A method for rapid reconstruction of radar electromagnetic characteristics of a local stealth coating peeling target

Abstract

The application discloses a radar electromagnetic characteristic fast reconstruction method for a local stealth coating falling target and belongs to the technical field of electromagnetic simulation. The application constructs a novel matrix equation, so that the calculation data of a full-coated target can be repeatedly used when the RCS of a local-coated target is calculated, and a PARDISO solver, a fast multipole algorithm and a preconditioning technology are used to accelerate the iteration process of the generalized minimum residual method, so that the iteration convergence process is further accelerated. The calculation cost of the method is far less than that of a method of refilling a matrix and performing calculation, and the influence of local coating change on the radar characteristics of the target can be accurately and efficiently evaluated in the scene of local coating change of the target.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic simulation technology, specifically relating to a method for rapid reconstruction of radar electromagnetic characteristics of targets with partially detached stealth coatings. Background Technology

[0002] The stealth capability of stealth weapon systems is mainly achieved through two aspects: shape design and stealth materials. Shape design is constrained by many factors, making the research and application of stealth materials crucial to stealth technology. However, in complex flight environments, the coating of stealth aircraft is prone to peeling and cracking, thus affecting the overall stealth performance of the aircraft. Therefore, the maintenance and upkeep of stealth aircraft is critical.

[0003] Currently, the main methods for detecting the quality of stealth aircraft coatings include conducting RCS (Radar Cross Section) 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, and when computation is large, they are time-consuming and costly. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for rapid reconstruction of radar electromagnetic characteristics of targets with partially detached stealth coatings. This method is used to perform rapid reconstruction calculations on partially coated targets, significantly reducing the time spent on recalculation.

[0005] The technical problem addressed by this invention is solved as follows:

[0006] A method for rapid reconstruction of radar electromagnetic properties of targets with partially detached stealth coatings includes the following steps:

[0007] Step 1: Discretize the fully coated target surface using a conformal triangular mesh, and define basis functions on each triangular mesh; construct the CFIE mixture field integral equation and discretize it using the Galerkin method to generate a system of linear equations. The CFIE mixed-field integral equation to be solved is given by A and B, where A and B are impedance matrices, b is the excitation term, and J is the current coefficient to be solved. The normalized magnetic flux coefficient is to be solved;

[0008] Step 2: Construct the impedance boundary conditions for the fully coated target. η s The relative surface impedance of the fully coated target;

[0009] Step 3: Simultaneously solve the CFIE mixed-field integral equations and impedance boundary conditions. Solve the simultaneous equations using the PARDISO method, the multilayer fast multipole MLFMA method, and the BD / SAI preconditioning method. / represents or , and calculate the J and corresponding to the fully coated target. The solution;

[0010] Step 4: For the precondition matrices corresponding to the self-group and near-field group in the impedance matrices A and B obtained in Step 3 using the BD / SAI preconditioning method, the aggregation term, transfer term, and configuration term of the far-field group obtained using the MLFMA method, the excitation term b, and the J and corresponding values ​​of the fully coated target calculated in Step 3. The solution is stored.

[0011] Step 5: For locally coated targets, discretize them using the same conformal triangular mesh as the fully coated targets, set the relative surface impedance of the uncoated metal parts to 0, and update the impedance boundary conditions.

[0012] Step 6: Simultaneously establish the CFIE mixed-field integral equations and the updated impedance boundary conditions; using the precondition matrices corresponding to the self-group and near-field group in the impedance matrices A and B stored in Step 4, the aggregation term, transition term, and configuration term of the far-field group, the excitation term b, and the updated impedance boundary conditions in Step 5, with the J and corresponding to the fully coated target stored in Step 4... Using the solution as the initial solution, the system of simultaneous equations is iteratively solved to obtain J and the corresponding local coating target. The solution;

[0013] Step 7: Based on the J and corresponding targets of the locally coated missiles The solution is used to calculate the radar cross section of the locally coated target.

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

[0015] Define the mixed-field integral equation, i.e., the CFIE equation, as follows: Where α and β are combination coefficients, β = 1 - α; EFIE represents the electric field integral equation, MFIE represents the magnetic field integral equation, and η0 represents the wave impedance in vacuum. This represents the surface normal vector of the fully coated target;

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

[0017]

[0018] Where Γ represents the surface of the fully coated target, and × represents the vector cross product; j represents the imaginary part, k represents the wave number, and X represents the unknown quantity. This indicates that the gradient is calculated with respect to the field point. This represents the divergence over the source point, where G is the scalar Green's function and dr′ represents the differential component of the source point location.

[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, we obtain the CFIE equation for the fully coated target surface as follows:

[0020]

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

[0022] The CFIE equations can be rewritten in matrix form as follows:

[0023]

[0024] The corresponding elements of the coefficient matrix are:

[0025]

[0026] Among them, A mn Let J represent the element in the m-th row and n-th column of the impedance matrix A, and let λ represent the trial function. n C is the current coefficient corresponding to the nth basis function. α，β (J n ;Γ n ) represents the mixed-field integral operator corresponding to the nth basis function, Γ n and Γ m Let B represent the nth and mth triangular meshes respectively, and let <> denote the inner product; mn This represents the element in the m-th row and n-th 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 as follows:

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

[0029]

[0030] Among them, the element in the m-th row and n-th column of the coefficient matrix P1 The element in the m-th row and n-th column of the coefficient matrix P2 [0] represents a vector of all zeros.

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

[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 elements of the impedance matrix into the self group, the near-field group, and the far-field group; for the far-field group, the MLFMA method is used to calculate the aggregation term, transition term, and collocation term corresponding to the elements of the impedance matrix.

[0033] For the self-group and the near-field group, the impedance matrix element values ​​are obtained by directly calculating them; the impedance matrix element values ​​of the self-group and the near-field group are preprocessed using BD preconditions or SAI preconditions to obtain the precondition matrix, and then the preprocessed CFIE linear equation system is obtained.

[0034] In step 2, the coefficient matrices P1 and P2 in the impedance boundary condition matrix equation are sparse matrices. During 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 solution is quickly obtained using the PARDISO solver. Then the current coefficient J and the current coefficient of this iteration are... Substituting the preprocessed CFIE equation into the left-hand side, we calculate the vector sum of the left-hand side of the CFIE equation to be solved; through iteration, we ensure that the difference between the vector sum of the left-hand side of the CFIE equation to be solved and the excitation term b is less than a set threshold, thus obtaining J and the corresponding full-coating target. The solution.

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

[0036] For locally coated targets, the same conformal triangular mesh as that used for fully coated targets is used for discretization.

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

[0038]

[0039] For the uncoated metal parts, η s =0; For locally coated portions, the relative surface resistance η s satisfy:

[0040]

[0041] Where, ε r μ is the relative permittivity of the coating material. r denoted as the relative permeability of the coating material, k0 as the wave number in vacuum, and d as the thickness of the coating material.

[0042] The beneficial effects of this invention are:

[0043] This invention provides a rapid reconstruction method for the radar electromagnetic characteristics of targets with partially detached stealth coatings, enabling fast reconstruction and calculation of the electromagnetic scattering characteristics of locally coated targets. The invention constructs a novel matrix equation, allowing reuse of computational data from fully coated targets when calculating the RCS of locally coated targets. Furthermore, it employs the PARDISO solver, the fast multipole algorithm, and preconditioning techniques to accelerate the iterative process of the generalized minimum residual method, further speeding up the iterative convergence process. The computational cost of this method is significantly lower than that of refilling the matrix and performing calculations. For scenarios involving changes in the local coating of a target, it can accurately and efficiently assess the impact of local coating variations on the target's radar characteristics. Attached Figure Description

[0044] Figure 1 This is a schematic diagram of a missile with full coating and a missile with partial coating in the method described in the embodiment;

[0045] Figure 2 This is a comparison chart of the results of localized missile coating using the method described in the embodiment and those obtained using commercial electromagnetic simulation software. Detailed Implementation

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

[0047] This embodiment provides a method for rapid reconstruction of radar electromagnetic characteristics of targets with localized stealth coating peeling off. 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 assess the impact of local coating changes on the target's radar characteristics, and promote the shift of stealth equipment maintenance from "periodic maintenance" to "performance threshold-triggered precision maintenance", thereby reducing operation and maintenance costs.

[0048] The schematic diagrams of the coated missile and the partially coated missile models in the method described in this embodiment are as follows: Figure 1 As shown, the target-coated missile is approximately 2 meters long, with an incident plane wave frequency of 1 GHz and an incident direction of (elevation angle θ = 0°, azimuth angle θ = 0°). The electric field polarization direction is along the x-direction.

[0049] Includes the following steps:

[0050] Step 1: Set the average mesh size of the triangular mesh to 0.1λ, and discretize the surface of the fully coated missile using a conformal triangular mesh; define basis functions on the triangular mesh, with a total of 40971 basis functions; the surface current of the fully coated missile is used as the equivalent current of the surface to be solved, and is represented by multiplying the current coefficient to be solved with the basis functions; establish the CFIE mixed field integral equation to be solved and discretize it using the Galerkin method to generate a system of linear equations. A and B are impedance matrices, b is the excitation term, and J is the current coefficient to be solved. The normalized magnetic flux coefficient is to be solved;

[0051] The specific process of step 1 is as follows:

[0052] Define the CFIE equation as follows: 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, and η0 represents the wave impedance in vacuum. This represents the surface normal vector of a missile with a fully coated surface.

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

[0054]

[0055] Where Γ represents the surface of the fully coated target, and × represents the vector cross product; j represents the imaginary part, k represents the wave number, and X represents the unknown quantity. This indicates that the gradient is calculated with respect to the field point. This represents the divergence over the source point, where G is the scalar Green's function and dr′ represents the differential component of the source point location.

[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 fully coated missile surface, we obtain the CFIE equation for the fully coated missile surface as follows:

[0057]

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

[0059] The above CFIE equation can be rewritten in matrix form as follows:

[0060]

[0061] The corresponding elements of the coefficient matrix are:

[0062]

[0063] Among them, A mn Let J represent the element in the m-th row and n-th column of the impedance matrix A, and let λ represent the trial function. n C is the current coefficient corresponding to the nth basis function. α，β (J n ;Γ n) represents the mixed-field integral operator corresponding to the nth basis function, Γ n and Γ m Let B represent the nth and mth triangular meshes respectively, and let <> denote the inner product; mn This represents the element in the m-th row and n-th column of the impedance matrix B. is the normalized magnetic flux coefficient corresponding to the nth basis function.

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

[0065] The specific process of step 2 is as follows:

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

[0067] Rewriting the above equation in matrix form, we get:

[0068]

[0069] Among them, the element in the m-th row and n-th column of the coefficient matrix P1 The element in the m-th row and n-th column of the coefficient matrix P2 [0] represents a vector of all zeros.

[0070] Step 3: Solve the system of linear equations corresponding to the CFIE mixed-field integral equations and impedance boundary conditions simultaneously. Utilize the PARDISO solution method, the multilevel fast multipole MLFMA method, and the BD / SAI preconditioning method to solve the system of equations, reducing the number of iterations and accelerating the iterative convergence process. Calculate J and... The solution.

[0071] The specific process of step 3 is as follows:

[0072] For the impedance matrices A and B in the CFIE equation of step 1, the MLFMA method is used to divide the elements of the impedance matrix into the self group, the near-field group, and the far-field group; for the far-field group, the MLFMA method is used to calculate the aggregation term, transition term, and collocation term corresponding to the elements of the impedance matrix.

[0073] For the self-group and the near-field group, the impedance matrix element values ​​are obtained by directly calculating them; the impedance matrix element values ​​of the self-group and the near-field group are preprocessed using BD preconditions or SAI preconditions to obtain the precondition matrix, and then the preprocessed CFIE linear equation system is obtained.

[0074] In step 2, the coefficient matrices P1 and P2 in the impedance boundary condition matrix equation are sparse matrices. During 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 solution is quickly obtained using the PARDISO solver. Then the current coefficient J and the current coefficient of this iteration are... Substituting the preprocessed CFIE equation into the left-hand side, calculate the vector summation result on the left-hand side of the CFIE equation (during the calculation, the self-group and near-field group can be directly calculated, while the far-field group is implemented using the MLFMA method); through iteration, ensure that the difference between the vector summation result on the left-hand side of the CFIE equation and the excitation term b is less than a set threshold, thus obtaining J and the corresponding values ​​for the fully coated missile. The solution.

[0075] Step 4: The precondition matrices corresponding to the self-group and near-field group in impedance matrices A and B, the aggregation terms, transition terms, and configuration terms of the far-field group, the excitation term b, and J and the corresponding terms for the fully coated missile. The solution is stored.

[0076] Step 5: For a target missile with partial coating, discretize it using the same mesh as the missile with full surface coating, set the relative surface impedance corresponding to the uncoated metal part to 0, and update the impedance boundary conditions and their corresponding coefficient matrices.

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

[0078] For missiles with partial coating, the same mesh as for fully coated missiles is used for discretization, and areas where the coating has peeled off are identified. In these areas, the missile's outer surface is metallic, satisfying the following conditions: The boundary conditions. Therefore, for the area where the coating has peeled off, the corresponding η of the area... s Setting the value to 0 and leaving other elements unchanged, we can obtain the impedance boundary condition equation satisfied by the locally coated missile surface, specifically:

[0079] The impedance boundary condition satisfied by the current coefficient and normalized magnetic flux coefficient on the surface of the target missile where local coating is applied is as follows:

[0080]

[0081] For the uncoated metal parts, η s =0; For locally coated portions, the relative surface resistance η s satisfy:

[0082]

[0083] Where j is the imaginary part symbol, ε rμ is the relative permittivity of the coating material. r denoted as the relative permeability of the coating material, k0 as the wave number in vacuum, and d as the thickness of the coating material.

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

[0085] Step 6: Simultaneously establish the CFIE mixed-field integral equations and the updated impedance boundary conditions; using the precondition matrices corresponding to the self-group and near-field group in the impedance matrices A and B stored in Step 4, the aggregation term, transition term, and configuration term of the far-field group, the excitation term b, and the coefficient matrix corresponding to the updated impedance boundary conditions in Step 5, along with the J and J corresponding to the surface-coated missile stored in Step 4... Using the solution as the initial solution, the system of simultaneous equations is iteratively solved to obtain J and the corresponding values ​​of the target missile with local coating. The solution.

[0086] Step 7: Based on the J and corresponding targets of the locally coated missiles The solution is used to calculate the radar cross section of the locally coated target missile, such as... Figure 2 As shown.

[0087] To demonstrate the effectiveness of this invention, the RCS (red line) of the locally coated missile calculated in step 7 is compared with the calculation results of the commercial electromagnetic simulation software FEKO (black dot). Figure 2 As shown in the figure, the present invention also has high calculation accuracy for more complex targets.

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

[0089] Table 1. Comparison of computation time for a base function set of 660,096.

[0090]

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

Claims

1. A method for rapid reconstruction of radar electromagnetic characteristics of targets with partially detached stealth coatings, characterized in that, Includes the following steps: Step 1: Discretize the fully coated target surface using a conformal triangular mesh, and define basis functions on each triangular mesh; construct the CFIE mixture field integral equation and discretize it using the Galerkin method to generate a system of linear equations. The CFIE mixed-field integral equation to be solved is given by A and B, where A and B are impedance matrices, b is the excitation term, and J is the current coefficient to be solved. The normalized magnetic flux coefficient is to be solved; Step 2: Construct the impedance boundary conditions for the fully coated target. η s The relative surface impedance of the fully coated target; Step 3: Simultaneously solve the CFIE mixed-field integral equations and impedance boundary conditions. Solve the simultaneous equations using the PARDISO method, the multilayer fast multipole MLFMA method, and the BD / SAI preconditioning method. / represents or , and calculate the J and corresponding to the fully coated target. The solution; Step 4: For the precondition matrices corresponding to the self-group and near-field group in the impedance matrices A and B obtained in Step 3 using the BD / SAI preconditioning method, the aggregation term, transfer term, and configuration term of the far-field group obtained using the MLFMA method, the excitation term b, and the J and corresponding values ​​of the fully coated target calculated in Step 3. The solution is stored. Step 5: For locally coated targets, discretize them using the same conformal triangular mesh as the fully coated targets, set the relative surface impedance of the uncoated metal parts to 0, and update the impedance boundary conditions. Step 6: Simultaneously establish the CFIE mixed-field integral equations and the updated impedance boundary conditions; using the precondition matrices corresponding to the self-group and near-field group in the impedance matrices A and B stored in Step 4, the aggregation term, transition term, and configuration term of the far-field group, the excitation term b, and the updated impedance boundary conditions in Step 5, with the J and corresponding to the fully coated target stored in Step 4... Using the solution as the initial solution, the system of simultaneous equations is iteratively solved to obtain J and the corresponding local coating target. The solution; Step 7: Based on the J and corresponding targets of the locally coated missiles The solution is used to calculate the radar cross section of the locally coated target.

2. The method for rapid reconstruction of radar electromagnetic characteristics of targets with partially detached stealth coatings according to claim 1, characterized in that, The specific process of step 1 is as follows: Define the mixed-field integral equation, i.e., the CFIE equation, as follows: Where α and β are combination coefficients, β = 1 - α; EFIE represents the electric field integral equation, MFIE represents the magnetic field integral equation, and η0 represents the wave impedance in vacuum. This represents the surface normal vector of the fully coated target; Define the hybrid field integral operator C α，β (J;Γ) is represented as: Where Γ represents the surface of the fully coated target, and × represents the vector cross product; j represents the imaginary part, k represents the wave number, and X represents the unknown quantity. This indicates that the gradient is calculated with respect to the field point. This represents the divergence over the source point, where G is the scalar Green's function and dr′ represents the differential component of the source point location. 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, we obtain the CFIE equation for the fully coated target surface as follows: Among them, E inc H represents the electric field of the incident plane wave. inc Indicates the magnetic field of the incident plane wave; The CFIE equations can be rewritten in matrix form as follows: The corresponding elements of the coefficient matrix are: Among them, A mn Let J represent the element in the m-th row and n-th column of the impedance matrix A, and let λ represent the trial function. n C is the current coefficient corresponding to the nth basis function. α，β (J n ;Γ n ) represents the mixed-field integral operator corresponding to the nth basis function, Γ n and Γ m Let B represent the nth and mth triangular meshes respectively, and let <> denote the inner product; mn This represents the element in the m-th row and n-th 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 targets with partially detached stealth coatings according to claim 2, characterized in that, The specific process of step 2 is as follows: The impedance boundary condition for a fully coated target is expressed as: Rewritten in matrix equation form as follows: Among them, the element in the m-th row and n-th column of the coefficient matrix P1 The element in the m-th row and n-th column of the coefficient matrix P2 [0] represents a vector of all zeros.

4. The method for rapid reconstruction of radar electromagnetic characteristics of targets with partially detached stealth coatings according to claim 3, characterized in that, The specific process of step 3 is as follows: 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 elements of the impedance matrix into the self group, the near-field group, and the far-field group; for the far-field group, the MLFMA method is used to calculate the aggregation term, transition term, and collocation term corresponding to the elements of the impedance matrix. For the self-group and the near-field group, the impedance matrix element values ​​are obtained by directly calculating the impedance matrix. The impedance matrix element values ​​of the self group and the near-field group are preprocessed using BD preconditions or SAI preconditions to obtain the precondition matrix, and then the preprocessed CFIE linear equation system is obtained. In step 2, the coefficient matrices P1 and P2 in the impedance boundary condition matrix equation are sparse matrices. During 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 solution is quickly obtained using the PARDISO solver. Then the current coefficient J and the current coefficient of this iteration are... Substituting the preprocessed CFIE equation into the left-hand side, we calculate the vector sum of the left-hand side of the CFIE equation to be solved; through iteration, we ensure that the difference between the vector sum of the left-hand side of the CFIE equation to be solved and the excitation term b is less than a set threshold, thus obtaining J and the corresponding full-coating target. The solution.

5. The method for rapid reconstruction of radar electromagnetic characteristics of targets with partially detached stealth coatings according to claim 4, characterized in that, The specific process of step 5 is as follows: For locally coated targets, the same conformal triangular mesh as that used for fully coated targets is used for discretization. The impedance boundary condition satisfied by the current coefficient and normalized magnetic current coefficient on the locally coated target surface is: For the uncoated metal parts, η s =0; For locally coated portions, the relative surface resistance η s satisfy: Where, ε r μ is the relative permittivity of the coating material. r denoted as the relative permeability of the coating material, k0 as the wave number in vacuum, and d as the thickness of the coating material.

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