# Interval Uncertainty Optimization Method for Electromagnetic Orbital Launcher
## 1 Introduction
The uncertainties can be classified as random, fuzzy, and unsure. According to the mechanism and physical meaning of the uncertainty factors, there are three uncertainty optimization theories, namely stochastic planning, fuzzy planning, and non-probabilistic, corresponding to three uncertainty models, namely the probabilistic model, fuzzy model, and convex model [15; 16]. In the field of the uncertainty optimization of electrical equipment, [PERSON] et al. [17] established an uncertainty optimization model using the interval order and interval probability density method for the processing of composite materials under strong impact loads with high difficulty and error, and they solved the model via the interval nested optimization method based on a radial basis function neural network. [PERSON] et al. [18] proposed a structural damage identification algorithm under an interval number optimization algorithm for the uncertainty damage identification problem, which considered the uncertainty in variables and provided support for structural health diagnosis under uncertainty. [PERSON] et al. [19] proposed an effective interval uncertainty powertrain suspension system analysis and design optimization method. The method takes the uncertainty parameters of the powertrain suspension system as interval variables and proposes an effective method to quickly calculate the inherent frequency of the system and decouple the lower and upper bounds, which improves the computational efficiency. [PERSON] et al. [20] proposed a method to solve nonlinear problems using an interval linear programming approach, which is based on the idea of transforming an uncertainty optimization problem into several sensitivity analysis and deterministic linear optimization problems to be solved sequentially. [PERSON] et al. [21] proposed an interval uncertainty optimization method for the dynamic responses of artillery structures considering robustness and economy, based on nonlinear interval programming and nested optimization solution strategies. [PERSON] et al. [22] established a wind-storage-vehicle capacity stochastic planning method for wind power output uncertainty with multi-scenario operation simulation, which can efficiently participate in source-load interactions and obtain a capacity configuration with better robustness. [PERSON] et al. [23] proposed a reliability design optimization method for wind turbine towers that can accurately take into account the uncertainty of wind loads and material properties, and the results showed that the optimal design of the tower can be accurately achieved to meet the target reliability. [PERSON] et al. [24] considered the uncertainty of the output power of distributed power sources, established a distribution network grid planning model based on fuzzy theory, and solved the model by combining it with genetic algorithm. Probabilistic and fuzzy models require sufficient uncertainty information to establish probability distribution functions and fuzzy affiliation functions, which is often difficult for practical engineering problems and the applications are more limited. From the perspective of uncertainty modeling, interval number optimization is a special case of convex model optimization. It uses the upper and lower bounds of uncertainty parameters, i.e., intervals, to describe the volatility of the values. Interval design optimization does not need to calculate the probability distribution functions of uncertain design variables, and it characterizes the uncertainty ranges of variables by interval ranges, which requires relatively low quantities and accuracy in data and is relatively easy to calculate. Thus, it has obvious advantages in practical engineering applications [25; 26]. Currently, the interval uncertainty optimization method has achieved more and better results in problems where explicit expressions can be established.