# Fast Optimization of the Installation Position of 5G-R Antenna on the Train Roof
## 3 A Fast Prediction Model for the Coupling Coefficient
### Setting of Prediction Model for the Coupling Coefficient

Table 3: Comparison of coupling coefficients of roof antennae with different frequencies. From Figure 3, it can be seen that, due to the reflection of the roof plane, the antenna pattern of the roof antenna (f = 2 GHz) is no longer symmetrical, but the shapes of the antenna patterns at the two installation positions are generally similar and have no significant changes. In addition, it can also be seen from Table 4 that the optimization of the installation position of the roof antenna with different operating frequencies has a small impact on the performances of the antenna. For the roof antenna (f = 2 GHz), the change in MLA is only 0.08 dbi, and MLD is reduced by 15\({}^{\circ}\), so the optimization of the installation position does not significantly affect the performances of the roof antenna. However, because of the difference in operating frequency, the two co-ordinates are also significantly different. This is due to the irregular phenomenon caused by the size of the roof antenna and other factors, so it is difficult to use the method of fitting the curve to predict. In addition, due to the irregular reflection of the roof plane and other environmental factors in practical applications, it is possible to affect the irregular variation of the attenuation characteristics of the radiant electric field intensity on the roof, so it is necessary to establish a more accurate prediction method for the coupling coefficient. However, it can still be seen from Table 3 that, among the 825 different positions in the dataset, the coupling coefficient can be reduced by up to 26.96 dB by optimizing the installation position of the roof antenna. Therefore, if the installation position of the roof antenna with the lowest coupling coefficient can be found, the EMI of pantograph arcing can be significantly reduced. Methods based on prediction model to obtain such locations will be more efficient than methods based on multiple electromagnetic simulations or methods based on engineering experience. As mentioned above, this paper will build a prediction model based on the BPNN algorithm and ELM algorithm, optimize it with the MEA and PSO algorithm, and propose a prediction model based on the MMNN. Block modeling was carried out according to the roof plane in the model, as shown in Figure 4.  
In reality, the contact line is generally located at the center line of the roof plane, that is, the X-axis in the figure, and the roof plane is symmetrically distributed accordingly, so only half of the roof plane area is considered in this paper. As can be seen from Figure 4, in the range of the roof antenna installation currently considered, the roof plane is divided into four modules, with X as 3 m and 14 m, and Y as 0.8 m as the dividing lines, respectively, and four different algorithms are used for block modeling. Finally, the coupling coefficient of the roof antenna at different installation positions is predicted efficiently based on the prediction model. The selection of the three dividing lines is based on the comparison of the prediction accuracy of different single-prediction models, and gives full play to their respective strengths as much as possible. The analysis of the results will be presented later. Figure 4: Modular modeling diagram. The accuracy of the BPNN prediction model and ELM prediction model is mainly affected by the parameters (weights and thresholds) between the neuron nodes of each layer in the structure, and these parameters are generated randomly, which may lead to a low prediction accuracy and instability [21]. To solve the above problems, the MEA and PSO algorithms are widely used to optimize the initial parameters, so that the prediction accuracy and stability of the prediction model have been significantly improved. Therefore, the MEA-BPNN prediction model and PSO-ELM prediction model will be constructed in this paper to predict the coupling coefficient of the roof antenna at different installation positions.