## 4 Results and Discussion  
In this paper, root mean square error (RMSE), mean absolute error (MAE), and maximum error (MAX Error) were used to quantitatively evaluate the performance of the proposed method. Their definitions are as follows:  
\[\text{RMSE}=\sqrt{\frac{1}{n}\sum_{i=1}^{n}(\hat{y}_{i}-y_{i})^{2}} \tag{9}\]  
\[\text{MAE}=\frac{1}{n}\sum_{i=1}^{n}|\hat{y}_{i}-y_{i}| \tag{10}\]  
\[\text{MAX Error}=\max|\hat{y}_{i}-y_{i}| \tag{11}\]  
The number of layers in RNN model was set to three layers--the first two layers were RNN layers, and the last layer was a fully connected layer. The number of neurons in the RNN model was set to 98, 156, and 50. The number of layers in the LSTM model was also set to three layers--the first two layers were LSTM layers, and the last layer was a fully connected layer. The number of neurons in the LSTM model was set to 86, 198, and 80. The parameters of GA-GRU is shown in Table 1. In addition, other parameters of RNN, LSTM, and GA-GRU were the same. For example, Adam was used as optimizer. The learning rate was equal to 0.0001. The epochs were set to 50. The batch size was set to 128. Mean square error (MSE) was used as a loss function. In order to make an assessment of the superiority of the proposed method, we compared the SOC estimation results of RNN, LSTM, and GA-GRU under different dynamic test conditions and different temperatures, namely, DST at 0 \({}^{\circ}\)C, FUDS at 10 \({}^{\circ}\)C, BJDST at 20 \({}^{\circ}\)C, DST at 30 \({}^{\circ}\)C, and US06 at 30 \({}^{\circ}\)C. The comparison results are shown in subfigure (a) of Figures 6-10. Their SOC errors are compared in subfigure (b) of Figures 6-10. The RMSE, MAE, and MAX error of RNN, LSTM, and GA-GRU are presented in Table 3.  
Figure 6: SOC estimation results and errors under DST at 0 \({}^{\circ}\)C. **(a)** Comparison of SOC estimation results under DST at 0 \({}^{\circ}\)C; **(b)** comparison of SOC estimation errors under DST at 0 \({}^{\circ}\)C.  
Figure 8: SOC estimation results and errors under BJDST at 20 \({}^{\circ}\)C. (**a**) Comparison of SOC estimation results under BJDST at 20 \({}^{\circ}\)C; (**b**) comparison of SOC estimation errors under BJDST at 20 \({}^{\circ}\)C.  
Figure 7: SOC estimation results and errors under FUDS at 10 \({}^{\circ}\)C. (**a**) Comparison of SOC estimation results under FUDS at 10 \({}^{\circ}\)C; (**b**) comparison of SOC estimation errors under FUDS at 10 \({}^{\circ}\)C.  
Figure 9: SOC estimation results and errors under DST at 30 \({}^{\circ}\)C. (**a**) Comparison of SOC estimation results under DST at 30 \({}^{\circ}\)C; (**b**) comparison of SOC estimation errors under DST at 30 \({}^{\circ}\)C.  
From the subfigure (a) of Figures 6-10, we see that these three prediction curves all were able to follow the real SOC curve. However, the green curve was the closest to the real one, which means that the GA-GRU model achieved the best prediction performance compared to the other two methods. Similarly, the same result can be concluded from subfigure (b) of Figures 6-10. For example, it can be found from the partial enlarged view of subfigure (a) in Figure 6 that the curve of GA-GRU and the curve of actual value were almost coincident, which means GA-GRU is able to estimate SOC well. However, the curves of LSTM and RNN were farther from the curve of actual value than the curve of GA-GRU. From subfigure (b) in Figure 6, we see that the SOC error values of GA-GRU were less than 1% and near to zero, and the SOC error values of LSTM and RNN were less than 10%. Therefore, compared with LSTM and RNN, GA-GRU performed better. As shown in Table 3, the statistical estimation results based on RMSE, MAE, and MAX error were calculated. Due to the similarity of the results of the five test cases, we used the SOC estimation result under DST at 30 \({}^{\circ}\)C as an example for discussion and analysis. The RMSE, MAE, and MAX error of the GA-GRU model under DST at 30 \({}^{\circ}\)C were 0.2017%, 0.2383%, and 1.3366%, respectively.