A method for quickly solving the local variation of broadband electromagnetic scattering characteristics of targets

Abstract

The present invention discloses a method for quickly solving the local change broadband electromagnetic scattering characteristics of a target. First, the frequency range, frequency interval and corresponding sampling calculation frequency of the analysis are determined; secondly, the type of the local change problem is determined and different forms of block impedance matrix equations are determined; then, the block impedance matrix under each sampling frequency is filled according to the impedance interpolation method and the local change problem is quickly solved using the local change method, and the inverse of the matrix impedance matrix only needs to be calculated once. Under different sampling calculation frequencies, the impedance matrix is ​​obtained by interpolation without recalculation; under the same sampling calculation frequency, the inverse of the matrix impedance matrix only needs to be calculated once without repeated calculation, and can be reused under different local change situations of the target. Compared with traditional methods, the present invention has a significant improvement in calculation efficiency for analyzing broadband electromagnetic scattering characteristics of local changes in the target.

Description

Technical Field

[0001] The invention relates to an efficient method for quickly solving the broadband electromagnetic scattering characteristics of a target with local changes, which is suitable for analyzing the broadband scattering problem after the target has local changes. Background Art

[0002] Local changes in the target are a common problem in the field of electromagnetic scattering. Usually, when solving such problems with traditional methods, the impedance matrix is ​​regenerated after the target changes. However, the repeatedly generated impedance matrix contains a lot of repeatedly calculated element information, which will reduce the efficiency of each solution. How to avoid repeatedly calculating the same impedance information is the key to improving the solution of such problems.

[0003] At the same time, in the field of electromagnetic scattering, people are no longer only concerned with the scattering characteristics of the target at a certain frequency point, but are often more concerned with the scattering characteristics of the target within a certain broadband. However, to analyze the broadband scattering characteristics of the target, it is necessary to repeatedly generate the impedance matrix at each sampling frequency point. Although the information of these impedance matrix elements is not repeated, direct calculation each time will also lead to reduced computational efficiency. How to improve the filling speed of the impedance matrix is ​​the key to improving the efficiency of solving such problems. Summary of the invention

[0004] Purpose of the invention: In order to solve the problem of broadband electromagnetic scattering after local changes of the target, the present invention proposes a fast solution method based on impedance interpolation, block inverse matrix formula and Sherman-Morrison-Woodbury (SMW) formula, which can significantly reduce the solution time of the broadband electromagnetic scattering problem after local changes of the target calculated by the moment method.

[0005] In order to achieve the above object, the technical solution of the present invention is achieved as follows:

[0006] A method for quickly solving the local variation broadband electromagnetic scattering characteristics of a target, characterized by comprising the following steps:

[0007] Step 1: Establish a surface integral equation for the local change problem of the target, then use a triangular mesh to discretize the surface of the original target model, and define the RWG basis function on two adjacent triangular meshes with common edges; according to the principle of the moment method and using the RWG basis function, discretize the surface integral equation to obtain the original matrix equation and the original impedance matrix corresponding to the original parent structure;

[0008] Step 2: According to the type of local change problem, the structure is divided into blocks based on the original matrix structure, and the original impedance matrix corresponding to the original matrix structure is written in the form of a block impedance matrix; when a subtractive local change occurs, the original matrix structure is divided into a remaining structure and a subtracted structure; when a plus local change occurs, the original matrix structure remains unchanged, and the target structure after the local change is divided into the original matrix structure and the plus structure;

[0009] Step 3: For the wide frequency band to be analyzed, four interpolation frequencies are selected, and the original impedance matrices at the four interpolation frequencies are calculated respectively. Four interpolation modified impedance matrices used for interpolation are obtained according to the original impedance matrices at the four interpolation frequencies;

[0010] Step 4: Use equally spaced sampling to determine each sampling frequency that needs to be calculated;

[0011] Step 5: For each sampling frequency, four interpolation coefficients at the corresponding sampling frequency are calculated according to the four interpolation frequencies, and the impedance matrix at the corresponding sampling frequency is obtained by interpolation through the four interpolation corrected impedance matrices and the four interpolation coefficients;

[0012] Step 6: Restore the interpolated impedance matrix to the original impedance matrix and solve the surface current;

[0013] Step 7: Calculate the far-field radar cross-section based on the solved surface current.

[0014] Preferably, the four interpolation frequencies are selected as follows:

[0015] f k =t k f h +(1-t k )f l , f k ∈(f l , f h ),

[0016] Where k = 0, 1, 2, 3, f l and f h are the lowest and highest frequencies of the wide band analyzed,

[0017] Preferably, the corresponding sampling frequency f is calculated by the following formula: c The four interpolation coefficients are: f k and f n are interpolation frequencies.

[0018] Preferably, four interpolation correction impedance matrices for interpolation are calculated based on the original impedance matrices at the four interpolation frequencies, and the interpolation correction impedance matrix elements are The calculation formula is as follows:

[0019] where z mn (f k ) is the sampling frequency f k The original impedance matrix element at mn is the distance between the mth basis function and the nth basis function.

[0020] The present invention has the following beneficial effects:

[0021] Compared with the existing solution methods, the method of the present invention for quickly solving the local change broadband electromagnetic scattering characteristics of the target is more efficient. The efficiency of the method of the present invention comes from two aspects. First, the impedance interpolation method improves the filling speed of the impedance matrix at each sampling frequency point. Compared with the original direct calculation of the impedance elements, which includes a large number of vector product operations and a large number of discrete integral operations, the impedance interpolation only involves multiplication and addition operations, and the operation efficiency is greatly improved; then the local change algorithm based on the block inverse matrix formula and the SMW formula avoids the repeated calculation of impedance elements when solving the local change problem. It only needs to calculate the parent impedance matrix once and invert it. The surface current of the changed target can be quickly obtained by the inverse of the parent impedance matrix, and the inversion operation of the large-dimensional matrix is ​​avoided in the process, which further improves the efficiency of the solution. Therefore, the method of the present invention for quickly solving the local change broadband electromagnetic scattering characteristics of the target has a significant improvement in calculation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 It is a schematic diagram of broadband reduction local variation of the present invention;

[0023] Figure 2 It is a schematic diagram of broadband plus local variation of the present invention;

[0024] Figure 3 This is a model diagram of a calculation example 1 of the broadband reduction local variation of the present invention;

[0025] Figure 4 This is a broadband single-station RCS result diagram before the target change of Example 1 of the present invention;

[0026] Figure 5 This is a broadband single-station RCS result diagram after the target change of Example 1 of the present invention;

[0027] Figure 6 This is the second calculation model of broadband plus local variation of the present invention Figure 1 ;

[0028] Figure 7 This is the second calculation model of broadband plus local variation of the present invention Figure 2 ;

[0029] Figure 8 This is a broadband single-station RCS result diagram when the target center cone of Example 2 of the present invention changes to 60°;

[0030] Fig. 9 This is a broadband single-station RCS result diagram when the target center cone of Example 2 of the present invention changes to 70°;

[0031] Fig.10 This is a broadband single-station RCS result diagram of all target change angles in Example 2 of the present invention; Specific implementation plan

[0032] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments.

[0033] This embodiment provides a method for quickly and efficiently solving the local variation broadband electromagnetic scattering characteristics of a target, comprising the following steps:

[0034] Step 1: Establish a surface integral equation for the local change problem of the target, then use a triangular mesh to discretize the surface of the original target model, and define the RWG basis function on two adjacent triangular meshes with common edges. According to the principle of the moment method and using the RWG basis function, the surface integral equation of the problem is discretized to obtain the original matrix equation and the original impedance matrix Z corresponding to the original parent structure. mm .

[0035] Assume that the moment method matrix equation corresponding to the original target is:

[0036] Z mm I m =V m

[0037] Among them, the generalized impedance matrix Z mm and the generalized voltage vector V m The elements are:

[0038]

[0039]

[0040] Where j represents the imaginary unit, k represents the wave number of the incident wave, η represents the wave impedance of free space, and T m and T n denote the triangular patches of the mth and nth RWG basis functions, G(r, r′) denotes the Green’s function of free space, and f m (r) and f m (r) represent the mth and nth RWG basis functions, E inc (r) is the incident electric field.

[0041] Step 2: According to the type of local variation problem, the structure is divided into blocks based on the original matrix structure, and the original impedance matrix corresponding to the original matrix structure is written in the form of a block impedance matrix;

[0042] like Figure 1 , when a local change occurs, the original target's matrix structure (original matrix structure) is divided into a residual structure and a subtracted structure, and the original impedance matrix Z corresponding to the original matrix structure is mm Becomes as follows Among them, Z rr and Z ss are the self-impedance matrices of the remaining structure and the subtracted structure, respectively, z rs and Z sr is the mutual impedance matrix between the remaining structure and the subtracted structure;

[0043] like Figure 2 When a local change occurs, the original matrix structure remains unchanged. The target structure after the local change is divided into the original matrix structure and the added structure. The original impedance matrix corresponding to the original matrix structure becomes as follows: Among them, Z mm and Z aa are the self-impedance matrices of the original matrix and the added structure, Z ma and Z am is the mutual impedance matrix between the original parent structure and the added structure.

[0044] Step 3: Analyze the wide frequency band (f l , f h ), f l and f h They are the lowest frequency and the highest frequency respectively, and four appropriate interpolation frequencies f are selected k ∈(f l , f h ), (k=0,1,2,3)

[0045] f k =t k f h +(1-t k )f l

[0046] in,

[0047]

[0048] The original impedance matrices at the four interpolation frequencies are calculated respectively, and four interpolation modified impedance matrices used for interpolation are obtained according to the original impedance matrices at the four interpolation frequencies. The modified impedance matrix elements are The calculation formula is as follows:

[0049] Where Zmn (f k ) is the frequency f k The original impedance matrix element at mn is the distance between the mth basis function and the nth basis function.

[0050] Step 4: Use equal-interval sampling to determine each sampling frequency that needs to be calculated. Assume that the sampling interval is f s , then the number of sampling frequencies that need to be calculated and analyzed is t=(f h -f l ) / f s +1, corresponding to the sampling frequency f c =f l +(c-1)f s , c=1,2,3…,t.

[0051] Step 5: For each sampling frequency, calculate the corresponding sampling frequency f according to the four interpolation frequencies c The four interpolation coefficients φ under k (f c )

[0052] Among them, f k and f h are sampling interpolation frequencies.

[0053] The corresponding sampling frequency f is obtained by interpolating four interpolation correction impedance matrices and four interpolation coefficients. c The impedance matrix under the condition, instead of the original Galerkin method, interpolates the impedance matrix elements The interpolation calculation formula is as follows:

[0054]

[0055] Step 6: The interpolated impedance matrix needs to be restored to the original impedance matrix to solve the surface current. The original impedance matrix element Z mn (f c ) is calculated as follows:

[0056]

[0057] At a certain sampling frequency, if the target undergoes a local change, then by determining the remaining structure during the change and the basis functions on the subtracted structure, the matrix equation z corresponding to the original target is mm I m =V m Can be written as

[0058]

[0059] Among them, Ir and I s are the current coefficients to be determined on the remaining structure and the subtracted structure, V r and V s are the voltage vectors on the remaining structure and the subtracted structure respectively; the equation to be solved at this time is Z rr I r =V r , but resolving Z rr It takes a lot of time, considering that Z has been solved once when the target has not changed at the beginning mm And find the inverse matrix Therefore, according to the block inverse matrix formula and SMW formula, we can get

[0060]

[0061]

[0062] Among them, I r is the surface current of the remaining structure, It's Z rr The inverse matrix of .

[0063] It is the formula of the original block matrix and its corresponding inverse matrix.

[0064] If the target undergoes a partial change, then by determining the remaining structure during the change and subtracting the basis functions on the structure, the matrix equation Z corresponding to the original target is mm I m =v m Can be written as

[0065]

[0066] The solution to the matrix equation is now

[0067]

[0068] According to the block inverse matrix formula

[0069]

[0070]

[0071] Among them, I m and I a are the current coefficients corresponding to the added structure and the parent structure, V a and V m are the voltage vectors corresponding to the added structure and the parent structure, is the inverse matrix of the parent structure's self-impedance matrix;

[0072] It is the formula of the original block matrix and its corresponding inverse matrix.

[0073]

[0074] Step 7: Calculate the far-field radar cross-section based on the obtained surface current.

[0075]

[0076] in,

[0077] E s (r) represents the scattered field, represents the obtained current vector, and J(r′) represents the target surface current vector.

[0078] The present invention is further described below by means of specific examples:

[0079] Example 1

[0080] This example verifies the accuracy of the method of the present invention. This example is a simple shape model of a PEC ball placed on a PEC plate. Figure 3 As shown. The radius of the sphere is 0.1m, the size of the plate is 1m×1m×0.1m, and the distance from the center of the sphere to the upper surface of the plate is equal to the radius. Calculate the target broadband single-station RCS before and after the PEC sphere is removed from the plate. The plane wave incident angle is (0°, 0°), and the polarization direction is θ. The calculation frequency band is from 300MHz to 600MHz, the frequency interval is 6MHz, and the number of sampling frequencies is 51. The example model is as shown in the attached Figure 3 The calculation results are shown in the attached Figure 4 and attached Figure 5 As shown, it can be seen that the resulting curves fit well.

[0081] Table 1 shows the comparison of the calculation time of the first example between the present invention and the traditional method. It can be seen that the calculation efficiency is improved.

[0082] Table 1 Calculation results of Example 1

[0083]

[0084] Example 2

[0085] This example verifies the high efficiency of the method of the present invention. This example is a simple cavity model containing a central cone. Figure 6 , Attachment Figure 7As shown, the cavity depth is 600mm, the bottom diameter is 500mm, the opening diameter is 400mm, the bottom diameter of the central cone is 150mm, and the distance from the bottom of the cavity is 5mm. The central cone angle α varies from 50° to 90°, and the angle interval is 10°. Calculate the broadband single-station RCS of these cavities containing central cones of different angles. The plane wave incident angle is (0°, 0°), and the polarization direction is θ. The calculation frequency band is from 1GHz to 2GHz, the sampling frequency interval is 20MHz, and the number of sampling frequencies is 51. From the attached Figure 8 , Attachment Fig. 9 and attached Fig.10 As can be seen from the results shown, the curves show good agreement.

[0086] Table 2 shows the comparison of the calculation time of the present invention and the traditional method for the second example. It can be seen that when the number of changes increases, the calculation efficiency of the present invention is greatly improved.

[0087] Table 2 Calculation results of Example 2

[0088]

Claims

1. A method for quickly solving the local variation broadband electromagnetic scattering characteristics of a target, characterized in that: The steps include: Step 1: Establish a surface integral equation for the local change problem of the target, then use a triangular mesh to discretize the surface of the original target model, and define the RWG basis function on two adjacent triangular meshes with common edges; According to the principle of moment method and using RWG basis function, the surface integral equation is discretized to obtain the original matrix equation and the original impedance matrix corresponding to the original matrix structure; Step 2: According to the type of local change problem, the structure is divided into blocks based on the original matrix structure, and the original impedance matrix corresponding to the original matrix structure is written into the form of a block impedance matrix; when a subtractive local change occurs, the original matrix structure is divided into a remaining structure and a subtracted structure; when an additive local change occurs, the original matrix structure remains unchanged, and the target structure after the local change is divided into the original matrix structure and the added structure; if any local change occurs, the additive and subtractive local change algorithms are combined to handle it; Step 3: For the wide frequency band to be analyzed, four interpolation frequencies are selected, and the original impedance matrices at the four interpolation frequencies are calculated respectively. Four interpolation modified impedance matrices used for interpolation are obtained according to the original impedance matrices at the four interpolation frequencies. The interpolation technology is applied to the block matrix generated by the local variation problem. Step 4: Use equally spaced sampling to determine each sampling frequency that needs to be calculated; Step 5: For each sampling frequency, four interpolation coefficients at the corresponding sampling frequency are calculated according to the four interpolation frequencies, and the impedance matrix at the corresponding sampling frequency is obtained by interpolation through four interpolation corrected impedance matrices and four interpolation coefficients, and the block matrix in the local change algorithm at the sampling frequency is interpolated; Step 6: Restore the interpolated impedance matrix to the original impedance matrix and use the local variation algorithm to solve the surface current; Step 7: Calculate the far-field radar cross-section based on the solved surface current.

2. The method for rapidly solving the local variation broadband electromagnetic scattering characteristics of a target according to claim 1, characterized in that: The four interpolation frequencies chosen are: f k =t k f h +(1-t k )f l ,f k ∈(f l ,f h ), Where k = 0, 1, 2, 3, f l and f h are the lowest and highest frequencies of the wide band analyzed, 3. The method for rapidly solving the local variation broadband electromagnetic scattering characteristics of a target according to claim 2, characterized in that: The corresponding sampling frequency f is calculated by the following formula c The four interpolation coefficients are: f k and f n are interpolation frequencies.

4. The method for rapidly solving the local variation broadband electromagnetic scattering characteristics of a target according to claim 1, characterized in that: Four modified interpolation impedance matrices are calculated based on the original impedance matrix at the four interpolation frequencies. The modified impedance matrix elements are The calculation formula is as follows: Where Z mn (f k ) is the interpolation frequency f k The original impedance matrix element at mn is the distance between the mth basis function and the nth basis function, and j is an imaginary unit.

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