A method for analyzing electromagnetic scattering characteristics of an electrically large conductor target

Abstract

The application discloses a method for analyzing electromagnetic scattering characteristics of an electrically large conductor target, and steps of the method comprise: dividing the conductor target to be analyzed into several blocks, expanding each block to obtain a self-impedance matrix; obtaining a new characteristic mode matrix based on the self-impedance matrix; constructing a reduction matrix by using a Galerkin method based on the new characteristic mode matrix; obtaining surface currents of the conductor target based on the reduction matrix; and analyzing electromagnetic scattering characteristics based on the surface currents; the application of the principal component analysis technology with a threshold not only reduces the number of characteristic modes, but also makes the orthogonality between new characteristic mode base functions better. The condition number of the reduction matrix constructed by using the Galerkin method is optimized, the convergence speed of iterative solution of the reduction matrix equation can be significantly accelerated, and the ability of the characteristic mode base function method for analyzing electromagnetic scattering problems of electrically large targets is improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of electromagnetic scattering characteristic analysis, and particularly relates to a method for analyzing electromagnetic scattering characteristics of an electrically large conductor target. BACKGROUND

[0002] In analyzing electromagnetic scattering characteristics of an electrically large target (such as an airplane, a missile, a tank, an antenna array, etc.), the existing solution is to divide the target to be analyzed into a plurality of smaller blocks, to obtain characteristic mode basis functions (CMBFs) for each block, and then to combine a multilevel fast multipole method, an adaptive integration method, etc. with the CMBF method to reduce matrix-vector multiplication operations. However, these methods do not improve the condition number of the reduced matrix or the convergence speed of iterative solution of the reduced matrix equation. Therefore, these methods are low in calculation efficiency and time-consuming in analyzing electromagnetic scattering characteristics of an electrically large target, which seriously hinders the application prospect of the method in target electromagnetic characteristic analysis, electromagnetic compatibility, antenna design and optimization, etc.

[0003] The CMBF method (CMBFM) is based on the principle of region division, divides the target into a plurality of smaller blocks, and extends each block outward to calculate the self-impedance matrix of each extended block. According to the characteristic mode theory of a conductor target, a generalized eigenvalue equation is constructed on each block, and a threshold condition is set according to the mode significance to solve the effective modes meeting the threshold condition as the CMBFs. Finally, a reduced matrix of a reduced order is constructed, which can usually be solved by using a direct method. However, as the electric size of the target increases, the number of CMBFs increases, and the dimension of the reduced matrix becomes larger and larger, so it is very difficult to solve the reduced matrix equation by using the direct method. SUMMARY

[0004] The application aims to provide a method for analyzing electromagnetic scattering characteristics of an electrically large conductor target to solve the problems in the prior art.

[0005] To achieve the above object, the application provides a method for analyzing electromagnetic scattering characteristics of an electrically large conductor target, which comprises the following steps:

[0006] dividing the conductor target to be analyzed into a plurality of blocks, extending each block to obtain a self-impedance matrix;

[0007] obtaining a new characteristic mode matrix based on the self-impedance matrix;

[0008] constructing a reduced matrix by using the Galerkin method based on the new characteristic mode matrix;

[0009] obtaining the surface current of the conductor target based on the reduced matrix;

[0010] analyzing electromagnetic scattering characteristics based on the surface current.

[0011] Optionally, the process of obtaining a new eigenmode matrix based on the self-impedance matrix comprises:

[0012] Based on the self-impedance matrix, an eigenvalue equation is constructed according to the eigenmode theory of a conductor target;

[0013] Based on the eigenvalue equation, an eigenvalue and an eigenvector corresponding to the eigenvalue are obtained;

[0014] The extended part of the eigenvector is removed to obtain an unextended eigenmode;

[0015] The unextended eigenmode is filled to obtain a filled matrix;

[0016] The filled matrix is standardized to obtain a covariance of the filled matrix and construct a covariance matrix;

[0017] A principal component matrix is obtained based on the covariance matrix, and the new eigenmode matrix is obtained based on the principal component matrix.

[0018] Optionally, the eigenvalue equation is as follows:

[0019]

[0020] wherein X i and R i are the imaginary part and the real part of the self-impedance matrix respectively, λ i is an eigenvalue, is an eigenvector corresponding to λ i .

[0021] Optionally, the process of obtaining an eigenvalue and an eigenvector corresponding to the eigenvalue based on the eigenvalue equation comprises:

[0022] Based on mode saliency, a threshold value is set, and an effective mode eigenvector corresponding to the eigenvalue is obtained according to the set threshold value.

[0023] Optionally, the dimension of the filled matrix is n x p, wherein n is the number of eigenmodes, and p is the number of unextended unknowns.

[0024] Optionally, the covariance matrix is as follows:

[0025]

[0026] wherein C i is a covariance matrix, n is the number of eigenmodes, Q i is a filled matrix, and T represents transposition.

[0027] Optionally, the process of obtaining a principal component matrix based on the covariance matrix comprises:

[0028] Eigenvalues and eigenvectors of the covariance matrix are obtained by singular value decomposition;

[0029] Eigenvalues of the covariance matrix are truncated by setting a threshold value;

[0030] The reserved eigenvalues of the covariance matrix are filled to obtain the principal component matrix.

[0031] Optionally, the process of obtaining the surface current of the conductor target based on the reduced matrix comprises:

[0032] Incomplete LU preconditioning is performed on the reduced matrix;

[0033] The preconditioned reduced matrix is solved by using an iterative method to obtain a coefficient matrix;

[0034] The surface current of the conductor target is obtained based on the coefficient matrix

[0035] The technical effects of the present application are:

[0036] After the principal component analysis technology with a threshold value is applied, the number of eigenmodes is reduced, and the orthogonality between the new eigenmode basis functions is better. The condition number of the reduced matrix constructed by using the Galerkin method is optimized, the convergence speed of the iterative solution of the reduced matrix equation can be significantly accelerated, and the ability of the eigenmode basis function method to analyze the electromagnetic scattering characteristics of large-size targets is improved. BRIEF DESCRIPTION OF DRAWINGS

[0037] The accompanying drawings, which form a part of this application, are included to provide a further understanding of the application and are incorporated in and constitute a part of this application. The embodiments of this application and their explanations are used to explain this application and do not constitute an improper limitation on this application. In the drawings:

[0038] Figure 1 The flowchart of the electromagnetic scattering characteristic analysis method of the large-size conductor target in the embodiment of the present application is shown.

[0039] Figure 2 The example result diagram of the electromagnetic scattering characteristic analysis method of the large-size conductor target in the embodiment of the present application is shown. DETAILED DESCRIPTION

[0040] It should be noted that the embodiments and features in the embodiments of the present application can be combined with each other without conflict. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0041] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0042] Example 1

[0043] like Figure 1 As shown, this embodiment provides a method for analyzing the electromagnetic scattering characteristics of electrically large conductor targets, including the following steps:

[0044] Step 1: Based on the characteristic mode basis function method, the electrically large conductor target to be analyzed is divided into M blocks, and then each block is expanded to obtain the self-impedance matrix. Based on the characteristic mode theory of conductor targets, the following is adopted: Constructing the generalized eigenvalue equation:

[0045]

[0046] In the formula, X i and R i They are respectively The imaginary and real parts, λ i For eigenvalues, For λ i The corresponding feature vector. Based on pattern saliency. Set a threshold τ and find the eigenvalues ​​that satisfy MS≥τ and their corresponding effective patterns.

[0047] Remove valid mode After obtaining the unexpanded eigenmodes from the extended part, these eigenmodes are padded row-wise to form matrix Q. i Its dimension is n×p, where n is the number of eigenmodes and p is the number of unexpanded unknowns. Then, for Q... i Standardization process, calculate Q i The covariance is calculated and the covariance matrix is ​​constructed as follows:

[0048]

[0049] In the formula, C i Let C be the covariance matrix with dimension n×n, and T denote the transpose. C is obtained through singular value decomposition. i The eigenvalues ​​and eigenvectors are used to truncate the eigenvalues ​​by setting a threshold σ. The eigenvectors corresponding to the retained eigenvalues ​​are the principal components. These principal components are used to fill the matrix W. i Then, the new eigenmode matrix of the i-th block after dimensionality reduction is finally obtained. for:

[0050]

[0051] In the formula, Let J be the k-th (k < n) eigenmodulus on the i-th block. Construct a new eigenmodulus basis function matrix J using the eigenmodulus of all blocks. CM .

[0052] Step 2: Construct the reduced matrix Z using Galilean's method R as follows:

[0053]

[0054] After performing incomplete LU preprocessing on the reduced matrix, the iterative method is then applied to solve the equation of the reduced matrix:

[0055] Z R α=V R (5)

[0056] In the formula, V R =(J CM ) T V. By solving equation (5) to obtain the coefficient matrix α, the surface current of the target can be obtained. Based on this surface current, the electromagnetic scattering characteristics of electrically large conductor targets can be analyzed.

[0057] Example 2

[0058] like Figure 2 As shown, this embodiment provides a specific implementation of a method for analyzing the electromagnetic scattering characteristics of electrically large conductor targets, including:

[0059] This embodiment uses the calculation of the bistatic radar cross section (RCS) of a missile with a length of 1m as an example. The incident excitation is a plane wave with an angle of... The frequency is 3.5 GHz. The target surface is partitioned at intervals of 0.1λ (λ is the wavelength of the incident plane wave), resulting in 28,864 RWG basis functions and 43,296 unknowns. The target is divided into 55 blocks, each expanded by 0.15λ, resulting in 91,588 unknowns. In this invention, the thresholds τ and σ are set to 0.001 and 0.968, respectively. While CMBFM yields 8,548 eigenmode basis functions, this invention yields 8,196 new eigenmode basis functions. Compared to CMBFM, the condition number of the reduced matrix constructed in this invention is reduced from 6.5771 × 10⁻⁶. 8 It decreased to 3.4137×10 4 Both CMBFM and this invention employ incomplete LU decomposition to process the reduced matrix and use iterative methods to solve the reduced matrix equation.

[0060] Table 1 gives the calculation time, iteration number and root mean square error of CMBFM and the method of the application. It can be seen that the iteration number is sharply reduced, the solution time is significantly reduced, and the final total calculation time is reduced by 44%. From the table, it can be seen that the calculation results of the method of the application are in good agreement with the MoM and CMBFM, and have high calculation accuracy. The example verifies the accuracy and high efficiency of the application. Figure 2 It can be seen that the calculation results of the method of the application are in good agreement with the MoM and CMBFM, and have high calculation accuracy. The example verifies the accuracy and high efficiency of the application.

[0061] Table 1

[0062]

[0063] In summary, after the effective modes are obtained by the characteristic mode basis function method, the extended part is removed to obtain unextended characteristic modes, and after the unextended characteristic modes are processed by the principal component analysis technology with threshold as new characteristic mode basis functions to construct a reduced matrix, the dimension of the matrix is reduced, the condition number of the matrix is optimized, the convergence of the iterative solution is accelerated, and the calculation time is reduced. The application has high calculation efficiency and accuracy when solving the electromagnetic scattering characteristics of the electrically large conductor target.

[0064] The above merely describes a preferred embodiment of the application, but the protection scope of the application is not limited thereto, and any person skilled in the art can easily think of changes or replacements within the technical scope disclosed by the application, which should be covered within the protection scope of the application. Therefore, the protection scope of the application should be subject to the protection scope of the claims.

Claims

1. A method of analyzing electromagnetic scattering properties of electrically large conductor objects, characterized by, The method comprises the following steps: dividing a conductor object to be analyzed into several blocks, expanding each block, and obtaining a self-impedance matrix; obtaining a new characteristic mode matrix based on the self-impedance matrix; constructing a reduction matrix by using the Galerkin method based on the new characteristic mode matrix; obtaining surface currents of the conductor object based on the reduction matrix; performing electromagnetic scattering characteristic analysis based on the surface currents; the process of obtaining a new characteristic mode matrix based on the self-impedance matrix comprises: constructing an eigenvalue equation according to a characteristic mode theory of a conductor object based on the self-impedance matrix; obtaining eigenvalues and characteristic vectors corresponding to the eigenvalues based on the eigenvalue equation; removing an expanded part of the characteristic vectors to obtain unexpanded characteristic modes; filling the unexpanded characteristic modes to obtain a filled matrix; performing standardization processing on the filled matrix to obtain a covariance of the filled matrix and construct a covariance matrix; obtaining a principal component matrix based on the covariance matrix and obtaining the new characteristic mode matrix based on the principal component matrix; the covariance matrix is as follows: where C i is the covariance matrix, n is the number of eigenmodes, Q i is the padding matrix, and T denotes the transpose; the process of obtaining a principal component matrix based on the covariance matrix comprises: obtaining eigenvalues and eigenvectors of the covariance matrix by using singular value decomposition; truncating the eigenvalues of the covariance matrix by setting a threshold; filling the retained eigenvalues of the covariance matrix to obtain the principal component matrix; the process of obtaining surface currents of the conductor object based on the reduction matrix comprises: performing incomplete LU preconditioning on the reduction matrix; obtaining a coefficient matrix by solving the preconditioned reduction matrix by using an iterative method; obtaining the surface currents of the conductor object based on the coefficient matrix.

2. The method of analyzing electromagnetic scattering characteristics of electrically large conductor objects of claim 1, wherein, the eigenvalue equation is as follows: where X i and R i are the imaginary and real parts of the self-impedance matrix, respectively, λ i is the eigenvalue, and v i is the corresponding eigenvector.

3. The method of claim 1, wherein the method is characterized by: the process of obtaining eigenvalues and characteristic vectors corresponding to the eigenvalues based on the eigenvalue equation comprises: setting a threshold based on mode saliency and obtaining eigenvalues and effective mode characteristic vectors corresponding to the eigenvalues according to the set threshold.

4. The method of claim 1, wherein the dimension of the filled matrix is n×p, wherein n is the number of characteristic modes and p is the number of unexpanded unknowns.

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