## 3 Sensitivity Analysis of Influencing Factors
### Random Forest Model  
The random forest is essentially an ensemble-learning based on decision trees, consisting of multiple decision trees formed by random sampling and the random selection of attributes, without any pruning action in the project of constructing decision trees. The algorithm solves quite adequately the overfitting problem that emerges from a single decision tree, and additionally tackles large-scale datasets with excellent fault tolerance for noisy and missing data. The random forest algorithm has a high prediction accuracy and robustness. The random forest model is employed to classify the importance of the variables related to karst tunnels in the following steps. The operational flow chart of the random forest model based on orthogonal experimental design is shown in Figure 9.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Target Variable** & **A1** & **A2** & **A3** & **A4** & **A5** & **A6** & **A7** & **A8** & **A9** & **A10** & **A11** \\ \hline \multirow{3}{*}{\(d\)} & F & \multirow{3}{*}{0.44} & F & \multirow{3}{*}{0.60} & F & \multirow{3}{*}{0.31} & \multirow{3}{*}{9.53} & \multirow{3}{*}{0.47} & \multirow{3}{*}{0.40} & \multirow{3}{*}{0.52} & \multirow{3}{*}{3.50} & \multirow{3}{*}{0.15} \\  & value & & & & & & & & & & \\ \cline{2-2} \cline{6-11}  & \(p\) value & 0.85 & 0.56 & 0.78 & 0.85 & 0.74 & 0.001 & 0.63 & 0.67 & 0.60 & 0.046 & 0.86 \\ \hline \multirow{3}{*}{S1} & F & \multirow{3}{*}{0.03} & F & \multirow{3}{*}{0.04} & \multirow{3}{*}{0.00} & \multirow{3}{*}{0.05} & \multirow{3}{*}{0.05} & \multirow{3}{*}{0.02} & \multirow{3}{*}{0.00} & \multirow{3}{*}{0.01} & \multirow{3}{*}{0.07} & \multirow{3}{*}{452.50} & \multirow{3}{*}{0.04} \\  & value & & & & & & & & & & & \\ \cline{2-2} \cline{6-11}  & \(p\) value & 0.97 & 0.97 & 1.00 & 0.95 & 0.95 & 0.98 & 1.00 & 0.99 & 0.94 & 0.00 & 0.97 \\ \hline \multirow{3}{*}{S1–S3} & F & \multirow{3}{*}{0.08} & F & \multirow{3}{*}{0.26} & \multirow{3}{*}{0.02} & \multirow{3}{*}{0.03} & \multirow{3}{*}{0.03} & \multirow{3}{*}{0.20} & \multirow{3}{*}{0.03} & \multirow{3}{*}{0.09} & \multirow{3}{*}{0.01} & \multirow{3}{*}{161.58} & \multirow{3}{*}{0.00} \\  & value & & & & & & & & & & & \\ \hline \multirow{3}{*}{S1–S3} & F & \multirow{3}{*}{0.93} & \multirow{3}{*}{0.78} & \multirow{3}{*}{0.98} & \multirow{3}{*}{0.97} & \multirow{3}{*}{0.82} & \multirow{3}{*}{0.97} & \multirow{3}{*}{0.92} & \multirow{3}{*}{0.99} & \multirow{3}{*}{0.00} & \multirow{3}{*}{1.00} \\  & value & & & & & & & & & & & \\ \hline \end{tabular}
\end{table}
Table 5: Analysis of variance (ANOVA).  
1. The original training set should be obtained. Initially, a bootstrap resampling technique is applied to generate a new set of training samples by randomly sampling various samples from the original training sample set in a relaxed manner;
2. The training sets and test sets should be divided from the original sample set following the appropriate ratio, and the root nodes and leaf nodes should be trained to determine the number of decision trees, the depth of decision trees, and the number of features to be applied to train the leaf nodes of each decision tree;
3. The trained random forest model should be adopted to predict the test set. The prediction accuracy should be adjusted until it fulfils the requirements of prediction accuracy. The variables of the trained random forest model should be subjected to feature importance analysis, the feature importance score of each influencing factor should be calculated, and the feature importance results should be visualised.