## 4 Simulation Experiment Example of FE Model Updating of Antenna  
We combined the content of Section 3 and the deformation data of the antenna primary reflector surface nodes under the conditions of a 35\({}^{\circ}\) elevation angle and gravity load. The 25 m radio telescope antenna primary reflector original FE model is updated. The modulus of elasticity parameters of the 52 types of bars, which are classified according to the different cross-sectional dimensions and lengths of the bars, are set as input variables to the antenna original FE model. The RMS value of the BUS upper chord node displacement is taken as the output response for parameter sensitivity analysis. According to the method shown in Section 3.2, the initial value of constant \(c\) is 1, and the random sampling range of elastic modulus parameters is 190-220 GPa. Using the original FE model of the antenna and the LHS experimental design method, 200 sets of input and output samples are obtained to fit the RBF surrogate model, which is used for parameter sensitivity analysis. According to the method shown in Section 3.2, 10 sets of samples are re-extracted, and the prediction results are calculated by using the antenna original FE model and the RBF surrogate model, respectively. The constant \(c\) is optimized with the objective function \(f\) function value less than 0.01. The optimization process and results are shown in Table 2 and Figure 9. After 20 iterations, the RBF surrogate model meets the accuracy requirements when the value of \(c\) is 69.4 and the value of function \(f\) is 0.61 \(\times\) 10\({}^{-2}\). Fitting the surrogate model for parameter sensitivity analysis took 1546 s.  
Using the RBF surrogate model and Sobol method to calculate 20,000 sets of random input and output samples, the sensitivity of these 52 elastic modulus parameters to the BUS deformation is obtained, as shown in Figure 10. It can be seen that the elastic modulus parameter of the bar numbered 50 is the most sensitive to the antenna primary reflector surface deformation. However, the antenna's primary reflector surface consists of multiple panels, each supported by multiple bars, and updating this parameter is not enough to correct the deformation of the entire surface. Compared with other bars, the elastic modulus of the seven bars, numbered 2, 4, 18, 20, 33, 48, and 50, is the most sensitive to the antenna primary reflector surface deformation. Therefore, we choose these seven parameters as \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Variable \(c\)** & **Objective Function Values** \\ \hline initial value & 1 & 0.74 \\ optimal values & 69.4 & 0.61 \(\times\) 10\({}^{-2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Optimization results of constant \(c\) of RBF model for parameter sensitivity analysis. Figure 9: The optimization iteration process of the constant \(c\) of the RBF model for parameter sensitivity analysis. Figure 14: The error distribution between the updated FE model and the antenna under the action of 35\({}^{\circ}\) elevation angle and gravity load. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**The Number of Parameters** & **2** & **4** & **18** & **19** & **33** & **49** & **50** \\ \hline Elastic modulus/GPa & 218.3 & 190.4 & 191.1 & 190.3 & 190.4 & 190.7 & 190.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameter optimization results. Figure 12: The optimization iteration process of the constant \(c\) of the RBF model for parameter optimization. Figure 13: Parameter optimization process. From Figures 6b and 14, it can be seen that the error between the FE model's RMS and the antenna's RMS at a 35\({}^{\circ}\) elevation angle is reduced from 0.019 mm to 0.013 mm, which is 36.8% lower than the original error.