# Interval Uncertainty Optimization Method for Electromagnetic Orbital Launcher
## 1 Introduction  
The armature plays a crucial role as one of the key components in the electromagnetic orbital launcher, and the design parameters of the armature directly affect the launcher's performance [1; 2]. However, in the armature design process, challenges arise in acquiring the design parameters, modeling the armature appropriately, and dealing with uncertainties associated with these design parameters. As a result, there has been limited research investigating the impact of the design parameters on the armature's performance and developing optimization methods for armature design. Nowadays, the most commonly used electrical equipment performance optimization scheme is a combination of a proxy model and algorithm to find the best solution, first based on existing data to establish a proxy model between the design parameters and performance data, and then using genetic algorithm [3], particle swarm optimization (PSO) [4], and the differential evolution algorithm [5] based on the proxy model. In the field of the deterministic optimization of electrical equipment, [PERSON] et al. [6] selected the efficiency and power density of an axial motor as the optimization objective and obtained the optimal Pareto solution set for the motor optimization variables by multi-objective genetic algorithm search, which improved the motor power density by 20.82%. [PERSON] et al. [7] used the response surface methodology combined with genetic algorithm to optimize the cogging torque of an axial flux permanent magnet motor. The results showed that the cogging torque could be reduced from 2.14 to 0.18 N\(\cdot\)m, and the peak-to-peak value of the torque ripple was only 3.5% of the rated output torque. Moreover, the values of the no-load back EMF and the rated output torque were almost invariable before andafter optimization. [PERSON] et al. [8] proposed an adaptive particle swarm optimization algorithm for reluctance motor optimization, which converged faster than the standard particle swarm optimization algorithm and had an improved ability to search for a better solution set. [PERSON] et al. [9] used a multiple swarm genetic algorithm with a strong search capability for the multi-objective optimization of the thrust density, thrust fluctuation, and loss using the dimensions of the permanent magnets and toroidal windings of a coreless permanent magnet linear synchronous motor as variables. It was verified that the optimal design results obtained by MPGA were in good agreement with the design objectives under different weight coefficients. [PERSON] et al. [10] optimized transformer winding shapes based on a fast non-dominated ranking genetic algorithm NSGA-II with an elite strategy, and the example validation results showed a 10% improvement in efficiency. [PERSON] et al. [11] used the simulated annealing algorithm as well as genetic algorithm to achieve the multi-objective optimal design of a high-temperature superconducting transformer's volume and loss. Here, three simple scenarios were considered for optimization: Scenario 1: one-variable and one-constraint two-objective functions; Scenario 2: two-variable and one-constraint three-objective functions; and Scenario 3: two-variable and one-constraint four-objective functions. [PERSON] et al. [12] analyzed the track geometry size characteristics based on a simulation model of an electromagnetic rail gun system and optimized the design of the track size using genetic algorithm, with the optimization objective of increasing the kinetic energy of the armature exit. The optimization of the design parameters of the electromagnetic orbital launcher can be achieved to a certain extent using these deterministic optimization methods, but the extensive uncertainties that exist in its design and service process are not considered, making it difficult to achieve a reliable design. In the optimization processes of electrical equipment, there are always uncertainties, such as loads, material properties, geometric characteristics, and boundary conditions [13; 14].