Radar electromagnetic characteristic rapid reconstruction method for local stealth coating falling target

Abstract

The invention discloses a radar electromagnetic characteristic rapid reconstruction method for a local stealth coating falling target, and belongs to the technical field of electromagnetic simulation. According to the method, a novel matrix equation is constructed, calculation data of a full-coating target can be repeatedly utilized when the RCS of the local coating target is calculated, meanwhile, a PARDISO solver, a fast multi-pole algorithm and a precondition technology are used for accelerating the iteration process of a generalized minimum residual method, and the iteration convergence process is further accelerated. The calculation cost of the method is far lower than that of a method of refilling a matrix and performing calculation, and the influence of local coating change on target radar characteristics can be accurately and efficiently evaluated for a scene of target local coating change.

Description

Technical Field

[0001] The present invention belongs to the technical field of electromagnetic simulation, and in particular relates to a method for rapidly reconstructing radar electromagnetic characteristics of a target with partially fallen stealth coating. Background Art

[0002] The stealth capability of stealth weapon systems is primarily achieved through both design and materials. Design is subject to numerous constraints, making the research and development of stealth materials crucial to stealth technology. However, in complex flight environments, the coatings on stealth aircraft are prone to peeling and cracking, compromising the aircraft's overall stealth performance. Maintenance of stealth aircraft is crucial.

[0003] Currently, the main methods for testing the quality of stealth aircraft coatings include conducting RCS measurements and evaluating them using electromagnetic simulation software. RCS measurements require specialized test sites and systems, which are time-consuming and costly. Traditional electromagnetic simulation algorithms are not optimized for localized coating targets, resulting in high computational complexity and a long, computationally expensive process. Summary of the Invention

[0004] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and provide a method for quickly reconstructing the radar electromagnetic characteristics of a target with partially peeled stealth coating, which is used to quickly reconstruct and calculate the locally coated target, greatly shortening the time spent on recalculation.

[0005] The technical problem proposed by the present invention is solved as follows:

[0006] A method for rapidly reconstructing radar electromagnetic characteristics of a target with partially lost stealth coating comprises the following steps:

[0007] Step 1: Use conformal triangular mesh to discretize the fully coated target surface, and then define basis functions on each triangular mesh; construct the CFIE mixed field integral equation and discretize it using the Galerkin method to generate a linear equation system As the CFIE hybrid field integral equation to be solved, where A and B are impedance matrices, b is the excitation term, and J is the current coefficient to be solved, is the normalized magnetic current coefficient to be solved;

[0008] Step 2: Construct the impedance boundary condition of the fully coated target η s is the relative surface impedance of the fully coated target;

[0009] Step 3: Combine the CFIE hybrid field integral equations and impedance boundary conditions to be solved, and use the PARDISO solution method, the multi-layer fast multipole MLFMA method and the BD / SAI preconditioning method to solve the simultaneous equations. / represents or, and calculate the J and corresponding to the full coating target. The solution;

[0010] Step 4: For the preconditioning matrices corresponding to the self group and the near zone group in the impedance matrices A and B obtained by the BD / SAI preconditioning method in step 3, the aggregation item, transfer item and configuration item of the far zone group obtained by the MLFMA method, the excitation item b, the J and corresponding to the full coating target calculated in step 3, The solution is stored;

[0011] Step 5: For the partially coated target, the same conformal triangular mesh as the fully coated target is used for discretization, the relative surface impedance corresponding to the uncoated metal part is set to 0, and the impedance boundary condition is updated;

[0012] Step 6: Combine the CFIE hybrid field integral equation and the updated impedance boundary condition; use the preconditioning matrix corresponding to the self group and the near zone group in the impedance matrices A and B stored in step 4, the aggregation item, transfer item and configuration item of the far zone group, the excitation item b, and the updated impedance boundary condition in step 5, and use the J and corresponding to the full coating target stored in step 4. The solution of is taken as the initial solution, and the simultaneous equations are solved iteratively to obtain J and The solution;

[0013] Step 7: Based on the J and The radar cross section of the partially coated target is calculated using the solution.

[0014] Furthermore, the specific process of step 1 is:

[0015] The mixed field integral equation, CFIE equation, is defined as: Among them, α and β are combination coefficients, β = 1-α; EFIE represents the electric field integral equation, MFIE represents the magnetic field integral equation, η0 represents the wave impedance in vacuum, The surface normal vector representing the fully coated target;

[0016] Define the mixed field integral operator C α，β (J; Γ) is expressed as:

[0017]

[0018] Where Γ represents the surface of the fully coated target, and × represents the vector cross product; j is the symbol of the imaginary part, k represents the wave number, X represents the unknown quantity, Indicates the gradient of the field point. Indicates the divergence of the source point, G is the scalar Green's function, and dr' represents the differential value of the source point position;

[0019] The above mixed field integral operator C α，β Substituting (J; Γ) into the electric field integral equation and magnetic field integral equation of the fully coated target surface, the CFIE equation of the fully coated target surface is obtained:

[0020]

[0021] Among them, E inc represents the electric field of the incident plane wave, H inc represents the incident plane wave magnetic field;

[0022] Rewrite the CFIE equation into a matrix equation form, expressed as:

[0023]

[0024] Among them, the corresponding elements of the coefficient matrix are:

[0025]

[0026] Among them, A mn represents the mth row and nth column element of the impedance matrix A, λ represents the test function, J n is the current coefficient corresponding to the nth basis function, C α，β (J n Γ n ) represents the mixed field integral operator corresponding to the nth basis function, Γ n and Γ m Represent the nth triangle mesh and the mth triangle mesh respectively, <> represents the inner product; B mn represents the element in the mth row and nth column of the impedance matrix B, is the normalized magnetic flux coefficient corresponding to the nth basis function.

[0027] Furthermore, the specific process of step 2 is:

[0028] The impedance boundary condition for the fully coated target is expressed as: Rewritten as a matrix equation:

[0029]

[0030] Among them, the element in the mth row and nth column of the coefficient matrix P1 is The element in the mth row and nth column of the coefficient matrix P2 [0] represents an all-zero vector.

[0031] Furthermore, the specific process of step 3 is:

[0032] For the impedance matrices A and B in the CFIE equation to be solved in step 1, the MLFMA method is used to divide the impedance matrix elements into self-group, near-zone group and far-zone group; for the far-zone group, the MLFMA method is used to calculate the aggregation terms, transfer terms and configuration terms corresponding to the impedance matrix elements;

[0033] For the self-group and the near-zone group, the impedance matrix element values ​​are directly calculated; the impedance matrix element values ​​of the self-group and the near-zone group are pre-conditioned using BD preconditioning or SAI preconditioning to obtain the pre-conditioned matrix, and then the pre-conditioned CFIE linear equation system is obtained;

[0034] In the impedance boundary condition matrix equation in step 2, the coefficient matrices P1 and P2 are sparse matrices. In each iteration of the generalized minimum residual method, the current coefficient J of the current iteration is substituted into the impedance boundary condition matrix equation, and the corresponding PARDISO solver is used to quickly solve it. Then the current coefficient J and Substitute the left side of the equal sign of the pre-processed CFIE equation and calculate the vector addition result on the left side of the equal sign of the CFIE equation to be solved; through iteration, make the difference between the vector addition result on the left side of the equal sign of the CFIE equation to be solved and the excitation term b less than the set threshold, and obtain J and corresponding to the full coating target The solution.

[0035] Furthermore, the specific process of step 5 is as follows:

[0036] For the local coating target, the same conformal triangle mesh as the full coating target is used for discretization;

[0037] The impedance boundary condition satisfied by the current coefficient and the normalized magnetic flux coefficient on the locally coated target surface is:

[0038]

[0039] Where, for the uncoated metal part, η s =0; for the local coating material part, the relative surface impedance η s satisfy:

[0040]

[0041] Among them, ε r is the relative dielectric constant of the coating material, μ r is the relative magnetic permeability of the coating material, k0 is the wave number in vacuum, and d is the thickness of the coating material.

[0042] The beneficial effects of the present invention are:

[0043] The method described in the present invention provides a method for rapidly reconstructing the radar electromagnetic characteristics of a target with partially depleted stealth coating, and is used to rapidly reconstruct and calculate the electromagnetic scattering characteristics of a partially coated target. The method constructs a novel matrix equation that reuses the calculated data of the fully coated target when calculating the RCS of the partially coated target. The method also utilizes a PARDISO solver, a fast multipole algorithm, and preconditioning techniques to accelerate the iterative process of the generalized minimum residual method, further accelerating the iterative convergence process. The computational cost of the method described in the present invention is far less than that of methods that refill the matrix and perform the calculations. For scenarios where the target's local coating changes, the method can accurately and efficiently assess the impact of the local coating change on the target's radar characteristics. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 Schematic diagram of the model of a fully coated missile and a partially coated missile in the method described in the embodiment;

[0045] Figure 2 This is a comparison chart of the results of the local coating missile in the method described in the embodiment and commercial electromagnetic simulation software. DETAILED DESCRIPTION

[0046] The present invention will be further described below with reference to the accompanying drawings and examples.

[0047] This embodiment provides a method for rapidly reconstructing the radar electromagnetic characteristics of a target with partially detached stealth coating. It provides an efficient and accurate electromagnetic reconstruction technology for scenarios where the target's local coating changes. It can be used to accurately and quickly evaluate the impact of local coating changes on the target's radar characteristics, promoting the maintenance of stealth equipment from "periodic maintenance" to "performance threshold-triggered precise maintenance," thereby reducing operation and maintenance costs.

[0048] The schematic diagram of the coated missile and partially coated missile model in the method described in this embodiment is as follows Figure 1 As shown, the length of the target coated missile is about 2m, the frequency of the incident plane wave is 1GHz, and the incident direction is (pitch angle θ=0°, azimuth angle ), the electric field polarization direction is along the x direction.

[0049] The following steps are involved:

[0050] Step 1: The average mesh size of the triangular grid is set to 0.1λ, and the surface of the fully coated missile is discretized using a conformal triangular grid; basis functions are defined on the triangular grid, and the number of basis functions is 40971; the surface current of the fully coated missile is used as the equivalent current of the surface to be solved, and is expressed by multiplying the current coefficient to be solved with the basis function; the CFIE mixed field integral equation to be solved is established and discretized using the Galerkin method to generate a linear equation system A and B are impedance matrices, b is the excitation term, and J is the current coefficient to be solved. is the normalized magnetic current coefficient to be solved;

[0051] The specific process of step 1 is:

[0052] Define the CFIE equation as: Where α is the combination coefficient, ranging from 0 to 1, and β = 1-α; EFIE represents the electric field integral equation, MFIE represents the magnetic field integral equation, η0 represents the wave impedance in vacuum, represents the surface normal vector of a fully coated missile;

[0053] Define the mixed field integral operator C α，β (J; Γ) is expressed as:

[0054]

[0055] Where Γ represents the surface of the fully coated target, and × represents the vector cross product; j is the symbol of the imaginary part, k represents the wave number, X represents the unknown quantity, Indicates the gradient of the field point. Indicates the divergence of the source point, G is the scalar Green's function, and dr' represents the differential of the source point position.

[0056] The above mixed field integral operator C α，β Substituting (J; Γ) into the electric field integral equation and magnetic field integral equation of the surface of the fully coated missile, the CFIE equation of the surface of the fully coated missile is obtained:

[0057]

[0058] Among them, E inc represents the electric field of the incident plane wave, H inc represents the incident plane wave magnetic field.

[0059] The above CFIE equation is rewritten into a matrix equation form, which is expressed as:

[0060]

[0061] Among them, the corresponding elements of the coefficient matrix are:

[0062]

[0063] Among them, A mn represents the mth row and nth column element of the impedance matrix A, λ represents the test function, J n is the current coefficient corresponding to the nth basis function, C α，β (J n Γ n) represents the mixed field integral operator corresponding to the nth basis function, Γ n and Γ m Represent the nth triangle mesh and the mth triangle mesh respectively, <> represents the inner product; B mn represents the element in the mth row and nth column of the impedance matrix B, is the normalized magnetic flux coefficient corresponding to the nth basis function.

[0064] Step 2: Generate a linear system of equations using the impedance boundary condition of the fully coated missile η s is the relative surface impedance of the fully coated missile;

[0065] The specific process of step 2 is:

[0066] The impedance boundary condition of a fully coated missile is expressed as:

[0067] Rewrite the above formula into matrix equation form, expressed as:

[0068]

[0069] Among them, the element in the mth row and nth column of the coefficient matrix P1 is The element in the mth row and nth column of the coefficient matrix P2 [0] represents an all-zero vector.

[0070] Step 3: Solve the linear equations corresponding to the CFIE hybrid field integral equation and the impedance boundary condition by using the PARDISO solution method, the multi-layer fast multipole MLFMA method and the BD / SAI preconditioning method to reduce the number of iterations and accelerate the iterative convergence process. Then, J and The solution.

[0071] The specific process of step 3 is:

[0072] For the impedance matrices A and B in the CFIE equation in step 1, the MLFMA method is used to divide the impedance matrix elements into self-group, near-zone group, and far-zone group; for the far-zone group, the MLFMA method is used to calculate the aggregation terms, transfer terms, and configuration terms corresponding to the impedance matrix elements;

[0073] For the self-group and the near-zone group, the impedance matrix element values ​​are directly calculated; the impedance matrix element values ​​of the self-group and the near-zone group are pre-conditioned using BD preconditioning or SAI preconditioning to obtain the pre-conditioned matrix, and then the pre-conditioned CFIE linear equation system is obtained;

[0074] In the impedance boundary condition matrix equation in step 2, the coefficient matrices P1 and P2 are sparse matrices. In each iteration of the generalized minimum residual method, the current coefficient J of the current iteration is substituted into the impedance boundary condition matrix equation, and the corresponding PARDISO solver is used to quickly solve it. Then the current coefficient J and Substitute the pre-processed CFIE equation into the left side of the equal sign and calculate the vector addition result on the left side of the CFIE equation (in the calculation process, the self group and the near zone group can be directly calculated, and the far zone group is realized by the MLFMA method); through iteration, the difference between the vector addition result on the left side of the CFIE equation and the excitation term b is less than the set threshold, and the J and corresponding to the fully coated missile are obtained. The solution.

[0075] Step 4: The preconditioning matrix corresponding to the self group and the near zone group in the impedance matrices A and B, the aggregation item, transfer item and configuration item of the far zone group, the excitation item b, the J and corresponding to the fully coated missile The solution is stored.

[0076] Step 5: For the partially coated target missile, the same mesh as that for the fully coated missile is used for discretization. The relative surface impedance corresponding to the uncoated metal part is set to 0, and the impedance boundary condition and its corresponding coefficient matrix are updated.

[0077] Furthermore, the specific process of step 5 is as follows:

[0078] For partially coated missiles, the same mesh as that for fully coated missiles is used for discretization, and the area where the coating has fallen off is identified. In the area where the coating has fallen off, the outer surface of the missile is metal, which satisfies Therefore, for the area where the coating falls off, the η of the corresponding area s Set it to 0 and keep other regional elements unchanged, and the impedance boundary condition equation satisfied by the local coated missile surface can be obtained, specifically:

[0079] The impedance boundary condition satisfied by the current coefficient and the normalized magnetic flux coefficient on the surface of the locally coated target missile is:

[0080]

[0081] Where, for the uncoated metal part, η s =0; for the local coating material part, the relative surface impedance η s satisfy:

[0082]

[0083] Among them, j is the symbol of the imaginary part, ε ris the relative dielectric constant of the coating material, μ r is the relative magnetic permeability of the coating material, k0 is the wave number in vacuum, and d is the thickness of the coating material.

[0084] The coefficient matrix corresponding to the impedance boundary condition is updated according to the relative surface impedance of the target missile currently coated locally.

[0085] Step 6: Combine the CFIE hybrid field integral equation and the updated impedance boundary condition; use the preconditioning matrix corresponding to the self group and the near zone group in the impedance matrices A and B stored in step 4, the aggregation term, transfer term and configuration term of the far zone group, the excitation term b, and the coefficient matrix corresponding to the impedance boundary condition updated in step 5, and use the J and corresponding to the surface fully coated missile stored in step 4. The solution of is taken as the initial solution, and the simultaneous equations are solved iteratively to obtain J and The solution.

[0086] Step 7: Based on the J and The radar cross section of the locally coated target missile is calculated using the solution of Figure 2 shown.

[0087] To demonstrate the effectiveness of the present invention, the RCS of the partially coated missile calculated in step 7 (red line) is compared with the calculation results of the commercial electromagnetic simulation software FEKO (black dots). Figure 2 As shown in the figure, it can be seen that the present invention also has higher calculation accuracy for more complex targets.

[0088] The method described in this example was used to calculate the RCS of a partially coated spherical target with 660,096 basis functions and an incident plane wave frequency of 1 GHz, with an iterative convergence threshold set to 0.01. The computation time required was calculated and compared with the time required by existing methods. The comparison results are shown in Table 1. As can be seen from the table, the computation time required by the present invention is significantly reduced compared to traditional algorithms, while maintaining higher accuracy. It can achieve the effect of rapidly reconstructing a partially coated target from a fully coated target. Using the fully coated target solution as the initial solution further improves computational efficiency.

[0089] Table 1 Comparison of calculation time when the number of basis functions is 660096

[0090]

[0091] The above description is only a specific embodiment of the present invention. Any feature disclosed in this specification, unless otherwise stated, can be replaced by other equivalent or alternative features with similar purposes; all disclosed features, or all steps in the methods or processes, except for mutually exclusive features and / or steps, can be combined in any way.

Claims

1. A method for rapid reconstruction of radar electromagnetic characteristics of a target with partially lost stealth coating, characterized in that: The following steps are involved: Step 1: Use conformal triangular mesh to discretize the fully coated target surface, and then define basis functions on each triangular mesh; construct the CFIE mixed field integral equation and discretize it using the Galerkin method to generate a linear equation system As the CFIE hybrid field integral equation to be solved, where A and B are impedance matrices, b is the excitation term, and J is the current coefficient to be solved, is the normalized magnetic current coefficient to be solved; Step 2: Construct the impedance boundary condition of the fully coated target η s is the relative surface impedance of the fully coated target; Step 3: Combine the CFIE hybrid field integral equations and impedance boundary conditions to be solved, and use the PARDISO solution method, the multi-layer fast multipole MLFMA method and the BD / SAI preconditioning method to solve the simultaneous equations. / represents or, and calculate the J and corresponding to the full coating target. The solution; Step 4: For the preconditioning matrices corresponding to the self group and the near zone group in the impedance matrices A and B obtained by the BD / SAI preconditioning method in step 3, the aggregation item, transfer item and configuration item of the far zone group obtained by the MLFMA method, the excitation item b, the J and corresponding to the full coating target calculated in step 3, The solution is stored; Step 5: For the partially coated target, the same conformal triangular mesh as the fully coated target is used for discretization, the relative surface impedance corresponding to the uncoated metal part is set to 0, and the impedance boundary condition is updated; Step 6: Combine the CFIE hybrid field integral equation and the updated impedance boundary condition; use the preconditioning matrix corresponding to the self group and the near zone group in the impedance matrices A and B stored in step 4, the aggregation item, transfer item and configuration item of the far zone group, the excitation item b, and the updated impedance boundary condition in step 5, and use the J and corresponding to the full coating target stored in step 4. The solution of is taken as the initial solution, and the simultaneous equations are solved iteratively to obtain J and The solution; Step 7: Based on the J and The radar cross section of the partially coated target is calculated using the solution.

2. The method for rapid reconstruction of radar electromagnetic characteristics of a target with partial stealth coating peeling off according to claim 1 is characterized in that: The specific process of step 1 is: The mixed field integral equation, CFIE equation, is defined as: Among them, α and β are combination coefficients, β = 1-α; EFIE represents the electric field integral equation, MFIE represents the magnetic field integral equation, η0 represents the wave impedance in vacuum, Represents the surface normal vector of the fully coated target; Define the mixed field integral operator C α，β (J; Γ) is expressed as: Where Γ represents the surface of the fully coated target, and × represents the vector cross product; j is the symbol of the imaginary part, k represents the wave number, X represents the unknown quantity, Indicates the gradient of the field point. Indicates the divergence of the source point, G is the scalar Green's function, and dr' represents the differential value of the source point position; The above mixed field integral operator C α，β Substituting (J; Γ) into the electric field integral equation and magnetic field integral equation of the fully coated target surface, the CFIE equation of the fully coated target surface is obtained: Among them, E inc represents the electric field of the incident plane wave, H inc represents the incident plane wave magnetic field; Rewrite the CFIE equation into a matrix equation form, expressed as: Among them, the corresponding elements of the coefficient matrix are: Among them, A mn represents the mth row and nth column element of the impedance matrix A, λ represents the test function, J n is the current coefficient corresponding to the nth basis function, C α，β (J n Γ n ) represents the mixed field integral operator corresponding to the nth basis function, Γ n and Γ m Represent the nth triangle mesh and the mth triangle mesh respectively, <> represents the inner product; B mn represents the element in the mth row and nth column of the impedance matrix B, is the normalized magnetic flux coefficient corresponding to the nth basis function.

3. The method for rapid reconstruction of radar electromagnetic characteristics of a target with partial stealth coating peeling off according to claim 2 is characterized in that: The specific process of step 2 is: The impedance boundary condition for the fully coated target is expressed as: Rewritten as a matrix equation: Among them, the element in the mth row and nth column of the coefficient matrix P1 is The element in the mth row and nth column of the coefficient matrix P2 [0] represents an all-zero vector.

4. The method for rapid reconstruction of radar electromagnetic characteristics of a target with partial stealth coating peeling off according to claim 3 is characterized in that: The specific process of step 3 is: For the impedance matrices A and B in the CFIE equation to be solved in step 1, the MLFMA method is used to divide the impedance matrix elements into self-group, near-zone group and far-zone group; for the far-zone group, the MLFMA method is used to calculate the aggregation terms, transfer terms and configuration terms corresponding to the impedance matrix elements; For the self-group and near-zone group, the impedance matrix element values ​​are directly calculated; Using BD preconditioning or SAI preconditioning to precondition the impedance matrix element values ​​of the self group and the near zone group, a preconditioning matrix is ​​obtained, and then a preconditioned CFIE linear equation system is obtained; In the impedance boundary condition matrix equation in step 2, the coefficient matrices P1 and P2 are sparse matrices. In each iteration of the generalized minimum residual method, the current coefficient J of the current iteration is substituted into the impedance boundary condition matrix equation, and the corresponding PARDISO solver is used to quickly solve it. Then the current coefficient J and Substitute the left side of the equal sign of the pre-processed CFIE equation and calculate the vector addition result on the left side of the equal sign of the CFIE equation to be solved; through iteration, make the difference between the vector addition result on the left side of the equal sign of the CFIE equation to be solved and the excitation term b less than the set threshold, and obtain J and corresponding to the full coating target The solution.

5. The method for rapid reconstruction of radar electromagnetic characteristics of a target with partial stealth coating peeling off according to claim 4 is characterized in that: The specific process of step 5 is: For the local coating target, the same conformal triangle mesh as the full coating target is used for discretization; The impedance boundary condition satisfied by the current coefficient and the normalized magnetic flux coefficient on the locally coated target surface is: Where, for the uncoated metal part, η s =0; for the local coating material part, the relative surface impedance η s satisfy: Among them, ε r is the relative dielectric constant of the coating material, μ r is the relative magnetic permeability of the coating material, k0 is the wave number in vacuum, and d is the thickness of the coating material.

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