# State of Health Estimation for Lithium-Ion Batteries Based on TCN-RVM
## 3 Results and Discussion
### Robustness Analysis  
Robustness is one of the core indicators for evaluating the reliability and adaptability of battery systems. To further verify the robustness of the TCN-RVM model, this study adopts a cross-validation analysis method, using CS2-36, CS2-37, and CS2-38 as training  
Figure 11: Prediction results for confidence intervals with CS2_35 as the training set. sets while using the remaining battery types as test sets to evaluate the estimation capability of the model. The prediction results obtained are shown in a table. As shown in Table 7, when CS2-36 is used as the training set, the model yields better prediction performance on the test set, with the maximum MAE and RMSE reaching 0.65% and 1.13%, respectively. The largest prediction error occurs when CS2-38 is used as the training set, with the maximum MAE and RMSE reaching 0.72% and 1.47%, respectively. This discrepancy may be attributed to the distribution differences among the data from different battery types. These differences may lead to incomplete coverage during model training, thereby limiting the generalization ability and resulting in larger prediction errors. In this cross-validation experiment, regardless of which battery type is used as the training set, the resulting RMSE and MAE do not exceed 1.5% and 0.75%, respectively. In summary, the proposed model demonstrates good robustness. To further comprehensively evaluate the generalization ability and robustness of the model from different aspects, in addition to the aforementioned cross-experiments based on different battery combinations, this paper also introduces a five-fold cross-validation strategy to analyze the prediction stability of the model within a single battery dataset. The specific method is as follows: each group of battery data is divided into five equal parts according to the time series; in turn, four folds are used as the training set, and the remaining one fold as the test set; after repeating this process five times, the average error indicators are calculated to more comprehensively evaluate the consistency of the model's performance under different data subset divisions. This validation method can effectively test the adaptability and robustness of the model to different sample divisions, and the validation results are shown in Table 8.  
As can be seen from the data in Table 8, the TCN-RVM model shows overall stable performance in the five-fold cross-validation. The average prediction errors of all batteries are relatively low, with the maximum MAE being 0.0075 and the maximum RMSE being 0.0096, both of which are below 1%. This indicates that the model still maintains good prediction accuracy and robustness under changes in sample divisions. In terms of the specific performance of each battery, CS2_38 achieves the optimal average error indicators in the five rounds of cross-validation, with MAE and RMSE being 0.0051 and 0.0069, respectively, showing that the model has a strong fitting ability for the data of this battery and the prediction results are more consistent. In contrast, the error of CS2_37 is slightly higher but still fluctuates within a small range, with an MAE of 0.0075 and RMSE of 0.0096, \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Battery** & \multicolumn{2}{c}{**CS2\_36**} & \multicolumn{2}{c}{**CS2\_37**} & \multicolumn{2}{c}{**CS2\_38**} \\ \cline{2-7}
**Model** & **MAE** & **RMSE** & **MAE** & **RMSE** & **MAE** & **RMSE** \\ \hline CS2\_35 & 0.0065 & 0.0113 & 0.0065 & 0.0133 & 0.0072 & 0.0147 \\ CS2\_36 & \(\backslash\) & \(\backslash\) & 0.0058 & 0.0074 & 0.0071 & 0.0088 \\ CS2\_37 & 0.0050 & 0.0066 & \(\backslash\) & \(\backslash\) & 0.0047 & 0.0062 \\ CS2\_38 & 0.0052 & 0.0071 & 0.0062 & 0.0086 & \(\backslash\) & \(\backslash\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Quantitative assessment of the SOH estimation results via cross-validation.