## 4 Analysis Results
### Capacity Degradation Trend Prediction  
Two experiments were carried out in this study. In the first experiment, seven cells were conducted. For each cell, 70% of the data was used for training, and the remaining 30% of the data was used to test the model. Table 2 shows the best parameters of the LSTM with attention and proposed models, such as lookback, batch size, neuro, steps per epoch, and epochs.  
The MAPE and root mean square error (RMSE) were selected as measure criteria for the test data, where RMSE is obtained by  
\[\text{RMSE}=\sqrt{\frac{1}{n}\sum_{t=1}^{n}\left(C_{t}-\hat{C}_{t}\right)^{2}} \tag{6}\]  
Table 3 shows the capacity degradation predictions of different models. The results indicate that the proposed model outperforms the other two single models and the conventional ensemble learning model. For example, on cell #2_5, the RMSE values of the GBR, LSTM with attention, conventional ensemble learning, and proposed models are 0.0290, 0.0121, 0.0198, and 0.0047, respectively. LSTM  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Models** & **Cells** & **Lookback** & **Batch Size** & **Neuro** & **Steps per Epoch** & **Epochs** \\ \hline \multirow{8}{*}{LSTM with attention} & 2\_5 & 8 & 21 & 15 & 45 & 59 \\  & 2\_6 & 8 & 27 & 38 & 20 & 41 \\  & 2\_11 & 9 & 23 & 26 & 58 & 65 \\  & 2\_12 & 7 & 23 & 20 & 58 & 55 \\  & 2\_14 & 9 & 26 & 20 & 54 & 41 \\  & 2\_18 & 9 & 23 & 16 & 57 & 32  
The MC dropout method is used for variance estimation to construct a prediction interval. The proposed model was run 100 times with random dropout, which will produce different output values. We can calculate the mean and variance of the prediction results from these different output values, and then use the conventional formula to construct the prediction interval. Figure 5 shows the prediction interval of the proposed model on 2_11 and 2_12 cells at a 95% confidence level, where LB is the lower boundary, and UB is the upper boundary. The narrow width of the interval indicates that the prediction result is more reliable and credible. The prediction uncertainty increases when the prediction point is far from the starting cycle of test data.  
In the second experiment, one or two cells were used as training data, and other cells were used as test data to verify the proposed model. The training data can be one cell or two cells. Table 5 lists the performances of different models. The average MAPE values of GBR, LSTM with attention, and the proposed model are 1.2734, 0.9029, and 0.7294. The results show that the proposed model performs better than the GBR model and the LSTM with the attention model in all cases. For the test data such as cells #3 and #2_27, two training cells can provide better predictive performance than one training cell. Figure 6 shows the prediction performance of the proposed model using one cell or two cells as training data for cell #2_27. This shows that the proposed model can accurately predict the degradation trend of lithium-ion battery capacity.  
Figure 4: Prediction performance of different models on cell #2_12: (**a**) prediction performance and (**b**) absolute error.  
Figure 5: Proposed model prediction intervals: (**a**) cell #2_11 cell and (**b**) cell #2_12.