Research Of Electromagnetic Finite Element And Antenna Pattern Function Based On Random Field

Uncertainty problems are widely existed in engineering problems,such as the geometrical errors in manufacturing and assembly,material properties of structures,and external environmental loads.These uncertainties will have a large impact on the stability and reliability of the performance of the structure.In this paper,we focus on the problem of spatial uncertainty problems,and using the random field model to describe the factors of uncertainty,such as the spatial uncertainty of material properties,and the deformation of the array's function surface,etc.Then devoleping numerical methods to solve and analyze the uncertainty problems.Firstly,introduces the basic principle of the random field,and then develops electromagnetic field finite element analysis method based on Poisson equation and phased array pattern function problem with random deformation.The main work of this paper is as follows:(1)An electromagnetic field stochastic finite element method based on Poisson equation is proposed to solve the electromagnetic field problem considering the spatial uncertainty of dielectric materials.In this part,firstly the basic principle and solution formula of the one-dimensional and two-dimensional problems of deterministic electromagnetic finite element method need to be deduced.Then according to uncertain factors encountered in the actual problem,the random field model is selected to describe the spatial uncertainty factor.And Using the KL expansion or EOLE expansion method for stochastic field expansion,and substitute to the deterministic equilibrium equation to obtain the stochastic equilibrium equation.Then using the perturbation method to solve it,the influence of the uncertainty parameter on the electromagnetic response can be obtained.Finally,the Monte Carlo method is used to verify the feasibility,accuracy and efficiency of the proposed method.(2)Based on the random field model,an uncertainty analysis method for phased array patterns is proposed.Focusing on the uncertain deformation of the function of phased array antenna,the random field model is used to describe the uncertainty deformation of the array.Then substitute it into antenna pattern function,so the influence of each unit on the overall electrical performance pattern can be calculated.Based on the superposition principle of the array antenna,we can get the influence of the overall array's pattern function by the uncertainty deformation.Last,compared with Monte Carlo method to verify the reliability and efficiency.