## 1 Introduction
[18] employed a topology optimization method with multiple objectives to achieve the goal of maximizing structural stiffness, combined with parametric optimization. By designing the layout of reinforced ribs and selecting appropriate size parameters, the root mean square (RMS) value of the mirror surface was ultimately reduced to 3.58 nanometers. [PERSON] et al. [19] reconstructed the layout and thickness of reinforced ribs using topology and size optimization, to minimize the ribs' weight. [PERSON] et al. [20] established an optimization model by setting the normal acceleration of a specific region as the topology optimization objective. The layout of the ribs was reconstructed, and different optimal layouts were obtained based on different excitation conditions. [PERSON] et al. [21] proposed an integrated approach that combined the topology of damping layers and the layout of stiffeners, achieving the goal of reducing the vibration of thin-walled reinforced structures in dynamic environments. The above papers are compared with the research in this paper, as shown in Table 1.  
To address the issues of thermal deformation during the in-orbit operation of the parabolic cylindrical reflector antenna of MICAP and the lack of a theoretical foundation for the selection of reinforced rib dimensions, this study proposes a comprehensive design approach integrating both topology optimization and parametric analysis. The primary objective of this research was to demonstrate the superiority of the optimized layout and dimensions of the reinforced ribs based on the topology optimization results, and to elucidate the impact of the reinforced ribs' height and thickness on the root mean square (RMS) of the reflector surface's deformation displacement. The remaining sections of this paper are organized as follows: In Section 2, we establish a theoretical model for the temperature field and external heat flux of the antenna in orbit and conduct simulation calculations. The lowest temperature of the antenna under extreme in-orbit conditions is obtained as the thermal excitation input for finite element thermal distortion analyses. Finite element thermal distortion analyses are then conducted on the antenna with the originally designed reinforced ribs based on empirical methods, as well as the antenna without reinforced ribs. In Section 3, the antenna undergoes topology optimization, parametric analysis, model reconstruction, and RMS comparison. Topology optimization's objective is minimizing the maximum thermal deformation within a designed region, and the response constraint is the volume fraction. Parametric analysis focuses on the height and thickness of reinforced ribs. The layout and dimensions of the reinforced ribs were reconstructed based on the topology optimization and parametric analysis. The influence pattern of the height and thickness on the RMS of the reflector surface was also obtained. After calculating the RMS of the reflector surface with the optimized reinforced ribs, RMS comparisons were made between the reflector surfaces without reinforced ribs, the original design reinforced ribs based on empirical methods, and the optimized reinforced ribs.