# Explainable Artificial Intelligence for State of Charge Estimation of Lithium-Ion Batteries
## Abbreviations \begin{tabular}{l l} \(R^{2}\) & R Squared \\
**AI** & Artificial Intelligence \\
**BMS** & Battery Management System \\
**CNN** & Convolutional Neural Network \\
**e-Golf** & Volkswagen e-Golf \\
**EV** & Electric Vehicle \\
**FNN** & Forward Neural Network \\
**GRU** & Gated Recurrent Unit \\
**I** & Current \\
**Li-ion** & Lithium Ion \\
**LSTM** & Long Short-Term Memory \\
**MAE** & Mean Absolute Error \\
**MSE** & Mean Squared Error \\
**NN** & Neural Network \\
**OCV** & Open-Circuit Voltage \\
**Q** & Calculated charge \\
**RMSE** & Root Mean Squared Error \\
**RNN** & Recurrent Neural Network \\
**SoC** & State of Charge \\
**SoH** & State of Health \\
**SoP** & State of Power \\
**SoX** & State of X \\
**V** & Voltage \\
**xAI** & Explainable Artificial Intelligence \\ \end{tabular} 
Figure A1: LSTM SoC prediction: SoC predictions (blue) versus real SoC (orange). (**a**) E1’s result. (**b**) E3’s result, trained only with CURRENT and VOLTAGE. (**c**) E3’s result, trained only with CURRENT and VOLTAGE as well as a reduced window size. Figure A2: Informer SoC prediction: SoC predictions (blue) versus real SoC (orange). (**a**) E1’s result. (**b**) E3’s result, trained only with CURRENT and VOLTAGE. Figure A4: ResNet-LSTM SoC prediction: SoC predictions (blue) versus real SoC (orange). **(a)** EI’s result. (**b**) E3’s result, trained only with CURRENT and VOLTAGE. \begin{table}
\begin{tabular}{l c c c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{\multirow{2}{*}{**Model**}} & \multicolumn{4}{c}{**Train**} & \multicolumn{4}{c}{**Validation**} & \multicolumn{4}{c}{**Test**} \\  & \(\mathbf{R^{2}}\) & **MSE** & **MAE** & **RMSE** & \(\mathbf{R^{2}}\) & **MSE** & **MAE** & **RMSE** & \(\mathbf{R^{2}}\) & **MSE** & **MAE** & **RMSE** \\ \hline
**LSTM** & 0.996 & \(3.4\times 10^{-4}\) & \(11.8\times 10^{-3}\) & \(18.5\times 10^{-3}\) & 0.993 & \(5.6\times 10^{-4}\) & \(14.7\times 10^{-3}\) & \(23.7\times 10^{-3}\) & 0.996 & \(2.9\times 10^{-4}\) & \(12.2\times 10^{-3}\) & \(17.1\times 10^{-3}\) \\
**GRU** & 0.995 & \(3.8\times 10^{-4}\) & \(12.6\times 10^{-3}\) & \(19.5\times 10^{-3}\) & 0.992 & \(6.2\times 10^{-4}\) & \(15.7\times 10^{-3}\) & \(25.5\times 10^{-3}\) & 0.995 & \(3.5\times 10^{-4}\) & \(13.3\times 10^{-3}\) & \(18.6\times 10^{-3}\) \\
**CNN-LSTM** & 0.994 & \(4.6\times 10^{-4}\) & \(14.6\times 10^{-3}\) & \(21.4\times 10^{-3}\) & 0.991 & \(7.3\times 10^{-4}\) & \(18.5\times 10^{-3}\) & \(27.1\times 10^{-3}\) & 0.994 & \(4.5\times 10^{-4}\) & \(15.4\times 10^{-3}\) & \(21.3\times 10^{-3}\) \\
**Informer** & 0.976 & \(1.9\times 10^{-3}\) & \(33.6\times 10^{-3}\) & \(43.6\times 10^{-3}\) & 0.973 & \(2.2\times 10^{-3}\) & \(35.8\times 10^{-3}\) & \(46.4\times 10^{-3}\) & 0.975 & \(1.9\times 10^{-3}\) & \(33.5\times 10^{-3}\) & \(43.4\times 10^{-3}\) \\
**ResNet** & 0.751 & \(1.94\times 10^{-3}\) & \(12.1\times 10^{-3}\) & \(19.3\times 10^{-2}\) & 0.769 & \(18.2\times 10^{-3}\) & \(11.5\times 10^{-2}\) & \(13.5\times 10^{-2}\) & 0.725 & \(20.4\times 10^{-3}\) & \(12.5\times 10^{-2}\) & \(14.3\times 10^{-2}\) \\
**ResNet-LSTM** & 0.496 & \(4.0\times 10^{-3}\) & \(50.4\times 10^{-3}\) & \(6.3\times 10^{-3}\) & 0.952 & \(3.8\times 10^{-3}\) & \(49.9\times 10^{-3}\) & \(61.7\times 10^{-3}\) & 0.948 & \(3.9\times 10^{-3}\) & \(49.4\times 10^{-3}\) & \(62.2\times 10^{-3}\) \\
**InceptionTime** & 0 & \(41.2\times 10^{-2}\) & \(57.8\times 10^{-2}\) & \(64.2\times 10^{-2}\) & 0 & \(37.0\times 10^{-2}\) & \(53.9\times 10^{-2}\) & \(60.8\times 10^{-2}\) & 0 & \(41.5\times 10^{-2}\) & \(58.3\times 10^{-2}\) & \(64.4\times 10^{-2}\) \\
**Fusion Hybrid** & 0.995 & \(3.5\times 10^{-4}\) & \(13.4\times 10^{-3}\) & \(18.7\times 10^{-3}\) & 0.996 & \(3.1\times 10^{-4}\) & \(13.2\times 10^{-3}\) & \(17.5\times 10^{-3}\) & 0.996 & \(3.0\times 10^{-4}\) & \(12.8\times 10^{-3}\) & \(17.3\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: E1’s NNs and E2’s Fusion Hybrid Model performance results for train, validation, and test sets according to the evaluation metrics.