# Machine Learning Techniques for Soil Characterization Using Cone Penetration Test Data
## 5 Results and Discussion
### Comparisons of ML Models  
Table 4 provides a summary of the evaluation results for the ML models. Based on our results, the DT model exhibited lower accuracy, as evidenced by a lower \(R^{2}\) on both training and testing data. The DT model recorded RMSE of 13.06 and 13.16, MAE of 10.27 m/s and 10.34 m/s, MAPE of 7.27% and 7.31%, and \(R^{2}\) of 0.95 and 0.94 on the training and testing datasets, respectively. Additionally, Spider charts were utilized to visualize and assess each model's efficiency relative to others (Figure 10). The spider chart shows that the DT model significantly diverged towards higher RMSE, MAPE, and MAE on both training and testing datasets in comparison to other ML models. The RF, SVM, and XGBoost models outperform the DT model in terms of RMSE, MAE, MAPE, and \(R^{2}\). All RF, SVM, and XGBoost models have lower error values and higher \(R^{2}\) scores, indicating higher accuracy and better performance in predicting \(V_{\rm S}\) from the input features. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{Models} & \multicolumn{8}{c}{Train dataset} \\ \cline{2-9}  & \(A10-I\) & RMSE & \(R^{2}\) & PI & SI & MAE & MAPE & \(U_{95}\) & Rank \\ \hline RF & 1 (1) & 0.46 (1) & 1 (1) & 0.002 (1) & 0.003 (1) & 0.24 (1) & 0.17 (1) & 1.24 (1) & 1 \\ SVM & 0.998 (2) & 1.11 (2) & 1 (1) & 0.005 (2) & 0.007 (2) & 0.37 (2) & 0.28 (2) & 3.07 (2) & 2 \\ DT & 0.78 (3) & 13.1 (4) & 0.95 (2) & 0.06 (4) & 0.08 (4) & 10.27 (4) & 7.23 (4) & 36.20 (4) & 4 \\ XGBoost & 1 (1) & 1.68 (3) & 1 (1) & 0.007 (3) & 0.01 (3) & 1.29 (3) & 0.87 (3) & 4.65 (3) & 3 \\ \hline \multirow{2}{*}{Models} & \multicolumn{8}{c}{Test dataset} \\ \cline{2-9}  & \(A10-I\) & RMSE & \(R^{2}\) & PI & SI & MAE & MAPE & \(U_{95}\) & Rank \\ \hline RF & 1 (1) & 0.96 (1) & 1 (1) & 0.004 (1) & 0.006 (1) & 0.50 (2) & 0.36 (2) & 2.66 (2) & 1 \\ SVM & 0.998 (2) & 1.36 (2) & 1 (1) & 0.006 (2) & 0.008 (2) & 0.38 (1) & 0.31 (1) & 2.3 (1) & 2 \\ DT & 0.77 (3) & 13.2 (4) & 0.94 (2) & 0.06 (4) & 0.08 (4) & 10.34 (4) & 7.31 (4) & 36.48 (4) & 4 \\ XGBoost & 1 (1) & 1.86 (3) & 1 (1) & 0.008 (3) & 0.01 (3) & 1.40 (3) & 0.94 (3) & 5.16 (3) & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Summary of evaluation results for each ML model using training and testing datasets. Figure 9: Scatter plots and frequency distributions of residuals. Figure 11 illustrates the performance of ML models in predicting \(V_{\rm S}\)  as evaluated using four performance metrics: \(U_{\rm S}\), \(A10-I,\ P1,\ \text{and}\ SI\). The results indicate that the DT model achieved lower performance in comparison to other models, as evidenced by its higher \(U_{\rm S}\), \(PI,\ \text{and}\ SI\) scores and lower \(A10-I\) values. On the other hand, the RF model demonstrated exceptional performance, outperforming the other models in terms of these performance indicators. In terms of \(SI\), the RF, SVM, and XGBoost models achieved excellent precision (EP), with \(SI<0.05\) on both the training and testing datasets. In contrast, the DT model achieved good precision with \(0.05<SI<0.1\) on the training and testing datasets. Overall, the RF model ranked first, outperforming the other three ML models, while the DT model ranked fourth. The SVM and XGBoost models ranked second and third, respectively. To further assess the performance of the ML models, a comparison was made between model-predicted \(V_{\rm S}\) values and estimated \(V_{\rm S}\) values based on existing empirical correlation. A correlation model was selected to estimate \(V_{\rm S}\) from CPT soundings. Equation (12) [80] was utilized for the estimation of \(V_{\rm S}\) from CPT soundings. \[V_{\rm S}=10^{0.31L+0.77}\times\sqrt{\left(q_{\rm c}-\sigma_{v0}\right)/p_{a}} \tag{12}\]  
where \(V_{\rm S}\) is soil shear wave velocity, \(I_{\rm c}\) is soil behavior type index, \(q_{\rm c}\) is cone tip resistance, \(\sigma_{v0}\) is total overburden pressure, and \(p_{a}\) is atmospheric pressure.