## 3 Case Study
### Collapse Risk Assessment Based on Site Inspection Data  
Site inspection evaluation indicators can be divided into four categories: design factors, geological factors, construction factors and management factors. Design factors include excavation span and depth-to-height ratio. Geological factors include surrounding rock grade and bias. Construction factors include the main stiffness of initial support, stratum reinforcement measures, excavation methods and waterproof and drainage measures. Management factors include monitoring and measurement, construction quality qualification, accuracy of geological survey and timeliness of main support. According to the Guide to Highway Bridge and Tunnel Construction Safety Risk Assessment, the above 12 judgment indicators are divided into four levels, as shown in Table 4.  
There are four collapse risk levels in the site inspection data set, which are Level I, Level II, Level III and Level IV. The number of features for each risk level is 12. The input of the test set is \(\{x_{1},\ldots,x_{12}\}\). The data label is tunnel collapse risk grade, which can be determined according to expert site investigation. The model output is the failure probability value of tunnel collapse. The predicted result is the collapse risk level corresponding to maximum value of collapse failure, which is compared with the data label values to obtain the model prediction accuracy. The number of features in the site inspection test set is 12, and the number of samples is 60. Due to the small number of samples, the neural network model is not applicable, so the Gradient Boosting Decision Tree model in traditional machine learning is chosen. The collapse risk assessment model is constructed by calling the GradientBoostingClassifier module in the scikit-learn library. The key parameters include n_estimators and learning_rate. The grid search method is used to find the optimal hyperparameters. The parameter search range of n_estimators is [60, 80, 100, 120, 14]. The parameter search range of learning_rate is [0.001, 0.01, 0.1, 1, 1.5, 2]. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Index**} & \multicolumn{2}{c}{**Probability**} & \multicolumn{2}  
An optimization search experiment is conducted for n_estimators and learning rate. The Receiver Operating Characteristic (ROC) Curve is used for model evaluation. The closer the ROC curve is to the vertical axis, the better the model performance is, conversely, the worse the model performance is. In addition, the model can be evaluated by AUC (area under the ROC curve). Macro-averaging and micro-averaging are different methods to achieve classification accuracy calculations, and both can be used to evaluate the model. The larger the value, the larger the area, the better the model performance. The result of model parameters training is shown in Figure 4.  
Figure 4a shows the results of model training when n_estimators is fixed value and learning_rate is the variable. Figure 4b shows the results of model training when learning_rate is fixed value and n_estimators is the variable. As learning_rate increases, AUC and ACC (Accuracy) first increases and then decreases. As n_estimators increases, AUC and ACC (Accuracy) first increases and then decreases. As can be seen from the figure, The