# Evaluation of Aeolian Sand Collapsibility Based on Physical Indicators in the Mu Us Desert, China
## 5 Construction of Collapsibility Evaluation Method
### Predicted Results and Evaluation After SVM Regression Model  
After the SVR regression model was established, the test set data were used as the input. The predicted results are listed in Table 7. The fitting degree (\(R^{2}\)) was 0.9503, the mean absolute error (MAE) was 0.0019136, and the root mean square error (RMSE) was 0.0023849. The training dataset was also input into the model. The predicted results are shown in Figure 10. The \(R^{2}\) of the training set of samples was 0.9986, while the \(R^{2}\) of all of the samples was 0.97449. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Serial Number** & \begin{tabular}{c} **Water Content** \\ **(\%)** \\ \end{tabular} & \begin{tabular}{c} **Dry Density** \\ **(g/cm\({}^{3}\))** \\ \end{tabular} & \
\begin{tabular}{c} **Specific** \\ **Gravity** \\ \end{tabular} & **Void Ratio** & **Saturation (\%)** &
\begin{tabular}{c} **Collapsibility** \\ **Coefficient** \\ \end{tabular} \\ \hline
1 & 3.4 & 1.51 & 2.65 & 0.749 & 12 & 0.04934 \\
2 & 4.0 & 1.51 & 2.66 & 0.759 & 14 & 0.02986 \\
3 & 4.2 & 1.57 & 2.66 & 0.699 & 14 & 0.02776 \\
4 & 3.4 & 1.57 & 2.66 & 0.697 & 13 & 0.03677 \\
5 & 4.5 & 1.52 & 2.62 & 0.723 & 16 & 0.02939 \\
6 & 4.3 & 1.52 & 2.67 & 0.751 & 15 & 0.02631 \\
7 & 4.4 & 1.58 & 2.65 & 0.680 & 17 & 0.02587 \\
8 & 5.3 & 1.58 & 2.66 & 0.687 & 21 & 0.00954 \\
9 & 5.3 & 1.59 & 2.64 & 0.663 & 21 & 0.00928 \\
10 & 5.1 & 1.59 & 2.64 & 0.664 & 20 & 0.01931 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Training samples used in the SVR model. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Serial** & \begin{tabular}{c} **Water** \\ **Content** \\ **(\%)** \\ \end{tabular} & \begin{tabular}{c} **Dry** \\ **Density** \\ **(g/cm\({}^{3}\))** \\ \end{tabular} & \begin{tabular}{c} **Specific** \\ **Gravity** \\ \end{tabular} & \begin{tabular}{c} **Void** \\ **Ratio** \\ **Ratio** \\ \end{tabular} & \begin{tabular}{c} **Saturation** \\ **(\%)** \\ \end{tabular} & \begin{tabular}{c} **Test** \\ **Collapsibility** \\ **Coefficient** \\ \end{tabular} & \
\begin{tabular}{c} **Predicted** \\ **Collapsibility** \\ **Coefficient** \\ \end{tabular} &
\begin{tabular}{c} **Relative** \\ **Error** \\ **(\%)** \\ \end{tabular} \\ \hline
1 & 4.0 & 1.55 & 2.64 & 0.703 & 15 & 0.02756 & 0.03155 & 14.48 \\
2 & 3.3 & 1.57 & 2.64 & 0.684 & 13 & 0.03874 & 0.03579 & \(-\)7.61 \\
3 & 4.2 & 1.54 & 2.65 & 0.727 & 15 & 0.02847 & 0.02954 & 3.76 \\
4 & 5.4 & 1.57 & 2.68 & 0.699 & 21 & 0.00905 & 0.009088 & 0.42 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison between the predicted value and the test value for the collapsibility coefficient. As listed in Table 7, the support vector regression machine had a strong fitting effect between the predicted value and test value. The error values (MAE and RMSE) were within the acceptable range and the \(R^{2}\) was relatively high. The relative error range of prediction was \(-7.61\) to \(14.48\%\); some of the relative error values were relatively large. Many factors caused these errors, such as the prediction, test conditions, ring-knife sample preparation, soil sample transportation process, and test process, which affected the accuracy of the predicted collapsibility coefficient. To compare the PSO-SVR prediction effect and consider the number of test samples, this study also selected a support vector regression machine based on k-fold cross-validation (CV-SVR) and multiple linear regression based on a factor analysis (MLR) to perform regression predictions on the samples. Similarly, after establishing the model, the two methods predicted not only the test set, but also the training set. The prediction results were as follows: the \(R^{2}\) of the CV-SVR was \(0.6026\) and the \(R^{2}\) of the MLR was \(0.89\). Figure 11 shows a comparison of the results. The PSO-SVR method was better than the MLR and CV-SVR methods in terms of regression accuracy; the MLR was better than the CV-SVR.