# State of Health Estimation for Lithium-Ion Batteries Based on TCN-RVM
## 3 Results and Discussion
### Comparison of Predictions by Different Models  
To verify the advantages of the proposed model in this paper, the CS2_35 battery was used as the training set, and the remaining batteries as the test sets to compare the performance of different models. The processed battery data were input into the CNN-GRU model, KELM model, and SVM model, which served as comparative models. Since TCN and CNN require a time delay step, the step size in this paper is set to two, thus necessitating a two-step-ahead prediction. This leads to the loss of data from the first and second cycles in the test set. Therefore, when comparing the prediction results of the models, the test set results of machine learning algorithms such as KELM and SVM also need to discard the first two cycles for comparison purposes.  
As can be seen in Figure 10, in the early stage of the test cycles, all four models exhibit a good capability in tracking the SOH degradation trajectory. Although the TCN-RVM model shows a slightly higher estimation accuracy, the difference is not significant. However, in the later stage of prediction, the estimation results of the CNN-GRU, KELM, and SVM models deviate increasingly from the actual values. This is because KELM and SVM produce obvious oscillation errors due to the capacity regeneration phenomenon, and their kernel functions can only fit local segments, failing to model the long-range decay trend, which in turn leads to the increase in errors in the later stage. The decrease in the estimation accuracy of the CNN-GRU model is due to the memory decay problem of GRU units; as the number of cycles increases, the loss rate of historical information rises significantly, eventually resulting in larger errors in the later stage.  
In contrast, the TCN-RVM model also demonstrates excellent performance in the later stage of prediction, with its prediction curve showing a high degree of consistency with the actual curve. This is because the model has a strong multi-source feature fusion capability: it automatically extracts dynamic temporal features of charge-discharge curves through TCN and fuses mechanistic features using RVM, realizing the complementarity of multimodal information and thereby effectively improving the prediction performance.  
The quantitative evaluation of the SOH estimation results using the four models is presented in Table 6. When applying the SVM model to estimate the SOH of batteries CS2_36, CS2_37, and CS2_38, the maximum RMSE and MAE reached 1.37% and 0.93%, respectively. For the KELM model, the maximum RMSE and MAE were 1.28% and 1.00%, respectively. For the CNN-GRU model, the maximum RMSE and MAE were 1.35% and 0.99%, respectively. All of these values are higher than those of the proposed TCN-RVM model, which achieved a maximum RMSE of 0.72% and MAE of 0.51%. The experimental results demonstrate that the proposed model outperforms other mainstream models in terms of prediction accuracy.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Battery** & \multicolumn{2}{c}{**TCN-RVM**} & \multicolumn{2}{c}{**CNN-GRU**} & \multicolumn{2}{c}{**KELM**} & \multicolumn{2}{c}{**SVM**} \\ \cline{2-9}
**Model** & **MAE** & **RMSE** & **MAE** & **RMSE** & **MAE** & **RMSE** & **MAE** & **RMSE** \\ \hline CS2\_36 & 0.0045 & 0.0058 & 0.0099 & 0.0115 & 0.0071 & 0.0121 & 0.0093 & 0.0131 \\ CS2\_37 & 0.0051 & 0.0070 & 0.0072 & 0.0090 & 0.0059 & 0.0084 & 0.0065 & 0.0086 \\ CS2\_38 & 0.0050 & 0.0072 & 0.0091 & 0.0135