A method, device and medium for fast analyzing wideband RCS based on MLFACA and CBFM

Abstract

The application discloses a method and device for fast analyzing wideband RCS based on MLFACA and CBFM, and a medium, wherein the method only performs MLFACA and generates a characteristic basis function set CBFs at the highest frequency of a wideband to be analyzed, and does not need to repeatedly perform MLFACA and generate CBFs at other frequencies in the wideband. The MLFACA is based on fast adaptive cross-sampling and butterfly algorithm, and decomposes an impedance sub-matrix of a far-field block pair into a product of several sparse matrices. In addition, the size of an outer matrix in the product representation obtained by the MLFACA is compressed by using the CBFs, so that a more efficient approximate representation is obtained. The approximate representation can be fixed in the entire frequency band, and the matrix elements thereof can be efficiently obtained by an impedance interpolation method, so that the calculation and generation of a complete impedance matrix at each frequency to be analyzed are avoided, and the filling efficiency of the impedance matrix of the far-field block pair is effectively improved.

Description

TECHNICAL FIELD

[0001] The present application relates to a method, device and medium for fast analyzing target wideband electromagnetic scattering, in particular to a method for fast solving target wideband RCS based on multilevel fast adaptive cross approximation (MLFACA) and characteristic basis function method (CBFM). BACKGROUND

[0002] Efficiently solving wideband electromagnetic scattering problem plays an important role in many fields, such as target recognition, stealth design, etc. The method of moments (MoM) is an effective means to analyze the electromagnetic scattering characteristics of targets. However, the traditional method of moments needs to reconstruct the impedance matrix equation and solve it at each frequency point when dealing with wideband electromagnetic scattering problems. When the number of analysis frequency points is large, the overall time will be extremely time-consuming.

[0003] In 2011, Wei Dong Li et al. proposed that by reasonably selecting four sample frequencies in the frequency band, the accuracy of the impedance interpolation of the method of moments can be improved. This method avoids repeated calculation of impedance elements at other frequency points in the frequency band, but still needs to generate and store four complete impedance matrices as interpolation samples, which is still a huge consumption of memory and time. In 2012, M. De Gregorio et al. proposed that the characteristic basis functions (CBFs) generated at the highest frequency of the frequency band to be solved contain the spatial behavior at lower frequencies, so the CBFs generated at the highest frequency can be reused at any frequency point in the entire frequency band, saving the time of repeatedly calculating CBFs. And because the characteristic basis function method (CBFM) effectively compresses the matrix size, the computational complexity required to solve the matrix equation is greatly reduced. Although this method effectively reduces the solving time and memory, it still needs to perform the process of generating a complete impedance matrix at each frequency point, which is extremely time-consuming. In 2015, Chen Xinlei et al. proposed a hybrid method combining multilevel fast adaptive cross approximation (MLFACA) and CBFM, which reduces the computational time and storage complexity of MoM to O(Nlog 2N) (MLFACA-CBFM reference: x. Chen. et al. Multilevel Fast Adaptive Cross-Approximation Algorithm With Characteristic Basis Functions. 《IEEE Traps. Antennas Propag.》2015, Vol. 63(No. 9), pp. 3994-4002). In 2023, Chen Xinlei et al. found that the significant Rao-Wilton-Glisson (RWG) basis functions selected at the highest frequency point of the frequency band to be analyzed by the Adaptive Cross Approximation (ACA) algorithm can capture the electromagnetic characteristics of lower frequencies. Therefore, these significant basis functions are applicable to any frequency point in the entire frequency band. Summary of the Invention

[0004] To rapidly analyze broadband electromagnetic scattering from a target, this paper proposes a hybrid method based on the Multi-Level Fast Adaptive Cross Approximation (MLFACA) and the Characteristic Basis Function Method (CBFM) for quickly solving the target's broadband RCS. This method performs MLFACA and generates characteristic basis functions (CBFs) only at the highest frequency in the analyzed frequency band, fully leveraging the broadband properties of ACA and CBFs across the entire frequency band. Combined with an impedance interpolation method, this method significantly reduces the time required to fill the impedance matrix of far-field block pairs at the expense of a small increase in memory consumption, effectively improving the efficiency of solving broadband RCS.

[0005] To achieve the above-mentioned purpose, the present invention adopts the following technical solutions:

[0006] A method for quickly analyzing broadband RCS based on MLFACA and CBFM, characterized by comprising the following steps:

[0007] Step 1: At the highest frequency f of the wide frequency band to be analyzed H Mesh the target model;

[0008] Step 2: Use octree to map the target f +1 layer of blocks, and classify any two blocks into near-field and far-field block pairs according to the distance between the blocks, where l f It is the finest layer number;

[0009] Step 3: Use the excitation-independent characteristic basis function method CBFM at the highest frequency f H For the thinnest layer f Each finest layer of the layer generates a set of characteristic basis functions;

[0010] Step 4: At the highest frequency f HThe multi-layer fast adaptive cross approximation (MLFACA) algorithm is used to decompose the impedance matrix of the far-field block pair into a product of several sparse matrices, and the outer sparse matrices in the product representation are compressed using a set of characteristic basis functions (CBFs) corresponding to the far-field block pair;

[0011] Step 5: Select a sample frequency, and calculate and store the sample impedance at the sample frequency;

[0012] Step 6: For any frequency f to be calculated in the frequency band c , the impedance interpolation method is used to generate the sparse matrices in the impedance matrix decomposition form of the far-field block pair;

[0013] Step 7: For any frequency f to be calculated in the frequency band c , the impedance matrix of the near-field block pair is directly calculated, compressed using a set of characteristic basis functions (CBFs) corresponding to the near-field block pair, and then the compressed impedance matrices of the far-field block pair and the near-field block pair are integrated to form a reduced matrix equation, and the equation is solved using an iterative solution method to calculate the RCS.

[0014] The present application fully utilizes the broadband properties of CBFs and ACA, and proposes the above-mentioned method for quickly analyzing the broadband electromagnetic scattering of a target based on MLFACA and CBFM.

[0015] The present application only performs multi-layer fast adaptive cross approximation (MLFACA) and generates a set of characteristic basis functions (CBFs) at the highest frequency of the broadband to be analyzed, without repeating the MLFACA and generating CBFs at other frequencies in the broadband. The MLFACA is based on Fast Adaptive Cross Sampling (FACS) and butterfly algorithm, and decomposes the impedance sub-matrix of the far-field block pair into a product of several sparse matrices. In addition, the size of the outer matrix in the product representation obtained by MLFACA is compressed using CBFs, thereby obtaining a more efficient approximate representation. This approximate representation can be fixed throughout the frequency band, and its matrix elements can be efficiently obtained through the impedance interpolation method, avoiding the calculation and generation of a complete impedance matrix at each frequency to be analyzed, effectively improving the filling efficiency of the impedance matrix of the far-field block pair. In summary, compared with the traditional MLFACA-CBFM hybrid method for solving broadband electromagnetic scattering problems, the present application avoids the repeated execution of MLFACA at the cost of slightly increasing the memory overhead, greatly reduces the time required for filling the impedance matrix, significantly reduces the time required for calculating the impedance, greatly improves the efficiency of calculating the broadband RCS, and is particularly advantageous in the case of analyzing a large number of frequency points. The present application has universality. BRIEF DESCRIPTION OF DRAWINGS

[0016] Figure 1It is the basic flow chart of the present invention.

[0017] Figure 2 It is a schematic diagram of the decomposition of the impedance matrix of the MLFACA pair of far-field blocks in the present invention.

[0018] Figure 3 It is a ship model analyzed in an embodiment of the present invention.

[0019] Figure 4 Result diagram of the embodiment of the present invention.

[0020] Figure 5 2 is an error analysis diagram of an embodiment of the present invention. DETAILED DESCRIPTION

[0021] In order to more clearly illustrate the technical features of this patent, this patent is described in detail below through specific implementation methods and in combination with its accompanying drawings.

[0022] Example 1

[0023] This embodiment provides a method for quickly analyzing broadband RCS based on MLFACA and CBFM. Figure 1 As shown, the following steps are included:

[0024] Step 1: For a given frequency range [f L , f H ], for the target model (such as Figure 3 shown) at the highest frequency f in the frequency band H Use an average size of λ for the model surface H / 10 triangulation grid, and then define the Rao-Wilton-Glisson (RWG) basis function on the grid, where λ H is the frequency f H The corresponding wavelength.

[0025] Step 2: Divide the target into multiple blocks according to the octree structure. The side length of the small cube in the finest block is defined as q. Here, the value of q is usually 0.5λ. H , 1.0λ H , 1.5λ H Then, we classify any two blocks according to their positional relationship, and define two blocks that are adjacent or have the same relationship as a near-field block pair, otherwise they are considered to be a far-field block pair.

[0026] Step 3: Use the excitation-independent characteristic basis function method CBFM at the highest frequency f H At the finest level f A set of feature basis functions is generated on each finest block of the layer.

[0027] Step 4: At the highest frequency fH The impedance matrix between the far-field block pair (i, j) in the l-th layer is decomposed into a form of multiplication of several sparse matrices using the multi-level fast adaptive cross approximation (MLFACA) algorithm, and the set of characteristic basis functions (CBFs) corresponding to the far-field block pair is used to compress two outer sparse matrices.

[0028] Consider the impedance matrix between the far-field block pair (i, j) in the l-th layer After L-layer MLFACA, it is decomposed into

[0029]

[0030] where A (p) , C (p) and B (L) are decomposed sparse sub-matrices, p = 1, 2, …, L, where L = l f -l+1. Figure 2 is the decomposition schematic diagram after 4-layer MLFACA.

[0031] Then, the CBFs corresponding to the far-field block pair (i, j) are used to compress the impedance matrix, and its expression is

[0032]

[0033] where, is the reduced matrix of , (·) H is the conjugate transpose of (·). J i and J j are the combined matrices of the CBFs belonging to block i and block j, respectively, which are also sparse matrices

[0034]

[0035] where J ·，g (g = 1, 2, …, G) is the CBFs generated on the g-th finest layer block within block i or block j, and G is the number of the finest layer blocks included in block i or block j.

[0036] Substitute (1) into (2) to get

[0037]

[0038] where, is the reduced matrix of A (1) , is the reduced matrix of B (L) , and are still sparse matrices.

[0039] Fifth step: select four sample frequencies f​s (s=1, 2, 3, 4), calculate and store the sample impedance at the sample frequency.

[0040] The sampling frequency is chosen based on

[0041] f s =(1-t s )·f L +t s ·f H (6)

[0042] Among them, t s is the frequency selection coefficient, which is expressed as

[0043]

[0044] Then, A is calculated based on the index of the significant RWG basis function selected when performing MLFACA in the fourth step. (p) (f s ), C (p) (f s ) and B (L) (f s ), where p = 1, 2, ..., L, s = 1, 2, 3, 4. Since A (p) (f s ), C (p) (f s ) and B (L) (f s ) are sparse matrices, so compared to filling the complete impedance matrix, a lot of time is saved. To be used as an interpolation sample, the impedance element z in the matrix is ​​also required. mn (f s ) to make corrections

[0045]

[0046] in, is the modified element, D mn is the distance between the mth RWG basis function and the nth RWG basis function.

[0047] The matrix after impedance element correction is recorded as and Then, the CBFs corresponding to the far-field block pair (i, j) are used to convert and Compressed to and Further reduce the storage space required. In this step, and as well as are stored as interpolated samples.

[0048] Step 6: For any frequency f to be calculated within the frequency band c , an impedance interpolation method is used to generate multiple sparse matrices in the impedance matrix decomposition form of the far-field block pairs.

[0049] At frequency f c , the corrected impedance element It can be obtained by interpolation through the following formula

[0050]

[0051] Among them, the interpolation coefficient

[0052] Then, z can be obtained mn (f c ),according to

[0053]

[0054] However, due to and represents the interaction between CBFs and RWG basis functions, and CBFs do not have actual physical centers, so the distance parameter D in (8) and (10) is mn Cannot be defined, so you need to first and Decompression

[0055]

[0056] Then with and For the sample, according to (9)(10), we can interpolate to get A (p) (f c ), C (p) (f c ) and B (L) (f c ), where p = 1, 2, ..., L. Finally, the CBFs corresponding to the far-field block pair (i, j) are used to map A (1) (f c ) and B (L) (f c ) compression, that is, The compressed sparse representation in (5).

[0057] Step 7: For any frequency f to be calculated within the frequency band c , directly calculate the impedance matrix of the near-field block pair, and compress it using the CBFs corresponding to the near-field block pair. Then, integrate the compressed impedance matrices of the far-field and near-field block pairs to form a reduced matrix equation, and use the iterative solution method to solve the equation and calculate the RCS.

[0058] The present invention will be further described below with a specific example:

[0059] The present invention is based on a ship model with a size of 35.6m×5.2m×5.0m (attached Figure 3 ) as an example to illustrate the advantages of the present invention. The frequency band to be analyzed is 30MHz to 300MHz, the calculation frequency interval is 10MHz, and there are 28 calculation frequency points in total. At the highest frequency of 300MHz, the model is calculated according to 0.1λ H Divide the triangular mesh and obtain 166515 RWG basis functions, where λ H is the wavelength corresponding to 300MHz. The incident angle of the incident wave is The polarization mode is θ polarization. With a side length of λ H The target is divided into octree blocks with the small cube as the finest block, and 6 layers are divided, with a total of 648 non-empty finest blocks. The adaptive cross approximation (ACA) threshold is set to 10 -3 ; The truncation threshold of the singular value decomposition used to generate the characteristic basis function is 10 -4 , the block expansion size of the finest layer is 0.3λ H The four sample frequencies selected are 40.2763, 113.3377, 216.6623 and 289.7237 MHz.

[0060] In this example, the proposed method takes 394.2 minutes and uses a peak memory of 9952 MB, while the traditional MLFACA-CBFM method takes 1094.0 minutes and uses a peak memory of 2838 MB. The proposed method uses 3.5 times more memory than the traditional MLFACA-CBFM method, but achieves a total time reduction of approximately 64.0%. Figure 4 The calculated broadband RCS numerical results show that the results of the two methods are in good agreement. Figure 5 The error between the two methods, i.e., the absolute value of the difference between the RCS values ​​(in dBsm) calculated by the two methods, is given. It can be seen that the error between the two methods is less than 0.03 dB. This example verifies the accuracy and applicability of the present invention.

Claims

1. A method for rapid analysis of broadband RCS based on MLFACA and CBFM, characterized in that: The steps include: Step 1: At the highest frequency f of the wide frequency band to be analyzed H Mesh the target model; Step 2: Use octree to map the target f +1 layer of blocks, and classify any two blocks into near-field and far-field block pairs according to the distance between the blocks, where l f It is the finest layer number; Step 3: Use the excitation-independent characteristic basis function method CBFM at the highest frequency f H For the thinnest layer f Each finest layer of the layer generates a set of characteristic basis functions; Step 4: At the highest frequency f H The impedance matrix of the far-field block pair (i, j) of the lth layer is converted into the impedance matrix of the far-field block pair (i, j) of the lth layer using the L-layer multi-layer fast adaptive cross approximation MLFACA algorithm. Decomposed into the form of multiplication of multiple sparse matrices, the expression is Among them A (p) , C (p) and B (L) are all sparse submatrices, p = 1, 2, ..., L; where L = l f -l+1; Then use the corresponding characteristic basis function set to compress the two external matrices A (1) and B (L) , making Compressed to The expression is in, yes The reduction matrix, It's A (1) The reduction matrix, It's B (L) The reduction matrix of J i and J j l in the i-th block and the j-th block respectively f The combination matrix of the characteristic basis function set generated on the layer block, J i and J j is a sparse matrix; Step 5: Select the sample frequency, calculate and store the sample impedance at the sample frequency; Step 6: For any frequency f to be calculated within the frequency band c , using the impedance interpolation method to generate multiple sparse matrices in the impedance matrix decomposition form of the far-field block pairs; Step 7: For any frequency f to be calculated within the frequency band c , directly calculate the impedance matrix of the near-field block pair, and compress it using the characteristic basis function set of the corresponding near-field block pair. Then, integrate the compressed impedance matrices of the far-field and near-field block pairs to form a reduced matrix equation, and use the iterative solution method to solve the equation and calculate the RCS.

2. The method for rapidly analyzing broadband RCS based on MLFACA and CBFM according to claim 1 is characterized in that: In step 5, select the sample frequency f s , s=1, 2, 3, 4, according to the index of the main basis function selected when executing the MLFACA algorithm in step 4, the corresponding sparse matrix A is calculated at the sample frequency (p) (f s ), C (p) (f s ) and B (L) (f s ); After compressing the outer matrix using the characteristic basis function set of the corresponding far-field block pair (i, j), store A (p) (f s ), p = 2, ..., L, C (p) (f s ), p = 1, 2, ..., L and and as interpolation samples.

3. The method for rapidly analyzing broadband RCS based on MLFACA and CBFM according to claim 2 is characterized in that: In step 6, first compress the matrix and Decompression Then, at frequency f c A is obtained by impedance interpolation method (p) (f c ), C (p) (f c ) and B (L) (f c ), and then use the characteristic basis function set of the corresponding far-field block pair (i, j) to compress and obtain and 4. An electronic device comprising a processor and a memory, characterized in that The memory is used for a program running on the processor, and the processor executes the program to implement the steps of the method for quickly analyzing broadband RCS based on MLFACA and CBFM according to any one of claims 1 to 3.

5. A storage medium, characterized in that The storage medium stores a program, and when the program is executed by a processor, the steps of the method for quickly analyzing broadband RCS based on MLFACA and CBFM according to any one of claims 1 to 3 are implemented.

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