A characteristic mode analysis method for penetrating electromagnetic scattering characteristics of targets

Abstract

The present invention discloses a characteristic mode analysis method for electromagnetic scattering characteristics of a penetrable target. The surface integral equations of the electric field and the magnetic field are linearly combined to establish a mixed integral equation. The equation is discretized by the method of moments to obtain a matrix equation of the penetrable target. The asymmetric complex matrix equation is converted into a symmetric form. The Gaussian elimination method is used to obtain a reduced matrix equation for the surface current. The real part and the imaginary part of the reduced matrix equation are separated to establish a generalized eigenvalue equation for the surface current. The characteristic current and the eigenvalue are calculated by a solver for the equation. The characteristic current is weighted and summed to obtain the induced current on the surface of the penetrable target, and the magnetic current is restored to obtain the radar cross section of the penetrable target. The electromagnetic scattering characteristics of the penetrable target are analyzed by analyzing the distribution of the radar cross section. The present invention proposes a new method for calculating the radar cross section, which expands the application range of the characteristic mode.

Description

Technical Field

[0001] The invention relates to the technical field of radar cross-section of penetrable targets and a characteristic mode analysis method of electromagnetic scattering characteristics of penetrable targets. Background Art

[0002] The characteristic mode is actually an inherent mode, and this method can be applied to any electromagnetic target structure. It is only related to the electromagnetic structure itself and the material, and has nothing to do with the external excitation source. The advantage of the characteristic mode method is that it can calculate multiple modes and analyze the mode current, the resonance characteristics of the mode, and the mode field at the same time. Through the analysis of the characteristic mode, the radiation and scattering mechanism of the electromagnetic target structure is more clearly demonstrated, which can reduce the repeated optimization process in solving the electromagnetic response problem of the antenna and the target structure, and can achieve accurate solution and analysis, thus providing a very convenient tool for calculating the electromagnetic response.

[0003] Since the electric field integral can be applied to both closed and open domain structures, the traditional metal characteristic mode theory is established based on the electric field integral equation. The discrete method of the moment method is applied and the RWG basis function is established to fill the impedance matrix according to the location of the field source point. Considering the weighted eigenvalue equation, the generalized eigenvalue equation of the traditional metal target can be obtained by taking the real part of the impedance matrix as the weighted matrix. The generalized eigenvalue equation can be solved by direct solution and iterative solution to calculate the characteristic mode current and eigenvalue. The integral equation and matrix equation form of metal targets and penetrable targets are different. The development process of the metal body characteristic mode theory has well inspired the subsequent research and development of the characteristic mode theory of more complex electromagnetic structures.

[0004] In the third chapter of the study on the characteristic mode theory and calculation method of complex electromagnetic structures (Huang Shaode, doctoral dissertation, University of Electronic Science and Technology of China), the generalized eigenvalue equation of PMCHW is mentioned. This method only solves the characteristic mode, and it is necessary to invent a better method to study the electromagnetic scattering characteristics of penetrable targets. Summary of the invention

[0005] The purpose of the present invention is to provide a characteristic mode analysis technology that can penetrate the electromagnetic scattering characteristics of a target. The invention of this method expands the application scope of the characteristic mode theory. The specific technical solution is as follows:

[0006] According to the equivalent principle of penetrable target surface, the surface integral equations of electric field and magnetic field are linearly combined to establish a mixed integral equation based on PMCHW formula. The moment method is used to discretize the equation to obtain the PMCHW matrix equation of the penetrable target.

[0007] A complex scalar factor is introduced to multiply the submatrix to transform the asymmetric PMCHW complex matrix equation into a symmetric form. The Gaussian elimination method is used to obtain the reduced matrix equation for the surface current. The real and imaginary parts of the reduced matrix equation are separated to establish the generalized eigenvalue equation for the surface current.

[0008] The generalized eigenvalue equation is solved by using a generalized eigenvalue equation solver to obtain the eigenvalue and characteristic current under the characteristic mode, and the characteristic current is weightedly summed to obtain the induced current that can penetrate the target surface, and the magnetic current is restored, and then the radar scattering cross section of the penetrable target is calculated;

[0009] By analyzing the characteristic patterns of penetrable targets, the PMCHW equation is first established by integrating discrete information. The filled impedance matrix in this equation is an asymmetric matrix. Complex scalar factors are introduced to convert the asymmetric matrix into a symmetric matrix. The characteristic mode theory is used to establish a generalized eigenvalue equation based on PMCHW. After solving the mode characteristic current and taking all the modes, the induced current can be accurately restored, and then the radar scattering cross section can be calculated.

[0010] Furthermore, the PMCHW equation is established based on different surface integral equations, and the impedance matrix in the equation is also based on the discrete segmentation information of the penetrable target, and this matrix is ​​an asymmetric structure.

[0011] Furthermore, the asymmetric impedance matrix needs to be converted into a symmetric matrix in order to establish a generalized eigenvalue equation using the eigenmode theory. The symmetry correction method is to multiply a single submatrix with a complex scalar factor.

[0012] Furthermore, the generalized eigenvalue equation is solved using a direct solution method, and this direct solution method uses the sgeev function in the LAPACK library to solve the characteristic current and the eigenvalue.

[0013] Furthermore, the characteristic current can be represented by the induced current through the superposition of weighted coefficients, which is used to replace the current column vector of the impedance matrix equation. The combination can obtain a matrix equation with the unknown number as the mode weighting factor, and the column vector of the mode weighting factor can be calculated, and the induced current can be restored. This induced current can be used to solve the radar scattering cross section.

[0014] Furthermore, the radar cross section is calculated from the characteristic current of all modes, and this value is very close to the actual radar cross section. When calculating the radar cross section, the induced current recovered from the characteristic current of some modes is used. Compared with the value of the full mode, it can be found that the value is also very similar. This method can simplify the calculation of the radar cross section.

[0015] The characteristic mode analysis technology of the electromagnetic scattering characteristics of a penetrable target of the present invention is to dissect and discretize the medium of the penetrable target, and in this process, node information, coordinate information, side length information, etc. can be obtained, so that the impedance matrix in the PMCHW equation based on the moment method can be filled. However, since the impedance matrix after filling is asymmetric, in order to be able to use the characteristic mode theory, the asymmetric matrix is ​​corrected, and the complex scalar factor is used to multiply it with its submatrix to correct it to symmetry. The solution vector is composed of induced current and magnetic current, and the right vector is filled according to the inner product of the incident excitation field and the trial function. The real and imaginary parts of the impedance matrix of the matrix equation are separated to form a generalized characteristic equation in the characteristic mode. Since the real and imaginary parts are both real symmetric matrices, the characteristic current and eigenvalue obtained after solving the equation using the function in the LAPACK library are also real numbers. The characteristic current obtained by solving can be used to represent the induced current by multiplying and summing with the weighting factor, and can be substituted into the matrix equation combination to obtain the matrix equation with the unknown number as the mode weighting factor. The induced current can be recovered. The radar cross section can be solved by using the recovered induced current. The radar cross section calculated by taking the induced current recovered from the partial mode current is very similar to the radar cross section value under the full mode. This method is simplified to the calculation of the radar cross section, and the analysis of electromagnetic scattering is also more accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 The flowchart of the characteristic mode method for analyzing the radar scattering cross section of a penetrable target according to the present invention is shown;

[0017] Figure 2 This is a schematic diagram of the structure of the penetrable target object according to the present invention;

[0018] Figure 3 The surface equivalence principle of the uniform penetrable target of the present invention is (a) external equivalence and (b) internal equivalence;

[0019] Figure 4 This is the radar cross section distribution diagram obtained by the present invention. DETAILED DESCRIPTION

[0020] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiment of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiment of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments, and the preferred embodiments of the present invention are given in the drawings. The present invention can be implemented in many different forms and is not limited to the embodiments described herein. On the contrary, the purpose of providing these embodiments is to make the understanding of the disclosure of the present invention more thorough and comprehensive. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0021] See also Figure 1 In an embodiment of the present invention, a characteristic mode analysis technology capable of penetrating electromagnetic scattering characteristics of a target is provided, and the method comprises the following steps:

[0022] S1: Use simulation software HFSS and ANSYS to model and discretize the penetrable target, obtain the node information, coordinate information and triangle unit information of the penetrable target model as the .rwg input file, set its operating frequency, dielectric constant, wavelength and polarization direction, and set the direction and size of the incident field;

[0023] In the simulation software HFSS, it is necessary to use basic operations to build a model, adjust the size of the model according to the size, position and other parameters of the model, and export the .sat file. Import the exported .sat file into ANSYS to dissect and discretize the surface of the penetrable target, set the dissection unit to triangle, the material number to 1, and set the dissection size to within one tenth of the wavelength to accurately calculate the radar cross section of the penetrable target model, so as to analyze the electromagnetic scattering characteristics. Model the penetrable target, perform discretization and other operations, obtain the node information, coordinate information and triangle unit information of the penetrable target model, and use the .rwg file as the input file of the program, and set its operating frequency, dielectric constant, polarization direction, and wavelength in the program. And determine the direction and size of the incident excitation field.

[0024] S2: According to the equivalent principle of the penetrable target surface, the surface integral equations of the electric field and the magnetic field are linearly combined to establish a mixed integral equation based on the PMCHW formula. The moment method is used to discretize the equation to obtain the PMCHW matrix equation of the penetrable target.

[0025] The PMCHW equation of the present invention is obtained based on the surface integral equation, and the derivation in the surface integral equation is also based on the surface equivalence principle, including external equivalence and internal equivalence. Figure 3In the external equivalent problem shown in , the total field inside the target that can penetrate is 0, and the external electric and magnetic fields are superimposed and remain unchanged. From the boundary conditions of the electromagnetic field, it can be seen that there must be an equivalent current source on the surface of the medium at this time. and equivalent magnetic current source and It is related to the tangential component of the total magnetic field on the outer surface of the medium. It is related to the tangential component of the total electric field on the outer surface of the total medium. Since the total field in the medium is 0, the medium parameters in the medium can be replaced by the parameters of the background medium without affecting the distribution of the electromagnetic field, such as Figure 3 As shown in the figure, the advantage of this is that the entire space becomes a uniform infinite free space with medium parameters (ε0, μ0), and the three-dimensional Green's function of the corresponding background medium can be used. At this time, the total field of the entire space is the superposition of the incident field and the scattered field, and both inside and outside the medium are through and Radiation is generated in free space. Therefore, according to the fact that the total field on the inner and outer surfaces of the medium is constant and the total field on the inner surface of the medium is zero, the following four integral equations are obtained:

[0026]

[0027] and They are determined by the tangential components of the total magnetic field and the total electric field on the outer surface of the medium, Similar to the principle of external equivalence problem, Figure 3 In the external equivalent problem shown, the total field inside the penetrable target remains unchanged, the superposition of the external electric field and magnetic field is 0, and the following four integral equations can also be obtained:

[0028]

[0029] Subtract the first from the seventh of the eight surface integral equations above to obtain an equivalent equation with the incident electric field on the right side: Subtracting the 2nd equation from the 8th equation yields an equivalent equation with the incident magnetic field on the right side, The above two equations are both implemented based on operators.

[0030] The mixed integral equation based on the PMCHW formula is a matrix obtained by discretization using the moment method, and the discretization method is to use triangulated units and RWG basis functions. The object operating frequency in the invention example is f = 300MHz, and the incident angle θ of the plane wave is inc =0,φ inc = 0 When the medium is a lossy medium, the dielectric constant is 2-j. The wavelength is 1 meter, and the length of the model segmentation unit needs to be set to one tenth of the wavelength, but the dielectric constant is 2-j, so the segmentation unit size is Among them, λ is the working wavelength, ε is the dielectric constant, and the unit can be divided into 0.07 meters. In the global information obtained after the division in ANSYS software, the number of triangular units is 5178, the number of nodes of the triangle is 2591, and the number of inner edges is 7767. The matrix equation obtained by discretization is In this equation, the unknowns are the current and magnetic current, and the vectors on the right are the excitations, which are the electric field and magnetic field respectively. In order to make the matrix equation more concise, the impedance matrix in the above matrix equation, [jωμ0(L d +L0)] can be expressed as Can be expressed [jω(ε d L d +ε0L0)] can be expressed as So the above equation can be written as follows: in, In the above equations, k ± , η ± , μ ± , ε ± are the wave number, intrinsic impedance, dielectric constant and permeability of the internal (-) and external (+) media respectively. n are the basis functions related to the method of moments (MOM), and <·,·,·> is the intersection of all subspaces.

[0031] S2: Introduce a complex scalar factor to multiply the submatrix, transform the asymmetric PMCHW complex matrix equation into a symmetric form, use Gaussian elimination to obtain the reduced matrix equation for the surface current, separate the real and imaginary parts of the reduced matrix equation, and establish the generalized eigenvalue equation for the surface current. The generalized eigenvalue solver is used to calculate the eigencurrent and eigenvalue under the eigenmode.

[0032] In the embodiment of the present invention, the impedance matrix of the discretized right-hand side of the PMCHW matrix equation can be represented by the matrix [Z], but the impedance matrix [Z] is not a symmetric matrix. Each single sub-matrix in the matrix [Z] is independently symmetric. The impedance matrix of this combined equation can be forced into a symmetric form by adding a complex scalar, thereby forming a new symmetric impedance operator. Therefore, the PMCHW equation is modified to be in the following form: Among them, the symmetrical impedance matrix Z is expressed as:

[0033]

[0034] Separate the real and imaginary parts of the symmetrical impedance matrix, apply the characteristic mode theory, and obtain the generalized eigenvalue equation based on the PMCHW equation; the above impedance matrix Z is operated on the real and imaginary parts, and the operation is as follows: Z = R + jX, Since Z is symmetry-corrected, the real and imaginary matrices are also symmetric. Considering the following weighted eigenvalue equation, ZJ n =υ n WJ n , where J n is the eigenvector, υ n is the eigenvalue. For any symmetric matrix W, the impedance matrix Z can be diagonalized. The orthogonality of the mode far field can be guaranteed only when [W] = [R]. Therefore, when [W] = [R] and υ n =1+jλ n When , we can get the following generalized eigenvalue equation, [X][J n ]=λ n [R][J n ].

[0035] The solution to the generalized eigenvalue equation is obtained by using the functions in the LAPACK library. First, the generalized eigenvalue equation is converted into a standard eigenvalue equation. [X] -1 [R][J n ]=λ n [R][J n ], where [X] -1 is the inverse matrix of the matrix [X]. The functions that implement this operation are sgetrf and sgetrs. To solve the above standard eigenvalue equation, the sgeev function in the LAPACK library is used to solve the characteristic current J n and eigenvalue λ n .

[0036] S3: According to the relationship between the characteristic current and the induced current, the characteristic current is weighted and summed to obtain the induced current that can penetrate the target surface, and the magnetic current is restored to calculate the radar cross section of the penetrable target. The electromagnetic scattering characteristics of the penetrable target are analyzed by the distribution of the radar cross section;

[0037] The generalized eigenvalue equations above have been solved. Eigenmodes A complete set of orthogonal modes are used to extend any induced currents generated by a particular external source to the far field. In other words, the induced current on a penetrable target can be written as a superposition of the eigenvalue currents: Correspondingly, the far field generated by the induced current is equal to the superposition of the characteristic fields, Among them, α nis the complex weighting coefficient in each mode. The above PMCHW correction matrix equation is simplified to the following form: Through the elimination method, the expression for calculating the magnetic current by the recovered induced current can be obtained: Μ=Z2 -1 (E-Z1) J. Thus, the unknown variables of the matrix equation, the current and the magnetic current, can be obtained.

[0038] Radar cross section is a physical quantity of the echo intensity generated by a penetrable target under radar wave irradiation, based on the assumption that the penetrable target scatters is isotropically. Its calculation formula is:

[0039] By taking the weighted sum of the characteristic currents in the characteristic mode, we can take all the modes and some of the modes to recover the induced current. The calculated induced current can be used to accurately calculate the radar cross section that can penetrate the target. Selecting the characteristic currents of the appropriate partial characteristic mode can also accurately calculate the radar cross section.

[0040] The induced current can be equal to J = α1J2 + α2J3 + ··· + α 125 J 125 In this recovery process, the number of currents in the partial mode is 125, and the radar cross section can be calculated. Comparing it with the radar cross section in the full mode, it is concluded that the radar cross section can be accurately calculated in the partial mode.

[0041] See also Figure 2 , the figure shows a method of calculating the radar cross section (RCS) of a penetrable target using the characteristic mode method described in the present invention. The method is analyzed and calculated under the penetrable target. The size of the object shows that the radius of the dielectric sphere is 1 meter, and the structure diagram of the object after analysis and segmentation in free space is shown in Figure 2 on the right

[0042] See also Figure 4, the figure shows a method of calculating the radar cross section (RCS) of a penetrable target using the characteristic mode method described in the present invention, and the scanning angle Theta of the radar cross section ranges from 0° to 180°. By comparing the radar cross section calculated in the full mode with the radar cross section in the partial mode, it can be concluded that the radar cross section can be accurately approximated by using the characteristic current of the partial mode. It can be clearly seen in the figure that the set Theta is the observation angle, and the observation range is 0° to 180°. In the entire Theta variation range, from 0° to 30°, the value of the radar cross section shows a downward trend, that is, the radiation capability of penetrating the target in this angle range is reduced. The observation angle is [115°, 125°], and the value shows an upward trend and increases by 30dB, that is, the radiation capability of penetrating the target in this angle range is gradually enhanced. At 0°, the value of the radar cross section is the largest, and the radiation capability at this time is also the strongest. At 110°, the value is as low as -30dB, and the radiation capability at this time is also the weakest. The radar cross section calculated by this method better analyzes the scattering and radiation characteristics of penetrable targets.

[0043] During the entire calculation process of the program, the input of the program is the discrete information of the model. The discrete method is to establish a discrete Figure 2 The penetrable target model shown in the figure is exported as a .sat file. The file is imported into ANSYS for surface segmentation. The segmented units are triangles. The information obtained from the segmentation includes node and coordinate information, edge information, and triangle unit information. This information is formed into a .lis file and put into the preprocessing program as an input file to obtain the final .RWG file. This file is used as the input file of the PMCHW-based characteristic model calculation program. The program is written and verified according to the above steps. The output data is displayed in EXCEL as follows: Figure 4 Finally, the program can use the characteristic mode method to calculate the radar cross section of the penetrable target, and analyze the electromagnetic scattering characteristics of the penetrable target through the distribution diagram of the radar cross section.

[0044] The above are only preferred embodiments of the present invention, but do not limit the patent scope of the present invention. Although the present invention is described in detail with reference to the above embodiments, those skilled in the art can still modify the technical solutions recorded in the above embodiments, or replace some of the technical features with equivalent ones. Any equivalent structure made by using the contents of the present invention specification and drawings, directly or indirectly used in other related technical fields, is also within the scope of patent protection of the present invention.

Claims

1. A method for analyzing characteristic modes of electromagnetic scattering characteristics of a penetrable target, the method comprising the following steps: Step 1: Use simulation software HFSS and ANSYS to model the penetrable target, perform discrete operations, obtain the node information, coordinate information and triangle unit information of the penetrable target model as the .rwg input file, set its operating frequency, dielectric constant, wavelength and polarization direction parameters, and set the direction and size of the incident field; Step 2: Linearly combine the surface integral equations of the electric field and the magnetic field to establish a mixed integral equation based on the PMCHW formula, discretize the equation using the moment method, and obtain the PMCHW matrix equation that can penetrate the target; Step 3: Introduce a complex scalar factor to multiply the submatrix, transform the asymmetric PMCHW complex matrix equation into a symmetric form, use Gaussian elimination method to obtain the reduced matrix equation for the surface current, separate the real part and the imaginary part of the reduced matrix equation, and establish the generalized eigenvalue equation for the surface current; The generalized eigenvalue solver is used to calculate the characteristic current and eigenvalue in the characteristic mode. Step 4: According to the relationship between the characteristic current and the induced current, the characteristic current is weighted and summed to obtain the induced current that can penetrate the target surface, and the magnetic current is restored, and then the radar scattering cross section of the penetrable target is calculated; Step 5: Analyze the electromagnetic scattering characteristics of the penetrable target through the distribution diagram of the radar scattering cross section; In step 1, according to the equivalent principle of the penetrable target surface, the internal field and the external field of the penetrable target change, and the surface integral equation of the electric field or magnetic field changing with the current source and the magnetic current source is obtained: Linearly combining the surface integral equations, we can get the right-hand side term as the incident electric field and the incident magnetic field Two operator equations; In the step 2, the mixed integral equation based on the PMCHW formula is obtained by the discrete method of the moment method and the selection of the appropriate The appropriate RWG basis function discretizes the mixed integral equation based on the PMCHW formula into the unknown quantity, which is the current and magnetic current The matrix equation The right side of the equation is the excitation term, which is the electric field and magnetic field. Simplifying the equation, we get the following form In step 3, a complex scalar factor is introduced for the asymmetric PMCHW complex matrix equation j, multiply the two sub-matrices on the secondary diagonal by the complex scalar factors j and -j respectively, Transform the asymmetric PMCHW complex matrix equation into a symmetric form; In step 3, the reduced matrix equation considers the weighted eigenvalue equation, takes the weighted matrix as the real part of the impedance matrix, Z=R+jX, and establishes the generalized eigenvalue equation for the surface current [X][J n ]=λ n [R][J n ].

2. The characteristic mode analysis method of electromagnetic scattering characteristics of a penetrable target according to claim 1, characterized in that: In the step 4, the characteristic currents in the characteristic modes are weighted and summed, and all or part of the modes are selected.

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