## 4 Simulation
### Comparison of Model Performances Using the Battery Dataset  
To compare the LIB SOH estimation performances of the LSTM neural network model using the DWT, as expressed in Table 4, the estimation accuracy was determined for each data point using the Equation below. Figure 9 shows the actual SOH values and SOH estimation graphs obtained using the neural network models. In Equations (22)-(25), n denotes the number of test data points. Here, RMSE represents the robustness of the estimation, MAE accuracy refers to the estimation accuracy of SOH, and MAX is the maximum error value. The SOH estimation accuracy using Normalization and LSTM for the voltage and temperature were 94.85% and 93.49%, respectively. The SOH estimation accuracy using CWT and CNN for the voltage and temperature were 96.82% and 94.68%, respectively. The SOH estimation accuracy using DWT and LSTM for the voltage and temperature were 98.92% and 96.45%, respectively. All three models exhibited excellent performance when using the voltage data. \[\text{Accuracy}(\%)=100-\text{RMSE}\times 100 \tag{22}\]  
\[\text{RMSE}(\%)=\sqrt{\frac{\sum_{i=1}^{n}(y_{i}-\hat{y}_{i})}{n}}\times 100 \tag{23}\]  
\[\text{MAE}(\%)=\frac{1}{n}\sum_{i=1}^{n}\lvert y_{i}-\hat{y}_{i}\rvert\ \times 100 \tag{24}\] \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Datasets** & **Method** & **Accuracy (\%)** & **RMS (\%)** & **MAE (\%)** & **MAX (\%)** \\ \hline \multirow{3}{*}{Temperature} & Normalization + LSTM & 93.49 & 6.51 & 4.13 & 17.39 \\  & CWT + CNN & 94.38 & 5.61 & 4.11 & 20.22 \\  & DWT + LSTM & 96.45 & 3.55 & 3.36 & 6.03 \\ \hline \multirow{3}{*}{Voltage} & Normalization + LSTM & 94.85 & 5.15 & 4.58 & 7.84 \\  & CWT + CNN & 97.71 & 2.29 & 1.80 & 4.98 \\ \cline{1-1}  & DWT + LSTM & 98.92 & 1.07 & 0.91 & 2.57 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of battery SOH estimation performance. Figure 8: Schematic diagram of the simulation system. (25)  
Figure 9: SOH estimation results: (**a,b**) are normalization + LSTM, (**c,d**) are CWT + CNN and (**e,f**) are DWT + LSTM. All three models exhibited excellent performance when using the voltage data. This is due to the time-dependent nature of the voltage and temperature data associated with the charging and discharging of lithium-ion batteries. In lithium-ion batteries, the internal resistance increases as the number of repetitions of charging and discharging increases. The continuity of the voltage curve that occurs at this time is superior to that of the temperature curve as shown in Figure 3. In particular, as the charge and discharge time elapses, the temperature curve becomes irregular and the continuity decreases. The learning algorithm applied in this study was able to solve the nonlinearity of the data to some extent. However, it was confirmed that the SOH estimation accuracy was relatively low because the temperature characteristic curve was very discontinuous. Instead, we found that the SOH accuracy was excellent for the same algorithm because the voltage curve had better continuity than the temperature curve. When comparing the performance of the model using wavelet and Normalization, it can be seen that the accuracy of the wavelet is high. This confirms that the proposed algorithm is advantageous for nonlinear battery data learning. The performance was verified by comparing the relative errors of the three models. A boxplot was then used to compare the performances of the three models to evaluate the variance of the relative error. The mathematical equation of the relative error is the same as in Equation (26). \[\text{RE}(\%)=\frac{|\hat{y}-y|}{y}\times 100 \tag{26}\]  
Here, \(\hat{y}\) and \(y\) are the estimated and actual SOH values, respectively. The boxplot mainly focused on the maximum, minimum, median, third quartile, and first quartile. In Table 5, IQR is the difference between the third quartile and the first quartile.