# Explainable Artificial Intelligence for State of Charge Estimation of Lithium-Ion Batteries
## 5 Discussion
### Evaluation of Main Themes
The results achieved by  
\begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{**Window**} & \multicolumn{2}{c}{**Train**} & \multicolumn{2}{c}{**Validation**} & \multicolumn{2}{c}{**Test**} \\ \cline{3-8}  & & **MSE** & **MAE** & **MSE** & **MAE** & **MSE** & **MAE** \\ \hline
**GRU** & 10 & \(8.6\times 10^{-4}\) & \(20.2\times 10^{-3}\) & \(1.2\times 10^{-3}\) & \(23\times 10^{-3}\) & \(10.3\times 10^{-4}\) (\(\spherical{5.1\times 10^{-4}}\)) & \(21.5\times 10^{-3}\) (\(\spherical{5.3\times 10^{-3}}\)) \\
**GRU** & 15 & \(7.6\times 10^{-4}\) & \(18.8\times 10^{-3}\) & \(1.1\times 10^{-3}\) & \(21.4\times 10^{-3}\) & \(9.1\times 10^{-4}\) (\(\spherical{3.9\times 10^{-4}}\)) & \(20.4\times 10^{-3}\) (\(\spherical{4.2\times 10^{-3}}\)) \\
**GRU** & 25 & \(6.7\times 10^{-4}\) & \(18.1\times 10^{-3}\) & \(9.5\times 10^{-4}\) & \(20.8\times 10^{-3}\) & \(7.9\times 10^{-4}\) (\(\spherical{2.7\times 10^{-3}}\)) & \(19.4\times 10^{-3}\) (\(\spherical{3.2\times 10^{-3}}\)) \\
**GRU** & 35 & \(5\times 10^{-4}\) & \(16.3\times 10^{-3}\) & \(7.4\times 10^{-4}\) & \(18.8\times 10^{-3}\) & \(6\times 10^{-4}\) (\(\spherical{0.8\times 10^{-4}}\)) & \(17.8\times 10^{-3}\) (\(\spherical{1.6\times 10^{-3}}\)) \\
**GRU** & 45 & \(3.8\times 10^{-4}\) & \(14\times 10^{-3}\) & \(6.2\times 10^{-4}\) & \(16.8\times 10^{-3}\) & \(5.1\times 10^{-4}\) (\(\spherical{0.1\times 10^{-4}}\)) & \(15.9\times 10^{-3}\) (\(\spherical{0.3\times 10^{-3}}\)) \\
**CNN** & 55 & \(5.6\times 10^{-4}\) & \(16.5\times 10^{-3}\) & \(8.1\times 10^{-4}\) & \(19.1\times 10^{-3}\) & \(7.1\times 10^{-4}\) (\(\spherical{0.0}\)) & \(18.3\times 10^{-3}\) (\(\spherical{0.1\times 10^{-3}}\)) \\
**CNN** & 53 & \(5.6\times 10^{-4}\) & \(16.6\times 10^{-3}\) & \(8.1\times 10^{-4}\) & \(19.2\times 10^{-3}\) & \(7.1\times 10^{-4}\) (\(\spherical{0.0}\)) & \(18.4\times 10^{-3}\) (\(\spherical{0.2\times 10^{-3}}\)) \\this Fusion Hybrid Model are shown in Table 4 and Figure 6 which were comparable, if not better than, the other NNs' performances. **Feature Analysis--Significance and Redundancy: We used xAI and importance estimate methods to evaluate the data features used for the estimation of SoC. ** We accomplished this in Section 4.3. Within the experiment, we utilized the xAI method, InputXGradient [27], and an importance estimate method, Pairwise Importance Estimate Extension (PIEE) [26], to evaluate what features were important for SoC estimation. The features we investigated were signals from EVs, where we found that some signals were prone to being over relied upon by the NNs. This was not obvious and would have otherwise been missed in our normal analysis. This is discussed in E3's _Results--Over-reliance_. Utilizing xAI's InputXGradient, we determined what signals from the set of available signals had higher relative importance. We verified this by retraining the NNs with the specific higher-importance signals. This result is available in Table 5 and is documented in E3's _Results--Signals_. We also observed that not all time steps within the input window were important according to the methods. We then proceeded to investigate whether it was possible to reduce the window size for the NNs based on the information of importance from PIEE. The results of this are available in Table 6 and are documented in E3's _Results--Time Steps of Input Window_, which showed that it is possible to reduce up to 9-25% of the input window without detrimentally affecting performance.