## 4 Experimental Results and Discussion
### Results of the Estimation Obtained for Constant Current and Variable Current with Aging Effect  
Figures 23-25 demonstrate that the effect of battery aging could affect the quality of the electrical and thermal data provided to the GRU, LSTM, and DNN neural networks, which might result in a decrease in their performance. The effect of battery aging can cause a decrease in the capacity of the battery, therefore reducing its life. This may impact the performance of neural networks, as these models are very sensitive to voltage and current \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Error** &
\begin{tabular}{c} **Error Calculation** \\ **Methods** \\ \end{tabular} & **SOC Profile** & **References** \\ \hline RF & 2.63\% & MAE & Discharge & [54] \\ EKF & 1.31\% & MAE & Discharge & [46] \\ DOB & 0.72\% & MAE & Discharge & [46] \\ SVR & 5.19\% & MAE & Discharge & [54] \\ SimpleRNN & 1.30\% & MAE & Discharge & [54] \\ GRU-RNN & 2.53\% & MAE & Discharge & [63] \\ RNN & 2.50\% & MAE & Discharge & [63] \\ DAE-GRU & 1.59\% & MAE & Discharge & [63] \\ DNN proposed & 0.19\% & MAE & Discharge & - \\ GRU proposed & 1.04\% & MAE & Discharge & - \\ LSTM proposed & 1.19\% & MAE & Discharge & - \\ AUTOENCOD-LSTM & 0.93\% & MAE & Discharge & [89] \\ LSTM-AHIF & 1.18\% & MAE & Discharge & [90] \\ LSTM & 2.36\% & MAE & Discharge & [90] \\ TBCC-AEKF & 2.51\% & MAE & Discharge & [91] \\ TBCC-APF & 1.36\% & MAE & Discharge & [91] \\ APF & 4.62\% & MAE & Discharge & [91] \\ ACK-QR-Hoo & 2.42\% & MAE & Discharge & [92] \\ AEKF & 7.26\% & MAE & Discharge & [91] \\ UKF & 1.05\% & MAE & Discharge & [38] \\ AEKF & 5.80\% & MAE & Charge/discharge & [93] \\ SVM & 16.10\% & MAE & Charge/discharge & [93] \\ LSTM-TL & 3.80\% & MAE & Charge/discharge & [93] \\ DNN proposed & 0.34\% & MAE & Charge/discharge & - \\ GRU proposed & 0.86\% & MAE & Charge/discharge & - \\ LSTM proposed & 1.08\% & MAE & Charge/discharge & - \\ ANN & 3.80\% & MAE & Charge/discharge & [94] \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Performance of different SoC methods. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **GRU** & **LSTM** \\ \hline Number of layers & 2 & 2 \\ \hline Layer size & 64, 32 & 64, 32 \\ \hline Dropout & 0.2 & 0.2 \\ \hline Batch size & 64 & 64 \\ \hline Epochs & 300 & 300 \\ \hline Learning rate & 0.001 & 0.001 \\ \hline Optimizer & Adam & Adam \\ \hline Loss function & MSE & MSE \\ \hline Number of parameters & 22,689 & 29,857 \\ \hline Reason for difference & GRU has two gates (reset and update). &
\begin{tabular}{c} LSTM has a more complex structure \\ with forget, input, and output gates. \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Description of parameters for gated recurrent unit (GRU) and long short-term memory (LSTM) models. variations, which may introduce computational errors. A decrease in performance can result, as the models can no longer produce accurate predictions or satisfactory results. In addition, the effect of aging can also affect the stability of electronic components, which can lead to failures and computational errors. Neural networks need a stable and reliable power supply to function properly, and the effect of aging can reduce this stability, resulting in decreased performance. Figure 23: Estimation of the SoC obtained at constant current with the aging effect. Figure 24: _Cont._  
The DNN model excels due to its ability to capture complex nonlinear relationships between input variables (current, voltage, temperature, aging effect) and output (SoC). The depth of the DNN enables it to extract relevant features at multiple levels of abstraction, improving the accuracy of SoC predictions. The DNN was trained with a diverse dataset covering different aging and temperature conditions, enabling the model to generalize efficiently. To avoid overlearning and improve model robustness, regularization techniques such as dropout were also used. The GRU is designed to model temporal sequences by capturing long-term dependencies in the data.