# 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
#### 3.6.3 Prediction Results and Errors of Prediction Model Based on MMNN  
In this paper, the \"selective\" multi-mode fast strategy is adopted to construct the prediction model. In combination with the above comparison and analysis of the prediction results of the two sub-module prediction models, when X \(\leq\) 14 m, the prediction accuracy of the MNN1 prediction model is higher, and, when X \(>\) 14 m, the prediction accuracy of the MMN2 prediction model is higher. Therefore, in order to further improve the prediction accuracy of the prediction model, this paper adopts the block prediction method; that is, \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{3}{c}{**X \(\leq\) 14 m**} & \multicolumn{3}{c}{**14 m \(<\) X \(\leq\) 25 m**} \\ \cline{2-6}  & **MSE** & **MAE** & **PREMax** & **MSE** & **MAE** & **PREMax** \\ \hline MNN2 & 0.361 & 0.511 & 1.95\% & 0.438 & 0.557 & 2.12\% \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Performance comparison 2 of prediction models (MNN2). Figure 9: Prediction results and relative prediction error of MNN2 in X direction: (**a**) comparison results in X direction (coupling coefficient ranges from \(-65\) to \(-30\)); and (**b**) PRE in X direction. the block integration strategy is used to optimize the output of the prediction results of MNN1 and MNN2, so as to build the prediction model of the coupling coefficient based on the MMNN. The main structure of the prediction model is shown in Figure 10. There are three steps in the model construction process. For the first step, when the installation position and working frequency of a set of roof antennae are input into the prediction model, the prediction model will first determine whether the horizontal co-ordinate X \(\leq\) 14 m is in the installation position. If the judgment result is \"Yes\", the prediction model will choose the MNN1 prediction model for prediction. In the second step, when MNN1 is selected, it will further determine whether X \(\leq\) 3 m, and then select the prediction result of sub-neural network 1 or sub-neural network 2 as the final prediction result of MNN1. In the third step, if X \(>\) 14 m, the prediction model will select MNN2 for the prediction analysis. As mentioned above, Y = 0.8 m  
From the comparison of the results in Figures 11 and 12, it can be seen that, at each different co-ordinate, the predicted value and expected value of the prediction model based on the MMNN are very similar, and the PRE is very low; that is, the prediction accuracy is very high. As can be seen from Table 10, for roof antennae with three different operating frequencies, the prediction model based on the MMNN has similar performance indices, with the maximum values being MSE\({}_{\text{Max}}\) = 0.003, MAE\({}_{\text{Max}}\) = 0.040, and PRE\({}_{\text{Max}}\) = 2.01. This fully proves that the prediction model established in this paper has a high accuracy when facing different roof antennae. As can be seen from Table 11, the MSE = 0.002, MAE = 0.033, and PRE\({}_{\text{Max}}\) = 1.52% of the prediction model based on the MMNN are the lowest compared with the other four prediction models, which fully proves the accuracy of the prediction model established in this paper. The prediction performance indices of the MEA-BP prediction model compared to the BP prediction model and the PSO-ELM prediction model compared to the ELM prediction model have all decreased, proving the effectiveness of the optimization algorithm. Next, the required computing time and occupied computer storage space obtained after a single prediction and a single electromagnetic simulation are given, as shown in Table 12.  
As can be seen from Table 12, the PRE of the prediction model based on the MMNN proposed in this paper is only 2.01%, and, compared with the electromagnetic simulation method, the operation time only accounts for about 1/40 of the electromagnetic simulation time, and the storage space is also greatly saved.