## 4 Model Results
### Parametric Analysis  
A parametric analysis was performed to examine the impact of each input feature on the bearing capacity (\(q_{rs}\)) of the composite foundation system studied in this research and to compare the predicted results obtained through the MPR algorithm with those obtained in the laboratory. Each input variable was changed between its minimum and maximum value, while other parameters remained constant with their mean values. The best-fit curves that illustrate the contribution of each input variable on \(q_{rs}\) are displayed in Figure 6a-d, along with a comparison with the experimental values for \(q_{rs}\) and also those predicted by the MPR models.  
The effectiveness of models can be evaluated by comparing their predicted values with the actual behavior of the system being analyzed. As shown in Figure 6a-d, the response of the bearing capacity (\(q_{rs}\)) to changes in the predictor properties, such as \(q_{u}\), \(t/D\), \(d/D\), and \(h/d_{sc}\) ratios, is consistent with laboratory results when using the MPR predictions. Figure 6a shows that \(q_{rs}\) increases as \(q_{u}\) increases, as can be seen in Figure 6a. In addition, an increase in both \(d/D\) and \(h/d_{sc}\) ratios leads to an increase in \(q_{rs}\) for the foundation system, as depicted in Figure 6c-d. Conversely, increasing the \(t/D\) ratio initially results in an increase in \(q_{rs}\) values, followed by a decrease thereafter  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Models** & \multicolumn{2}{c}{**MPR**} & \multicolumn{2}{c}{**SVR-ERBF**} & \multicolumn{2}{c}{**SVR-RBF**} & \multicolumn{2}{c}{**SVR-POLY**} & \multicolumn{2}{c}{**ANFIS**} \\ \hline
**Metrics** & **Train** & **Test** & **Train** & **Test** & **Train** & **Test** & **Train** & **Test** & **Train** & **Test** \\ \hline \(R^{2}\) & 0.994 & 0.983 & 0.999 & 0.989 & 0.980 & 0.975 & 0.976 & 0.965 & 0.996 & 0.981 \\
**RMSE** & 13.010 & 15.655 & 4.30 & 11.45 & 17.63 & 17.51 & 20.63 & 23.93 & 7.90 & 13.80 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Evaluating the performance of the MPR model vs. prior black-box models for predicting the bearing capacity.  
of about 0.22. In general, the results indicate that the MPR models perform well, as confirmed by the experimental results and the variation in \(q_{rs}\) due to changes in the factors affecting the bearing capacity of the studied composite ground. Regarding the observed disparity between the experimentally best-fit curve and the scattered experimental points in Figure 6c,d, it should be recognized that this may affect the confidence in the proposed MPR model. However, it is important to note that the primary goal of the MPR model is to capture the overall trend and behavior of the system rather than perfectly fitting every individual data point. The scattered nature of the experimental points may be attributed to various factors, including inherent variability in the material properties and experimental conditions. Despite the observed disparity, the proposed MPR model provides a reasonable approximation of the overall trend and constitutes a valuable tool for understanding the general behavior of the composite foundation system. The authors believe that further research, including refining experimental procedures and incorporating additional data, may help improve the model's performance in the future.