## 4 Case Study
### Analysis of Prediction Results for Ventilation Local Resistance Coefficient  
Considering the engineering layout, maintenance ventilation characteristics, and local resistance characteristics, the diameter of the tunnel, the diameter of the air duct, the number of the air duct, and the airflow speed of the outlet are selected in this paper as the input variables of the IAJS-HKRVM prediction model, and the local resistance coefficient is selected as the output variable. The values or ranges of each input variable are shown  
Figure 8: Wind velocity distribution cloud map (**a**) and vector map (**b**) in the longitudinal section of the water transmission tunnel.  
Figure 7: Comparison of local loss coefficient simulation and test value under different bifurcation angles and flow diversion ratios (**(a)**—5\({}^{\circ}\); **(b)**—10\({}^{\circ}\); **(c)**—15\({}^{\circ}\)).  
in Table 3. A total of 68 groups of samples are obtained by random sampling, and the response values of each group of samples are calculated based on the three-dimensional numerical model of maintenance ventilation in Section 4.1. In the numerical simulation process of the 68 groups of samples, their main difference lies in the physical model and the settings of the boundary conditions. Changes in the number of air ducts, the diameter of the air ducts, and the diameter of the tunnel will lead to changes in the physical model, and changes in the airflow speed of the outlet will lead to changes in the setting of the boundary conditions.  
Among the 68 groups of samples obtained based on the three-dimensional numerical simulation model, 50 groups are randomly selected as the training set, and the other 18 groups are selected as the test set. The local resistance coefficient of water transmission tunnel maintenance ventilation is predicted by the IAJS-HKRVM prediction model established in this paper. The learning curves of the fitness of the train set and test set are shown in Figure 9. The comparison between the prediction results and the numerical simulation results is shown in Figure 10.  
It can be seen from Figure 9 that the fitness function value of the training set is smaller than that of the test set. Moreover, when the model is trained for about 60 iterations, the fitness curves of the training set and the test set begin to converge and there is little difference between the fitness values of the training set and the test set. Therefore, the model has a good generalization ability. As shown in Figure 10, the ventilation local  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Input Variable** & **Unit** & **The Values or Ranges** \\ \hline Diameter of air duct & m & 1-2 \\ Number of air duct & / & \(1,2,3,4\) \\ Diameter of tunnel & m & 5-8 \\ Airflow speed of outlet & m/s & 3-10 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The values or ranges of each input variable.  
Figure 10: Comparison of local resistance coefficient prediction value and simulation value.  
Figure 9: The learning curves of the fitness of train set and test set.  
resistance coefficient of the combined tee structure predicted by the IAJS-HKRVM model has a high consistency with the numerical simulation results, and the residual difference between the predicted value and the simulated value at each test sample point is within the allowable range. Therefore, the hybrid prediction model for the local resistance coefficient of water transmission tunnel maintenance ventilation proposed in this paper can efficiently and accurately predict the local resistance coefficient under different working conditions and can be used to predict the local resistance coefficient of the combined tee structure of the water transmission tunnel.