## 4 Simulation
### Comparison of Model Performances Using the Battery Dataset
The relative errors of different SOHs are compared in Figure 10 and the data are described in Table 6.  
The estimation accuracies of the SOH were compared in the case of using temperature data. When comparing the LSTM with normalization, the variance of the relative error of the LSTM was narrow and maximum value small. In addition, it was confirmed that there were no outliers in the relative error for the LSTM; however, outliers occurred when using normalization. Although the estimation accuracy of the CNN, comparing CNN and normalization, was high, the variance of the error was wide and the maximum value relatively large. Outliers existed in both models. When comparing the LSTM and CNN, it was confirmed that the variance of the relative error of the LSTM was narrow and maximum value smaller. The LSTM did not have outliers, but CNN had outliers. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Methods** & **Datasets** & **Maximum** & **Third Quartile** & **Median** & **First Quartile** & **Maximum** & **Outlier** \\ \hline Normalization & Voltage & 0.1546 & 0.1153 & 0.0800 & 0.0394 & 0.0002 & 0\% \\ + LSTM & Temperature & 0.1120 & 0.0527 & 0.0267 & 0.0074 & 0.0007 & 1.08\% \\ \hline \multirow{2}{*}{CWT + CNN} & Voltage & 0.2300 & 0.0495 & 0.0261 & 0.012 & 0.0004 & 5.37\% \\  & Temperature & 0.4237 & 0.0879 & 0.0436 & 0.0191 & 0.0001 & 6.45\% \\ \hline \multirow{2}{*}{DWT + STM} & Voltage & 0.0262 & 0.0212 & 0.0142 & 0.0071 & 0.0000 & 0\% \\  & Temperature & 0.0849 & 0.0698 & 0.0849 & 0.0349 & 0.0019 & 0\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Relative error of different methods. \begin{table}
\begin{tabular}{l l} \hline \hline
**Indicator** & **Definitions** \\ \hline Maximum & The smallest data larger than median \(1.5*\) IQR (Interquartile range) \\ Third quartile & The middle value between the median and the highest value of the dataset \\ Median & The middle value of the dataset \\ First quartile & The middle value between the median and the highest value of the dataset \\ Minimum & The highest value larger than median \(-1.5*\) IQR \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Relative error of different methods. For the voltage data case, the estimation accuracies of the SOH were compared. When comparing the LSTM with normalization, the variance of the relative error of the LSTM was narrow and the maximum value small. In both models, there were no outliers in the relative error. When the CNN and normalization are compared, the variance of the relative error of CNN was narrow and the maximum value small. However, there was an outlier for CNN, but not for normalization. Finally, when comparing LSTM and CNN, it can be seen that the variance and maximum value of the relative error of the LSTM were small, and there were no outliers. One reason for this difference between the two models was possibly the difference in learning. The CNN model did not consider the historical values based on time because it learned the entire image information, which was not related to a specific time. In contrast, the LSTM model was trained while considering the historical values based on time. Therefore, in terms of the SOH estimation accuracy of the LIB, the LSTM training method was more appropriate and fully reflects changes in the characteristic values (voltage and temperature) of the lithium ions caused by charging and discharging over time.