## 4 Results and Discussion
### Variable Importance  
To analyze the impact of feature variables on the prediction results of the LSTM model, the partial dependence plot (PDP) method was introduced to explain the output of the model. PDP, a common method for local interpretation [61], visualizes the marginal effect of single features on the prediction results of the LSTM model by taking all the possible values of the input variables as the horizontal axis and the average value of the output variables as the vertical axis, thereby reflecting the impact of different values of important features on the prediction results of the LSTM model. Figure 13 shows the PDPs of the influencing variables \(T_{w}\) and \(Q_{w}\), in which the two features do not interact strongly with other model inputs. Clearly, the air temperature \(T_{f_{out}}\) is directly correlated with the trickling water temperature \(T_{w}\), while \(T_{f_{out}}\) is inversely related to the trickling water flow rate \(Q_{w}\). The reason is that the heat absorption during evaporation of the trickling water with relatively high flow rate in the roadway causes the conversion of part of the sensible heat in the airflow into latent heat. For prediction of the airflow relative humidity \(RH_{out}\), both upwelling water temperature and flow rate are positively correlated with \(RH_{out}\), which is expected. In addition, after increasing to a certain extent, the upwelling water temperature and flow rate almost have no influence on the airflow temperature, but start to have evident influence on the airflow humidity. As can be seen from Figure 13, the latent heat and sensible heat variations of airflow in the water upwelling section of roadway are rather complex, so a useful mathematical model can hardly be established to predict the influence of the thermal upwelling water on airflow humidity and temperature at the end of the roadway. \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Prediction Model**} & \multicolumn{2}{c}{**Temperature**} & \multicolumn{2}{c}{**Relative Humidity**} \\ \cline{2-5}  & **MSE** & \(\mathbf{R^{2}}\) & **MSE** & \(\mathbf{R^{2}}\) \\ \hline PCA-LSTM-GA & 5.871310 \(\times\)\(10^{-6}\) & 0.9915 & 3.2413 \(\times\)\(10^{-4}\) & 0.9462 \\ \hline PCA-RNN-GA & 7.2956 \(\times\)\(10^{-6}\) & 0.9862 & 3.3891 \(\times\)\(10^{-4}\) & 0.9407 \\ \hline PCA-BP-GA & 8.4125 \(\times\)\(10^{-6}\) & 0.9841 & 3.5692 \(\times\)\(10^{-4}\) & 0.9359 \\ \hline PCA-XGBoost-GA & 2.16435 \(\times\)\(10^{-6}\) & 0.9617 & 3.7128 \(\times\)\(10^{-4}\) & 0.9243 \\ \hline \end{tabular}
\end{table} 
Table 4: Error of prediction results of different models. Figure 13: Partial dependence plots of water temperature \(T_{w}\) and flow rate \(Q_{w}\) for predicting air temperature \(T_{f_{out}}\) (**a,b**) and air \(RH\)\(RH_{out}\) (**c,d**) at the end of the roadway with water trickling. The importance scores (ISs) of input features were calculated in the hope of clarifying their importance. The calculation was conducted using the random forest model based on the mean decrease impurity of modes and depth of the tree for a variable [57; 62]. Figure 14a shows the IS results for air temperature \(T_{f_{out}}\) prediction. Interestingly, the water temperature \(T_{w}\) and flow rate \(Q_{w}\) have a small influence on the airflow temperature at the end of the roadway, for which the IS is 0.002. The results also indicate that the degrees of importance of the variables to \(T_{f_{out}}\) follows the order: surrounding rock temperature (IS 0.661) \(>T_{f_{in}}\) (IS 0.264) \(>RH_{in}\) (IS 0.067). This means that, in respect of roadway cooling, researchers and engineers should pay more attention to heat dissipation from surrounding rocks. The roadway airflow temperature accumulates during long-distance transport, and the surrounding rock temperature contributes most of the heat. The shorter the distance of a surrounding rock section to the prediction point, the more important the temperature of this section.