## 3 Results and Discussion
### Simulation  
In this section, different SVR models were used to simulate and evaluate FOS. Based on this step, optimization models are developed. The data used in this study include 80 data samples. Due to different conditions, 6 input parameters of these models were used without change. For more accurate evaluation, the data were divided into two parts: training and testing. Different and optimal conditions were designed to determine the superior models. Finally, the best model that could provide suitable conditions for different data for FOS prediction was determined. Each parameter has a specific effect on the data and results of the models. Visualization of a correlation matrix of slope data is shown in Figure 4. In Figures 5-10, the effect of each parameter on the output is investigated. Using these figures, the input data can be examined more accurately. These data can provide specific conditions and significant changes in model results. However, important ranges can also be identified through various studies. With the help of these cases, proper accuracy in FOS simulation and optimization can be achieved. This research has considered these cases in the simulations. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parameter** & **Type** & **Min** & **Max** & **Average** &
\begin{tabular}{c} **Standard** \\ **Deviation** \\ \end{tabular} & **Median** \\ \hline \(\gamma\) & input & 14 & 31.3 & 22.9337 & 4.0706 & 22 \\ \(c\) & input & 6.94 & 150.05 & 40.4358 & 33.1699 & 30 \\ \(\phi\) & input & 10 & 45 & 28.8924 & 8.6297 & 30.075 \\ \(\beta\) & input & 18 & 59 & 36.2587 & 10.3505 & 37.5 \\ _ru_ & input & 0 & 0.5 & 0.1936 & 0.1515 & 0.25 \\ \(H\) & input & 8.23 & 565 & 149.1659 & 142.6898 & 96.1 \\ FOS & target & 2.31 & 0.65 & 1.3305 & 0.3369 & 1.2495 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The main statistical information of the dataset. Figure 3: The main flowchart of the current research. Figure 4: Correlation matrix (aka correlalogram) plot of slope data. Figure 5: Density-FOS changes. Figure 6: C-FOS changes. Figure 7: \(\phi\)-FOS changes. Table 5 provides the simulation results for four different SVR models. To achieve the best conditions of each model, parametric analysis was performed to determine the optimal parameters of each model. As can be seen, both polynomial and RBF models provide better conditions for FOS simulation. The RBF model with an accuracy of \(R^{2}=0.947\) shows that a more appropriate assessment can be made than other models to simulate the problem in this research. Figure 11 indicates the simulation results for four models. As can be seen, the data are simulated with higher accuracy by the RBF model. The model developed in this step is evaluated using optimization algorithms to determine the optimal conditions of the parameters used for FOS. Figure 12 shows the error changes of the models. Using this figure, the range of changes from prediction values to actual values can be obtained. As can be seen, the RBF model provides limited error variations. This indicates that for different samples, the predicted data are in the appropriate range and a good ability to perform them is observed. Figure 10: Ru-FOS changes. Figure 9: H-FOS changes. Figure 11: Simulation results for FOS based on various support vector regression (SVR) models. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**SVR Model** & \begin{tabular}{c} **Optimal** \\ **Parameters** \\ \end{tabular} & \
\begin{tabular}{c} **Result** \\ **RMSE** \\ \end{tabular} &
\begin{tabular}{c} **MAE** \\ \end{tabular} \\ \hline
**Linear** & - & 0.267 & 0.284 & 0.236 \\
**Polynomial** &
\begin{tabular}{c} g = 0.3, c = 0.09, \\ d = 3 \\ g = 0.42 \\ g = 0.03, c = 0 \\ \end{tabular} & 0.868 & 0.120 & 0.086 \\
**RBF** &
\begin{tabular}{c} g = 0.42 \\ g = 0.03, c = 0 \\ \end{tabular} & 0.947 & 0.076 & 0.046 \\
**Sigmoid** &
\begin{tabular}{c} g = 0.03, c = 0 \\ \end{tabular} & 0.214 & 0.294 & 0.243 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of various models for simulation of FOS.