## 1 Introduction  
In space equipment, it is necessary to detect the output torque, stiffness, precision, and other indicators of the joint of the space manipulator in the ground simulation test to ensure the reliability of the operation [1, 2]. Compared with ordinary bearings, gas bearings have the characteristics of extremely low friction resistance, clean media, and good adaptability to high-speed rotational environments [3]. They show great application prospects for improving the accuracy of the ground tests of space manipulator joints. [PERSON] et al. summarized the research developments of aerostatic bearings and pointed out that the applications of aerostatic bearings are affected by low load capacity and stability [4]. However, the development of high-speed machinery and high-precision machinery has demanded higher performance of aerostatic bearings. Therefore, a reliable optimization design method is needed to design the structural parameters of aerostatic bearings. There are many structural parameters and physical parameters that affect the static performance of aerostatic bearings. In the design process, there is a competitive relationship between improving bearing capacity and reducing gas consumption. Therefore, optimizing parameters while considering the static performance of aerostatic bearings has become the key to the design of aerostatic bearings. [PERSON] et al. used the DIRECT and simulated annealing (SA) algorithms to design the air slider. They found that the DIRECT algorithm is more efficient in solving the non-linear slider optimization problem [5]. [PERSON] et al. used the hypercube segmentation method instead of the genetic algorithm to optimize the air-bearing parameters. This algorithm shows the characteristics of a wide calculation range and a small calculation amount [6]. [PERSON] et al. used a hybrid genetic optimization algorithm to calculate the optimal parameters of air bearing and verified the reliability of the optimization design using experiments [7]. [PERSON] et al. used the maximum Mach number to predict bearing dynamic stability. Accordingly, they established the optimization model to improve stiffness and eliminate micro-vibration [8]. [PERSON] et al. established two theoretical models of an ultra-low-friction cylinder to calculate the cylinder's performance. Then, they optimized the cylinder's structure using a constrained optimal design method [9]. The particle swarm optimization algorithm (PSO) is an evolutionary algorithm that simulates bird predation. It is simple to implement and has been successfully applied to multi-objective optimization problems [10]. [PERSON] et al. converted two optimization objective functions into a single objective function using the linear weighting method. Then, they used the PSO algorithm to find the optimal combination of design variables [11]. [PERSON] et al. proposed an external archive-guided multi-objective particle swarm optimization algorithm (AgMOPSO) and introduced the update mechanism of the archive. They verified that AgMOPSO effectively improves the convergence speed when dealing with multi-objective test problems [12]. [PERSON] et al. proposed a double-loop multi-objective particle swarm optimization algorithm to solve the problem when there are uncertain variables in the optimization process [13]. [PERSON] used MOPSO to optimize the structural parameters of the turbofan engine and verified the convergence of MOPSO by comparing the Pareto front with four solutions obtained using the single-objective optimization algorithm [14]. [PERSON] et al. improved the distribution of sub-problems using a weight vector adjustment strategy instead of Euclidean distance to divide congestion degrees [15]. [PERSON] et al. used a coupled multi-objective optimization algorithm to optimize the screw centrifugal blood pump and the Latin hypercube sampling method to generate an initial sample with a more uniform distribution [16].