# Optimization of Multistage Coilgun Based on Neural Network and Intelligent Algorithm
## 1 Introduction  
Electromagnetic launchers are currently under the spotlight of military studies as they surpass mechanical and chemical launchers because of their high initial speed, long range, good controllability, low cost, fast response speed, and silent, light- and smoke-free emission [1; 2; 3]. A synchronous induction coilgun (SICG) is a popular type of electromagnetic launcher. It is mainly composed of a driving coil, a driving circuit, a pulse power source, and a projectile. It uses the magnetic traveling wave generated by the pulse to accelerate a projectile. By simply increasing the number of drive coils, an SICG can accelerate large-mass loads to very high speeds, which makes it a hot topic of research [4; 5; 6].  
A multi-stage SICG (MSSICG) usually has the same parameters for components such as the driving coil and a projectile due to processing and cost constraints. Therefore, the feed time of each driving coil of an MSSICG becomes the crucial factor to determine the final muzzle velocity of the projectile [7; 8; 9], for which the number of coils can be increased to achieve the desired muzzle velocity. An inappropriate feed time often leads to undesirable outcomes.  
The current methods for optimizing the feed time of MSSICGs mainly include the orthogonal experimental method and intelligent algorithms. The orthogonal experimental method can obtain reliable results with fewer tests, but its optimization results are limited by the range of the selected level, and its convergence speed is slow, so it is difficult to determine data trends [10]. On the other hand, intelligent algorithms, such as genetic algorithms (GAs) [11], ant colony algorithms (ACOs) [12], simulated annealing (SA) algorithms [13], etc., can more easily determine the global optimal solution, so they are morefavored. However, obtaining the global optimal solution usually requires many calculations executed via iteratively calling the circuit model, which is very time consuming. Therefore, to save a great deal of calculation time, it is recommended to replace the current filament model with the predictive model in the optimization process. For example, [PERSON] et al. [14] used three typical machine learning methods, namely, LSSVM, KELM, and ESN, to perform non-parametric modeling of a five-level SICG. The results showed that the error between the predictive model and the current filament model was only 2.9%. However, these machine learning methods can only handle fixed-length inputs. Additionally, they can only learn the input information at the current moment and will not refer to the input information at other moments. However, when the number of coils of an MSSICG is used as the optimization target, the number of feeds will change, which means that the length of the input will also change. At the same time, there is a strong sequential relationship between each feed time, so it is necessary to develop a machine learning method that is not constrained by the fixed length input space and can store the state of the previous input and combine it with the current input.  
This paper uses a particle swarm optimization (PSO) [15] algorithm based on the prediction model of the gated recurrent unit (GRU) neural network [16] to optimize the feed time of an MSSICG. By optimizing the feed time, we aim to achieve a final projectile muzzle velocity of 50 m/s with the minimum number of coil stages, thereby reducing costs and increasing efficiency.