# State of Health Estimation for Lithium-Ion Batteries Based on TCN-RVM
## 4 Conclusions  
This paper first shows that lithium-ion batteries inevitably undergo complex electrochemical aging during their service. Accurately estimating the SOH of lithium-ion batteries has become an important issue in battery development. Therefore, this paper proposes an SOH estimation method for lithium-ion batteries based on incremental capacity curves and TCN-RVM. The main work is as follows:  
(1) First, by analyzing the battery charging experimental curves and IC curves, five types of health factors from the IC curves were extracted as input variables for the prediction model, including the peak value, peak position, left and right area of the peak, and total area. Their mutual information values are all above 3.9, indicating a good nonlinear dependence. Subsequently, the Pearson and Spearman correlation coefficient methods were used to quantitatively analyze the correlation between these health factors and battery SOH. The results show that the absolute values of the correlation coefficients between the two are all close to one, indicating that the selected health factors have strong correlations with SOH and are reasonable as input features. (2) Leveraging TCN's advantage in efficiently capturing multi-scale dependencies in long sequences and RVM's ability to integrate physical insights, a TCN-RVM model is constructed. The Adam optimization algorithm is used for model training. The proposed method is evaluated using the University of Maryland's lithium-ion battery dataset, where battery CS2_35 is used as the training set and the remaining batteries are used for testing. Comparative experiments with the CNN-GRU, KELM, and SVM models show that the proposed TCN-RVM model achieves maximum RMSE and MAE values of only 0.72% and 0.51%, respectively, significantly outperforming the baseline models. (3) To assess the model's transferability, cross-sample prediction experiments are conducted using different battery data as training sets and the remaining batteries as test sets. The results indicate that the increases in RMSE and MAE after changing the training samples are minimal, demonstrating the proposed method's strong generalization ability and stability across different battery samples. In conclusion, the proposed SOH estimation method based on the combination of incremental capacity curves and the TCN-RVM model exhibits excellent performance in terms of prediction accuracy, model robustness, and transfer capability. However, the TCN-RVM method proposed in this paper still has some limitations. The embedding of the battery mechanism is insufficient, as it relies on data-driven approaches and lacks electrochemical mechanistic constraints, which requires further research. Another issue that needs to be focused on is that the proposed method adopts a static temperature assumption but fails to conduct in-depth verification of the applicability of this quasi-static assumption under different temperature conditions. Meanwhile, the influence of thermal effects has not been taken into account in the feature extraction process. Nevertheless, the temperature factor is crucial for the application of this method in scenarios with drastic changes in ambient temperature, only by fully considering the influence of temperature can the effectiveness of the method in such scenarios be ensured. It should also be noted that accelerated aging experiments may introduce potential biases in model generalization, as the aging mechanisms and characteristics under accelerated conditions might not fully align with those of naturally aged batteries without direct comparative validation, which could thus exert adverse effects on the generalization ability of the model. These limitations motivate us to further optimize the proposed method. In future research, we will investigate the applicability of this method to batteries cycled under constant power-constant voltage (CP-CV) charging protocols and more dynamic operating protocols.