## 3 Results
### Neural Network Models and SHAP Analysis
#### 3.1.3 Neural Network Model and SHAP Analysis for Case 3
The results in Table 7 show that the contribution of feature \(f\) to the prediction of \(R_{a}\), \(F_{c}\), and \(F_{f}\) is smaller compared to the contribution of \(r_{i}\), with values of 19.31%, 21.31%, and 19.52%, respectively, while the contribution to the prediction of \(F_{p}\) is almost the same as the contribution of \(r_{i}\), with a value of 26.74%. The SHAP values' contribution of feature \(a_{p}\) to the prediction of \(F_{p}\) and \(F_{f}\) is 42.23% and 40.75%, respectively, while its contribution to the prediction of \(R_{a}\) and \(F_{c}\) drops to 16.79% and 16.60%, respectively. Table 8 depicts the evaluation metrics for the performance of the developed models on \(R_{a}\), \(F_{c}\), \(F_{p}\), and \(F_{f}\): the coefficient of determination (\(R^{2}\)), mean squared error (\(MSE\)), and mean absolute error (\(MAE\)). It can be seen that the developed models demonstrate good performance. The model has the best performance in the prediction of \(R_{a}\), with a coefficient of determination of 92.19%, mean squared error of 0.008, and mean absolute error of 0.0553. In case 1, the cutting speed \(v_{c}\) had the lowest impact on all outputs, where the higher values of cutting speed increased the values of \(R_{a}\) and \(F_{f}\), and the lower values of cutting speed \(v_{c}\) increased \(F_{c}\) and \(F_{p}\). In situations where the lower values of cutting speed \(v_{c}\) increased \(F_{c}\) and \(F_{p}\), the depth of cut \(a_{p}\) had the highest impact, and in situations where the higher values of cutting speed increased the values of \(R_{a}\) and \(F_{f}\), the feed rate \(f\) had the highest impact. Both with an increase in \(a_{p}\) and \(f\), the values of all outputs increased. However, the low value of \(R^{2}\) showed that these input variables did not explain the variability of \(R_{a}\) well, while the variabilities of all forces were explained with high percentages. The impact of the input variables in case 2 was different compared to case 1 for all outputs, except for the main cutting force \(F_{c}\). The depth of cut \(a_{p}\) had the highest importance for \(R_{a}\), \(F_{c}\), and \(F_{f}\), and it was the second most important variable for \(F_{p}\). The values of all outputs increased with the higher values of \(a_{p}\). The feed rate \(f\) had the lowest impact on \(R_{a}\) and the highest impact on \(F_{p}\). It was the second most important variable for \(F_{c}\) and \(F_{f}\). With an increase in \(f\) values, the values of all outputs increased. Also, as was the case in case 1, these variables did not explain the variability of \(R_{a}\) well. However, the variability of \(F_{p}\) in case 2 was not explained well, as was the case in case 1. The variabilities of forces \(F_{c}\) and \(F_{f}\) were explained with high percentages. In case 3, the insert radius \(r_{i}\) was included as an additional variable because data from both types of inserts were included in the analysis. In cases 1 and 2, \(R_{a}\) had the smallest \(R^{2}\), and in case 3, as the variable \(r_{i}\) was included, the \(R^{2}\) increased to 68.32%. The insert radius \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Input Feature** & \(r_{i}\) & \(v_{c}\) & \(f\) & \(a_{p}\) \\ \hline \(R_{a}\) & 59.83\% & 4.07\% & 19.31\% & 16.79\% \\ \(F_{c}\) & 26.23\% & 4.81\% & 26.74\% & 42.23\% \\ \(F_{p}\) & 54.22\% & 7.86\% & 21.31\% & 16.60\% \\ \(F_{f}\) & 34.46\% & 5.27\% & 19.52\% & 40.75\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Contributions of features \(r_{i}\), \(v_{c}\), \(f\), and \(a_{p}\) to \(R_{a}\), \(F_{c}\), \(F_{p}\), and \(F_{f}\) for case 3. \(r_{i}\) contributed to explaining the variability of \(R_{a}\) with a large percentage. Also, based on the SHAP analysis, it could be seen that the insert radius had the greatest impact on the value of \(R_{a}\).