## 3 Updating Method for FE Model of Antenna
### Establishment of Original FE Model and Analysis of Model Error  
Based on the antenna design diagram and ANSYS APDL 2022 software, we established the parametric original FE model of the antenna reflector shown in Figure 4a, which includes 28,132 elements and 24,135 nodes. Modeling omits the alidade, uses a mass element to equate the primary reflector surface, with the mass element being set on the upper chord node of the BUS, and uses beam and shell elements to simulate the rest of the antenna's structure, simplifying the connecting parts between the components and applying full-degree-of-freedom constraints at the nodes at the ends of the pitch axis. After applying the gravity load to the model, we calculated the deformation for an elevation angle of 35\({}^{\circ}\) and updated the FE model for this condition.  
As shown in Figure 5, we measured the deformation of the primary reflecting surface by photogrammetry. Firstly, we arranged the marking points on the antenna reflecting surface. Then, we used a 25-ton crane to suspend the basket to carry the measurement personnel holding a camera with a measurement accuracy of 5 \(\upmu\)m + 5 \(\upmu\)m/m to take pictures of the antenna in front of the reflecting surface. Finally, we measured the displacement data of the marking points distributed on the primary reflecting surface under the action of gravity load. The number of these marker points is 1640.  
The deformation data of 1640 points randomly distributed on the main reflector surface under gravity load were obtained by the photogrammetric method under a 35\({}^{\circ}\) elevation angle working condition. The RMS of the antenna primary reflector surface nodes' half-path length errors is 0.321 mm, and the distributions of errors are as shown in Figure 6a. We use the deformation data and the cubic polynomial interpolation method to process  
Figure 4: Antenna reflector under gravity and 35\({}^{\circ}\) elevation angle: (**a**) the original FE model; (**b**) the deformation.  
424 upper chord nodes in the original FE model BUS. The RMS's error between the original FE model and the antenna is 0.019 mm, as shown in Figure 6b.  
It is not difficult to see from Figure 6b that the positions of more significant errors are located on the primary reflector's outer side, which indicates that the antenna backup part shown in Figure 7a significantly influences the deformation of the primary reflector. This part of the backup is a double-layer structure in which the bars are divided into ring, radiation, and inclined beams, as shown in Figure 7b-d. The initial values of the different bars' elastic modulus parameters are 206 GPa.  
Due to the rotationally symmetric nature of the BUS, we chose 1/16 of the entire BUS to show its division. As shown in Figure 8, we divided the backup structure shown in Figure 7 into 52 parts based on the bars' different locations, cross-sectional sizes, and lengths. We set the bars' elastic modulus as the input variables of the original finite element model of the antenna, which has 52 in total. In the FEA model, we take as output the displacements of the upper chord nodes of the backstay structure, as shown in Figure 8a. The number of these nodes is 424.  
Figure 5: Measurement of primary reflective surface deformation.  
Figure 6: Antenna reflector deformation errors under gravity and 35\({}^{\circ}\) elevation angle: (**a**) the distributions of the antenna primary reflector surface nodes’ half-path length errors; (**b**) the error distribution between the original FE model and the antenna.