Research On EMC Uncertainty Simulation Method Based On The Generalized Polynomial Approximation Theory

In the Electromagnetic Compatibility analysis,various uncertain factors existing in the actual engineering environment should be considered,in order to improve the credibility of the simulation results.As a traditional uncertainty analysis method,the Monte Carlo Method has low computational efficiency,which makes it difficult to implement complex Electromagnetic Compatibility simulation analysis.Based on the generalized Polynomial Approximation theory,this paper has constructed an efficient general solution method for uncertainty analysis in Electromagnetic Compatibility simulation.Meanwhile,a series of key issues have also been discussed,such as the dimensional disaster problem,the validity evaluation problem and the arithmetic convergence judgment problem.The uncertainty parameters are modeled by random variables to obtain stochastic Maxwell's equations.Using the Stochastic Galerkin Method,the inner product on both sides of the stochastic Maxwell's equations is calculated,and a certain augmented Maxwell's equations can be got.Then the uncertainty analysis results in the form of chaotic polynomial are obtained by combining the Finite Difference Time Domain Method.When considering the material parameter uncertainty and excitation source parameter uncertainty,the Stochastic Galerkin Method and the Monte Carlo Method have the same computational accuracy.When considering the geometric parameter uncertainty,the computational accuracy of the Stochastic Galerkin Method is lower than that of the Monte Carlo Method.Using the Stochastic Collocation Method,the collocation points are selected according to the random variables.With the help of the Finite Difference Time Domain Method,the certain Maxwell's equations are solved at the collocation points,and then the simulation results can be given according to the numerical integration technique or multidimensional Lagrange interpolation technique.As a result,the solution to the stochastic Maxwell's equations is finally achieved without changing the solver.It is proved that the Stochastic Collocation Method has high computational accuracy,especially when dealing with simulation problems considering geometric parameter uncertainty.In this case,the character that there is no need to change the solver makes the Stochastic Collocation Method have the same calculation accuracy as the Monte Carlo Method,which is better than the Stochastic Galerkin Method.So far,the stochastic Maxwell's equations can be solved by selecting either Stochastic Collocation Method or Stochastic Collocation Method,in order to complete the analysis of Electromagnetic Compatibility uncertainty problem.When the number of required random variables is large,the computational efficiency of the generalized Polynomial Approximation theory will drop sharply.In order to solve this problem,a rapid sensitivity analysis strategy is firstly adopted,which uses the Richardson Extrapolation Method to improve the sensitivity calculation process of random variables in the Method of Moment,so the reduction of the number of random variables is achieved.For the Stochastic Collocation Method,the collocation points selection scheme based on the Dimension-reduced Sparse Grid Strategy is proposed,which is used to change the intrinsic property of the exponential relationship between the number of matching points and the number of random variables.In this case,the number of required deterministic simulations is greatly reduced,and then the computational efficiency of the Stochastic Collocation Method is improved.Based on the Genetic Algorithm,the Dimension-reduced Sparse Grid Strategy is improved by establishing an approximate random variable model,so that it is no longer limited by the form of random variables.In order to solve the validity evaluation problem of the uncertainty analysis results and the convergence determination problem of the uncertainty analysis method,the Mean Equivalent Area Method is proposed.In the method,the equivalent uniform distribution is used to instead of the true probability density distribution,to approximate calculate the common area between the probability density curve of the uncertainty analysis results and the probability density curve of the standard data.Then the validity evaluation of the uncertainty analysis results is given.Meanwhile,the Mean Equivalent Area Method is used to quantitatively calculate the similarity degree of the uncertainty analysis results under adjacent orders,so as to judge whether the generalized Polynomial Approximation theory has been converged.Finally,the computational electromagnetic method proposed in this paper is applied to the actual Electromagnetic Compatibility prediction,and the shielding effectiveness analysis of the metal box considering the uncertainty input and the transmission impedance prediction of the shielded cables considering the random effect are realized respectively.