## 3 Experimental Results  
For SVR, a total of 243 datasets were learned for five factors and three levels. Table 4 presents the prediction results. Upon using a polynomial kernel, an MSE of 0.005 was obtained when \(C=100\), \(\varepsilon=0.001\), and \(\gamma=1\), which was the closest value to 0. Additionally, the coefficient of determination (\(R^{2}\)), which is often used as a measure to confirm the suitability in regression, demonstrated a value of 0.999, which indicated good performance. The value of \(R^{2}\) approaching 1 signifies higher accuracy, as calculated by Equation (3), where \(y_{p}\), \(y_{r}\), and (\(\overline{y_{r}}\)) represent the predicted value, experimental value, and average experimental value, respectively. Furthermore, the accuracy of the model predicted using SVR was compared with that of the regression analysis, which is the existing optimal design method. Equation (4) shows the regression equation. The value of \(R^{2}\) was used to compare the prediction accuracy of the two methods. As shown in Figure 10, the red series represents the accuracy \(R^{2}\) of the prediction model learned with SVR, and the blue series represents the accuracy of the \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**C** & \(\varepsilon\) & \(\gamma\) & \(R^{2}\) & **MSE** \\ \hline \multirow{8}{*}{1} & & 0.01 & 0.774618 & 1108.673 \\  & & 0.001 & 0.1 & 0.952339 & 234.4494 \\  & & 1 & 0.972326 & 136.1297 \\  & & 0.01 & 0.773669 & 1113.338 \\  & & 0.01 & 0.952469 & 233.8078 \\  & & 1 & 0.972222 & 136.6425 \\  & & 0.01 & 0.773267 & 1115.316 \\  & & 0.1 & 0.947284 & 259.3131 \\  & & 1 & 0.962545 & 184.2419 \\ \hline \multirow{8}{*}{10} & & 0.01 & 0.892491 & 528.8427 \\  & & 0.001 & 0.1 & 0.990984 & 44.34811 \\  & & 1 & 0.99999 & 0.005441 \\  & & 0.01 & 0.892264 & 529.9624 \\  & & 0.01 & 0.991071 & 43.92448 \\  & & 1 & 0.999901 & 0.487326 \\  & & 0.01 & 0.888727 & 547.3592 \\  & & 0.1 & 0.989523 & 51.5357 \\  & & 1 & 0.990298 & 47.7243 \\ \hline \multirow{8}{*}{100} & & 0.01 & 0.940883 & 290.8004 \\  & & 0.1 & 0.998267 & 8.526889 \\  & & 1 & 0.99999 & 0.005441 \\  & & 0.01 & 0.941529 & 287.6255 \\ \cline{1-1}  & 0.01 & 0.1 & 0.998556 & 7.104295 \\ \cline{1-1}  & & 1 & 0.999901 & 0.487326 \\ \cline{1-1}  & & 0.01 & 0.94643 & 263.5146 \\ \cline{1-1}  & 0.1 & 0.994346 & 27.81252 \\ \cline{1-1}  & & 1 & 0.990298 & 47.7243 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results of SVR. values calculated using the regression equation. The design variables used as test data arbitrarily designated values that were not used for learning and modeled only those values that met the constraints. \[R^{2}=1-\frac{\sum(y_{r}-y_{p})^{2}}{\sum(y_{r}-\overline{y}_{r})^{2}} \tag{3}\]  
\[Y_{1}=166.73+0.930x_{1}+(-0.288)x_{2}+0.1339x_{3}+(-0.0863)x_{4}+(-46.029)x_{5} \tag{4}\]  
On comparing a total of 16 test datasets, the SVR prediction model showed high prediction accuracy, with an \(R^{2}\) of 0.94. Meanwhile, the regression equation showed an \(R^{2}\) of 0.70. On comparing all the test data values presented in Figure 10, it was seen that the SVR prediction values were similar to those of FEA. As the relationship between the dependent variables and the independent variables was not two-dimensional, the accuracy of SVR was higher than that of the regression equation, which considers only two-dimensional relationships. Therefore, the optimal design was implemented using the SVR prediction model, and design variable values were derived to minimize effective stress within the limited conditions. As the optimal design result, when the design variables were \(x_{1}=120^{\circ}\), \(x_{2}=90^{\circ}\), \(x_{3}=30\) mm, \(x_{4}=0\) mm, and \(x_{5}=4.8\) mm, the prediction with SVR confirmed that the effective stress was 47.8 MPa. The results show that the effective stress was reduced by 80%, as compared to that of 250 MPa obtained for the existing design model; and, moreover, it was structurally stable with a safety rate of 5.86.