## 3 Results
### Neural Network Models and SHAP Analysis
#### 3.1.3 Neural Network Model and SHAP Analysis for Case 3  
Figure 10 shows a SHAP summary plot for \(R_{a}\). In Figure 10, it can be seen that higher values of the insert radius \(r_{i}\) are clustered to the left of the SHAP value equal to zero, indicating that higher \(r_{i}\) values decrease the values of \(R_{a}\). Lower \(r_{i}\) values are clustered to the right of the SHAP value equal to zero, indicating that lower \(r_{i}\) values increase the values of \(R_{a}\). Also, in Figure 10, it can be seen that lower \(f\), \(a_{p}\), and \(v_{c}\) values decrease the model's \(R_{a}\) prediction, while higher values increase the model's \(R_{a}\) prediction. As can be seen in Figure 10, the \(v_{c}\) feature has a much lower impact on predicting \(R_{a}\) compared to \(f\) and \(a_{p}\). The SHAP values presented in Figure 10 show that \(r_{i}\) has the highest impact on the model's prediction and is the most important feature in predicting \(R_{a}\), followed by \(f\), \(a_{p}\), and \(v_{c}\). Figure 11 presents a SHAP summary plot for the prediction of \(F_{c}\). As can be seen in Figure 11, higher values of \(a_{p}\) and \(f\) cluster to the right of the SHAP value equal to zero and have positive impacts on the prediction of \(F_{c}\), while lower values have negative impacts. Contrarily, higher values of the \(r_{i}\) and \(v_{c}\) features cluster to the left of the SHAP value equal to zero and have negative impacts on the prediction of \(F_{c}\), while lower values have positive impacts. This plot shows that \(a_{p}\) is the most impactful feature, followed by \(f\), \(r_{i}\), and \(v_{c}\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Metrics** & \(R_{a}\) & \(F_{c}\) & \(F_{p}\) & \(F_{f}\) \\ \hline \(R^{2}\) & 38.66\% & 93.03\% & 34.04\% & 83.92\% \\ \(MSE\) & 0.0224 & 0.0042 & 0.0528 & 0.0107 \\ \(MAE\) & 0.0901 & 0.0500 & 0.1802 & 0.0784 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Evaluation of the model’s performance on \(R_{a}\), \(F_{c}\), \(F_{p}\), and \(F_{f}\) for case 2. Figure 10: Impact of \(r_{i}\), \(v_{c}\), \(f\), and \(a_{p}\) on \(R_{a}\) based on SHAP values for case 3. A SHAP summary plot for the passive force \(F_{p}\) is presented in Figure 12. It can be seen that higher values of feature \(r_{i}\) have negative impacts on the prediction of \(F_{p}\), while lower values have positive impacts. Higher values of \(f\), \(a_{p}\), and \(v_{i}\) have positive impacts on the prediction, while lower values have negative impacts. Figure 12 shows that the most impactful feature \(r_{i}\) is followed by \(a_{p}\) and \(v_{i}\). The SHAP summary plot for the feed force \(F_{f}\) is depicted in Figure 13. Features \(a_{p}\) and \(f\) show positive impacts when their values are high and negative impacts for their lower values. Contrarily, higher values of features \(r_{i}\) and \(v_{c}\) have negative impacts, while lower values have positive impacts and increase the model's prediction. Feature \(a_{p}\) is the most important in the prediction model, followed by \(r_{i}\), \(f\), and \(v_{c}\). Figure 11: Impact of \(r_{i}\), \(v_{c}\), \(f\), and \(a_{p}\) on \(F_{c}\) based on SHAP values for case 3. Figure 12: Impact of \(r_{i}\), \(v_{c}\), \(f\), and \(a_{p}\) on \(F_{p}\) based on SHAP values for case 3. Table 7 shows the percentages of features' contributions to \(R_{a}\), \(F_{c}\), \(F_{p}\), and \(F_{f}\). Feature \(r_{i}\) has the highest impact on \(R_{a}\) and \(F_{c}\). In Table 7, it can be seen that \(r_{i}\) feature's SHAP values contribute 59.83% and 54.22% to the prediction of \(R_{a}\) and \(F_{c}\), while its contribution to the prediction of \(F_{p}\) and \(F_{f}\) drops to 26.23% and 34.36%, respectively. Also, in Table 7, it can be seen that there is a very small contribution of feature \(v_{c}\) to the prediction of all four models' outputs \(R_{a}\), \(F_{c}\), \(F_{p}\), and \(F_{f}\), with values of 4.07%, 7.86%, 4.81%, and 5.27%, respectively.