A fast accuracy evaluation method for electromagnetic characteristics simulation of aerial targets using radar

Abstract

The present invention discloses a fast accuracy assessment method for simulating electromagnetic characteristics of aerial target radar, and belongs to the field of electromagnetic simulation technology. The method of the present invention performs fast self-assessment of radar electromagnetic characteristics simulation errors based on the law of conservation of energy, and can perform error assessment on simulation results without reference solutions, thus avoiding the large amount of cost required to generate reference solutions; the near-field coupling matrix is ​​quickly obtained using a multi-layer fast multipole method, thus avoiding point-by-point calculation of the near field, greatly reducing the calculation cost, and improving the calculation efficiency; it can efficiently and accurately judge whether the simulation results of the radar electromagnetic characteristics of aerial targets meet the accuracy requirements required for the design, thus avoiding design errors caused by inaccurate simulation results, shortening the iteration cycle, and realizing fast and high-precision simulation of the electromagnetic characteristics of aerial target radars.

Description

Technical Field

[0001] The invention belongs to the technical field of electromagnetic simulation, and in particular relates to a fast accuracy evaluation method for simulating electromagnetic characteristics of aerial target radar. Background Art

[0002] In practical applications, it is neither necessary nor realistic to achieve completely error-free electromagnetic scattering simulation results. Instead, the goal of electromagnetic scattering simulation is to control the error within an acceptable range for a specific application scenario. This requires an accurate assessment of the overall accuracy of the calculation results.

[0003] The efficient implementation of accuracy evaluation is an important part of the electromagnetic simulation of aerial target radar. It can quickly and accurately determine whether the simulation results of the radar electromagnetic characteristics of aerial targets meet the accuracy requirements of the design, avoid design errors caused by inaccurate simulation results, and shorten the design iteration cycle. The commonly used simulation error evaluation methods in the prior art can be roughly divided into two categories.

[0004] The first type compares the results with reference solutions (such as analytical solutions and measured solutions). Evaluation methods based on reference solutions are often very expensive. Generating numerical reference solutions requires solving the problem in a higher-dimensional discrete space, which not only increases the computational complexity but also may introduce potential convergence problems, especially for ill-conditioned system matrices. Acquiring measured solutions as reference solutions through experiments requires a lot of financial and time resources, which limits its feasibility in practical applications of electromagnetic property simulation.

[0005] The second type of method does not require a reference solution, and usually evaluates the simulation error based on physical principles. The prior art "Novel monopolar MFIE MoM-discretization for the scattering analysis of small objects" discloses a method for evaluating errors using the phenomenon that the field strength inside an ideal conductor is zero, and the prior art "The error cross-section method for quantifying the error inelectromagnetic scattering problems" discloses a method for evaluating the accuracy of electromagnetic simulation based on the principle of conservation of energy. The above-mentioned prior arts all achieve accurate evaluation of simulation errors, but the above-mentioned prior arts all have technical problems in the process of calculating simulation errors, which involve the need for a large number of near-field calculations, thereby bringing a significant computational burden and making it difficult to be widely implemented in practical applications of electromagnetic property simulation. Summary of the invention

[0006] The object of the present invention is to overcome the defects of the prior art and provide a fast accuracy evaluation method for simulating electromagnetic characteristics of aerial target radar.

[0007] The technical problem proposed by the present invention is solved in this way:

[0008] A fast accuracy evaluation method for simulating electromagnetic characteristics of aerial target radar includes the following steps:

[0009] Step 1. Perform triangular meshing on the model surface of the aerial target;

[0010] Step 2. Discretize the target surface current based on the RWG basis function on the divided model surface triangular mesh, and establish the electric field integral equation; solve the electric field integral equation to obtain the target surface current distribution of the aerial target;

[0011] Step 3. Establish an absorbed power calculation surface surrounding the aerial target and divide the calculation surface into triangular meshes; define the RWG basis function on the divided triangular mesh of the calculation surface to discretize the scattered tangential electric field and the scattered tangential magnetic field respectively;

[0012] Step 4. Use the target surface current distribution of the aerial target to characterize the discrete scattered tangential electric field and scattered tangential magnetic field; perform Galerkin test on the discrete scattered tangential electric field and scattered tangential magnetic field, generate and solve a linear equation system, obtain the electric field coefficient and the magnetic field coefficient, and then obtain the scattered tangential electric field and the scattered tangential magnetic field;

[0013] Step 5. Calculate the absorbed power of the aerial target using the scattered tangential electric field and the scattered tangential magnetic field, and use the modulus of the absorbed power as the evaluation error of the current radar electromagnetic characteristic simulation result;

[0014] Step 6. Determine whether the evaluation error of the current radar electromagnetic characteristics simulation result is less than the preset error threshold. If so, the current radar electromagnetic characteristics simulation result is determined to be credible, and the target surface current distribution of the current air target is output; otherwise, the current radar electromagnetic characteristics simulation result is determined to be unreliable, the model surface triangular mesh is encrypted, and return to step 2.

[0015] Furthermore, the specific process of step 2 is:

[0016] For any model surface triangle mesh, the discretized target surface current It is expressed as:

[0017] ;

[0018] Where, 1≤n≤N, N is the number of common edges of the triangular mesh on the surface of the current model; is the current coefficient corresponding to the nth common side, is the RWG basis function corresponding to the nth common edge;

[0019] The target surface current The discrete form of is substituted into the electric field integral equation, and the Galerkin method is used for testing. The electric field integral equation is expressed in the form of a matrix equation, specifically:

[0020] ;

[0021] in, is the impedance matrix, is the vector to be solved, is the excitation vector;

[0022] Impedance Matrix The element in row m and column n It is expressed as:

[0023] ;

[0024] Among them, 1≤m≤N, and RWG basis functions and The domain of For the field point, is the source point, represents the Green's function, is the wave number, represents the divergence of the field point. represents the divergence of the source point. and Respectively and The differential of

[0025] Excitation vector The element in row m It is expressed as:

[0026] ;

[0027] ;

[0028] in, is an imaginary unit, is the incident wave angular frequency, is the free space permeability, For the field The incident electric field at

[0029] Vector to be solved The element in the nth row is , solve the matrix equation, obtain the current coefficients, and then obtain the target surface current .

[0030] Furthermore, in step 3, the closest distance between the absorbed power calculation surface S and the aerial target is greater than 0.5λ, where λ is the wavelength corresponding to the angular frequency of the incident wave.

[0031] Furthermore, in step 3, for any computational surface triangle mesh, the discrete scattered tangential electric field and scattered tangential magnetic field They are:

[0032] ;

[0033] ;

[0034] Among them, 1≤q≤Q, Q is the number of common edges of the triangle mesh of the current calculation surface, is the RWG basis function corresponding to the qth common edge; and They respectively represent the electric field coefficient and magnetic field coefficient corresponding to the qth common edge.

[0035] Furthermore, the specific process of step 4 is as follows:

[0036] Select the RWG basis function defined on the computational surface S As a test function, the Galerkin test is performed on the scattered tangential electric field and scattered tangential magnetic field on the calculation surface S, and the following two sets of linear equations are obtained:

[0037] ;

[0038] ;

[0039] Among them, 1≤p≤Q, It means to find the inner product;

[0040] In the above two sets of linear equations, the discrete scattered tangential electric field on the left side of the equal sign is and scattered tangential magnetic field The target surface current distribution of the aerial target is characterized, and then written into matrix equations and solved to obtain the electric field coefficient and magnetic field coefficient, and then the discrete scattered tangential electric field is obtained. and scattered tangential magnetic field .

[0041] Furthermore, in step 4, for the left side of the two sets of linear equations, the target surface current distribution of the aerial target is used to represent the discrete scattered tangential electric field. and scattered tangential magnetic field , specifically:

[0042] ;

[0043] ;

[0044] in, is the free space dielectric constant, ▽ indicates the gradient, It means to find the curl;

[0045] The excitation matrices in the matrix equation form corresponding to the two sets of linear equations are obtained by using the multi-layer fast multipole method.

[0046] Furthermore, the specific process of step 5 is as follows:

[0047] Calculate the absorbed power of an aerial target:

[0048] ;

[0049] Among them, S represents the calculation surface, Re represents the real part, and They represent the tangential electric field and tangential magnetic field on the calculation surface respectively, and the superscript * indicates the conjugate. To calculate the unit normal vector of the surface, To calculate the differential of the surface; , , and are the incident tangential electric field and the incident tangential magnetic field, respectively;

[0050] Evaluation error of current radar electromagnetic characteristics simulation results for:

[0051] ;

[0052] in, Indicates the modulus value.

[0053] Furthermore, in step 6, 0.0001 is selected as the preset error threshold.

[0054] The beneficial effects of the present invention are:

[0055] The method of the present invention performs rapid self-evaluation of radar electromagnetic characteristics simulation errors based on the law of conservation of energy, and can perform error evaluation on simulation results without a reference solution, thereby avoiding the large amount of cost required to generate a reference solution. The method of the present invention utilizes a multi-layer fast multipole method to quickly obtain a near-field coupling matrix, thereby avoiding point-by-point calculation of the near field, greatly reducing the computational cost, and improving computational efficiency, thereby achieving rapid and efficient electromagnetic simulation accuracy evaluation. The method of the present invention can efficiently and accurately determine whether the simulation results of the radar electromagnetic characteristics of an aerial target meet the accuracy requirements required for the design, avoid design errors caused by inaccurate simulation results, shorten the iteration cycle, and achieve rapid and high-precision simulation of the electromagnetic characteristics of aerial target radars. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 is a comparison diagram of error convergence curves of the metal spherical model in the method described in the embodiment;

[0057] Figure 2 It is a comparison diagram of the error convergence curves of the metal square model in the method described in the embodiment. DETAILED DESCRIPTION

[0058] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0059] This embodiment provides a rapid accuracy assessment method for simulating electromagnetic characteristics of aerial target radar, comprising the following steps:

[0060] Step 1. Perform triangular meshing on the model surface of the aerial target;

[0061] Step 2. Discretize the target surface current based on the RWG basis function on the divided model surface triangular mesh, and establish the electric field integral equation; solve the electric field integral equation to obtain the target surface current distribution of the aerial target;

[0062] The specific process of step 2 is:

[0063] For any model surface triangle mesh, the discretized target surface current It is expressed as:

[0064] ;

[0065] Where, 1≤n≤N, N is the number of common edges of the triangular mesh on the surface of the current model; is the current coefficient corresponding to the nth common side, is the RWG basis function corresponding to the nth common edge;

[0066] The target surface current The discrete form of is substituted into the electric field integral equation EFIE, and the Galerkin method is used for testing. The electric field integral equation EFIE is expressed in the form of a matrix equation, specifically:

[0067] ;

[0068] in, is the impedance matrix, is the vector to be solved, is the excitation vector;

[0069] Impedance Matrix The element in the mth row and nth column is represented as:

[0070] ;

[0071] Among them, 1≤m≤N, and RWG basis functions and The domain of For the field point, is the source point, represents the Green's function, is the wave number, represents the divergence of the field point. represents the divergence of the source point. and Respectively and The differential of

[0072] Excitation vector The m-th row element is represented as:

[0073] ;

[0074] ;

[0075] in, is an imaginary unit, is the incident wave angular frequency, is the free space permeability, For the field The incident electric field at

[0076] Vector to be solved The element in the nth row is , solve the matrix equation to obtain the current coefficients , and then get the target surface current .

[0077] Step 3. Establish an absorbed power calculation surface surrounding the aerial target, divide the calculation surface into triangular meshes, define RWG basis functions on the divided calculation surface triangular meshes, and discretize the scattered tangential electric field and scattered tangential magnetic field respectively;

[0078] In this embodiment, the closest distance between the absorbed power calculation surface S and the aerial target is greater than 0.5λ, where λ is the wavelength corresponding to the angular frequency of the incident wave.

[0079] In step 3, for any computational surface triangle mesh, the discrete scattered tangential electric field and scattered tangential magnetic field The specific expansion processes are:

[0080] ;

[0081] ;

[0082] Among them, 1≤q≤Q, Q is the number of common edges of the triangle mesh of the current calculation surface, is the RWG basis function corresponding to the qth common edge; and They respectively represent the electric field coefficient and magnetic field coefficient corresponding to the qth common edge.

[0083] Step 4. Use the target surface current distribution of the aerial target to characterize the discrete scattered tangential electric field and scattered tangential magnetic field; perform Galerkin test on the discrete scattered tangential electric field and scattered tangential magnetic field, generate and solve a linear equation system, obtain the electric field coefficient and the magnetic field coefficient, and then obtain the scattered tangential electric field and the scattered tangential magnetic field;

[0084] The specific process of step 4 is:

[0085] Select the RWG basis function defined on the computational surface S As a test function, the Galerkin test is performed on the scattered tangential electric field and scattered tangential magnetic field on the calculation surface S, and the following two sets of linear equations are obtained:

[0086] ;

[0087] ;

[0088] Among them, 1≤p≤Q, It means to find the inner product;

[0089] In the above two sets of linear equations, the discrete scattered tangential electric field on the left side of the equal sign is and scattered tangential magnetic field The target surface current distribution of the aerial target is characterized, and then written into matrix equations and solved to obtain the electric field coefficient and magnetic field coefficient, and then the discrete scattered tangential electric field is obtained. and scattered tangential magnetic field .

[0090] Among them, for the left side of the equal sign of the two sets of linear equations, the target surface current distribution of the aerial target is used to represent the discrete scattered tangential electric field and scattered tangential magnetic field , specifically:

[0091] ;

[0092] ;

[0093] in, is the free space dielectric constant, ▽ indicates the gradient, It means to find the curl;

[0094] The excitation matrices in the matrix equation form corresponding to the two sets of linear equations are obtained by using the multi-layer fast multipole method, which characterizes the near-field coupling from the aerial target to the calculation surface.

[0095] Step 5. Calculate the absorbed power of the aerial target using the scattered tangential electric field and the scattered tangential magnetic field, and use the modulus of the absorbed power as the evaluation error of the current radar electromagnetic characteristic simulation result;

[0096] The specific process of step 5 is:

[0097] Calculate the absorbed power of an aerial target:

[0098] ;

[0099] Among them, Re represents the real part, and They represent the electric field and magnetic field on the calculation surface S, respectively. The superscript * indicates that the conjugate is taken. To calculate the unit normal vector of surface S, To calculate the differential of surface S, and represent the tangential electric field and tangential magnetic field on the calculation surface S respectively;

[0100] ;

[0101] ;

[0102] in, and are the incident tangential electric field and the incident tangential magnetic field, respectively;

[0103] Evaluation error of current radar electromagnetic characteristics simulation results for:

[0104] ;

[0105] in, Indicates the modulus value.

[0106] Step 6. Determine whether the evaluation error of the current radar electromagnetic characteristics simulation result is less than the preset error threshold. If so, the current radar electromagnetic characteristics simulation result is determined to be credible, the target surface current distribution of the current air target is output, and the air target radar electromagnetic characteristics simulation is completed; otherwise, the current radar electromagnetic characteristics simulation result is determined to be unreliable, the model surface triangular mesh is encrypted, and return to step 2.

[0107] In principle, the error threshold in step 6 can be a positive value close to 0. In this embodiment, 0.0001 is selected as the preset error threshold.

[0108] According to the law of conservation of energy, a perfect conductor target in a lossless medium will not absorb any energy. Therefore, when a uniform plane wave is irradiated on it, its absorbed power should be 0. However, due to the existence of numerical solution errors, the absorbed power calculated by the actual algorithm of the method described in this embodiment is not 0; the larger the modulus of the calculated absorbed power, the larger the simulation error. Therefore, the method described in this embodiment uses the modulus of the target absorbed power as an effective evaluation of the electromagnetic scattering simulation error.

[0109] This embodiment first gives calculation examples of metal spherical models and metal square models, and compares the absorbed power error calculated by the method described in this embodiment with the RCS error calculated based on the reference solution evaluation method. The error convergence curves of the two as the grid is encrypted are shown as follows: Figure 1 and Figure 2 As shown. Among them, the reference solution of the metal spherical model is obtained by Mie series calculation, while the reference solution of the metal square model is obtained by grid calculation with a size of 0.012λ. It can be seen that the absorption power error curve obtained by the method described in this embodiment is basically consistent with the convergence slope of the RCS error curve obtained based on the reference solution, which proves that the method described in this embodiment can accurately reflect the convergence of the simulation error as the grid is encrypted, and indicate the size of the simulation error. Therefore, it can be used as a means of error evaluation, and then used to achieve fast and high-precision simulation of the electromagnetic characteristics of air target radars.

[0110] This embodiment also gives a calculation example of a metal aircraft to demonstrate the efficiency of the proposed method in error assessment. The metal aircraft is 17.9m long, 12m wide, and 5.7m high. The calculation frequency is 300MHz, and the initial grid unit size is about 0.2λ. The absorption power error calculated by the initial grid is 0.000204, which is greater than the selected threshold of 0.0001, so the initial grid needs to be encrypted to improve the accuracy. The encrypted grid size is about 0.15λ, and the calculated absorption power error is 0.00000676, which meets the set threshold requirements. In the case of the initial grid, the calculation time of the method described in this embodiment and the prior art is 9s and 307s respectively; in the case of the encrypted grid, the calculation time of the method described in this embodiment and the prior art is 16s and 569s respectively. It can be seen that the calculation time required by the method described in this embodiment is much less than that of the prior art, which proves the efficiency of the method described in this embodiment for realizing the fast and high-precision simulation of the electromagnetic characteristics of the air target radar.

[0111] The above description is only a specific implementation mode of the present invention. Any feature disclosed in this specification, unless otherwise stated, can be replaced by other alternative features that are equivalent or have similar purposes; all the disclosed features, or all the steps in the methods or processes, except for mutually exclusive features and / or steps, can be combined in any way.

Claims

1. A fast accuracy assessment method for simulating electromagnetic characteristics of aerial target radar, characterized in that: The following steps are involved: Step 1. Perform triangular meshing on the model surface of the aerial target; Step 2. Discretize the target surface current based on the RWG basis function on the triangular mesh of the model surface and establish the electric field integral equation; Solve the electric field integral equation to obtain the target surface current distribution of the aerial target; Step 3. Establish an absorbed power calculation surface surrounding the aerial target and divide the calculation surface into triangular meshes; define the RWG basis function on the divided triangular mesh of the calculation surface to discretize the scattered tangential electric field and the scattered tangential magnetic field respectively; Step 4. Use the target surface current distribution of the aerial target to characterize the discrete scattered tangential electric field and scattered tangential magnetic field; perform Galerkin test on the discrete scattered tangential electric field and scattered tangential magnetic field, generate and solve a linear equation system, obtain the electric field coefficient and the magnetic field coefficient, and then obtain the scattered tangential electric field and the scattered tangential magnetic field; Step 5. Calculate the absorbed power of the aerial target using the scattered tangential electric field and the scattered tangential magnetic field, and use the modulus of the absorbed power as the evaluation error of the current radar electromagnetic characteristic simulation result; Step 6. Determine whether the evaluation error of the current radar electromagnetic characteristic simulation result is less than a preset error threshold. If so, determine that the current radar electromagnetic characteristic simulation result is credible, and output the target surface current distribution of the current air target; Otherwise, it is determined that the current radar electromagnetic characteristics simulation result is unreliable, the triangular mesh of the model surface is encrypted, and the process returns to step 2.

2. The rapid accuracy assessment method for air target radar electromagnetic characteristics simulation according to claim 1, characterized in that: The specific process of step 2 is: For any model surface triangle mesh, the discretized target surface current It is expressed as: ； Where, 1≤n≤N, N is the number of common edges of the triangular mesh on the surface of the current model; is the current coefficient corresponding to the nth common side, is the RWG basis function corresponding to the nth common edge; The target surface current The discrete form of is substituted into the electric field integral equation, and the Galerkin method is used for testing. The electric field integral equation is expressed in the form of a matrix equation, specifically: ； in, is the impedance matrix, is the vector to be solved, is the excitation vector; Impedance Matrix The element in row m and column n It is expressed as: ； Among them, 1≤m≤N, and RWG basis functions and The domain of For the field point, is the source point, represents the Green's function, is the wave number, represents the divergence of the field point. represents the divergence of the source point. and Respectively and The differential of Excitation vector The element in row m It is expressed as: ； ； in, is an imaginary unit, is the incident wave angular frequency, is the free space permeability, For the field The incident electric field at Vector to be solved The element in the nth row is , solve the matrix equation, obtain the current coefficients, and then obtain the target surface current .

3. The rapid accuracy assessment method for air target radar electromagnetic characteristics simulation according to claim 1, characterized in that: In step 3, the closest distance between the absorbed power calculation surface S and the aerial target is greater than 0.5λ, where λ is the wavelength corresponding to the angular frequency of the incident wave.

4. The rapid accuracy assessment method for air target radar electromagnetic characteristics simulation according to claim 2, characterized in that: In step 3, for any computational surface triangle mesh, the discrete scattered tangential electric field and scattered tangential magnetic field They are: ； ； Among them, 1≤q≤Q, Q is the number of common edges of the triangle mesh of the current calculation surface, is the RWG basis function corresponding to the qth common edge; and They respectively represent the electric field coefficient and magnetic field coefficient corresponding to the qth common edge.

5. The rapid accuracy assessment method for air target radar electromagnetic characteristics simulation according to claim 4 is characterized in that: The specific process of step 4 is: Select the RWG basis function defined on the computational surface S As a test function, the Galerkin test is performed on the scattered tangential electric field and scattered tangential magnetic field on the calculation surface S, and the following two sets of linear equations are obtained: ； ； Among them, 1≤p≤Q, It means to find the inner product; In the above two sets of linear equations, the discrete scattered tangential electric field on the left side of the equal sign is and scattered tangential magnetic field The target surface current distribution of the aerial target is characterized, and then written into matrix equations and solved to obtain the electric field coefficient and magnetic field coefficient, and then the discrete scattered tangential electric field is obtained. and scattered tangential magnetic field .

6. The rapid accuracy assessment method for air target radar electromagnetic characteristics simulation according to claim 5 is characterized in that: In step 4, for the left side of the two sets of linear equations, the target surface current distribution of the aerial target is used to represent the discrete scattered tangential electric field. and scattered tangential magnetic field , specifically: ； ； in, is the free space dielectric constant, ▽ indicates the gradient, It means to find the curl; The excitation matrices in the matrix equation form corresponding to the two sets of linear equations are obtained by using the multi-layer fast multipole method.

7. The rapid accuracy assessment method for air target radar electromagnetic characteristics simulation according to claim 6 is characterized in that: The specific process of step 5 is: Calculate the absorbed power of an aerial target: ； Among them, S represents the calculation surface, Re represents the real part, and They represent the tangential electric field and tangential magnetic field on the calculation surface respectively, and the superscript * indicates the conjugate. To calculate the unit normal vector of the surface, To calculate the differential of the surface; , , and are the incident tangential electric field and the incident tangential magnetic field, respectively; Evaluation error of current radar electromagnetic characteristics simulation results for: ； in, Indicates the modulus value.

8. The rapid accuracy assessment method for air target radar electromagnetic characteristics simulation according to claim 1, characterized in that: In step 6, 0.0001 is selected as the preset error threshold.

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