## 4 Results and Discussion
### Feature Importance  
Understanding feature importance isn't just about model performance, it also helps us connect the model's decisions to what's happening inside the battery. In our Extra Trees Regressor, Cycle Count is a key predictor when included as seen in Figure 15. The same pattern holds across the other models, too. Now, in the absence of Cycle Count the most important feature was time at 4.15 V as seen in Figure 16, which makes sense since operating near high voltages is known to accelerate SEI (Solid Electrolyte Interphase) layer growth and can lead to lithium plating on the anode surface. Both are key contributors to battery aging. Another top feature, the voltage drop between 3.6 V and 3.4 V, reflects how quickly a battery loses voltage during discharge, which tends to happen faster as the battery degrades. Features like time under constant current and maximum discharge voltage are closely tied to how well the battery holds and delivers energy, which naturally decline with use. Linear Regression places significant emphasis on maximum discharge voltage  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**References** & **ML Model** & **MSE** & **RMSE** & **MAE** & **R\({}^{2}\)** & \
\begin{tabular}{c} **Training** \\ **Time** \\ \end{tabular} &
\begin{tabular}{c} **Prediction** \\ **Time** \\ \end{tabular} \\ \hline
[9] & Support Vector Machine (SVM) & – & 115 & – & 0.90 & – & – \\
[10] & Random Forest Optimization & 2148.865 & 46.35 & 36.88 & 0.97 & – & – \\ \hline
[53] &
\begin{tabular}{c} Adaptive Deep \\ Neural Network (ADNN) \\ \end{tabular} & – & 6.66 & – & 0.93 & – & – \\ \hline
[11] & Random Forest & 14.11 & 3.75 & 2.09 & 0.99 & – & 0.06 \\ \hline Proposed &
\begin{tabular}{c} Random Forest with Extra Trees \\ Regressor \\ \end{tabular} & 10.23 & 3.66 & 1.99 & 0.99 & 7.34 & 0.05 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison table with existing related works.  
and minimum charge voltage, optimizing predictions based on their linear relationship with the RUL as seen in Figure 17. Overall, the model's top features align well with known chemical degradation processes, which helps support the reliability of its predictions.  
The feature importance for the Artificial Neural Network (ANN) model was determined using permutation-based analysis. The results highlight that Discharge Time is the most significant predictor as seen in Figure 18, contributing the most to the model's accuracy, followed by Max Voltage Discharge and Time at 4.15 V. Features such as Decrement  
Figure 16: Feature importance scores for the Extra Trees Regressor model without Cycle Count.  
Figure 17: Feature importance for the Linear Regression model.  
Figure 15: Feature importance scores for the Extra Trees Regressor with cycle count.  
(3.6 V-3.4 V) and Time Constant Current also show moderate importance, while Min Voltage Charge and Charging Time have comparatively lower impacts. While Random Forest and Extra Trees provide built-in ways to understand which features are most important, LSTM models don't offer the same level of interpretability out of the box. Although there are advanced methods like permutation importance or SHAP values that can be used, they tend to be more complex and computationally heavy, especially for time-series models like LSTM. To keep the analysis focused and practical, feature importance was only explored for the models where it could be done more directly and clearly. This algorithm analysis underscores the critical role of discharge-related features in predicting the RUL of Li-ion batteries, providing valuable insights for model optimization.