Uncertainty Propagation Analysis Of Electromagnetic Parameters And Its Application

As an important medium in the fields of power electronics,communication and remote detection,electromagnetic field analysis of its distribution and propagation characteristics is currently a hot topic.As the main theoretical basis of electromagnetic field analysis,computational electromagnetics plays an important role in the electromagnetic engineering.A series of methods have already been proposed to solve complex electromagnetic engineering problems,such as finite-difference-time-domain(FDTD),method of moments(MoM)and finite element method(FEM),etc.However,as electromagnetic engineering problems become more and more complex,extreme and high precision requirements,deterministic electromagnetic field analysis methods are difficult to meet the calculation requirements,and many uncertain factors ignored previously need to be considered,such as dimensional deviations,dielectric material performance fluctuations,excitation amplitude-phase and working conditions,etc.Although the uncertain electromagnetic field analysis has long been concerned and developed,the research in this field still needs to be developed,especially for those complex electromagnetic field problems considering spatial uncertainty of dielectric material and the multi-source uncertainty of microwave devices.There are still a series of technical difficulties to be solved in the fields of electromagnetic field analysis considering spatial uncertainty of heterogeneous dielectric materials parameters and electromagnetic response calculation under multi-source uncertain parameters.To this end,this thesis systematically studies the uncertainty propagation analysis of the electromagnetic field,and strives to make some tentative and exploratory work in the uncertainty modeling and calculation methods.Based on the uncertainty analysis of electromagnetic field,an electromagnetic stochastic finite element method(EMSFEM),an electromagnetic interval finite element method(EMIFEM)and an interval vector finite element method(IVFEM)are developed by considering the spatial distribution characteristics of dielectric materials.Moreover,amplitude and phase uncertainty propagation analysis are carried out for the improtant microwave device,i.e.Transmit/Receive modules(T/R modules)under multi-source uncertainty parameters in the active phased array antenna system.Finally,it is expected to provide fast and efficient calculation tools for the uncertainty analysis of complex electromagnetic field problems,and hope that in the future it can be applied to electromagnetic field uncertainty analysis of active phased array antennas,ship remote detection,deep space exploration and so on.Based on this idea,the work carried out and completed in this paper is as follows:(1)An electromagnetic stochastic finite element method(EMSFEM)is presented to calculate the statistical moments of electromagnetic problems with spatially uncertain dielectric parameters.Firstly,the random field model of the dielectric material is represented by the Karhunen-Loève(K-L)expansion and inserted into the scalar Helmholtz wave equations.The stochastic equilibrium equations are thus constructed according to the node-based finite element method.Secondly,the first order and second order perturbation stochastic finite element methods are developed for calculating the statistical moments of electromagnetic responses.(2)The interval field model that only needs the upper and lower bounds of the spatially uncertain parameters is introduced into the electromagnetic analysis,and an electromagnetic field interval finite element method(EMIFEM)is proposed to deal with the electromagnetic field problem of the material parameters with spatial uncertainty.By measuring the electromagnetic parameter characteristics of the medium by the interval field model,the interval K-L expansion is introduced to describe the interval field characteristics.In the construction process of the interval field,only the variation boundary of the dielectric material of any spatial point is needed instead of the exact probability distribution,thus effectively reducing the dependence on a large number of samples;then the interval field model is introduced into the scalar Helmholtz wave equation to measure the spatial uncertainty of the dielectric material,and the node-based finite element method is used to construct the interval equilibrium equation.A perturbation interval finite element method for electromagnetic field problems is proposed,which can efficiently calculate the upper and lower boundaries of the electromagnetic response under spatial uncertainty.(3)Based on the existing vector finite element method(VFEM)and the above-mentioned interval field model,an interval vector finite element method(IVFEM)is proposed,which can deal with the eigenvalue problem of dielectric-filled waveguides with material spatial uncertainty.Firstly,the interval field model is used to measure the spatial uncertainty of the dielectric-filled waveguide,and it is described by the interval K-L expansion.Then,by embedding the interval field model into the waveguide standard generalized eigenvalue equation,a perturbation interval vector finite element method suitable for the eigenvalue problem of dielectric-filled waveguides is developed,which can accurately and efficiently solve the upper and lower bounds the eigenvalues of the dielectric-filled waveguide.(4)The sensitivity analysis method based on variance decomposition and the arbitrary chaotic polynomial based on moment(MBaPC)are utilized to analyze the influence of multi-source uncertainty parameters on the amplitude and phase of T/R components.First,an electromagnetic numerical simulation model of the actual T/R component is constructed.Then,based on the model,a sensitivity analysis is performed to determine sensitive parameters for the amplitude difference and p hase difference between the input and output electromagnetic signals.Third,MBaPC is used to efficiently solve the fourth-order statistical moments of amplitude difference and phase difference.Finally,based on the principle of maximum entropy and the fourth-order statistical moment information,the probability distribution function(PDF)of the amplitude difference and phase difference of the T/R component is fitted.