## 3 Sensitivity Analysis of Influencing Factors
### Feature Importance Ranking
However, in the analysis of variance (ANOVA), the F-value observed by A10 (tunnel buried depth) was 452.50, and the P-value was 0.00, which was statistically significant. The \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Ranking of**} & \multicolumn{2}{c}{**The first category**} & \multicolumn{4}{c}{**The Secondary Category**} & \multicolumn{4}{c}{**The Third Category**} \\ \cline{3-11}  & **Influencing Factors** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **11** \\ \hline \multirow{2}{*}{\(d\)} & first test & A6 & A10 & A11 & A3 & A1 & A5 & A2 & A7 & A8 & A4 & A9 \\ \cline{2-11}  & second test & A6 & A10 & A11 & A1 & A3 & A2 & A5 & A7 & A8 & A9 & A4 \\ \hline \multirow{2}{*}{S1} & first test & A10 & A10 & A10 & A11 & A8 & A6 & A11 & A4 & A5 & A7 & A2 \\ \cline{2-11}  & second test & A10 & A10 & A10 & A6 & A8 & A11 & A3 & A4 & A5 & A2 & A7 \\ \hline \multirow{2}{*}{S1–S3} & first test & A10 & A10 & A10 & A10 & A11 & A2 & A9 & A8 & A1 & A7 & A5 & A4 \\ \cline{2-11}  & second test & A10 & A10 & A10 & A11 & A8 & A11 & A9 & A7 & A4 & A5 \\ \hline \hline \end{tabular}  
* The meaning of each symbol in the table is as follows: \(d-\)vertical displacement, S1—the first principal stress, S3—the third principal stress. The influencing factors in the red area are the first category of influencing factors, which means that the feature importance of such influencing factors is the greatest. The influencing factors in the orange region are the secondary category of influencing factors. This indicates that the feature importance of such influencing factors is of secondary importance. The influencing factors in the yellow area are the third category of influencing factors, which means that the feature importance of such influencing factors is minimal.  
\end{table} 
Table 6: The ranking of feature importance. two influencing factors with the largest feature importance obtained by the orthogonal experimental design and random forest algorithm are the same as the calculation results obtained by the orthogonal experimental design and range analysis method. The three least important influencing factors in the feature importance ranking obtained by the orthogonal experimental design and random forest algorithm were A5 (internal friction angle), A7 (the diameter of the karst cave), and A2 (Poisson's ratio). The three least sensitive influencing factors in the calculation results obtained by the orthogonal test design and range analysis method were A8 (the clear distance between tunnel and karst cave), A3 (geotechnical weight), and A7 (the diameter of the karst cave). In the calculation results of the most insensitive influencing factors, the calculation results of the two methods were not exactly the same. When taking the main stress difference as the target variable, the three influencing factors with the greatest feature importance were A10 (tunnel buried depth), A6 (tunnel diameter), and A3 (geotechnical weight) in the two test results obtained by applying the orthogonal test design and random forest algorithm. In the calculation results obtained by the orthogonal experimental design and range analysis method, the three most sensitive influencing factors were A10 (tunnel buried depth), A2 (Poisson's ratio), and A6 (tunnel diameter). And the results calculated by these two methods were basically the same. However, in the analysis of variance (ANOVA), the F-value observed by A10 (tunnel buried depth) was 161.58, and the P-value was 0.00, which was statistically significant. In the order of sensitivity obtained by the two methods, it is shown that the two influencing factors A10 (tunnel buried depth) and A6 (tunnel diameter) had the greatest impact on the construction safety of karst tunnels with the main stress field as the target variable.