10.13373/j.cnki.cjrm.XY23070015 |
| IEEE | [1] Chuanyu Bie, Hongling Liu, Xueqing Wang, Yuping Zhang, and Biao Gao, "Battery Capacity Prediction Based on Pearson Correlation and RBF Neural Network," Chinese Journal of Rare Metals, vol. 49, no. 7, pp. 1119-1126, 2025, doi: 10.13373/j.cnki.cjrm.XY23070015. keywords: {retired battery;Pearson correlation coefficient method;RBF （radial basis function） neural network;capacity prediction} |