## 5 Result and Discussion  
### Comparison of Models  
This section evaluates the model's efficacy. Figures 8 and 9 depict the training and testing dataset's prediction performance in regression form, respectively, while Tables 4 and 5 provide a summary of the relevant data.  
In terms of training, the XGBoost model produced the best prediction results (i.e., \(R^{2}\) = 0.971, \(MAE\) = 47.518 and \(RMSE\) = 66.844) compared to AdaBoost (i.e., \(R^{2}\) = 0.957, \(MAE\) = 56.671 and \(RMSE\) = 82.495), RF (i.e., \(R^{2}\) = 0.952, \(MAE\) = 58.366 and \(RMSE\) = 79.240), DT (i.e., \(R^{2}\) = 0.932, \(MAE\) = 68.912 and \(RMSE\) = 94.304) and SVM (i.e., \(R^{2}\) = 0.887, \(MAE\) = 88.801 and \(RMSE\) = 123.375). This is also confirmed by the results of _MARE_, _NSE_ and _RSR_ in  
Figure 8: Measured Pu versus Estimated Pu for training models using (**a**) XGBoost, (**b**) AdaBoost, (**c**) RF, (**d**) DT, and (**e**) SVM.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Testing Set**} \\ \hline
**Model** & \(R^{2}\) & _MAE_ **(kN)** & _RMSE_ **(kN)** & _MARE_ **(\%)** & _NSE_ & _RSR_ \\ \hline XGBoost & 0.955 & 59.929 & 80.653 & 6.600 & 0.950 & 0.225 \\ \hline AdaBoost & 0.950 & 70.383 & 90.665 & 8.252 & 0.936 & 0.253 \\ \hline RF & 0.945 & 69.030 & 86.348 & 8.014 & 0.942 & 0.241 \\ \hline DT & 0.925 & 74.450 & 99.822 & 8.775 & 0.923 & 0.278 \\ \hline SVM & 0.878 & 98.320 & 128.027 & 10.991 & 0.873 & 0.357 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Summary of Testing model.  
\(R^{2}=0.945\), \(MAE=69.030\), \(RMSE=86.348\), \(MARE=8.014\), \(NSE=0.942\), and \(RSR=0.241\)), DT (i.e., \(R^{2}=0.0.925\), \(MAE=74.450\), \(RMSE=99.822\), \(MARE=8.775\), \(NSE=0.923\), and \(RSR=0.278\)) and SVM (i.e., \(R^{2}=0.878\), \(MAE=98.320\), \(RMSE=128.027\), \(MARE=10.991\), \(NSE=0.873\), and \(RSR=0.357\)) as shown in Table 5.  
Comparing the above performance measures the proposed XGBoost model performed better than the AdaBoost, RF, DT and SVM. From these statistical analysis and prediction capabilities, we can state that the XGBoost model has good accuracy prediction for pile bearing capacity.  
The sensitivity results of the XGBoost model were assessed using [PERSON]'s [67] method for assessing the impact of input variables on \(P_{u}\). This approach, which has been used in several investigations [22; 28; 68; 69; 70], is as follows:  
\[r_{ij}=\frac{\sum_{k=1}^{n}(x_{im}\times x_{om})}{\sqrt{\sum_{k=1}^{n}x_{im} \sum_{k=1}^{n}x_{om}{}^{2}}} \tag{19}\]  
as \(n\) represents the number of values (i.e., 140); \(x_{im}\) and \(x_{om}\) denotes input and output variables, respectively. For each input parameter, the \(r_{ij}\) value ranges from zero to one, with the greatest \(r_{ij}\) values indicating the efficient output variable (i.e., \(Pu\)).  
Figure 10 shows the \(r_{ij}\) scores for all input variables. Figure 10 demonstrates that SPT blow count at pile shaft (N\({}_{\text{S}}\)) (\(r_{ij}=0.985\)) has the greatest effect on the \(Pu\).  
With the use of the Taylor diagram (see Figure 11), we investigated the model's efficiency further. The better the performance, the closer each produced model's point is to the observed point location. The models demonstrated the best predictive capability, while the XGBoost method had a greater correlation and a lesser \(RMSE\).