CN111914420B - Self-adaptive nested multipoint source method for extracting electromagnetic characteristics of metal target - Google Patents

Self-adaptive nested multipoint source method for extracting electromagnetic characteristics of metal target Download PDF

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CN111914420B
CN111914420B CN202010771903.5A CN202010771903A CN111914420B CN 111914420 B CN111914420 B CN 111914420B CN 202010771903 A CN202010771903 A CN 202010771903A CN 111914420 B CN111914420 B CN 111914420B
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王珂琛
许建华
刘军
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Abstract

The invention discloses a self-adaptive nested complex point source method for extracting the electromagnetic property of a metal target, which realizes the quick and accurate electromagnetic modeling and property extraction of the metal target. The invention aims to solve the problem of self-adaptive grouping modeling aiming at different target characteristics. Aiming at the regular characteristics of the actual metal target appearance, the self-adaptive grouping of the electromagnetic model is realized so as to ensure the reasonable distribution and the efficient utilization of computing resources. And after the target is subjected to adaptive grouping modeling, reasonable and effective parameter settings are automatically selected according to the distribution of the basis functions in the group and the electrical size of the group by using an adaptive cross approximation method and the calculation precision, so that the target electromagnetic characteristics are accurately and efficiently extracted.

Description

Self-adaptive nested multipoint source method for extracting electromagnetic characteristics of metal target
Technical Field
The invention relates to the technical field of electromagnetic modeling and feature extraction methods of metal targets, in particular to a self-adaptive nested complex point source method for extracting electromagnetic characteristics of a metal target.
Background
The actual target has a complex multi-scale geometric shape and electromagnetic characteristics, and the electromagnetic characteristics of the target cannot be obtained by using a traditional analytic means, so that the electromagnetic modeling and feature extraction method for the complex multi-scale target is also widely concerned, and the method can be divided into a differential classification method and an integral classification method according to the technical principle. The micro classification method is most widely applied to a Finite Difference Time Domain (FDTD) method and a Finite Element Method (FEM) method, but the micro classification method requires a truncated boundary to be established, which increases the calculation scale. The integration method does not require the establishment of a truncation boundary, and typical methods include a Surface Integral Equation (SIE) method and a volume surface integral equation (vsee) method. However, for target analysis problems with complex multi-scale geometries, discrete modeling may result in more computational unknowns and multi-scale meshes, which may substantially increase computational time and memory requirements. In order to solve the problem, researchers have proposed a plurality of fast methods for reducing the computational complexity, such as a fast multipole method, an adaptive integration method, and the like, which all use a uniform grouping method and a uniform parameter setting during electromagnetic modeling, so that the practical problem with a complex structure can cause non-uniform distribution of basis functions in a group, which leads to unreasonable distribution of computational resources, and further limits the computational efficiency.
At present, two problems exist in the electromagnetic modeling and characteristic extraction method for the target: the first is that the existing method adopts a uniform grouping method during electromagnetic modeling, and the method has high efficiency for uniformly distributed targets under ideal conditions and causes the influence of non-uniform distribution of calculation resources on calculation efficiency due to the fact that calculation unknowns are unevenly distributed for actual targets with multi-scale structures; secondly, the uniform grouping method has a uniform rule for setting parameters, and has no targeted treatment for the condition of uneven distribution of the basis functions, so that the calculation precision is uncontrollable, and the calculation accuracy is reduced.
Disclosure of Invention
The invention designs a self-adaptive nested complex point source method for quickly extracting the electromagnetic characteristic of a metal target aiming at the requirement of extracting the electromagnetic characteristic of the metal target, realizes quick and accurate electromagnetic modeling and characteristic extraction of the metal target, and is characterized in that the self-adaptive nested complex point source method with quasi-linear computation complexity is used for realizing the quick and accurate electromagnetic modeling and characteristic extraction of the metal target with a multi-scale structure on the basis of a surface integral equation method. The technical problems to be solved include: 1. the group modeling problem is adaptive to different target characteristics. Aiming at the regular characteristics of the actual target appearance, the self-adaptive grouping of the electromagnetic model is realized so as to ensure the reasonable distribution and the efficient utilization of computing resources. 2. The method is characterized by solving the problem of parameter selection of a self-adaptive nested complex point source method. After the target is subjected to adaptive grouping modeling, reasonable and effective parameter settings are automatically selected according to the distribution of the basis functions in the group and the electrical size of the group by using an adaptive cross approximation method and the calculation precision, so that the target electromagnetic characteristics are accurately and efficiently extracted.
The technical scheme of the invention is as follows: a self-adaptive nested multipoint source method for extracting electromagnetic characteristics of a metal target comprises the following steps:
step 1, establishing a physical model of a corresponding target, and using subdivision software to subdivide the surface of an object by using triangles to obtain structural information of the physical model, wherein the structural information comprises numbers of the triangles and coordinates of each node to represent a basis function;
step 2, carrying out self-adaptive grouping on the subdivided model by utilizing a multi-layer self-adaptive grouping technology to obtain a multi-layer grouping structure;
step 3, after grouping is completed, establishing an equivalent surface in each layer according to the size of each group, and uniformly distributing the complex point sources on the equivalent surface according to the number of the complex point sources of each layer;
step 4, when the two groups interact, the interaction between the complex point sources with effective action is selected, and the automatic selection of the effective complex point sources is completed by adopting a self-adaptive cross approximation method and utilizing approximate precision setting;
and 5, according to an equivalent principle, the interaction between the basis functions in the two groups is equivalent to the interaction between effective complex point sources on an equivalent surface, as shown in a formula 1:
equation 1:
Figure BDA0002616956670000031
in equation 1:
Figure BDA0002616956670000032
representing the interaction matrix between the l-th layer observation group O and the source group S,
Figure BDA0002616956670000033
subgroup O representing observation group O in finest layer LchildThe aggregate matrix of the internal basis functions,
Figure BDA0002616956670000034
for each from the finest layer L to the L-th layer of the observation group OThe transfer matrices of the layer subgroups complex point sources are multiplied,
Figure BDA0002616956670000035
representing the transition matrix between complex point sources of observation set O and source set S,
Figure BDA0002616956670000036
for the transfer matrix multiplication of the complex point sources of the subgroups of layers L from the L-th layer to the finest layer L for the source group S,
Figure BDA0002616956670000037
indicating that the source set S is in the finest layer L subgroup SchildA configuration matrix of internal basis functions;
and 6, obtaining a current coefficient corresponding to the target discrete basis function according to the solution method combining the surface integral equation in the step 5, and then representing the electromagnetic property of the target by using the current coefficient and the basis function.
In the above, in step 2, the multi-layer adaptive grouping technology is used to perform adaptive grouping on the subdivided model to obtain a multi-layer grouping structure, and the specific steps are as follows: after the divided models are grouped primarily, the threshold value of the maximum number of basis functions with the same size group in each layer is set, when the number of basis functions in one group is larger than the threshold value, the group needs to be subdivided again according to the grouping technology until the number of basis functions in each group meets the threshold value requirement, the size of each group is controlled in a self-adaptive mode according to the distribution of the basis functions, and the basis functions are distributed in each group relatively and uniformly.
In the above, the step 3 of establishing the equivalent surface according to each group of sizes includes the specific steps of: establishing equivalent plane by using the geometric center of each group as center, wherein the equivalent plane can be in proper shape according to different characteristics of the model, for example, the two-dimensional structure can be selected to have radius of
Figure BDA0002616956670000038
A circle of multiple group size, or a square of 3/2 times group size side length, the three-dimensional structure can be chosen to have a radius
Figure BDA0002616956670000039
A sphere of multiple group size, or a cube of 3/2 times group size on a side.
In the above, the solution method of the combined surface area equation in step 6 obtains the current coefficient corresponding to the target discrete basis function, and then the electromagnetic characteristic of the target is represented by using the current coefficient combined basis function, and the specific representation form is as follows:
Figure BDA0002616956670000041
ES(r) is the scattered field at the far field r point, j is the imaginary sign, k represents the wave number, η represents the free space wave impedance, r' represents the position of the basis function where the current coefficient is located,
Figure BDA0002616956670000042
represents the unit direction vector of r', JθAnd JφRespectively representing current coefficients
Figure BDA0002616956670000043
And
Figure BDA0002616956670000044
and (4) components. The expression of the target radar scattering cross section is as follows:
Figure BDA0002616956670000045
sigma denotes the radar scattering cross section, EincThe incident field is shown.
The technical scheme adopted by the invention is as follows: 1. aiming at the characteristic that the actual metal target is irregular in shape, the self-adaptive grouping of the electromagnetic model is realized, so that the reasonable distribution and the efficient utilization of computing resources are ensured. 2. After the target is subjected to adaptive grouping modeling, reasonable and effective parameter setting is automatically selected according to the calculation precision by using an adaptive cross approximation method based on the radiation directivity of a complex point source and according to the distribution of the number of basis functions in a group and the electrical size of the group, so that the electromagnetic characteristics of the target can be accurately and efficiently extracted.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a two-dimensional schematic diagram of preliminary grouping using a multi-layer grouping technique.
FIG. 3 is a two-dimensional diagram of the present invention for adaptive grouping based on the distribution of basis functions.
FIG. 4 is a schematic diagram of the distribution of complex point sources on an equivalent spherical surface according to the present invention.
Fig. 5 is a schematic view of a model aircraft of the present invention.
FIG. 6 is a diagram illustrating the results of analyzing the electromagnetic scattering properties of a target according to an embodiment of the present invention.
Detailed Description
In order to facilitate understanding of the present invention, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the present invention belongs, in conjunction with the accompanying drawings and the specific embodiments. The terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, the term "and/or" includes any and all combinations of one or more of the associated listed items.
An embodiment of the present invention is a self-adaptive nested complex point source method for rapidly extracting electromagnetic characteristics of a metal target, which includes the following specific steps as shown in fig. 1:
step 1, establishing a corresponding physical model of a problem to be solved, and using subdivision software to subdivide the surface of an object in a triangular manner to obtain structural information of the physical model, wherein the serial number of the triangle and coordinates of each node are used for expressing a basis function;
step 2, performing adaptive grouping on the analyzed problems by using a multilayer adaptive grouping technology, as shown in fig. 2-3, setting a threshold of the maximum number of basis functions with the same size group at each layer, and when the number of basis functions in one group is greater than the threshold, subdividing the group again according to the multilayer grouping technology until the number of basis functions in each group meets the threshold requirement, so that the size of each group is adaptively controlled according to the distribution of the basis functions, the basis functions are relatively uniformly distributed in each group, and further, the balanced distribution of computer resources is ensured, as shown in fig. 3; the method comprises the following steps of carrying out self-adaptive grouping on a subdivided model by utilizing a multi-layer self-adaptive grouping technology to obtain a multi-layer grouping structure, wherein the method specifically comprises the following steps: after the divided models are grouped primarily, the threshold value of the maximum number of basis functions with the same size group in each layer is set, when the number of basis functions in one group is larger than the threshold value, the group needs to be subdivided again according to the grouping technology until the number of basis functions in each group meets the threshold value requirement, the size of each group is controlled in a self-adaptive mode according to the distribution of the basis functions, and the basis functions are distributed in each group relatively and uniformly.
Step 3, after grouping is completed, establishing an equivalent surface in each layer according to the size of each group, and uniformly distributing the complex point sources on the equivalent surface according to the number of the complex point sources of each layer; as shown in fig. 4, the step 3 of establishing the equivalent surface according to each group of sizes includes the following specific steps: establishing equivalent plane by using the geometric center of each group as center, wherein the equivalent plane can be in proper shape according to different characteristics of the model, for example, the two-dimensional structure can be selected to have radius of
Figure BDA0002616956670000051
A circle of multiple group size, or a square of 3/2 times group size side length, the three-dimensional structure can be chosen to have a radius
Figure BDA0002616956670000052
A sphere of multiple group size, or a cube of 3/2 times group size on a side.
And 4, because the complex point source has the radiation directivity of the complex point source, the interaction between the complex point sources with effective action can be selected when the two groups interact, in order to achieve controllable precision, the self-adaptive cross approximation method is adopted to finish the automatic selection of the effective complex point source by utilizing the approximate precision setting, namely, the approximate precision is firstly determined, and then the effective complex point source for determining the interaction between the two groups is selected according to the method of compressing the interaction matrix by the self-adaptive cross approximation method.
And 5, according to an equivalent principle, the interaction between the basis functions in the two groups is equivalent to the interaction between effective complex point sources on an equivalent surface, as shown in a formula 1:
equation 1:
Figure BDA0002616956670000061
in the above equation 1:
Figure BDA00026169566700000612
representing the interaction matrix between the l-th layer observation group O and the source group S,
Figure BDA0002616956670000062
subgroup O representing observation group O in finest layer LchildThe aggregate matrix of the internal basis functions,
Figure BDA0002616956670000063
for the transfer matrix multiplication of the complex point sources from the finest layer L to the ith layer subset for the observation group O,
Figure BDA0002616956670000064
representing the transition matrix between complex point sources of observation set O and source set S,
Figure BDA0002616956670000065
for the transfer matrix multiplication of the complex point sources of the subgroups of layers L from the L-th layer to the finest layer L for the source group S,
Figure BDA0002616956670000066
indicating that the source set S is in the finest layer L subgroup SchildA configuration matrix of internal basis functions.
And 6, obtaining a current coefficient corresponding to the discrete basis function of the target according to the solving method of combining the step 5 with the surface integral equation, and representing the electromagnetic property of the target by using the current coefficient and the basis function. The specific representation is as follows:
Figure BDA0002616956670000067
ES(r) is the scattered field at the far field r point, j is the imaginary sign, k represents the wave number, η represents the free space wave impedance, r' represents the position of the basis function where the current coefficient is located,
Figure BDA0002616956670000068
represents the unit direction vector of r', JθAnd JφRespectively representing current coefficients
Figure BDA0002616956670000069
And
Figure BDA00026169566700000610
component, the expression of the target radar scattering cross section is:
Figure BDA00026169566700000611
sigma denotes the radar scattering cross section, EincThe incident field is shown.
Typical simulation of the target electromagnetic characteristics is performed on the above embodiment, and the simulation is implemented on a personal computer with a main frequency of 2.83GHz and a memory of 8GB, such as an aircraft model shown in fig. 5, where the model size is 9.56 mx 6.70 mx 2.13m, the calculation frequency is 300MHz, and the unknown quantity is 24414. The aircraft model in the embodiment has a multi-scale structure, in order to accurately fit a target model, finer grids need to be adopted for subdivision fitting at a nose, a wing and the like, so that the grids have the multi-scale characteristic, the target model is subjected to self-adaptive grouping by adopting the technology of the invention, a multi-layer grouping structure is arranged at a place where the grids are dense, and a larger group size and a smaller number of layers are adopted for grouping at a place where the grids are sparse. The self-adaptive nested complex point source method and the traditional moment method are respectively adopted for analysis, the incident angle is theta 0 degree,
Figure BDA0002616956670000072
observation ofAt an angle of
Figure BDA0002616956670000073
The electromagnetic scattering properties analyzed by the two methods are shown in fig. 6, and it can be seen from fig. 6 that the results of the two methods are very consistent. Corresponding memory and calculation time are shown in table 1, table 1 is a memory and calculation time comparison table, and it can be seen from the table that the adaptive nested multiple-point source method of the present invention is superior to the existing mature traditional moment method in calculation efficiency.
TABLE 1 memory vs. calculated time
Figure BDA0002616956670000071
The technical scheme adopted by the invention is as follows: 1. aiming at the characteristic that the actual target is irregular in shape, the self-adaptive grouping of the electromagnetic model is realized, so that the reasonable distribution and the efficient utilization of computing resources are ensured. 2. After the target is subjected to adaptive grouping modeling, reasonable and effective parameter settings are automatically selected according to the calculation precision by using an adaptive cross approximation method based on the radiation directivity of a complex point source and according to the distribution of the number of basis functions in a group and the electrical size of the group, so that the electromagnetic characteristics of the target can be accurately and efficiently extracted.
The technical features mentioned above are combined with each other to form various embodiments which are not listed above, and all of them are regarded as the scope of the present invention described in the specification; also, modifications and variations may be suggested to those skilled in the art in light of the above teachings, and it is intended to cover all such modifications and variations as fall within the true spirit and scope of the invention as defined by the appended claims.

Claims (4)

1. A self-adaptive nested multipoint source method for extracting electromagnetic characteristics of a metal target is characterized by comprising the following steps:
step 1, establishing a physical model of a corresponding target, and using subdivision software to subdivide the surface of an object by using triangles to obtain structural information of the physical model, wherein the structural information comprises numbers of the triangles and coordinates of each node to represent a basis function;
step 2, carrying out self-adaptive grouping on the subdivided model by utilizing a multi-layer self-adaptive grouping technology to obtain a multi-layer grouping structure;
step 3, after grouping is completed, establishing an equivalent surface in each layer according to the size of each group, and uniformly distributing the complex point sources on the equivalent surface according to the number of the complex point sources of each layer;
step 4, when the two groups interact, the interaction between the complex point sources with effective action is selected, and the automatic selection of the effective complex point sources is completed by adopting a self-adaptive cross approximation method and utilizing approximate precision setting;
and 5, according to an equivalent principle, the interaction between the basis functions in the two groups is equivalent to the interaction between effective complex point sources on an equivalent surface, as shown in a formula 1:
equation 1:
Figure FDA0003513338710000011
in equation 1:
Figure FDA0003513338710000012
representing the interaction matrix between the l-th layer observation group O and the source group S,
Figure FDA0003513338710000013
subgroup O representing observation group O in finest layer LchildThe aggregate matrix of the internal basis functions,
Figure FDA0003513338710000014
for the transfer matrix multiplication of the complex point sources from the finest layer L to the ith layer subset for the observation group O,
Figure FDA0003513338710000015
representing the transition matrix between complex point sources of observation set O and source set S,
Figure FDA0003513338710000016
is the l-th layer from the source set SMultiplication of the transfer matrices to the complex point sources of the subgroups of layers of the finest layer L,
Figure FDA0003513338710000017
indicating that the source set S is in the finest layer L subgroup SchildA configuration matrix of internal basis functions;
step 6, obtaining a current coefficient corresponding to the target discrete basis function according to the solution method combining the surface integral equation in the step 5, and then representing the electromagnetic property of the target by using the current coefficient and the basis function; the solving method of the combined surface area equation obtains a current coefficient corresponding to a target discrete basis function, and then the electromagnetic characteristic of the target is represented by using the current coefficient combined basis function, wherein the specific representation form is as follows:
Figure FDA0003513338710000021
ES(r) is the scattered field at the far field r point, j is the imaginary sign, k represents the wave number, η represents the free space wave impedance, r' represents the position of the basis function where the current coefficient is located,
Figure FDA0003513338710000022
represents the unit direction vector of r', JθAnd JφRespectively representing current coefficients
Figure FDA0003513338710000023
And
Figure FDA0003513338710000024
component, the expression of the target radar scattering cross section is:
Figure FDA0003513338710000025
sigma denotes the radar scattering cross section, EincThe incident field is shown.
2. The adaptive nested complex point source method for extracting the electromagnetic property of the metal target according to claim 1, wherein in the step 2, the self-adaptive grouping of the subdivided models is performed by using a multilayer self-adaptive grouping technology to obtain a multilayer grouping structure, and the specific steps are as follows: after the divided models are grouped primarily, the threshold value of the maximum number of basis functions with the same size group in each layer is set, when the number of basis functions in one group is larger than the threshold value, the group needs to be subdivided again according to the grouping technology until the number of basis functions in each group meets the threshold value requirement, the size of each group is controlled in a self-adaptive mode according to the distribution of the basis functions, and the basis functions are distributed in each group relatively and uniformly.
3. The adaptive nested multipoint source method for extracting the electromagnetic characteristics of the metal target according to claim 1, wherein the step 3 is to establish equivalent surfaces according to each group of sizes, and the specific steps are as follows: an equivalent plane is established centered on the geometric center of each group.
4. The adaptive nested complex point source method for extracting the electromagnetic property of the metal target according to claim 2, wherein the equivalent surface is a two-dimensional structure or a three-dimensional structure; the two-dimensional structure has a selected radius of
Figure FDA0003513338710000026
A circle of multiple group size, or a square of length 3/2 times the group size; the three-dimensional structure has a selected radius of
Figure FDA0003513338710000031
A sphere of multiple group size, or a cube of 3/2 times group size on a side.
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