# Lithium-Ion Battery Capacity Prediction with GA-Optimized CNN, RNN, and BP
## 4 Results and Discussion
The prediction results obtained by averaging five iterations for 40, 70, and 100 training data are presented in Tables 7 and 8. Based on these results, the GA-CNN model exhibited the best performance overall. The best prediction results for all training data across all batteries are summarized in Table 9. The table lists the algorithms that achieved the best performance based on RMSE values. Except for the 70 training data of the B0006 battery, the algorithms that performed well in terms of RMSE also demonstrated high performance in other evaluation metrics. For this particular training dataset, the GA-RNN algorithm was selected because it delivered good results in three out of five parameters, primarily focusing on RMSE. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Train Num.** & **Algorithm** & **MSE (\%)** & **RMSE (\%)** & **NRMSE (\%)** & **MAE (\%)** & **R\({}^{2}\)** \\ \hline \multirow{3}{*}{**40**} & GA-CNN & **0.1562** & **3.9527** & **5.9004** & **3.3071** & **0.9505** \\  & GA-BP & 3.5468 & 18.8328 & 28.1128 & 16.9141 & 0.8425 \\  & GA-RNN & 8.9822 & 29.9703 & 44.7385 & 26.9203 & 0.6633 \\ \hline \multirow{3}{*}{**70**} & GA-CNN & 0.8756 & 9.3572 & 21.2776 & 8.5259 & **0.8548** \\  & GA-BP & 0.5710 & 7.5563 & 17.1824 & **5.3343** & 0.8038 \\  & GA-RNN & **0.4670** & **6.8336** & **15.5391** & 5.3855 & 0.7026 \\ \hline \multirow{3}{*}{**100**} & GA-CNN & **0.2006** & **4.4784** & **15.0062** & **3.8496** & **0.7991** \\  & GA-BP & 1.7621 & 13.2744 & 44.4795 & 11.3466 & 0.4473 \\ \cline{1-1}  & GA-RNN & 2.1116 & 14.5315 & 48.6919 & 13.3263 & 0.4031 \\ \hline \end{tabular}  
* The best results are indicated in **bold**.  
\end{table} 
Table 6: Battery B0006 performance parameters. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Train Num.** & **Algorithm** & **MSE (\%)** & **RMSE (\%)** & **NRMSE (\%)** & **MAE (\%)** & **R\({}^{2}\)** \\ \hline \multirow{3}{*}{**40**} & GA-CNN & **0.2766** & **5.2588** & **10.3894** & **4.6970** & **0.9999** \\  & GA-BP & 8.0148 & 28.3105 & 55.9306 & 24.6709 & 0.6640 \\  & GA-RNN & 7.0370 & 26.5274 & 52.4080 & 22.6094 & 0.3318 \\ \hline \multirow{3}{*}{**70**} & GA-CNN & **0.0008** & **0.2794** & **0.8348** & **0.2576** & **0.9999** \\  & GA-BP & 0.0234 & 1.5281 & 4.5659 & 1.0706 & 0.9885 \\  & GA-RNN & 1.2446 & 11.1560 & 34.4457 & 8.7653 & 0.6568 \\ \hline \multirow{3}{*}{**100**} & GA-CNN & **0.0001** & **0.1176** & **0.5635** & **0.0951** & **0.9996** \\  & GA-BP & 0.0027 & 0.5212 & 2.4981 & 0.4355 & 0.9997 \\ \cline{1-1}  & GA-RNN & 0.1750 & 4.1839 & 20.0532 & 3.3743 & 0.8629 \\ \hline \end{tabular}  
* The best results are indicated in **bold**.  
\end{table} 
Table 5: Battery B0005 performance parameters. The charts of the prediction outcomes provided in the tables for all batteries for each of the training types and for every model are displayed in Figure 11. Additionally, the percentage point errors of the best prediction algorithms are shown in Figure 12. These algorithms are given in Table 9 with their training numbers. Here, the training data are displayed with zero error. As can be seen from the graphs, percentage errors start with the test data. Table 10 summarize the RMSE and R\({}^{2}\) values from various studies on battery life prediction types such as capacity, SOH, and RUL. The data in this table include results obtained from studies conducted on NASA data. The methods used to improve the prediction accuracy are also indicated in the studies. As shown in the table, the performance of the proposed method is generally superior in all results except for the prediction using