CN112733364A - Foil strip cloud scattering rapid calculation method based on impedance matrix blocking - Google Patents
Foil strip cloud scattering rapid calculation method based on impedance matrix blocking Download PDFInfo
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Abstract
The invention belongs to the technical field of calculation of a large-volume foil cloud cluster radar scattering cross section, and discloses a foil cloud scattering rapid calculation method, which uses a linear moment method theory to perform preliminary calculation on the foil cloud cluster radar scattering cross section; the calculated result is compared with a moment method calculated result of the RWG basis function, the number of the subdivision units of the foil strip by the line moment method is greatly reduced while the result is accurate, the calculation speed of the cloud scattering characteristic of the foil strip is improved, and the calculated result is obtained more quickly; for the geometrically discontinuous electromagnetic target such as the foil cloud, the electromagnetic target is divided into a plurality of sub-regions according to the actual situation, the current matrix of each sub-region is calculated in parallel in a blocking mode, the current matrix of the whole region is solved, the electromagnetic scattering property of the foil cloud is obtained, and the acceleration of solving is realized; and error compensation, namely, the coupling effect of partial foil strips between every two adjacent spherical areas is considered, so that the obtained electromagnetic current is closer to the real electromagnetic current, and the calculated quantity and the convergence of the result are balanced.
Description
Technical Field
The invention belongs to the technical field of calculation of mass foil cloud cluster radar scattering cross sections, and particularly relates to a foil cloud scattering rapid calculation method based on impedance matrix blocking.
Background
At present: foil strips are a widely used type of passive interferent. The definition of foil strips by IEEE in terms of construction and function is as follows: the aerial interferent formed by aluminum or strip-shaped or sheet-shaped fibers coated with metal on the surface hinders the radar from identifying the true target in the modes of false target or noise interference and the like. Since world war ii, foil strips have become widely used as an important interference technique against radar, and the main advantages of foil strips used for interference techniques are: low manufacturing cost, simple structure, easy manufacturing and the like. Therefore, the method is widely applied to the field of national defense.
Early studies were mainly directed to theoretical analysis and estimation of radar cross-section (RCS) of foil cloud. At present, a plurality of scattering calculation algorithms for the foil strip cloud cluster exist, including an analytical method, a semi-analytical method, a medium method, an iterative method, a moment method, a Monte Carlo method and the like. The analytic method and the moment method have high precision, and the cloud RCS under the condition of small number can be calculated; the semi-analytical method has high precision and high speed under the condition that the foil cloud cluster structure is not complex, and can calculate the cloud cluster RCS of a large number of foil strips; the medium method can treat a large number of high-density clouds; the iterative method is fast, and can process the cloud cluster mixed by various foil strips; the Monte Carlo method can simulate the average of cloud clusters of any shape, structure and spatial distribution thereof, and can handle the conditions of large quantity and high density, and the relationship between the average value and the simulation times is not large.
Through the analysis of the algorithms, different calculation algorithms can be obtained and are usually suitable for different calculation requirements. However, the above various foil strip cloud cluster radar scattering calculation (estimation) technologies also have several significant disadvantages: firstly, although the accuracy of calculating the scattering cross section of the foil cloud radar by an analytical method and a moment method is high, the calculated amount is large, the speed is low, the number of foil strips is limited, and a large number of simultaneous equations need to be solved; the precision and speed of the semi-analytical method calculation depend on the complexity of the cloud cluster structure and the number of foil strips, and the division size and the division level need to be determined manually; the static model cannot be accurately described by a medium method; the iterative method cannot process spherical and complex structured clouds and needs to consider multiple scattering; the Monte Carlo method has a large calculation amount, the precision of spatial distribution is related to the simulation times, and multiple scattering needs to be considered.
Through the above analysis, the problems and defects of the prior art are as follows:
(1) the existing numerical method can ensure the accuracy, but the calculation efficiency is too low, and for foil strip clouds consisting of millions of foil strips, the calculation of the electromagnetic scattering property by the numerical method needs to consume a large amount of time and computer memory resources.
(2) The existing Monte Carlo method can effectively simulate the scattering characteristics of large-scale foil strip cloud to radar waves, but the calculation accuracy cannot be guaranteed because the method is based on the statistical principle.
The difficulty in solving the above problems and defects is: in order to solve the above technical problems, the following technical difficulties mainly exist: how to improve the speed of calculating the electromagnetic scattering property of the foil cloud while ensuring the accuracy of calculating the electromagnetic scattering of the foil cloud by a numerical method.
The significance of solving the problems and the defects is as follows: on the premise of ensuring the precision, the fast calculation of the scattering cross section of the foil cloud cluster radar is realized, and the calculation efficiency and the universality are solved as fast as possible; the application range of the precise algorithm of the numerical method in practical engineering is enlarged, and the development cycle of electromagnetic related equipment in the national defense science and technology field and the civil and civil field of China is shortened.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a method for rapidly calculating cloud scattering of a foil strip.
The invention is realized in such a way that a foil cloud scattering rapid calculation method based on impedance matrix blocking comprises the following steps:
calculating RCS of single and multiple foil strips by combining the specific steps of calculating foil strip cloud RCS by a linear moment method, comparing the calculated RCS with the calculated result of a moment method by using RWG basis functions, and verifying the correctness of the linear moment method;
by comparing the dividing units by the RWG basis function moment method and the line moment method, the applicability and the superiority of the foil strip calculated by the line moment method are proved;
for the foil cloud which is a geometrically discontinuous electromagnetic target, the foil cloud is divided into a plurality of sub-areas according to the actual situation, because the sub-areas are geometrically disconnected with each other, the current continuity problem does not exist between the areas, the current matrix of each sub-area is calculated in parallel in a blocking mode, and the current matrix of the whole area is solved;
error compensation, dividing the target into n sub-regions according to the geometry of the original problem. Each subregion extends a part to its adjacent subregion and forms the overlap region, makes the electromagnetic current who obtains more approximate true electromagnetic current.
Further, the foil strip scattering characteristic is calculated by solving a late position integral formula based on a moment method of the foil strip cloud scattering rapid calculation method based on the impedance matrix blocks, namely, firstly, grid division is carried out on the scattering body, the integral equation is converted into a matrix equation [ V ] ═ Z ] [ I ] by the discrete integral formula, and the current of the surface of the scattering body is obtained;
in a known applied field EiBy the effect of (a) the charge density σ and the current density on the conductor S
The equation (c) can be obtained by the following method. Expressing sigma and by late bit integration
The generated scattered field EsAnd using the boundary condition on S, the formula is summarized as follows:
for thin wires, the following approximation is made: assuming that current flows only in the direction of the wire axis; the current and charge density can be approximated as a line current
And σ on the lead axis; boundary conditions are used only on the axial component of the electric field at the surface of the wire;
the formula becomes:
wherein l is a variable along the axial direction of the wire, and R is the distance from a source point on the wire axis to a surface field point of the wire;
for the equation, the above equation is further refined by dividing the wire into N small segments, approximating the integral as a sum, I and q being constants on each small segment, and approximating the derivative with finite differences using finite difference methods:
also, similarly have
And
defining a matrix:
[V]＝[Z][I]；
for [ Z)]Solving is carried out by
Substitution into
Simply arrange to obtain [ Z ]]Another method is to directly obtain [ Z ] by using two isolated elements]；
bonding of
To
The formula can be obtained:
wherein ：
obtaining a [ Z ] matrix;
to obtain [ I]＝[Y][V]Wherein [ Y ] is]The matrix is composed of]The matrix is obtained by inversion, and after the current on each section of the foil strip is obtained, the current is regarded as N current elements
The far-zone magnetic vector position of the antenna array is as follows:
after the magnetic vector position of the far zone is obtained, the relation between the electric field of the far zone and the magnetic vector position is determined as follows:
obtaining the far-field electric field, and then considering the polarization form of the receiver
The radar scattering cross section can be obtained:
further, the foil strip cloud scattering rapid calculation method based on the impedance matrix blocking is characterized in that foil strips are subdivided by using a pulse basis function through comparison of calculation results of a moment method and a linear moment method of RWG basis functions.
Further, when the foil cloud complex electricity large-scale matrix equation [ Z ] [ I ] ═ V ] is solved by the foil cloud fast computing method based on the impedance matrix block, considerable storage and long computing time are consumed, for a foil cloud type geometrically discontinuous electromagnetic target, the foil cloud type geometrically discontinuous electromagnetic target is divided into a plurality of sub-regions according to actual conditions, and as the sub-regions are not geometrically connected with each other, the continuity problem of current does not exist between the regions, the current matrix of each sub-region is computed in parallel in the block mode, and the current matrix of the whole region is solved.
Further, for the foil strip such as the thin metal wire structure, a foil strip cloud with the volume of V is divided into a plurality of spherical subareas with the diameter of 4 lambda until all the foil strips are covered; and respectively calculating the current on each foil in the spherical sub-areas in parallel to obtain the current distribution on the overall foil cloud, obtain the electromagnetic scattering property of the foil cloud, and realize the acceleration of the solution.
Further, according to the error compensation of the foil strip cloud scattering rapid calculation method based on the impedance matrix blocks, the target is divided into n sub-regions according to the geometric structure of the original problem, each sub-region extends a part to the adjacent sub-region to form an overlapping region, and the obtained electromagnetic flow is closer to the real electromagnetic flow.
Further, selecting a middle point of a connecting line of the centers of every two subregions, continuously dividing a plurality of subregions by taking the point as a sphere center, wherein the newly formed subregions are partially overlapped with the original subregions, and the selection of the sizes of the subregions has considerable influence on the calculated amount and the convergence; the larger the overlap between the regions is, the more the calculation amount for each region is increased, the better the convergence of iterative solution of the whole problem is, and the required iteration times are correspondingly reduced, and vice versa.
Another object of the present invention is to provide a foil strip cloud scattering computing system for implementing the foil strip cloud scattering fast computing method based on impedance matrix blocking, the foil strip cloud scattering computing system comprising:
the first result comparison module is used for calculating RCS of single and multiple foil strips by combining the specific steps of calculating RCS of a foil strip cloud by a linear moment method, comparing the RCS with the calculation result of the moment method of the RWG basis function and verifying the correctness of the linear moment method;
the second result comparison module is used for comparing the bin number by the moment method and the line moment method of the RWG basis function;
the current matrix acquisition module is used for dividing a foil strip cloud which is a geometrically discontinuous electromagnetic target into a plurality of sub-regions according to the actual situation, and the sub-regions are geometrically disconnected with each other, so that the current continuity problem does not exist among the regions, the current matrix of each sub-region is calculated in a block-by-block parallel mode, and the current matrix of the whole region is solved;
and the error compensation module is used for dividing the target into n sub-regions according to the geometric structure of the original problem. Each subregion extends a part to its adjacent subregion and forms the overlap region, makes the electromagnetic current who obtains more approximate true electromagnetic current.
The invention also aims to provide a system for calculating the scattering cross section of the massive foil cloud cluster radar, which is used for realizing the method for quickly calculating the foil cloud scattering based on the impedance matrix blocking.
By combining all the technical schemes, the invention has the advantages and positive effects that: the method is combined with the specific steps of calculating the foil cloud RCS by using the linear moment method to calculate the RCS of single or multiple foil strips, and compared with the calculation result of the moment method using the RWG basis function to verify the correctness of the linear moment method. According to the method, the calculated results of the moment method and the linear moment method of the RWG basis function are compared, so that the quantity of the subdivision units of the foil strip by the linear moment method is greatly reduced while the precision is ensured. The foil strips are subdivided by utilizing the pulse basis functions, the number of unknown quantities can be reduced to a great extent while the calculation accuracy is ensured, and the scale of an equation is reduced, so that the calculation speed of the cloud scattering characteristics of the foil strips is improved, and the calculation results are obtained more quickly. For the complex and large electrical problem of the foil cloud, when a matrix equation [ Z ] [ I ] ═ V ] is solved by using a linear moment method, the method consumes considerable storage and long calculation time. For the foil cloud which is a geometrically discontinuous electromagnetic target, the foil cloud is divided into a plurality of sub-areas according to the actual situation, because the sub-areas are geometrically disconnected with each other, the current continuity problem does not exist between the areas, the current matrix of each sub-area is calculated in parallel in a blocking mode, and then the current matrix of the whole area is calculated; for the thin metal wire structure of the foil strips, the coupling effect is weaker and weaker along with the increase of the foil strip spacing, and the coupling effect between the foil strips can be ignored when the spacing is 3-4 lambda (lambda is the incident wavelength), so that the coupling effect between the foil strips can be ignored when the spacing between the foil strips is larger (larger than 4 lambda). Therefore, a cloud of foil strips with a volume V can be divided into several spherical subregions with a diameter of 4 λ until all foil strips are covered. Therefore, the current on each foil in the spherical sub-regions can be respectively calculated in parallel, and then the current distribution on the overall foil cloud can be obtained, so that the electromagnetic scattering property of the foil cloud can be obtained, and the further acceleration of the solution is realized.
The invention compensates for errors. The result obtained by the partition parallel computing solution and the integral solution of the problem by directly adopting a linear moment method has certain error, and certain coupling effect is inevitably generated between every two small areas, so that the coupling effect of partial foil strips between every two adjacent small areas needs to be further considered. The target is divided into n sub-regions according to the geometry of the original problem. Each subregion extends a part to its adjacent subregion and forms the overlap region, makes the electromagnetic current who obtains more approximate true electromagnetic current.
The invention selects the middle point of the connecting line of the centers of every two subregions, and continuously divides a plurality of subregions by taking the point as the sphere center, the newly formed subregions can be partially overlapped with the original subregions, and the selection of the sizes of the subregions has considerable influence on the calculated amount and the convergence. The larger the overlap between the regions, the more the calculation amount per region will increase, but the better the convergence of the iterative solution of the whole problem will be, and the number of iterations required will be correspondingly smaller, and vice versa. Therefore, the influence of the two is comprehensively considered in the actual solution, and the optimal size of the overlapping area is selected.
The invention adopts the concept of 'divide-and-conquer' to greatly improve the analysis capability of the moment method on the large-size target. And decomposing the target to be solved into a plurality of small subproblems, extending a part of buffer area from each subarea to the adjacent area to form a new iteration area, and solving each subarea by adopting a linear moment method. Compared with the RWG basis function moment method, the line moment method generates less unknown quantity for a single region, and when the method is used for solving, only the computer resource is ensured to meet the maximum sub-region. The overlapped region decomposition utilizes the buffer region to enable the current obtained by the solution to approximate to the real current distribution, the algorithm idea is clear, and the reliability is high.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed to be used in the embodiments of the present application will be briefly described below, and it is obvious that the drawings described below are only some embodiments of the present application, and it is obvious for those skilled in the art that other drawings can be obtained from the drawings without creative efforts.
Fig. 1 is a flowchart of a foil strip cloud scattering fast calculation method based on impedance matrix blocking according to an embodiment of the present invention.
FIG. 2 is a schematic structural diagram of a foil cloud scattering computing system according to an embodiment of the present invention;
in fig. 2: 1. a first result comparison module; 2. a second result comparison module; 3. a current matrix acquisition module; 4. and an error compensation module.
Fig. 3 is a basic principle flow chart of the algorithm provided by the embodiment of the invention.
Fig. 4 is a schematic view of a fine metal wire structure according to an embodiment of the present invention.
Fig. 5 is a schematic sectional view of a fine metal wire structure according to an embodiment of the present invention.
Fig. 6 is a schematic diagram illustrating the discrete positions of the electric scale according to an embodiment of the present invention.
Fig. 7 is a schematic split view of a foil strip according to an embodiment of the present invention.
Fig. 8 is a diagram of a partition structure of a cloud of foil strips according to an embodiment of the present invention.
Fig. 9 is a schematic diagram illustrating the definition of the coupling region between sub-regions according to the embodiment of the present invention.
Fig. 10 is a schematic diagram of a foil strip cloud partition numbering rule provided in an embodiment of the present invention.
Fig. 11 is a supplementary schematic diagram of an impedance matrix element provided in an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Aiming at the problems in the prior art, the invention provides a foil strip cloud scattering fast calculation method based on impedance matrix blocking, and the invention is described in detail below with reference to the accompanying drawings.
As shown in fig. 1, the foil strip cloud scattering fast calculation method based on impedance matrix blocking provided by the invention comprises the following steps:
s101: and calculating the RCS of the single or multiple foil strips by combining the specific steps of calculating the RCS of the foil strip cloud by using a linear moment method, and comparing the RCS with the calculation result of the moment method by using the RWG basis function to verify the correctness of the linear moment method.
S102: by comparing the calculation results of the moment method and the linear moment method of the RWG basis function, the quantity of the subdivision units of the foil strip by the linear moment method is greatly reduced while the precision is ensured.
S103: for the electromagnetic target such as the foil cloud with discontinuous geometry, the electromagnetic target is divided into a plurality of sub-areas according to the actual situation, because the sub-areas are not geometrically connected with each other, the current continuity problem does not exist between the areas, the current matrix of each sub-area is calculated in parallel in a blocking mode, and then the current matrix of the whole area is calculated.
S104: error compensation, dividing the target into n sub-regions according to the geometry of the original problem. Each subregion extends a part to its adjacent subregion and forms the overlap region, makes the electromagnetic current who obtains more approximate true electromagnetic current.
A person skilled in the art can also perform other steps to perform the foil cloud scattering fast calculation method based on impedance matrix blocking provided by the present invention, and the foil cloud scattering fast calculation method based on impedance matrix blocking provided by the present invention shown in fig. 1 is only one specific embodiment.
As shown in fig. 2, the foil strip cloud scattering computing system provided by the present invention includes:
the first result comparison module 1 is used for calculating RCS of single and multiple foil strips by combining the specific steps of calculating RCS of foil strip cloud by a linear moment method, comparing the RCS with the calculation result of the moment method of RWG basis function, and verifying the correctness of the linear moment method;
the second result comparison module 2 is used for comparing the calculation results of the moment method and the line moment method of the RWG basis function;
the current matrix acquisition module 3 is used for dividing the foil cloud which is a geometrically discontinuous electromagnetic target into a plurality of sub-regions according to the actual situation, and the sub-regions are geometrically disconnected with each other, so that the current continuity problem does not exist among the regions, the current matrix of each sub-region is calculated in parallel in a blocking manner, and the current matrix of the whole region is calculated;
and the error compensation module 4 is used for dividing the target into n sub-regions according to the geometric structure of the original problem. Each subregion extends a part to its adjacent subregion and forms the overlap region, makes the electromagnetic current who obtains more approximate true electromagnetic current.
The technical solution of the present invention is further described below with reference to the accompanying drawings.
The foil cloud scattering rapid calculation method based on impedance matrix blocking uses a linear moment method theory to perform preliminary calculation on the foil cloud cluster radar scattering cross section; the calculated result is compared with a moment method calculated result of the RWG basis function, the number of the subdivision units of the foil strip by the linear moment method is greatly reduced while the result is accurate, the cloud scattering characteristic calculation speed of the foil strip is preliminarily improved, and the calculated result is obtained more quickly; for the geometrically discontinuous electromagnetic target such as the foil cloud, the electromagnetic target is divided into a plurality of sub-regions according to the actual situation, the current matrix of each sub-region is calculated in parallel in a blocking mode, and then the current matrix of the whole region is worked out, so that the electromagnetic scattering property of the foil cloud can be obtained, and the further acceleration of the solution is realized; and (4) carrying out error compensation, and further considering the coupling effect of partial foil strips between every two adjacent spherical areas, so that the obtained electromagnetic flow is closer to the real electromagnetic flow, and the calculated amount and the convergence of the result are balanced.
The invention aims to solve the problem of accelerated calculation of the electromagnetic scattering (radar scattering cross section) problem of the cloud cluster of the foil strips. Primarily calculating the scattering cross section of the foil strip cloud radar by using a linear moment method theory; then, the calculation result is compared with a moment method calculation result of the RWG basis function, the number of the subdivision units of the foil strip by the line moment method is greatly reduced while the result is accurate, the cloud scattering characteristic calculation speed of the foil strip is preliminarily improved, and the calculation result is obtained more quickly; then, for the geometrically discontinuous electromagnetic target such as the foil cloud, the electromagnetic target is divided into a plurality of sub-regions according to the actual situation, the current matrix of each sub-region is calculated in parallel in a blocking mode, and then the current matrix of the whole region is worked out, so that the electromagnetic scattering property of the foil cloud can be obtained, and the further acceleration of the solution is realized; and finally, error compensation is carried out, and the coupling effect of partial foil strips between every two adjacent spherical areas is further considered, so that the obtained electromagnetic flow is closer to the real electromagnetic flow, and the calculated amount and the convergence of the result are balanced.
The invention relates to a foil strip cloud scattering rapid calculation method based on an impedance matrix blocking method, which comprises the following steps:
the method comprises the following steps of firstly, calculating RCS of single and multiple foil strips by combining with the specific step of calculating foil strip cloud RCS by a linear moment method, comparing the RCS with the calculation result of the moment method by using RWG basis functions, and verifying the correctness of the linear moment method.
Basic theory of linear moment method:
(1) basic principle of moment method
Assuming the to-be-solved field problem can be described by the following operator equation:
L(f)＝g (1)
where L represents one of a differential or integral linear operator. g denotes the known function source and f denotes the response function. The response function f expands linearly within the domain of definition of L as:
in the formula anRepresenting unknown scalar coefficients to be solved, fnReferred to as basis functions. The summation of infinite terms is carried out in the above formula, but only finite terms can be carried out in the actual solving process. In the formula, the linear characteristic of the operator L can be obtained by substituting the formula:
then selecting a proper function w in the value range of L1,w2,…wmTaking the inner product of the two sides of the above formula as a test function to obtain:
where m is 1,2,3 … N, this system of linear equations can be written as a matrix as follows:
[lmn][an]＝[gm] (5)
in the formula ：
suppose an impedance matrix, [ l ]mn]Non-singularity, [ a ]n]Can be obtained by the following equation:
[an]＝[lmn]-1[gm] (9)
a to be solvednSubstituting the formula to obtain f.
In summary, the core factor affecting the accuracy of the moment method is the basis function fnAnd weight function wnIf f and g are defined in the same space, then f can be takenn＝wnCommonly referred to as the Galois method.
wherein fn and wnMust be linearly independent. Influence fn and wnThe factors selected are:
calculating the difficulty degree of matrix elements;
calculating precision to be solved:
③ good state matrix lmn]-1The realizability of (a);
and fourthly, the convergence speed of the matrix is high or low.
(2) The method is applied to a linear moment method of foil strips, wherein the moment method is used for calculating the scattering characteristics of the foil strips by solving a late position integral formula, namely, firstly, grids of a scattering body are divided, then, an integral equation is converted into a matrix equation [ V ] ═ Z ] [ I ] by a discrete integral formula, and therefore the current of the surface of the scattering body is obtained. Other useful parameters, such as field pattern, input impedance, RCS, etc., can be calculated from the corresponding equations, as long as the current distribution is known.
Assuming that the field E is applied at a known external fieldiBy the effect of (a) the charge density σ and the current density on the conductor S
The equation (c) can be obtained by the following method. Expressing sigma and by late bit integration
The generated scattered field EsAnd using the boundary condition on S, the formula is summarized as follows:
For thin wires, the following approximation is made: 1. it is assumed that the current flows only in the direction of the wire axis. 2. The current and charge density being approximatedConsidered as a line current
And σ on the lead axis. 3. The boundary conditions are only used on the axial component of the electric field at the surface of the wire.
Thus, the above equation becomes:
where l is a variable along the axis of the wire and R is the distance from a source point on the axis of the wire to the surface field point of the wire.
For the above equation, we can use a wire divided into N small segments and approximate the integration as a sum. At this point, I and q are constants on each segment, and the derivatives are approximated by finite differences using finite difference methods.
Also, similarly have
And
it can be seen that each σ can be represented by each I.
Can be written in a form containing only I (n) we can consider
The expression N equations is a single equation with terminal pairs
The voltage applied to each port is approximately Ei·Δln. Thus, a matrix is defined:
[V]＝[Z][I] (24)
for the solution of [ Z ], the values of-can be substituted and simply arranged to obtain [ Z ], and the other method is to directly obtain [ Z ] by using two isolated elements.
The integral in (b) has the same form, expressed as:
binding to formula (la) can result:
wherein ：
therefore, in summary, the [ Z ] matrix can be obtained.
Then [ I ] can be obtained]＝[Y][V]Wherein [ Y ] is]The matrix is composed of]The inversion of the matrix is equivalent to taking the pulse function as the basis function of both current and charge, and the point matching as the weight function. After obtaining the current on each segment of the foil strip, it can be regarded as N current elements
The far-zone magnetic vector position of the antenna array is as follows:
after the magnetic vector position of the far zone is obtained, the relation between the electric field of the far zone and the magnetic vector position is determined as follows:
thereby obtaining far-zone electric field, and then considering polarization form of receiver
The radar scattering cross section can be obtained:
and secondly, comparing the calculation results of the moment method of the RWG basis function with the calculation results of the line moment method, and greatly reducing the number of the subdivision units of the foil strip by the line moment method while ensuring the precision. The foil strips are subdivided by utilizing the pulse basis functions, the number of unknown quantities can be reduced to a great extent while the calculation accuracy is ensured, and the scale of an equation is reduced, so that the calculation speed of the cloud scattering characteristics of the foil strips is improved, and the calculation results are obtained more quickly.
And thirdly, for the complex electrical problem of the foil cloud, when a matrix equation [ Z ] [ I ] ═ V ] is solved by using a linear moment method, considerable storage and long calculation time are consumed. For the electromagnetic target such as the foil cloud with discontinuous geometry, the electromagnetic target is divided into a plurality of sub-areas according to the actual situation, because the sub-areas are not geometrically connected with each other, the current continuity problem does not exist between the areas, the current matrix of each sub-area is calculated in parallel in a blocking mode, and then the current matrix of the whole area is calculated.
Specifically, for the thin metal wire structure such as the foil strips, the coupling effect becomes weaker with the increase of the foil strip spacing, and is negligible when the spacing is 3-4 λ (λ is the incident wavelength), so that the coupling effect between the foil strips can be ignored when the spacing between the foil strips is larger (larger than 4 λ). Therefore, a cloud of foil strips with a volume V can be divided into several spherical subregions with a diameter of 4 λ until all foil strips are covered. Therefore, the current on each foil in the spherical sub-regions can be respectively calculated in parallel, and then the current distribution on the overall foil cloud can be obtained, so that the electromagnetic scattering property of the foil cloud can be obtained, and the further acceleration of the solution is realized.
And fourthly, carrying out error compensation on the previous step. The result obtained by the partition parallel computing solution and the integral solution of the problem by directly adopting a linear moment method has certain error, and certain coupling effect is inevitably generated between every two small areas, so that the coupling effect of partial foil strips between every two adjacent small areas needs to be further considered. The target is divided into n sub-regions according to the geometry of the original problem. Each subregion extends a part to its adjacent subregion and forms the overlap region, makes the electromagnetic current who obtains more approximate true electromagnetic current.
Specifically, the midpoint of the connecting line of the centers of every two subregions is selected, the point is taken as the sphere center to continuously mark out a plurality of subregions, the newly formed subregions can be partially overlapped with the original subregions, and the selection of the sizes of the subregions has considerable influence on the calculated amount and the convergence. The larger the overlap between the regions, the more the calculation amount per region will increase, but the better the convergence of the iterative solution of the whole problem will be, and the number of iterations required will be correspondingly smaller, and vice versa. Therefore, the influence of the two is comprehensively considered in the actual solution, and the optimal size of the overlapping area is selected.
The basic schematic block diagram of the algorithm of the present invention is shown in fig. 3.
(1) Firstly, uniformly distributed foil strip clouds are established in a cubic range with a volume of V, the spatial distribution and orientation information of the foil strip clouds are read, and the reading format of data is as follows (as shown in Table 1):
wherein the serial number is the serial number of each foil strip, (x, y, z) is the coordinate of the central point of the foil strip, and the unit is meter,
is the orientation of the foil strip in radians.
Table 1 foil strip cloud data storage format table
Secondly, each foil strip is segmented (taking 10 segments as an example), and all foil strip segmentation information numbers are stored in a table, wherein the table comprises the coordinates of the upper end point, the coordinates of the lower end point, the coordinates of the center of each segment and the corresponding serial numbers of the foil strips, and the table is shown in table 2.
Table 2 data storage format table of upper end point, lower end point and central point of foil strip cloud segment
(2) Substituting data into a line moment method theory to calculate according to the spatial distribution and orientation information of the foil strip cloud: respectively carrying out construction of an integral equation, dispersion of the integral equation, a matching process, calculation of matrix elements and calculation of a radiation far field, and specifically comprising the following steps:
construction of integral equation
For a thin metal wire with radius a in the uniform medium space, length l in the axial direction, as shown in fig. 4; the generated electromagnetic field satisfies the following conditions:
wherein ：
wherein ,
and
are respectively a field point
Electric field, magnetic vector and electric scale; if the radius and length of the thin line satisfy a < lambda, a < l, thenIt can be considered that: 1. the wire only has axial current, and the current in the circumferential direction on the surface of the wire and the current on two end faces of the wire can be ignored; 2. current flow being axial only
Flowing, with line current
Instead of the bulk current density, the charge linear density σ may be used instead of the charge bulk density ρ; 3. the current distribution is only related to the length of the wire and not to the radius.
Under assumptions, the expression of the magnetic vector bits and the electric scale bits can be approximated as:
wherein ：
for field points on the surface of the wire, according to the boundary conditions satisfied:
comprises the following steps:
integral equation dispersion
The linear moment method uses a pulse basis function to disperse an integral equation. The thin metal wire is divided into N segments as shown in FIG. 5, and the length of the segment N is expressed as Deltaln，
Represents the distance between n and n +1,
representing the distance between n and n-1.
The unknown current density on the thin metal wire can be expressed as:
wherein ,
is the impulse basis function, and I (n) is the expansion coefficient;
the expression is as follows:
in the formula ,
and the axial unit vector of the wire on the nth segment is shown, and the direction is from the starting point of the wire to the end point. Will magnetic vector position
Discretizing into N partitions with the pulse basis function is as follows:
since the basis function is a pulse basis function, the wire has a charge density σ at the junction of the line segments, and is 0 at other positions, as shown in fig. 5, and the relationship between the charge density and the current of the nth segment is:
electric mark position
Can then be calculated from the charge density σ (n)+) (N ═ 0,1, 2.., N), since
And I (0) ═ I (N +1) ═ 0, the beacon bits are discretized into N +1 subdivisions:
wherein
③ selecting and matching process
The weight function of the matching is
According to the formula, there are:
in the formula ：
wherein ：
substituting the formula and the formula into the formula to obtain:
the above equation is simplified to a matrix form:
ZI＝V (54)
the calculation formula of the impedance matrix is as follows:
the voltage matrix element calculation mode is as follows:
and fourthly, calculating matrix elements, wherein for a linear moment method, the key point of calculating the impedance matrix elements is to calculate the electric mark position of the unit charge on the nth section at the point m:
in calculating the electric scale position
When, the selected integral interval is Deltaln +Or Δ ln -Corresponding to the two halves of the wire. The electric scale bit can thus be replaced by the sum of the integrals over the two half-segments
in the formula ,
represents n-As a result of the integration over the n-half segment,
represents n to n+Integration results over half the segment. For the
The calculation can be discussed in two cases of a far zone and a near zone, but the calculation amount is increased, and the method is not suitable for a scene with particularly many subdivision units. The general calculation method is as follows:
assuming that the subdivision units are sufficiently large and the length of each unit is sufficiently small, the method comprises the following steps
Can be expressed as:
in the formula ：
in the above equation, a is the wire radius, z' is the coordinates of the source point, (z, ρ) is the coordinates of the field point,
radiation far field calculation
The radiation field expression of the current element in the maximum radiation direction is as follows:
according to reciprocity definition:
an expression can be derived for the radiation field:
simplifying to obtain:
therefore, the method comprises the following steps:
according to the approximate relationship of the far zone, there are both amplitude and phase
wherein 
Is the vector from the origin of coordinates to the nth segment center of the wire, and then substituted into
The following can be obtained:
the field generated by the antenna in the far zone can be seen as spherical wave, i.e. with transverse electric field Eθ and EφFree of radial electric field ErIf extracted
And
then E can be obtained respectivelyθ and EφThe total field expression can be written as:
(3) and comparing the result obtained in the step with the calculation results of the moment method and the linear moment method of the RWG basis function, and greatly reducing the number of the subdivision units of the foil strip by the linear moment method while ensuring the precision. The foil strips are subdivided by utilizing the pulse basis functions, the number of unknown quantities can be reduced to a great extent while the calculation accuracy is ensured, and the scale of an equation is reduced, so that the calculation speed of the cloud scattering characteristics of the foil strips is improved, and the calculation results are obtained more quickly.
Specifically, when the RWG basis function is selected as the basis function, the surface of the foil strip is divided into a plurality of small triangles, the induced current on the common edge of each triangle is calculated, and finally the calculation result is obtained according to the expression of the far-field RCS. The RWG basis function is a deformed pulse basis function, the basis function is defined on two adjacent triangular bins, and is a bin pair, and the definition formula is as follows:
when the scattering characteristics of the three-dimensional target are calculated by using the RWG basis functions, the three-dimensional target needs to be subdivided by using a small triangle, then the current distribution of each surface element is calculated, and finally the scattering field information is solved. However, for the thin linear model of the foil strip, when a triangular surface element is used for splitting, a large number of splitting units are needed to ensure good fitting of the geometric model, so that the RWG basis function is not suitable for calculating the scattering characteristic of the foil strip.
Due to the special model of the thin and long metal wires of the foil strips, the induced currents of the foil strips are distributed along the length direction, so that the pulse basis function which is difficult to solve a three-dimensional target is suitable for the foil strips, the current on the foil strips can be better split by using the pulse basis function, and the current distribution on the foil strips can be more accurately described only by splitting the foil strips into a plurality of sections along the length direction.
FIG. 7 shows the difference between the splitting of a foil strip by RWG basis function and the splitting of a foil strip by pulse basis function, wherein for a foil strip applied to a radar frequency of 3GHz, the length is 0.05m, the diameter is 0.001m, and when the RWG basis function is adopted, a large number of splitting units are needed for fitting the fine line structure of the foil strip, and the foil strip is split into 468 small triangles, so that the calculation can be well completed; however, for the subdivision of the pulse basis function, the description of the current distribution of the foil strip can be completed only by about 20 subdivision units. Therefore, the foil strips are divided by using the pulse basis function, the number of unknown quantities can be reduced to a great extent while the calculation accuracy is ensured, and the scale of the equation is reduced, so that the calculation speed of the cloud scattering characteristic of the foil strips is improved, and the calculation result is obtained more quickly.
(4) For the foil strip such a fine metal wire structure, the coupling effect becomes weaker with the increase of the foil strip spacing, which is negligible when the spacing is 3-4 λ (λ is the incident wavelength), so that when the spacing between the foil strips is larger (larger than 4 λ)When desired), the coupling effect between the foil strips can be neglected. Therefore, as shown in fig. 8, a cubic foil cloud with a volume V may be divided into a plurality of cubic sub-areas with a side length of 4 λ until all foil strips are covered, the partitioned foil cloud data is stored according to the form of table 3, and then substituted into an impedance element calculation formula, where the form of the impedance matrix equation is shown as the formula, where Z is11,Z22,…,ZnnIs the impedance element in each partition. In this way, the current on each foil strip in these cube sub-regions can be calculated separately in parallel, as shown in the equation. And then the current distribution on the overall foil cloud can be obtained, so that the electromagnetic scattering property of the foil cloud can be obtained, and the further acceleration of the solution is realized.
Table 3 foil strip cloud data partition mark storage format table
| Number of foil strips | x | y | | Area code | |
| 1 | |||||
| 2 | |||||
| …… | …… | …… | …… | …… |
[Z11][I1]＝[V1],[Z22][I2]＝[V2],…,[Znn][In]＝[Vn] (71)
(5) Error compensation is performed. The result obtained by the partition parallel computing solution and the integral solution of the problem by directly adopting a linear moment method has certain error, and certain coupling effect is inevitably generated between every two small areas, so that the coupling effect of partial foil strips between every two adjacent small areas needs to be further considered. The target is divided into n sub-regions according to the geometry of the original problem. Each sub-area and the adjacent sub-area form a coupling area, so that the obtained electromagnetic flow is closer to the real electromagnetic flow.
Specifically, the midpoint of the central connecting line of every two subregions is selected, a plurality of subregions are continuously divided by taking the midpoint as the center, the newly formed subregions can be partially overlapped with the original subregions, and the selection of the sizes of the subregions has considerable influence on the calculated amount and the convergence. The larger the overlap between the regions, the more the calculation amount per region will increase, but the better the convergence of the iterative solution of the whole problem will be, and the number of iterations required will be correspondingly smaller, and vice versa. Therefore, the influence of the two is comprehensively considered in the actual solution, and the optimal size of the overlapping area is selected. Now, a spherical area with a diameter of 4 lambda is selected as a mutual coupling area of two adjacent cubic subregions, and as shown in fig. 9, a coupling area exists between the first region and the second region, between the first region and the third region, between the second region and the fourth region, and between the third region and the fourth region in a sectional view. After the coupling area is divided, each sub-area divided in the previous step is renumbered, and the numbering rule is as follows: the sub-region where a certain vertex of the cube is located is taken as a No. I region, the vertex is taken as a sphere center, and the radius of the sub-region gradually increases to form concentric spheres which intersect with the sub-regions, as shown in FIG. 10. Numbering the subsequent sub-regions according to the sequence of intersection, numbering the sub-regions according to the rule of top to bottom, left to right, front to back and back to back if a certain sphere is intersected with a plurality of sub-regions at the same time, and then storing the foil strip cloud data partition marks in the table 3 again.
With the center of the coupling area as the center, the foil strips and the corresponding foil strip serial numbers in the coupling area are screened out, and the total impedance matrix is newly supplemented, the supplemented effect is shown in fig. 11, wherein the dotted line part is the filling of new matrix elements considering the coupling between the areas (i) and (ii), the areas (i) and (iii), the areas (ii) and (iv), and the areas (iii) and (iv). And solving the supplemented matrix equation, so that the obtained electromagnetic flow is closer to the real electromagnetic flow.
The technical effects of the present invention will be described in detail with reference to the simulation examples.
Firstly, simulation conditions: the simulation adopts foil strip clouds of different numbers uniformly distributed in a cube, and the parameters are shown in table 4, wherein the parameters comprise the volume size of the cube, the frequency of an incident plane wave, an incident angle, the number of foil strips and the like.
Table 4 simulation conditions list
Second, comparison of simulation results
The results of the single station RCS calculations before and after acceleration by the linear moment method were compared, as shown in table 5:
TABLE 5 comparison of the results
According to the comparison of results, the error of the calculation result before and after acceleration is within 10%, and the solving time is remarkably shortened, so that the calculation efficiency of the simple-type large-volume foil cloud is obviously improved.
The above description is only for the purpose of illustrating the present invention and the appended claims are not to be construed as limiting the scope of the invention, which is intended to cover all modifications, equivalents and improvements that are within the spirit and scope of the invention as defined by the appended claims.
Claims (8)
1. A foil cloud scattering fast calculation method based on impedance matrix blocking is characterized by comprising the following steps:
calculating RCS of single and multiple foil strips by combining with the specific steps of calculating RCS of foil strip cloud by a linear moment method theory, comparing with a calculation result of a moment method by using RWG basis functions, and verifying the correctness of the linear moment method;
comparing the subdivision quantity of the foil strips by a moment method and a linear moment method of RWG basis functions to verify the improvement of the calculation efficiency of the linear moment method;
for the foil cloud which is a geometrically discontinuous electromagnetic target, the foil cloud is divided into a plurality of sub-areas according to the actual situation, because the sub-areas are geometrically disconnected with each other, the current continuity problem does not exist between the areas, the current matrix of each sub-area is calculated in parallel in a blocking mode, and the current matrix of the whole area is solved;
and error compensation, namely dividing the target into n sub-regions according to the geometric structure of the original problem, wherein each sub-region extends a part to the adjacent sub-region to form an overlapping region, so that the obtained electromagnetic flow is closer to the real electromagnetic flow.
2. The fast foil cloud scattering calculation method based on impedance matrix blocking according to claim 1, wherein the moment method of the fast foil cloud scattering calculation method based on impedance matrix blocking calculates the scattering characteristics of the foil by solving a late bit integration formula, that is, firstly, the scatterer is divided into grids, and the discrete integration formula converts the integration equation into a matrix equation [ V ] ═ Z ] [ I ], so as to obtain the current of the scatterer surface;
in a known applied field EiBy the effect of (a) the charge density σ and the current density on the conductor S
The equation (c) can be obtained by expressing the sum of sigma by integrating the late bits
The generated scattered field EsAnd using the boundary condition on S, the formula is summarized as follows:
for thin wires, the following approximation is made: assuming that current flows only in the direction of the wire axis; the current and charge density can be approximated as a line current
And σ on the lead axis; boundary conditions are used only on the axial component of the electric field at the surface of the wire;
the formula becomes:
wherein l is a variable along the axial direction of the wire, and R is the distance from a source point on the wire axis to a surface field point of the wire;
for the equation, the above equation is further refined by dividing the wire into N small segments, approximating the integral as a sum, I and q being constants on each small segment, and approximating the derivative with finite differences using finite difference methods:
also, similarly have
And
defining a matrix:
[V]＝[Z][I]；
for [ Z)]Solving is carried out by
Substitution into
Simply arrange to obtain [ Z ]]The other one isThe method is to directly obtain [ Z ] by using two isolated elements]；
bonding of
To
The formula can be obtained:
wherein ：
obtaining a [ Z ] matrix;
to obtain [ I]＝[Y][V]Wherein [ Y ] is]The matrix is composed of]The matrix is obtained by inversion, and after the current on each section of the foil strip is obtained, the current is regarded as N current elements
The far-zone magnetic vector position of the antenna array is as follows:
after the magnetic vector position of the far zone is obtained, the relation between the electric field of the far zone and the magnetic vector position is determined as follows:
obtaining the far-field electric field, and then considering the polarization form of the receiver
The radar scattering cross section can be obtained:
3. the impedance matrix blocking-based foil cloud scattering fast calculation method as claimed in claim 1, wherein the impedance matrix blocking-based foil cloud scattering fast calculation method divides the foil by using a pulse basis function by comparing a moment method of RWG basis function with a line moment method.
4. The method for foil cloud scattering fast calculation based on impedance matrix blocking according to claim 1, wherein when a matrix equation [ Z ] [ I ] ═ V ] is solved for a complex electrical large scale of the foil cloud by using a linear moment method, the foil cloud scattering fast calculation method based on impedance matrix blocking consumes considerable storage and long calculation time, and for an electromagnetic target such as a foil cloud with geometrical discontinuity, the electromagnetic target is divided into several sub-regions according to actual conditions, and since the sub-regions are geometrically disconnected with each other, the current continuity problem does not exist between the regions, the current matrix of each sub-region is calculated in parallel by blocking, and the current matrix of the whole region is solved.
5. The impedance matrix blocking-based foil cloud scattering fast calculation method according to claim 4, wherein for a foil strip such as a thin metal wire structure, a foil strip cloud cluster with a volume of V is divided into a plurality of spherical subregions with a diameter of 4 λ until all foil strips are covered; and respectively calculating the current on each foil in the spherical sub-areas in parallel to obtain the current distribution on the overall foil cloud, obtain the electromagnetic scattering property of the foil cloud, and realize the acceleration of the solution.
6. The impedance matrix blocking-based foil cloud scattering fast calculation method as claimed in claim 1, wherein the error compensation of the impedance matrix blocking-based foil cloud scattering fast calculation method divides the target into n sub-regions according to the geometric structure of the original problem, and each sub-region extends a part to its adjacent sub-region to form an overlap region, so that the obtained electromagnetic flow is closer to the real electromagnetic flow.
7. The impedance matrix blocking-based foil cloud scattering fast calculation method of claim 6, wherein a midpoint of a connecting line of centers of every two subregions is selected, a plurality of subregions are continuously divided by taking the midpoint as a sphere center, the newly formed subregions are partially overlapped with the original subregions, and the selection of the sizes of the subregions has a considerable influence on the calculation amount and the convergence; the larger the overlap between the regions is, the more the calculation amount for each region is increased, the better the convergence of iterative solution of the whole problem is, and the required iteration times are correspondingly reduced, and vice versa.
8. A massive foil cloud radar scattering cross section computing system is characterized in that the massive foil cloud radar scattering cross section computing system is used for realizing the foil cloud scattering rapid computing method based on impedance matrix blocking according to any one of claims 1 to 7.
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| CN113806933A (en) * | 2021-09-15 | 2021-12-17 | 西安电子科技大学 | Method for acquiring ideal conductor carrier platform broadband RCS (radar cross section) based on satellite emission source |
| CN113935157A (en) * | 2021-09-27 | 2022-01-14 | 中国人民解放军32802部队 | Cross-scale multi-mechanism fusion electromagnetic scattering numerical solving method |
| CN117784042A (en) * | 2023-11-30 | 2024-03-29 | 西安电子科技大学 | Calibration alignment error correction method under foil cloud measurement scene |
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| CN111123225A (en) * | 2019-12-25 | 2020-05-08 | 西安电子科技大学 | Sea background foil strip cloud scattering method based on vector transport theory |
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| CN111123225A (en) * | 2019-12-25 | 2020-05-08 | 西安电子科技大学 | Sea background foil strip cloud scattering method based on vector transport theory |
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| CN113806933A (en) * | 2021-09-15 | 2021-12-17 | 西安电子科技大学 | Method for acquiring ideal conductor carrier platform broadband RCS (radar cross section) based on satellite emission source |
| CN113935157A (en) * | 2021-09-27 | 2022-01-14 | 中国人民解放军32802部队 | Cross-scale multi-mechanism fusion electromagnetic scattering numerical solving method |
| CN117784042A (en) * | 2023-11-30 | 2024-03-29 | 西安电子科技大学 | Calibration alignment error correction method under foil cloud measurement scene |
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