# Real-Time State Evaluation System of Antenna Structures in Radio Telescopes Based on a Digital Twin
## 4 Real-Time Simulation Construction of Antenna Physical Field  
### Finite Element Simulation  
The structure of the 26 m radio telescope is shown in Figure 5. The structure adopts a modified Cassegrain antenna and an omnidirectional controllable central body symmetrical azimuth-elevation wheel-rail antenna seat. Among them, the primary reflector is the key part of antenna design and optimization, and it is also the main load-bearing mechanism for many kinds of loads, so the structure of the primary reflector of the antenna is taken as a research object for further investigation.  
To verify the feasibility and effectiveness of the DT state monitoring and evaluation method, this paper mainly studies the static structural state of the antenna primary reflector under gravity and steady-state wind load.  
Figure 4: QEM algorithm diagram.  
The steady-state wind load can be calculated as follows:  
\[F=0.5\rho v^{2}C_{F}A \tag{7}\]  
where \(\rho\) is the air density at standard atmospheric pressure; \(v\) denotes wind speed; \(C_{F}\) is the wind coefficient; \(A\) is the characteristic area. The wind coefficient \(C_{F}\) is obtained according to the wind tunnel test data of the approximate body [20].  
Based on the above conditions, the finite element model of the primary reflector of the antenna is established, and the load and boundary conditions are applied at the same time. For the wind load, the wind pressure is equivalent to the concentrated load of each node of the reflector. The concentrated load is calculated according to the load area of the node, and it is decomposed in three directions along the coordinate axis to complete the node load assignment. Figure 6 is the finite element model and wind direction definition diagram of the primary reflector of the 26 m antenna. Among them, the wind direction angle is defined as the angle between the normal vector of the center of the elevation axis in the horizontal plane and the inverse vector of the incoming wind direction.  
Taking 10 m/s steady wind as an example, the deformation of the antenna back-up structure under different elevation angles is calculated. The results are shown in Figure 7. Figure 7 represents the axial structural deformation under the condition of a 90\({}^{\circ}\) elevation angle and a 0\({}^{\circ}\) wind direction; Figure 7b represents the axial structural deformation under the condition of a 45\({}^{\circ}\) elevation angle and a 45\({}^{\circ}\) wind direction; Figure 7c,d respectively represent the axial deformation cloud diagram of the structure under the equivalent fluid-solid coupling field when gravity is applied at the same time under the above two  
Figure 5: Twenty-six-meter radio telescope.  
Figure 6: Finite element model and wind direction angle definition diagram of the primary reflector of the 26 m antenna.  
conditions. The results show that the deformation of the antenna backup structure increases gradually from the center to the periphery under the condition of a 90\({}^{\circ}\) elevation angle, and the maximum deformation position appears at the outermost edge. Under the condition of a 45\({}^{\circ}\) elevation angle, the deformation of the top and bottom edges of the antenna back-up structure is the largest. At the same time, under the action of only wind load, its deformation trend corresponds to the changing trend of the wind pressure coefficient [21].