## 3 Sensitivity Analysis of Influencing Factors
### Feature Importance Ranking  
To measure the contribution of each input variable to the training and testing results of the random forest model, the random forest algorithm was applied to rank the characteristic importance of factors affecting the stability of the rock and soil masses around the tunnel and the karst cave. However, by applying the orthogonal experimental design and random forest algorithm, variable significance analyses were performed by calculating the reduction in prediction error for out-of-bag samples. The feature importance measurement is the average of the difference between the original prediction error and the prediction error on out-of-bag samples by randomly upsetting a certain eigenvalue. The data collected with  
Figure 9: The operational flow chart. vertical displacement as the target variable could be the original dataset, and the accuracy results of the random forest model test set are shown in Figure 10a,b. In the first test of the trained random forest model, the scatters are 93.75% within the 95% prediction interval. In the second test result, 94.90% of the scatter points are located within the 95% prediction interval, which demonstrates that the combination of the orthogonal experimental design method and the random forest model has a high prediction accuracy, and the fitting effect of the model could achieve the arithmetic requirements. Nevertheless, owing to the randomness of sampling and the randomness of selecting attributes of the random forest algorithm, there are a certain amount of differences in the feature importance results and the sensitivity ranking of each influencing factor obtained from each calculation. Upon this basis, the most representative calculations were selected for sensitivity analyses employing a multiple-operation approach. It is shown in Figure 10c that these 11 influences are classified into three categories of importance parameters in terms of the degree of characteristic importance, with the first category having the highest sensitivity, the second the secondary, and the third the lowest. With vertical displacement as the response variable, the results of the two tests indicated that the first type of parameters included A6 (tunnel diameter), A10 (tunnel buried depth), and A11 (excavation dimension); and the third type of parameters included A8 (clear distance between the tunnel and the karst cave), A4 (cohesion), and A9 (location of the karst cave). As shown in Figure 10d,e, the scatters in the first test of the random forest model are located in 99.35% of the 95% prediction intervals, considering the first principal stress as the target variable. The scatters in the second test are located within the 95% prediction interval 99.30% of the time. The method also maintains a high prediction accuracy at this time. As shown in Figure 10f, in the results of the first test, the parameters of the first category were A10 (tunnel buried depth), A9 (location of the karst cave), and A3 (geotechnical weight); the parameters of the third category were A5 (internal friction angle), A7 (diameter of the karst cave), and A2 (Poisson's ratio). In the results of the second test, the first type of parameters included A10 (tunnel depth), A9 (location of the karst cave), and A1 (elastic modulus), and the third type of parameters included A5 (internal friction angle), A2 (Poisson's ratio), and A7 (diameter of the karst cave). In Figure 10g,h, with the principal stress difference as the response variable, the scatters of the random forest model are located in 98.33% of the 95% prediction intervals in the first test, and the percentage of the scatters in the second test that are located within the 95% prediction interval is 98.49%. It shows that the model has a high prediction accuracy and a high fitting effect of the model.