## 3 Control of Thermal Deformation Optimization Strategy
### Multi-Objective Optimization Design
#### 3.3.2 Multi-Objective Optimization Design of Reference Support  
The design of the reference bracket is restricted by many factors, and how to balance the selection of all factors needs to be carried out according to the results of topology optimization. The first factor to consider is mass constraints. Aerospace products strive to meet the design requirements with a smaller structural mass. In this paper, the density method is adopted for topology optimization, and the minimum total volume is set as the optimization objective. The displacement of the reference bracket caused by the whole satellite temperature field is taken as the displacement input of the reference bracket. The precise temperature control of the reference bracket can be achieved within the fluctuation range of \(\pm 1\)\({}^{\circ}\)C. According to the temperature fluctuation range as the temperature data, the thermal deformation caused by the temperature fluctuation of the bracket is calculated, and the deformation caused by the bracket itself is taken as the constraint to constrain the changes in the optical axis angle of the star-sensor and laser communication load. The above constraints can be used to optimize the design of the reference bracket when determining the location of the star sensor and laser communication load on the satellite bus. The current topology optimization design method is often used to optimize the design of spacecraft weight reduction, which can deal with this kind of problem well [17; 28]. The relative position relationship between the star sensor and the laser communication load on the satellite is also one of the variables affecting the design result. In this paper, the installation location of the star sensor is also taken as an optimization objective. Laser communication load turntables usually have a universal frame structure, a single reflector structure, and a latent structure. The laser communication load in this system adopts the latent configuration, as shown in Figure 14. During the layout of the satellite, the installation position of the star sensor and the avoidance of the rotation range of the rotating laser communication load turntable should be considered. In this paper, the range above the rotating area of the rotating table of the rotating laser communication load is set as the area where the star sensor can be laid out. With \(\varphi_{i}\) as the optimization variable,  
Figure 13: Flexible isolation device. topology optimization iterations are carried out for different positions. The mathematical relationship expression is shown below. \[\left\{ \begin{array}{ll}Find\ \ \varphi_{i}\\ \min\ V\\ s.t.\ \ \varphi_{i}^{\prime}\leq\varphi_{i}\leq\varphi_{i}^{u}\\ d_{j}\leq d_{j}^{u}\\ f_{1}\geq f_{1}^{l}\end{array} \right. \tag{3}\]  
where the \(V\) represents the above equation represents the total volume, \(d_{j}\) represents the displacement constraint, \(f_{1}\) represents the fundamental frequency constraint, \(u\) and \(l\) represents the upper and lower limits of the design objectives and design variables. Figure 15 shows the principle of optimization iteration. The optimization of the position determined by the star sensor is transformed into a routine topology optimization process. In addition to the topology optimization process, we add a loop about the \(\varphi_{i}\) optimization variable. The \(\varphi_{i}\) is traversed with a certain step size, and the topology optimization results of each position are compared, judged, and selected. The optimization analysis results are shown in Figure 16, and density distributions under different conditions \(\varphi_{i}\) are obtained. The total volume results of topology optimization were extracted and shown in Figure 17. With the change in angle, the total volume has a trend of first rising and then falling. When \(\varphi_{i}=0^{\circ}\) or \(\varphi_{i}=70^{\circ}\), the total volume is the smallest.