# Explainable Artificial Intelligence for State of Charge Estimation of Lithium-Ion Batteries
## 4 Experiments and Results
### E3: SoC Estimation Guided by xAI and Importance Estimates
**Results--Over-reliance:** A thorough evaluation was conducted for the following features, which were taken from Table 3:  
* CURRENT
* VOLTAGE_CELL_MIN* VOLTAGE_CELL_MAX
* VOLTAGE_DIFF
* T_CELL_AVG
* T_CELL_MIN
* T_DIFF
* SOC_REAL
* MILEAGE
* CUMULATIVE_DE
* CUMULATIVE_CE
* CUM_CE_DIFF  
The list of features was determined via expert opinions and established existing works [7; 10; 18] regarding SoC. It served as a comprehensive list to measure the relative importance between the signals. InputXGradient's averaged results of relative importance between the signals from the different NNs are presented in Figure 7. The figure indicates that the models over-rely on CUMULATIVE_DE for SoC estimation. Further investigation revealed that the signal was moderately correlated with SoC, where a Pearson correlation coefficient of 0.554 was measured. This suggests that the models were learning the correlation instead of utilizing the signals for their intended purpose of estimating SoC. This information was not obvious from the dataset and would not have been discovered without the use of xAI. Afterwards, we experimented with different subsets of features as inputs and repeated the procedure to learn the contributions of the features. It was found that the models tended to over-rely on MILEAGE and CUMULATIVE_DE. Therefore, necessary adjustments were made, such as discarding some sessions. **Results--Signals:** After the investigation of correlation reliance, we made necessary adjustments to the signals and established a condensed set of features for measuring relative importance based on expert opinions. These were as follows:  
* CURRENT
* VOLTAGE
* VOLTAGE_DIFF
* T_CELL_AVG  
Figure 7: Signal Importance: Importance based on xAI’s InputXGradient. CUMULATIVE_DE’s importance is abnormally high. * T_DIFF
* CUMULATIVE_DE
* CUM_CE_DIFF  
This set of condensed signals were used to retrain the different NNs, and xAI's InputXGradient was applied again. The results, demonstrated in Figure 8, showed that CURRENT and VOLTAGE were both considered to have a higher relative importance within this set of condensed signals. This outcome concurs with expert opinions and the basis of SoC. We additionally verified the relative importance of the features by retraining the NNs with only CURRENT and VOLTAGE to compare the results of SoC estimation. This is shown in Table 5. We focused on CNN-LSTM and GRU since the xAI results were obtained from these two corresponding models. The visuals of CNN-LSTM and GRU are available in Figure 4b and Figure 5b, respectively. We only focus on the results from the test set in order to be representative when applying the changes to a real application, where it would be impossible to perform any further tuning. Based on the differences from the respective metrics between the architectures, MSE with a difference of up to \(3\times 10^{-4}\) and MAE with a difference of approximately \(3\times 10^{-3}\), we can conclude that there were minimum changes between the performances of SoC estimation. This shows that the NNs trained with only these two features exhibit comparable performance to NNs trained with the condensed set of features. Interestingly, the SoC estimations of ResNet and InceptionTime improved when using only CURRENT and VOLTAGE; this is supported by Figure A3 and Figure A5, respectively, in Appendix A. This further reinforces the importance of the two features within the signals. An extended version of Table 5 can be found in Appendix A's Table A2. **Results--Time Steps of Input Window:** The previous outcome regarding the signals' relative importance revealed that VOLTAGE and CURRENT are particularly important for SoC estimation. It can also be observed that not all time steps within the input window were considered equally important in Figure 8.  
Therefore, we also investigated the importance of time steps within the multivariate time series context. Specifically, we wanted to know if we could make an informed decision regarding the window size for our input.