CN114722589B - Method for rapidly solving three-dimensional target double-station RCS - Google Patents
Method for rapidly solving three-dimensional target double-station RCS Download PDFInfo
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Abstract
The invention discloses a method for rapidly solving a three-dimensional target double-station RCS, which relates to the field of electromagnetic numerical calculation and can effectively improve the solving efficiency of the three-dimensional electric large conductor target double-station RCS. First, a region decomposition strategy is used to solve the effective mode of each block and construct a feature modulus basis function. Then, the induced current is subjected to sparse conversion by adopting a characteristic mode basis function. And finally, constructing a low-dimensional compressed sensing model and reconstructing the induced current. The invention provides a new sparse basis construction method for a moment method based on compressed sensing, realizes sparse conversion of induced current on the surface of a three-dimensional target, and improves filling and solving efficiency of a matrix equation.
Description
Technical Field
The invention relates to the technical field of electromagnetic numerical computation, in particular to a method for rapidly solving a three-dimensional target double-station RCS.
Background
Analysis of a target double-station Radar Cross Section (RCS) is a theoretical basis of radar detection, target identification, aerospace and other technologies, and has important significance in the military field. Among a plurality of electromagnetic numerical algorithms, a moment method (MoM) has become one of the most dominant algorithms for solving the target double-station RCS problem due to the advantages of high precision, strong adaptability and the like. The core idea of the moment method is to use proper basis functions and weight functions to discrete an electromagnetic integral equation into a matrix equation for solving. However, since the generated impedance matrix is a dense matrix of full rank, both memory consumption and computation time increase dramatically as the target electrical size increases.
As an improved algorithm of a moment method, the moment method based on compressed sensing can convert a high-dimensional matrix equation into a low-dimensional compressed sensing model, and an efficient recovery algorithm is adopted to accurately reconstruct induced current. The method can remarkably reduce the calculation complexity of a moment method, thereby reducing the solving time of the electric large target double-station RCS. In this method, in order to construct a compressed sensing model, the induced current needs to be sparsely transformed on a suitable sparse basis. For the scattering problem of a two-dimensional target, the traditional sparse basis, such as discrete cosine transform and discrete Fourier transform, can effectively realize sparse conversion of surface induced current. However, for the three-dimensional object scattering problem, the surface induced current discretized with the Rao-Wilton-Glisson (RWG) basis function is not sparse on these conventional sparse bases, and thus cannot construct a compressed sensing model. Therefore, the application of this algorithm in three-dimensional target two-station RCS problems is severely limited.
Disclosure of Invention
The invention aims to provide a method for rapidly solving three-dimensional target double-station RCS, so as to solve the problems in the background technology. According to the invention, a group of characteristic mode basis functions are quickly constructed by adopting a regional decomposition strategy and used for realizing sparse conversion of surface induced current, and meanwhile, the solving efficiency of the target double-station RCS is improved by adopting an incompletely filled impedance matrix and an efficient recovery algorithm.
In order to achieve the above purpose, the technical scheme of the invention is realized by the following basic steps:
step 1: dividing the conductor target surface into a plurality of smaller blocks, expanding each block, and calculating the self-impedance matrix of each expanded block.
Step 2: according to the characteristic model theory of the conductor target, a generalized characteristic value equation on each block is constructed, a threshold condition is set according to the mode significance, and an effective mode meeting the threshold condition is solved.
Step 3: and removing the numerical value of the corresponding expansion part in the effective mode to obtain the characteristic mode of each unexpanded block, and constructing a group of characteristic mode basis functions by adopting the characteristic modes to carry out sparse conversion on the surface induced current.
Step 4: the impedance matrix and the excitation vector are randomly extracted according to rows, and the matrix equation is converted into a low-dimensional compressed sensing model.
Step 5: and reconstructing an induced current coefficient by adopting a recovery algorithm, and solving the induced current of the target surface.
Step 6: and (5) according to the result obtained in the step (5), solving the target double-station RCS.
Compared with the prior art, the invention has the advantages that:
1. The invention realizes sparse conversion of the induced current on the three-dimensional target surface by adopting the characteristic mode basis function which is quickly constructed based on the regional decomposition strategy.
2. The incompletely filled impedance matrix can obviously reduce the filling time of a matrix equation, and the low-dimensional compressed sensing model can efficiently solve the surface induced current through a recovery algorithm, so that the solving efficiency of the three-dimensional target double-station RCS is greatly improved.
Drawings
FIG. 1 is a basic flow chart of the method of the present invention.
FIG. 2 is a schematic diagram of the result of the method of the present invention.
Detailed Description
The basic flow diagram of the method of the invention is shown in fig. 1, and the implementation of the technical scheme is further described in detail below with reference to the accompanying drawings:
Step 1: dividing the conductor target surface into a plurality of smaller blocks, the matrix equation zj=v in the moment method is rewritten as:
Wherein Z ii and The self-impedance matrix and the transimpedance matrix are respectively obtained, V i is incident excitation on the ith block, J i is surface induced current, m is the number of blocks, each block is expanded, and the self-impedance matrix of each expanded block is calculated
Step 2: according to the characteristic mode theory of the conductor target, the self-impedance matrix of the expanded block is adoptedConstructing a generalized eigenvalue equation:
wherein X i and R i are each Lambda i is the eigenvalue,Is the eigenvector corresponding to the eigenvalue lambda i. Pattern dependent significanceSetting a threshold tau, and solving a characteristic value meeting MS not less than tau and a corresponding effective mode by adopting an iteration method
Step 3: removing active modesThe corresponding expansion part value in the block is used for obtaining the characteristic mode of each unexpanded block
In the method, in the process of the invention,For the kth feature mode on the ith block, K is the number of active modes on the ith block. The feature mode basis function J CM is constructed using feature modes over all blocks:
And sparse conversion is carried out on the induction current J:
J＝JCMa (5)
Where a is a weight coefficient vector.
Step 4: the impedance matrix Z and the excitation vector V are randomly extracted according to rows and are respectively used as an observation matrix Z and an observation value V, and a matrix equation in a moment method is converted into a compressed sensing model by combining a characteristic mode basis function:
ZJCMa＝V (6)
step 5: and (5) reconstructing an induced current coefficient vector a by adopting a recovery algorithm, and bringing the vector a into a formula (5) to solve the induced current of the target surface.
Step 6: and (5) according to the surface induced current obtained in the step (5), solving the target double-station RCS.
The process of the present invention will now be further illustrated by the following detailed examples, it being apparent that the embodiments described are only some, but not all, of the embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention takes as an example a double station RCS calculating a conductor cube of side length 1 m. The incident excitation being a plane wave having an angle ofThe frequency was 800MHz. Splitting the cube surface at 0.1λ (λ is the wavelength of the incident plane wave) intervals yields 24309 unknowns in total. The target is divided into 26 blocks, each extended by 0.15 lambda. The method and the traditional MoM are adopted to solve the target double-station RCS respectively. In the present invention, the threshold τ is 0.001, and the number of randomly extracted lines is 1/3 of the unknowns. In conventional MoM, an iterative approach is employed.
As can be seen from FIG. 2, the calculation result of the method of the present invention is better matched with the conventional MoM, and has higher calculation accuracy. Table 1 shows the calculated time and relative root mean square error for the method of the present invention and for a conventional MoM. It can be seen that the fill time and solution time are reduced by 43% and 66%, respectively, resulting in a 51% reduction in total computation time. This example verifies the accuracy and efficiency of the present invention.
TABLE 1
| Method of | Filling time/s | Solving time/s | Total time/s | RCS error/% |
| Traditional MoM | 375.3 | 205.1 | 580.4 | - |
| The invention is that | 212.4 | 68.2 | 280.6 | 0.9 |
In summary, the invention realizes sparse conversion of the three-dimensional target surface induced current by constructing a group of characteristic mode basis functions based on region decomposition, and converts the traditional MoM matrix equation into a low-dimensional compressed sensing model, thereby remarkably reducing the calculation time. The method has higher calculation efficiency and precision when solving the three-dimensional electric large conductor target double-station RCS.
Claims (4)
1. A method for rapidly solving a three-dimensional target double-station RCS is characterized by comprising the following steps:
step 1: dividing the conductor target surface into a plurality of smaller blocks, expanding each block, and calculating a self-impedance matrix of each expanded block;
Step 2: according to the characteristic model theory of the conductor target, constructing a generalized characteristic value equation on each block, setting a threshold condition according to the mode significance, and solving an effective mode conforming to the threshold condition;
step 3: removing the numerical value of the corresponding expansion part in the effective mode to obtain a characteristic mode of each unexpanded block, and constructing a group of characteristic mode basis functions by adopting the characteristic modes to carry out sparse conversion on the surface induced current;
Step 4: randomly extracting an impedance matrix and an excitation vector according to rows, and converting a matrix equation into a low-dimensional compressed sensing model;
Step 5: reconstructing an induced current coefficient by adopting a recovery algorithm, and solving the induced current of the target surface;
Step 6: and (5) according to the result obtained in the step (5), solving the target double-station RCS.
2. The method of claim 1, wherein in step 1, the conductor target surface is divided into a plurality of smaller blocks, and then the matrix equation zj=v in the moment method is rewritten as:
Wherein Z ii and The self-impedance matrix and the transimpedance matrix are respectively obtained, V i is incident excitation on the ith block, J i is surface induced current, m is the number of blocks, each block is expanded, and the self-impedance matrix of each expanded block is calculated
3. The method for rapidly solving a three-dimensional object two-station RCS according to claim 1, wherein in step 2, the self-impedance matrix of the expanded block is adopted according to the characteristic modulus theory of the conductor objectConstructing a generalized eigenvalue equation:
wherein X i and R i are each Lambda i is the eigenvalue,Is the feature vector corresponding to the feature value lambda i according to the mode significanceSetting a threshold tau, and solving a characteristic value meeting MS not less than tau and a corresponding effective mode by adopting an iteration method
4. The method for rapidly solving a three-dimensional target dual-station RCS according to claim 1, wherein in step 3, the active mode is removedThe corresponding expansion part value in the block is used for obtaining the characteristic mode of each unexpanded block
In the method, in the process of the invention,For the kth eigenmode on the ith block, K is the number of active modes on the ith block, and eigenmode basis functions J CM are constructed using eigenmodes on all blocks:
And sparse conversion is carried out on the induction current J:
J＝JCMa (5)
Where a is a weight coefficient vector.
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| CN107145732A (en) * | 2017-05-03 | 2017-09-08 | 安徽理工大学 | A kind of method based on the rapid solving target list station Electromagnetic Scattering Characteristics for improving CBFM |
| CN108647183A (en) * | 2018-04-02 | 2018-10-12 | 北京环境特性研究所 | Multiple RCS data interpolating methods based on compressed sensing |
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| CN112329204B (en) * | 2020-10-11 | 2022-08-16 | 南京理工大学 | Method for rapidly analyzing electromagnetic characteristic model of repetitive structure by considering carrier platform coupling |
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| CN107145732A (en) * | 2017-05-03 | 2017-09-08 | 安徽理工大学 | A kind of method based on the rapid solving target list station Electromagnetic Scattering Characteristics for improving CBFM |
| CN108647183A (en) * | 2018-04-02 | 2018-10-12 | 北京环境特性研究所 | Multiple RCS data interpolating methods based on compressed sensing |
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