# Fast Optimization of the Installation Position of 5G-R Antenna on the Train Roof
## 3 A Fast Prediction Model for the Coupling Coefficient
### Prediction Results and Errors
#### 3.6.2 Prediction Results and Errors of MNN2 Prediction Model  
As mentioned above, in this paper, when Y = 0.8 m is taken as the dividing line in MNN2, the sub-neural network 3 prediction model and sub-neural network 4 prediction model are constructed based on the ELM algorithm and PSO-ELM algorithm, respectively, when Y > 0.8 m and Y \(\leq\) 0.8 m. Similarly, the optimal number of neurons in the hidden layer of the ELM algorithm was determined by the trial-and-error method, and the parameters of the PSO-ELM algorithm are shown in Table 7. The prediction results are shown in Table 8.  
As can be seen from Table 8, when Y > 0.8 m, the PERMax of sub-neural network 3 (Sub-NN3) and sub-neural network 4 (Sub-NN4) in MNN2 are 2.11% and 1.93%, respectively, and the other two prediction performance indices are similar. However, the prediction model of sub-neural network 3 is only based on the ELM algorithm and does not need to \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**X \(\leq\) 14 m**} & \multicolumn{3}{c}{**14 m \textless{}X \(\leq\) 25 m**} \\ \cline{2-7}  & **MSE** & **MAE** & **PREMax** & **MSE** & **MAE** & **PREMax** \\ \hline MNN1 & 0.009 & 0.081 & 0.31\% & 1.062 & 0.863 & 3.33\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Performance comparison 2 of prediction models (MNN1). \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Acceleration factor c\({}_{1}\) & 2.49445 \\ Acceleration factor c\({}_{2}\) & 2.49445 \\ Number of iterations & 200 \\ Maximum velocity & \(1\) \\ Minimum velocity & \(-1\) \\ Maximum position & \(5\) \\ Minimum position & \(-5\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Parameters of the PSO-ELM algorithm. Figure 8: Prediction results and relative prediction error of MNN1 in X direction: (**a**) comparison results in X direction (coupling coefficient ranges from \(-70\) to \(-30\)); and (**b**) PRE in X direction. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**0.8 m \(\leq\) Y \(\leq\) 1 m (14 m \textless{}X \(\leq\) 25 m)**} & \multicolumn{3}{c}{**Y \textless{} 0.8 m (14 m \textless{}X \(\leq\) 25 m)**} \\ \cline{2-7}  & **MSE** & **MAE** & **PREMax** & **MSE** & **MAE** & **PREMax** \\ \hline Sub-NN3 (ELM) & 0.003 & 0.041 & 2.11\% & 0.006 & 0.072 & 3.32\% \\ Sub-NN4 (PSO-ELM) & 0.001 & 0.032 & 1.93\% & 0.003 & 0.043 & 2.14\% \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Performance comparison 1 of prediction models (MNN2). be combined with PSO, and the structure of the prediction model is simpler, so it has better engineering practicability. As above, among the 10 predictions, sub-neural network 3 has a higher prediction accuracy for one time, which also shows the instability of the prediction model constructed by the PSO-ELM algorithm. When Y \(<\) 0.8 m, the PREMax of sub-neural network 3 and sub-neural network 4 are 3.32% and 2.14%, respectively, and the other two prediction performance indices of sub-neural network 4 are also smaller, achieving a higher prediction accuracy, which reflects the role of the optimization algorithm PSO. Therefore, in this paper, Y = 0.8 m is taken as the dividing line in MNN2, and the integrated strategy is used to establish a prediction model based on sub-neural network 3 when Y \(\geq\) 0.8 m. When Y \(<\) 0.8 m, a prediction model is established based on sub-neural network 4, and the output of the two is optimized, and the prediction result of MNN2 is finally obtained. The corresponding RPE is shown in Figure 9.  
As can be seen from Figure 9a, the predicted value and expected value of the prediction model based on MNN2 are close to each other, and, as can be seen from Figure 9b, the prediction accuracy of MNN2 is relatively average. From the comparison between Figures 8 and 9, it can also be seen that, when X \(\leq\) 14 m, the RPEMax of MNN1 and MNN2 are approximately 0.31% and 1.95%, respectively.