Method and device for rapidly analyzing broadband RCS based on MLFACA and CBFM, and medium

Abstract

The invention discloses a method, equipment and medium for rapidly analyzing broadband RCS based on MLFACA and CBFM, and the method only executes MLFACA and generates a feature basis function set CBFs at the highest frequency of a broadband to be analyzed, and does not need to repeat MLFACA and generate CBFs again at other frequencies in the broadband. The MLFACA decomposes an impedance sub-matrix of a far-field block pair into a product of several sparse matrixes based on fast adaptive cross sampling and a butterfly algorithm. In addition, the size of an outer matrix in product representation obtained by MLFACA is compressed by using CBFs, so that more efficient approximate representation is obtained. The approximate representation can be fixed in the whole frequency band, matrix elements can be efficiently obtained through an impedance interpolation method, it is avoided that a complete impedance matrix is generated through calculation at each frequency to be analyzed, and the filling efficiency of the impedance matrix of the far field block pair is effectively improved.

Description

Technical Field

[0001] The present invention relates to a method, a device and a medium for quickly analyzing target broadband electromagnetic scattering, and in particular to a method for quickly solving target broadband RCS based on multi-layer fast adaptive cross approximation (MLFACA) and characteristic basis function method (CBFM). Background Art

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

[0003] In 2011, WeiDong Li et al. proposed that the accuracy of moment method impedance interpolation can be improved by reasonably selecting four sample frequencies within the frequency band. This method avoids the repeated calculation of impedance elements at other frequency points within the frequency band, but it still needs to generate and store 4 complete impedance matrices as interpolation samples, which still consumes a lot of memory and time. In 2012, M. De Gregorio et al. proposed that the characteristic basis function (CBF) generated at the highest frequency of the frequency band to be calculated contains the spatial behavior at lower frequencies. Therefore, 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. Moreover, 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 solution 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 of multilevel fast adaptive cross approximation (MLFACA) combined with CBFM, which reduced the computational time and storage complexity of MoM calculation of single-frequency electromagnetic scattering problems to O(Nlog 2N) (MLFACA-CBFM reference: x.Chen.et.MultilevelFastAdaptiveCross-ApproximationAlgorithmWithCharacteristicBasisFunctions.IEEETraps.AntennasPropag.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, so these significant basis functions are applicable to any frequency point in the entire frequency band. Summary of the invention

[0004] Aiming at the problem of fast analysis of broadband electromagnetic scattering of targets, the present invention proposes a hybrid method based on multi-layer fast adaptive cross approximation (MLFACA) and characteristic basis function method (CBFM) for fast solution of broadband RCS of targets. This method only performs MLFACA and generates characteristic basis functions (CBFs) at the highest frequency of the frequency band to be analyzed, fully utilizes the broadband properties of ACA and CBFs in the entire frequency band, and combines the impedance interpolation method to significantly reduce the filling time of the impedance matrix of the far-field block pair at the cost of a small increase in memory consumption, effectively improving the efficiency of solving broadband RCS.

[0005] In order 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 Meshing the target model;

[0008] Step 2: Use the 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 impedance matrix of the far-field block pair is decomposed into a multiplication of multiple sparse matrices using the multi-layer fast adaptive cross approximation MLFACA algorithm, and the two outer sparse matrices are compressed using the characteristic basis function set of the corresponding far-field block pair;

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

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

[0013] 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.

[0014] The present invention makes full use of the broadband properties of CBFs and ACA, and proposes the above-mentioned method for quickly analyzing target broadband electromagnetic scattering based on MLFACA and CBFM. Compared with the prior art, the present invention has the following beneficial effects:

[0015] The present invention only performs multi-layer fast adaptive cross approximation (MLFACA) and generates characteristic basis function sets (CBFs) at the highest frequency of the wide frequency band to be analyzed, without repeating MLFACA and generating CBFs at other frequencies within the broadband. MLFACA decomposes the impedance submatrix of the far-field block pair into the product of several sparse matrices based on Fast Adaptive Cross Sampling (FACS) and the butterfly algorithm. In addition, the size of the outer matrix in the product representation obtained by MLFACA is compressed by CBFs, thereby obtaining a more efficient approximate representation. This approximate representation can be fixed within the entire frequency band, and its matrix elements can be efficiently obtained by the impedance interpolation method, avoiding the calculation and generation of a complete impedance matrix at each frequency to be analyzed, and effectively improving the filling efficiency of the impedance matrix of the far-field block pair. In summary, for solving broadband electromagnetic scattering problems, compared with the traditional MLFACA-CBFM hybrid method, the present invention avoids the repeated execution of MLFACA at the cost of slightly increasing memory overhead, greatly reduces the time required to fill the impedance matrix, significantly reduces the time required to calculate impedance, and greatly improves the efficiency of calculating broadband RCS. Especially when a large number of frequency points need to be analyzed, the advantages of the present invention are more obvious, and the method is universal. BRIEF DESCRIPTION OF THE 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 by the embodiment of the present invention.

[0019] Figure 4 It is a result diagram of an 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 elaborated in detail below through a specific implementation method and in combination with its accompanying drawings.

[0022] Embodiment 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 triangulated mesh, and then defined the Rao-Wilton-Glisson (RWG) basis function on the mesh, 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 usual value of q is 0.5λ. H , 1.0λ H , 1.5λ H ; Then, according to the positional relationship between any two blocks, classification is performed, and two blocks with adjacent or identical relationships are defined as near-field block pairs, otherwise they are considered to be far-field block pairs.

[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 characteristic basis functions is generated on each finest block of the layer.

[0027] Step 4: At the highest frequency fH The impedance matrix of the far-field block pair is decomposed into the form of multiplication of multiple sparse matrices using the multi-layer fast adaptive cross approximation (MLFACA) algorithm, and the two outer sparse matrices are compressed using the characteristic basis function set (CBFs) corresponding to the far-field block pair.

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

[0029]

[0030] Among them A (p) , C (p) and B (L) are all decomposed sparse submatrices, p = 1, 2, ..., L, where L = l f -l+1. Figure 2 yes Schematic diagram of the decomposition after 4 layers of MLFACA.

[0031] Then, the CBFs compression impedance matrix corresponding to the far-field block pair (i, j) is used, which is expressed as

[0032]

[0033] in, yes The reduction matrix of H is the conjugate transpose of (·). i and J j is the combination matrix of CBFs belonging to block i and block j respectively, which are also sparse matrices

[0034]

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

[0036] Substituting (1) into (2), we get

[0037]

[0038] in, Yes A (1) The reduction matrix of It is B (L) The reduction matrix of and It is still a sparse matrix.

[0039] Step 5: Select 4 sample frequencies fs (s=1, 2, 3, 4), the sample impedance is calculated and stored 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, expressed as

[0043]

[0044] Then, A is calculated based on the index of the significant RWG basis function selected when performing MLFACA in step 4. (p) (f s ), C (p) (f s ) and B (L) (f s ), where p = 1, 2, ..., L, s = 1, 2, 3, 4. (p) (f s ), C (p) (f s ) and B (L) (f s ) are sparse matrices, so compared to filling in a 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 form of impedance matrix decomposition for 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, we can get z 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 Unzip

[0055]

[0056] Then with and For samples, 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 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.

[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 ) is used 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 get 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. H The target is divided into octree blocks using the small cubes 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 finest layer block expansion size 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 present invention takes 394.2 minutes and occupies a peak memory of 9952MB, while the traditional MLFACA-CBFM takes 1094.0 minutes and occupies a peak memory of 2838MB. The memory cost of the present invention is 3.5 times that of the traditional MLFACA-CBFM, but it achieves a total time reduction of about 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, that is, the absolute value of the difference between the RCS (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 quickly analyzing 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 Meshing the target model; Step 2: Use the 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 is decomposed into a multiplication of multiple sparse matrices using the multi-layer fast adaptive cross approximation MLFACA algorithm, and the two outer sparse matrices are compressed using the characteristic basis function set of the corresponding far-field block pair; 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 an impedance interpolation method to generate multiple sparse matrices in the form of an impedance matrix decomposition of 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 4, the impedance matrix of the far-field block pair (i, j) of the layer is After L-layer MLFACA decomposition, it can be 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 characteristic basis function set corresponding to the far-field block pair (i, j) to compress the two outer matrices A (1) and B (L) It is then approximately expressed as in, yes The reduction matrix of is the reduction matrix of A(1), is the reduction matrix of B(L); J i and J j are l in the i-th block and 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.

3. The method for quickly analyzing broadband RCS based on MLFACA and CBFM according to claim 2 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 corresponding to the 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.

4. The method for rapidly analyzing broadband RCS based on MLFACA and CBFM according to claim 3 is characterized in that: In step 6, first compress the matrix and Unzip 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 5. 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 4.

6. 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 4 are implemented.

Images