## 4 Analysis and Comparison of the Model Performance
### Comparative Analysis of Multi-Types Model  
To evaluate the superiority of the proposed model, comparisons were made with a DNN without feature fusion. Additionally, common supervised learning methods such as XGBoost, Decision Tree Regression (DTR), and Random Forest Regression (RFR) were included in the comparative analysis. Table 4 displays the optimal key parameters or structures for these supervised learning models, which were obtained through a grid search method. The performance of the proposed method, as well as other comparative methods, is presented in Table 5. The proposed method outperforms the other methods and exhibits the best generalization. The R-squared (\(R^{2}\)) values for the proposed model on the training set are 0.938, 0.908, 0.987, 0.991, and 0.965, respectively. On the validation set, the \(R^{2}\) values are 0.910, 0.821, 0.779, 0.687, and 0.768, respectively. All models perform well on the test set, but only FDNN and DNN achieve \(R^{2}\) values above 0.8. FDNN outperforms DNN with a 0.03 improvement in \(R^{2}\) on the training set and a 0.089 improvement in R\({}^{2}\) on the test set, indicating that FDNN exhibits better generalization. Although DTR has the highest \(R^{2}\) on the training set, it has the lowest \(R^{2}\) on the test set. Figure 10: Change of loss function during training process in training and test datasets. To demonstrate the improvement in predictive performance resulting from the inclusion of additional input parameters, the geometric parameters were used as the base parameters. Geological, support, and construction parameters were incorporated as subsequent parameters, resulting in the creation of seven different datasets with varying parameter compositions, as outlined in Table 6. _MAE_ and \(R^{2}\) were selected as performance metrics for subsequent model training on these diverse datasets. The _MAE_ values for all models under different inputs are shown in Figure 12. In the subsequent analysis, geometric parameters were used as the foundational parameters. The performance improvement resulting from DS1-DS3 indicates that geological parameters have the most significant impact on model performance across all models. For DS4-DS6, the combination of geological and construction parameters in the database yields favorable performance improvements for all models. FDNN, DNN, and XGBoost models consistently outperform DRT and RFR models in both training and testing phases on DS1-DS7 datasets. The model performance ranking, from highest to lowest, is as follows: FDNN, DNN, XGBoost, RFR, and DRT. The proposed FDNN model exhibits the best performance across datasets with different parameter combinations, showcasing its robustness and superior performance. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{5}{c}{**Training Set**} & \multicolumn{5}{c}{**Test Set**} \\ \cline{2-10}  & _MAE_ & _MSE_ & _RMSE_ & _R_\({}^{2}\) & _MAE_ & _MSE_ & _RMSE_ & _R_\({}^{2}\) \\ \hline FDNN & 0.046 & 0.004 & 0.059 & 0.938 & 0.043 & 0.003 & 0.053 & 0.910 \\ DNN & 0.054 & 0.005 & 0.072 & 0.908 & 0.058 & 0.007 & 0.081 & 0.821 \\ XGBoost & 0.054 & 0.006 & 0.075 & 0.987 & 0.143 & 0.049 & 0.222 & 0.779 \\ DTR & 0.115 & 0.126 & 0.354 & 0.991 & 1.114 & 2.954 & 1.721 & 0.687 \\ RFR & 0.482 & 0.447 & 0.661 & 0.965 & 0.943 & 2.182 & 1.485 & 0.768 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Performances of models. Figure 11: Results of prediction and measurement under training and test datasets. (**a**) Training set. (**b**) Test set. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Model**} & \multicolumn{2}{c}{**Key Parameters**} \\ \hline DNN & Input-BN-FC(176)-FC(100)-FC(80)-FC(40)-FC(20)Dropout(0.1)-Output \\ XGBoost & max\_depth: 7; learning rate: 0.1005; n\_estimators: 36; objective: reg: squarederror’; booster: 'gbtree’ \\ DTR & max\_depth: 10; random\_state: 30 \\ RFR & max\_depth: 7; random\_state: 30 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameters of models.