## 6 System Evaluation and Model Prediction Performance
### Models Prediction Performance  
Table 2 presents the performance results of five distinct models trained on the FELL platform to forecast the SoH of electric vehicle batteries over the subsequent 7 days. Among these models, the LSTM model achieved the lowest MSE of 0.73, indicating superior predictive accuracy compared to the others. Correspondingly, LSTM demonstrated the  
Figure 11: Distribution plots of SoH estimated using the EKF. (**a**) SoH distribution plot estimated using EKF. (**b**) SoH KDE plot estimated using EKF. Figure 10: Predicting the state of health over time: EKF estimation of BMW i3 Electric Vehicle’s 60 Ah Lithium Battery. lowest RMSE of 0.85, emphasizing its superior ability to capture the variability of SoH values. Furthermore, LSTM yielded the lowest MAE of 0.74, highlighting its effectiveness in minimizing prediction errors. In terms of percentage-based metrics, LSTM attained the lowest MAPE of 1.02% and the lowest SMAPE of 1.01%, further accentuating its superior performance in accurately predicting SoH values. Conversely, the MLP model exhibited the highest values for MSE, RMSE, MAE, MAPE, and SMAPE among the models, indicating relatively poorer predictive performance. Overall, the LSTM model emerges as the most effective in forecasting the SoH of electric vehicle batteries over the next 7 days, closely followed by the GRU and multi-head attention transformer models, while the MLP and CNN models demonstrate lower predictive accuracy. Table 3 depicts the performance results of five models trained on the FELL platform to predict the SoH of electric vehicle batteries over the next 120 days. Among these models, the LSTM architecture achieved the lowest MSE of 2.91, signifying its superior predictive accuracy compared to the other models. Furthermore, LSTM demonstrated the lowest RMSE of 1.70, indicating its capability in effectively capturing the variability of SoH values throughout the 120-day forecast period. Additionally, LSTM yielded the lowest MAE of 1.50, emphasizing its proficiency in minimizing prediction errors. In terms of percentage-based metrics, LSTM also attained the lowest MAPE of 2.29% and the lowest SMAPE of 2.26%, further illustrating its superior performance in accurately predicting SoH values over the extended forecast period. Conversely, the MLP model exhibited the highest MSE, RMSE, MAE, MAPE, and SMAPE values among the models, indicating its relatively poorer predictive performance. Overall, the LSTM model emerges as the most effective in forecasting the SoH of electric vehicle batteries over the subsequent 120 days, closely followed by the GRU model, while the MLP, CNN, and Multi-head Attention Transformer models display lower predictive accuracy. The structure of the model predicting electric vehicle battery SoH over the next 120 days is outlined as follows: the MLP model consists of an input layer with 128 neurons, followed by two hidden layers with 64 and 32 neurons, and an output layer with 120 neurons, resulting in a total of 15,064 trainable parameters. The LSTM model comprises an LSTM layer with 128 units, followed by two LSTM layers with 64 and 32 units, and a fully connected dense layer with 16 units, resulting in a total of 130,952 trainable parameters. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Models**} & \multicolumn{5}{c}{**Forecast Steps = 7 Days**} \\ \cline{2-6}  & **MSE** & **RMSE** & **MAE** & **MAPE** & **SMAPE** \\ \hline MLP & 15.21 & 3.90 & 3.17 & 3.99 & 4.09 \\ CNN & 18.75 & 4.33 & 3.70 & 5.50 & 5.40 \\ LSTM & 0.73 & 0.85 & 0.74 & 1.02 & 1.01 \\ GRU & 4.79 & 2.19 & 1.96 & 2.71 & 2.66 \\ Multi-head Attention Transformer & 5.05 & 2.25 & 1.91 & 2.87 & 2.84 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Prediction performance results of five distinct models trained on the FELL platform to forecast the SoH of electric vehicle batteries over the subsequent 7 days.