# Thermal Environment Prediction for Metro Stations Based on an RVFL Neural Network
## 3 Measurement Process
### Results and Analysis
#### 3.4.2 Prediction Performance of Thermal Model Based on RVFLNN  
From the above analysis, the training parameters were finally determined--that is, the number of hidden layer nodes is 400 and the range of \(w\) and \(b\) is [\(-\)1, 1]. Hence, the thermal model based on RVFLNN was built with the above parameters. Figure 7 gives the comparison results of the prediction data with the experimental data. Figure 8 shows the relative error of the prediction and experimental data. The relative error can be calculated with the equation  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & & & (a) S2 & & & & & \\ \hline Number of Nodes & 20 & 50 & 100 & 200 & 300 & 400 & 600 & 800 & 1000 \\ \(E_{\text{train}}\)\(\times 10^{-3}\) & 3.687 & 3.435 & 3.404 & 3.438 & 3.333 & 3.284 & 3.271 & 3.235 & 3.224 \\ \(E_{\text{validation}}\)\(\times 10^{-3}\) & 4.532 & 4.201 & 4.144 & 4.119 & 4.067 & 3.991 & 3.972 & 3.910 & 3.941 \\ \hline  & & & & & & & & & & \\ \hline Number of Nodes & 20 & 50 & 100 & 200 & 300 & 400 & 600 & 800 & 1000 \\ \(E_{\text{train}}\)\(\times 10^{-3}\) & 4.657 & 4.391 & 4.294 & 4.162 & 4.126 & 4.122 & 3.958 & 3.930 & 3.920 \\ \(E_{\text{validation}}\)\(\times 10^{-3}\) & 6.011 & 5.807 & 5.490 & 5.452 & 5.528 & 5.613 & 5.487 & 5.502 & 5.494 \\ \hline  & & & & (c) S4 & & & & & \\ \hline Number of Nodes & 20 & 50 & 100 & 200 & 300 & 400 & 600 & 800 & 1000 \\ \(E_{\text{train}}\)\(\times 10^{-3}\) & 3.229 & 2.866 & 2.791 & 2.720 & 2.695 & 2.660 & 2.629 & 2.600 & 2.585 \\ \(E_{\text{validation}}\)\(\times 10^{-3}\) & 6.880 & 6.760 & 6.714 & 6.824 & 6.773 & 6.846 & 6.763 & 6.821 & 6.773 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Effects of different numbers of hidden layer nodes on model performance.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{\(\lambda\)} & **\(\omega\),b c [\(-\)0.5, 0.5]** & **\(\omega\),b c [\(-\)1, 1]** & **\(\omega\),b c [\(-\)2, 2]** \\ \cline{2-5}  & \(E_{\text{validation}}\)\(\times 10^{-3}\) & \(E_{\text{validation}}\)\(\times 10^{-3}\) & \(E_{\text{validation}}\)\(\times 10^{-3}\) \\ \hline
0.05 & 5.554 & 5.596 & 5.917 \\
0.1 & 5.557 & 5.586 & 5.667 \\
0.5 & 5.485 & 5.464 & 5.632 \\
1 & 5.478 & 5.455 & 5.447\[E_{relative}=\left|\frac{T_{\text{sim},i}-T_{\text{exp},i}}{T_{\text{exp},i}} \right|\times 100\% \tag{11}\]  
where \(T_{\text{exp},i}\) and \(T_{\text{sim},i}\) are the experimental data and the prediction data, respectively.  
Figure 8: _Cont._  
Figure 7: Comparison of predicted data with experimental data.  
1. The temperature change in the metro station is influenced by many factors and its change rule is relatively complicated. The presented model based on the RVFLNN can reveal this rule very well: its fitting error and prediction error are both very small.
2. Comparison of the predicted data and experimental data shows that the maximum absolute error is about 0.4 \({}^{\circ}\)C and the maximum relative error is about 2.5%.
3. The test error shown in Table 3 is sometimes a little higher than the validation error in the three different RVFLNN models. This can also be seen in Figures 7 and 8.  
The model accuracy has reached a good level and the presented modeling method can be used for future temperature prediction in metro stations.