## 3 A Fast Prediction Model for the Coupling Coefficient
### Structure of the Cascade PSO-BP Neural Network  
A cascade neural network can combine multiple networks of the same kind or different networks into a multi-layer structure, with the advantages of a fast learning speed and no need for the backward propagation of error signals. The cascade neural network model established in this paper is composed of two identical PSO-BP networks. The main structure of the prediction model is shown in Figure 8.  
In the PSO-BP cascade neural network model, neural network I does not directly input into neural network II, but instead calculates the electric field strength at the roof antenna through the coupling coefficient. The field strength at the roof antenna is calculated by Equation (3):  
\[\mathrm{S=E_{r}-E_{w}} \tag{3}\]  
where \(\mathrm{E_{r}}\) is the electric field strength at the roof antenna, in dB\(\mathrm{\SIUnitSymbolMicro m}\); \(\mathrm{E_{w}}\) is the electric field strength at the window, in dB\(\mathrm{\SIUnitSymbolMicro m}\); \(\mathrm{S}\) is the coupling coefficient, defined as the ratio of  
\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 & 300 \\ Maximum velocity & \(1\) \\ Minimum velocity & \(-1\) \\ Maximum position & 5 \\ Minimum position & \(-5\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameters of the PSO-BP algorithm.  
Figure 8: Structure of the proposed cascade neural network prediction model.  
Figure 7: PSO-BP neural network topology.  
the electric field strength at the roof antenna to the electric field strength at the window. The electric field strength at the roof antenna is used as the input to neural network II. At the same time, the input of neural network I is also used as the input of neural network II to predict the coupling coefficient of the electric field strength between the window position and the roof antenna port. This means that there are three steps in the model construction process.  
For the first step, the model in Figure 3 is used to obtain the field data. The antenna position is assumed to be constant and the window probe position is varied by 1 m in the y direction and 0.4 m in the z direction. The dataset is then pre-processed to extract feature components, which are used as inputs into the neural network model. In this paper, 80 percent of the data from the above sample set is randomly selected as the training set, and the remaining 20 percent is used as the validation set. The training set data is used to train the PSO-BP neural network I, which is validated by the validation set.  
In the second step, the measured field data received by the window probe is used to predict the coupling coefficient with the PSO-BP neural network I, and the field strength at the roof antenna is calculated. The field strength at the roof antenna is the input of the PSO-BP neural network II.  
The third step is to train the PSO-BP neural network II. The input data contains both simulation data and measurement data. This will improve the accuracy of the model. The output of the PSO-BP neural network II is the coupling coefficient. Similarly, the electric field strength at the roof antenna is calculated using Equation (3).  
By further comparing and analyzing the prediction results of the proposed cascade neural network with a single neural network, it can be concluded that the prediction accuracy of the cascade neural network prediction model is significantly improved. The specific analysis of the prediction results will be given below.