## 4 Experimental Results and Discussion
### Results of the Estimation Obtained at Variable Current without Aging Effect  
An accurate and efficient comparison of the experimentally measured SoC of a lithium-ion 18650 cell from the NASA PCOE research center and the simulated SoC of a _LiCoO\({}_{2}\)_ battery (see reference [43]) was performed. The results indicated a perfect correspondence between both strategies. These two strategies should be subjected to the same current profile and tested under the same conditions. In addition, the performance of the proposed neural network was tested with both types of data mentioned above and with the same current profile, as shown in Figure 6a. The experimental charge and discharge cycles were simulated using the software mentioned above, taking into account the effect of the operating temperature applied to the SoC of a _LiCoO\({}_{2}\)_ cell. The collected data were subsequently used for testing and validating the performance of the proposed DNN, GRU, and LSTM networks. The results of the SoC prediction in two distinct scenarios are discussed. There are several reasons why a comparative study of simulation and experimental data is interesting for the SoC estimation using DNN, GRU, and LSTM. First, \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **RMSE (\%)** & **MAE (\%)** & **MSE (10\({}^{-3}\))** & **R\({}^{2}\)** \\ \hline DNN & 0.290 & 0.190 & 0.008 & 0.9999 \\ GRU & 3.379 & 1.047 & 1.140 & 0.9828 \\ LSTM & 3.797 & 1.198 & 1.440 & 0.9773 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: State of charge prediction errors for the different proposed models  
Figure 9: Instrumentation platform to collect electrical and thermal data for a battery experiment. experimental data can provide accurate information about the actual battery behavior, while simulation data can be used to generate larger and more diverse datasets, which can improve the performance of machine learning models. Moreover, simulation data serve the purpose of replicating scenarios challenging or even impossible to emulate through experimentation, such as extreme charge and discharge conditions. Through the comparison of results from experimental and simulated data, it is possible to validate the efficacy of deep learning models and identify the most reliable for estimating the SoC. This combination offers a comprehensive understanding of a battery's potential and constraints, facilitating the refinement of SoC estimation algorithms for enhanced accuracy and reliability. In the first scenario, experimentally measured data were used to train and validate the proposed models. Then, in the second scenario, the data obtained from the simulation were used to validate the effectiveness of the proposed model in estimating the SoC on the one hand, and on the other hand, to confirm the reliability of the simulation data to train and validate the discussed models. Figures 11 and 12 demonstrate the utilization of a four-layer DNN architecture. In that configuration, the initial three layers consisted of nine neurons each, with the final layer containing a single neuron. The performance evaluation of the network revealed that the predicted SoC, denoted in red, closely followed the reference SoC depicted in blue. The DNN results indicated a mean error of under 0.5% for the experimental data and a maximum error of less than 2.4%. Additionally, simulation data exhibited a mean error below 0.4% and a maximum error under 2.5%. The slight variance in precision observed between the simulation and experimental tests of the DNN could be attributed to the utilization of a new battery in the simulation, as opposed to the battery employed in the experimental setup. The latest results demonstrated that the DNN model provided a reliable estimate of the SoC. To evaluate the performance of that method, the MAE [86], MSE, RMSE [87], and coefficient of determination R2 were used, which were obtained by calculating predicted and real values. They were used to assess network performance.