## 4 Discussion  
To further analyze the performance of the WO-DBN model, a comparison study between WO-DBN, DBN, ANN and another deep learning method called long short-term memory (LSTM) has been conducted. For the DBN model, the trial-and-error method is generally used to determine its hyperparameters, which can be described as follows. (1) According to the experience, the possible ranges of hyperparameters have been determined. (2) Several sets of hyperparameter combinations have been selected in their possible ranges by the experimental design or other methods, and these hyperparameter combinations have been used for prediction. (3) The prediction errors of models by the different combinations of hyperparameters have been used for comparison, that is, the evaluation indexes of the prediction models have been compared. The parameter combination with the smallest prediction error has been selected as the final hyperparameters of the prediction model. Figure 11: Prediction results of the structure response for the utility tunnel: (**a**) Vertical displacement at the mid span of the structure roof; (**b**) Horizontal stress at the mid span of the structure roof. By using the trial-and-error method, the determined hyperparameters of the DBN model are summarized in Table 5.  
As one typical artificial intelligence method, the ANN is generally used for prediction study [27; 35; 36; 37]. Therefore, it is used here for comparison. By using the trial-and-error method, too, its hyperparameters can be determined, which are summarized in Table 6.  
It should be noted that, in Table 6, \(n_{1}\) and \(n_{2}\) are neuron numbers for the first and second hidden layers, respectively. \(\eta\) is the learning rate, and _Epoch_ is the maximum iteration number. Moreover, for the LSTM which belongs to the recurrent neural network (RNN) [38], it is one generally used deep learning method for the prediction study [38; 39]. Therefore, here, for a comparison with the new deep learning model (WO-DBN), the LSTM is applied. By using the trial-and-error method, the hyperparameters of LSTM can also be determined. Because the determined structure of LSTM is the same as that of ANN, the hyperparameters of LSTM are also summarized in Table 6.  
By using the determined parameters in Tables 5 and 6, the prediction models for the response of the utility tunnel structure based on DBN, ANN and LSTM can be constructed. For comparison, the prediction results of the DBN, ANN and LSTM models are also shown in Figure 11. From Figure 11, it can be found that there are some differences between the prediction results of the three models (DBN, ANN and LSTM) and the real test results, and the results of WO-DBN approach the real data more. Therefore, the prediction results of the new WO-DBN model are the best, which are much better than those of the three models. Moreover, to compare the four models (WO-DBN, DBN, ANN and LSTM) more clearly, the quantitative evaluation indexes (RMSE, MAE and R) of the four prediction models are summarized in Table 7.  
From Table 7, it can be found that, both for the vertical displacement and for the horizontal stress, the computing errors of the WO-DBN model are all much less than those of the three other models (DBN, ANN and LSTM). For example, the R for the vertical displacement by WO-DBN is 0.9742, which is much larger than those by DBN (0.8642), ANN (0.7585) and LSTM (0.8435). The R for the horizontal stress by WO-DBN is 0.6825, which is also much larger than those by DBN (0.5011), ANN (0.3411) and LSTM (0.5145). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Parameters** & \(\mathbf{n_{1}}\) & \(\mathbf{n_{2}}\) & \(\mathbf{\eta}\) & _Epoch_ \\ \hline ANN & Values & 32 & 16 & 0.01 & 50 \\ LSTM & Values & 16 & 8 & 0.001 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Parameters of the ANN and LSTM models.