## 4 Results and Discussion
### Analysis of Factors Screening  
Feature selection plays an important role in machine learning, as it manually or automatically selects input features that contribute significantly to the target variable. This selection is an important step to be considered while constructing ML models [44]. After the initial selection of input parameters in predicting horizontal displacements of the enclosure, to avoid the occurrence of dimensional catastrophe and overfitting and, at the same time, to improve the model's accuracy, it is necessary to rely on feature selection for further screening of the input parameters.  
The Pearson correlation coefficient [45] was used to calculate the linear correlation between the horizontal displacement of the envelope and each eigenvector. The Pearson correlation coefficient was used to calculate the linear correlation between the horizontal displacement of the enclosure and each eigenvector. The calculated formula is as follows:  
\[r=\frac{\sum_{i=1}^{n}{(x_{i}-\overline{x})(y_{i}-\overline{y})}}{\sqrt{\sum _{i=1}^{n}{(x_{i}-\overline{x})}^{2}}\sqrt{\sum_{i=1}^{n}{(y_{i}-\overline{y} )}^{2}}} \tag{6}\]  
where \(r\) denotes the Pearson correlation coefficient, \(x_{i},y_{i}\) denote the values of the \(x\) and \(y\) variables, and \(\overline{x},\overline{y}\) denote the mean of the variables in the sample, respectively. The Pearson's correlation coefficient lies between \(-1\) and \(1\). The greater the absolute value of the coefficient (\(\left|\,r\,\right|\)), the stronger the correlation between the variables.  
According to the Pearson correlation coefficient heatmap illustrated in Figure 9, the correlation results of each feature factor do not meet the conditions for achieving a high or strong correlation. Here, only feature factors with \(\left|\,r\,\right|>0.1\), indicating at least a weak correlation with the target value, are considered for selection. The feature factors in the dataset Set_1 comprise D, ACT, EL, WBP, AF, SS1, SS2, and PS. The target value is HD. In contrast, Set_2 comprises all feature factors.  
Table 6 shows the specific composition of the formed Set_1 and Set_2 datasets. These different datasets were fed into the optimal RF for model training and then evaluated. The precision assessment for each result is shown in Table 7. The 5-fold cross validation and the test set result all indicate that the performance of Set_2 is better than Set_1.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dataset** & **Target Value** & **Characteristic Factor** \\ \hline Set\_1 & HD & D, ACT, EL, WBP, AF, SS1, SS2, PS; \\ Set\_2 & HD & D, ACT, WL, EL, WBP, AF, SS2, SS1, PS, ST, BS, CS; \\ \hline \hline \end{tabular}
\end{table}
Table 6: Composition of different datasets.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Feature Selection**} & \multirow{2}{*}{**Dataset**} & \multirow{2}{*}{**\(\mathbf{R^{2}}\)**} & \multirow{2}{*}{**MAE**} & \multirow{2}{*}{**RMSE**} & \multirow{2}{*}{**\(\mathbf{R^{2}}\)**} & \multirow{2}{*}{**MAE**} & \multirow{2}{*}{**RMSE**} \\ \cline{5-6}  & & & & & & & & \\ \hline Pearson & Set\_1 & 0.9746 & 1.5108 & 3.1614 & 0.9734 & 1.5093 & 3.1987 \\ None & Set\_2 & 0.9907 & 0.8629 & 1.9165 & 0.9905 & 0.8621 & 1.9156 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Accuracy ratings of RF’s prediction results for the three datasets.