CN112733364B - Foil cloud scattering rapid calculation method based on impedance matrix partitioning - Google Patents
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Abstract
The invention belongs to the technical field of calculation of a general foil cloud cluster radar scattering cross section, and discloses a quick calculation method of foil cloud scattering, which uses a linear moment theory to perform preliminary calculation on the foil cloud cluster radar scattering cross section; the calculation result is compared with the calculation result of the moment method of the RWG basis function, the number of split 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 calculation result is obtained more quickly; for the geometrically discontinuous electromagnetic target of the foil cloud, dividing the geometrically discontinuous electromagnetic target into a plurality of sub-areas according to actual conditions, calculating the current matrix of each sub-area in parallel in a blocking manner, solving the current matrix of the whole area, obtaining the electromagnetic scattering characteristic of the foil cloud, and realizing the acceleration of solving; error compensation, considering the coupling effect of partial foil strips between every two adjacent spherical areas, so that the obtained electromagnetic flow is more approximate to the actual electromagnetic flow, and the calculated amount and the convergence of the result are balanced.
Description
Technical Field
The invention belongs to the technical field of calculation of radar cross sections of a large quantity of foil cloud clusters, and particularly relates to a foil cloud scattering rapid calculation method based on impedance matrix partitioning.
Background
At present: foil strips are a widely used passive jammer. The IEEE defines foil strips in terms of construction and function as follows: the air interference object formed by strip-shaped or sheet-shaped fibers coated with metal on the surface of the aluminum object can prevent the radar from identifying the true object in a false object or noise interference mode. Since the second world war, foil strips have been widely used as an important interference technique against radar, and the foil strips are used for the interference technique with the main advantages that: lower manufacturing cost, simple structure, easy manufacturing, etc. So that the method is widely applied in the field of national defense.
Early studies were mainly directed to theoretical analysis and estimation of Radar Cross Section (RCS) of foil cloud analysis. At present, a plurality of scattering calculation algorithms for foil cloud clusters are available, 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 resolution method and the moment method have high precision, and cloud cluster RCS under the condition of small quantity can be calculated; the semi-analytic method has high precision and high speed under the condition that the cloud cluster structure of the foil strips is not complex, and can calculate the cloud cluster RCS of a large number of foil strips; the medium method can process large quantity and high density cloud clusters; the iteration method is high in speed, and can process the cloud clusters mixed by various foil strips; the Monte Carlo method can simulate the average of cloud clusters with any shape, structure and spatial distribution, and can handle the conditions of large quantity and high density, and the average value has little relation with the simulation times.
By analyzing the algorithms, the method can obtain that different calculation algorithms are suitable for different calculation requirements. However, the above various foil cloud radar scattering calculation (prediction) techniques also have several significant disadvantages: firstly, calculating the foil cloud radar cross section by an analytic method and a moment method, wherein although the accuracy is high, the calculation amount is large, the speed is low, the number of foil is limited, and a large number of simultaneous equations are needed to be solved; the precision and speed of the semi-analytic 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 medium method can not accurately describe the static model; the iterative method cannot process spherical and complex-structured clouds and needs to consider multiple scattering; the Monte Carlo method has large calculation amount, the accuracy of spatial distribution is related to the simulation times, and multiple scattering needs to be considered.
Through the above analysis, the problems and defects existing in the prior art are as follows:
(1) The existing numerical method can ensure accuracy, but has low calculation efficiency, and for a foil cloud consisting of a plurality of millions of foils, a great deal of time and computer memory resources are consumed for calculating the electromagnetic scattering characteristics of the current numerical method.
(2) The existing Monte Carlo method can simulate the scattering characteristics of large-scale foil cloud to radar waves more efficiently, but because the method is based on a statistical principle, the calculation accuracy cannot be guaranteed.
The difficulty of solving the problems and the defects is as follows: in order to solve the technical problems, the following technical difficulties are mainly presented: how to improve the speed of calculating the electromagnetic scattering characteristics of the foil cloud while ensuring the accuracy of calculating the electromagnetic scattering of the foil cloud by a numerical method.
The meaning of solving the problems and the defects is as follows: on the premise of ensuring the precision, the rapid calculation of the radar cross section of the foil cloud cluster is realized, and the calculation efficiency and universality are solved as quickly as possible; the application range of the numerical method, namely the accurate algorithm, in actual engineering is enlarged, and the development period of electromagnetic related equipment in the national defense technology field and the civil and civil field of China is shortened.
Disclosure of Invention
Aiming at the problems existing in the prior art, the invention provides a rapid calculation method of foil cloud scattering.
The invention discloses a foil cloud scattering rapid calculation method based on impedance matrix partitioning, which comprises the following steps:
calculating RCS of single and multiple foil strips by combining specific steps of calculating RCS of foil strip cloud by a line moment method, comparing with a calculation result of the moment method by using RWG basis functions, and verifying correctness of the line moment method;
comparing the split units of the RWG basis function moment method and the line moment method to prove the applicability and superiority of the line moment method in calculating foil strips;
For the geometrically discontinuous electromagnetic target of the foil cloud, dividing the foil cloud into a plurality of sub-areas according to actual conditions, wherein the sub-areas are geometrically disconnected, the problem of continuity of current does not exist between the areas, and the current matrix of each sub-area is calculated in parallel in a blocking manner to obtain the current matrix of the whole area;
error compensation, dividing the target into n sub-regions according to the original problem geometry. Each sub-region extends to a part of the adjacent sub-region to form an overlapping region, so that the obtained electromagnetic flow is more approximate to the actual electromagnetic flow.
Further, the moment method of the foil cloud scattering rapid calculation method based on impedance matrix segmentation calculates the scattering characteristics of foil by solving a delay integral formula, namely firstly dividing grids of a scattering body, and converting the integral formula into a matrix formula [ V ] = [ Z ] [ I ] by using a discrete integral formula to obtain the current of the surface of the scattering body, wherein [ Z ] is an impedance matrix, [ I ] is a current matrix and [ V ] is a voltage matrix;
at a known applied field E i Under the influence of (a) the charge density sigma and the current density on the conductor S
The equation of (2) can be obtained by the following method. Sigma and +.>
Generated scattered field E s And using the boundary conditions on S, the formula is generalized as follows:
wherein ,
is the magnetic vector position, RIs the distance between the field point and the source. For thin wires, the following approximation is made: assuming that the current flows only in the wire shaft direction; the current and charge density can be approximated as line current +.>
Sigma on the wire spool; the boundary conditions are used only on the axial component of the wire surface electric field;
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 shaft to a field point on the surface of the wire;
for the equation, we use dividing the wire into N segments, approximating the integral to sum, I and q are constants on each segment, and approximating the derivative with finite difference using finite difference method, we further develop the above equation as:
also, similarly there are
and
Defining a matrix:
[V]＝[Z][I]；
for [ Z ]]Solving can be to
Substitution into
Simplifying the arrangement to obtain Z]Another method is to directly find [ Z ] by using two isolated elements]；
bonding of
The formula can be obtained:
wherein ：
obtaining a [ Z ] matrix;
obtain [ I ]]＝[Y][V]Wherein [ Y ]]The matrix is composed of Z]Inverting the matrix to obtain the current on each segment of the foil strip, and treating the current as N current elements 
The far-zone magnetic sagittal position is:
after obtaining the far-field magnetic sagittal position, the relation between the far-field electric field and the magnetic sagittal position is used for:
obtaining the far-field electric field and considering the polarization form of the receiver
Radar cross-section can be obtained:
further, the rapid calculation method of foil strip cloud scattering based on impedance matrix partitioning is characterized in that foil strips are split by utilizing a pulse basis function through comparison of a moment method of RWG basis function and a calculation result of a line moment method.
Further, when the impedance matrix block-based foil cloud scattering rapid calculation method solves a matrix equation [ Z ] [ I ] = [ V ] on complex electricity of foil cloud by using a line moment method, considerable storage and longer calculation time are required to be consumed, the geometrically discontinuous electromagnetic target of the foil cloud is divided into a plurality of sub-areas according to actual conditions, the sub-areas are geometrically disconnected, and the problem of continuity of current does not exist between the areas, the current matrix of each sub-area is calculated in parallel in blocks, and the current matrix of the whole area is calculated.
Further, for foil strip such metallic thin wire structures, a cloud of foil strips of volume V is divided into a number of spherical subregions of diameter 4λ until all foil strips are covered; and respectively calculating the currents on all foil strips in the spherical subareas in parallel to obtain the current distribution on the overall foil strip cloud, obtain the electromagnetic scattering characteristics of the foil strip cloud, and realize the acceleration of solving.
Further, according to the error compensation of the foil cloud scattering rapid calculation method based on the impedance matrix partitioning, the target is divided into n sub-areas according to the original geometric structure of the problem, and each sub-area extends to a part of the adjacent sub-area to form an overlapping area, so that the obtained electromagnetic flow is more approximate to the actual electromagnetic flow.
Further, selecting the midpoint of the central connecting line of every two subregions, continuously dividing a plurality of subregions by taking the midpoint as the sphere center, wherein the newly formed subregions are partially overlapped with the original subregions, and the selection of the subregion sizes has a considerable influence on the calculation amount and the convergence; the larger the overlap between regions, the more computation for each region increases, the better the convergence of the overall problem iteration solution, and the correspondingly fewer the number of iterations needed, and vice versa.
Another object of the present invention is to provide a foil cloud scattering computing system for implementing the impedance matrix blocking-based foil cloud scattering rapid computing method, the foil cloud scattering computing system comprising:
the first result comparison module is used for calculating the RCS of the single foil strip and the multiple foil strips by combining the specific steps of calculating the RCS of the foil strip cloud by a line moment method, comparing the RCS with the calculation result of the moment method by using the RWG basis function, and verifying the correctness of the line moment method;
The second result comparison module is used for comparing the number of the subdivision surface elements through a moment method of the RWG basis function and a line moment method;
the current matrix acquisition module is used for dividing the foil cloud which is a geometrically discontinuous electromagnetic target into a plurality of subareas according to actual conditions, wherein the subareas are geometrically disconnected, so that the problem of current continuity does not exist between the subareas, the current matrix of each subarea is calculated in parallel in a blocking manner, and the current matrix of the whole area is obtained;
and the error compensation module is used for dividing the target into n sub-areas according to the original geometric structure of the problem. Each sub-region extends to a part of the adjacent sub-region to form an overlapping region, so that the obtained electromagnetic flow is more approximate to the actual electromagnetic flow.
The invention further aims to provide a general foil cloud radar cross section calculation system which is used for realizing the foil cloud scattering rapid calculation method based on the impedance matrix partitioning.
By combining all the technical schemes, the invention has the advantages and positive effects that: the method provided by the invention is used for calculating the RCS of the foil cloud by combining the specific steps of calculating the RCS of the foil cloud by using the line moment method, calculating the RCS of single and multiple foil strips, and comparing with the calculation result of the moment method by using the RWG basis function, and verifying the correctness of the line moment method. According to the invention, the calculated results of the RWG basis function moment method and the line moment method are compared, so that the number of split units of the foil strip by the line moment method is greatly reduced while the accuracy is ensured. The impulse basis function is utilized to divide the foil strips, the number of unknown quantities can be reduced to a great extent while the calculation accuracy is ensured, the scale of the equation is reduced, and therefore the calculation speed of the cloud scattering characteristics of the foil strips is improved, and the calculation result is obtained more quickly. For the complex electric problem of the foil cloud, when a matrix equation [ Z ] [ I ] = [ V ] is solved by using a line moment method, the method needs to consume considerable storage and longer calculation time. For the geometrically discontinuous electromagnetic target of the foil cloud, the foil cloud is divided into a plurality of sub-areas according to actual conditions, as the sub-areas are geometrically disconnected with each other, the problem of continuity of current does not exist between the areas, and the current matrix of each sub-area is calculated in parallel in a blocking manner, so that the current matrix of the whole area is obtained; for foil strips, which are thin metal wire structures, the coupling effect becomes weaker as the spacing between the foil strips increases, which is negligible already at a spacing of 3-4 λ (λ being the incident wavelength), so that the coupling effect between the foil strips can be ignored when the spacing between the foil strips is larger (greater than 4 λ). Therefore, a cloud of foil strips of volume V can be divided into several spherical subregions of diameter 4λ until all foil strips are covered. Thus, the currents on the foil strips in the spherical subareas can be calculated in parallel respectively, and further the current distribution on the overall foil strip cloud can be obtained, so that the electromagnetic scattering characteristics of the foil strip cloud can be obtained, and further acceleration of solving is realized.
The invention performs error compensation. The result obtained by carrying out the integral solution on the problem by the partition parallel calculation solution and directly adopting a line 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-region extends to a part of the adjacent sub-region to form an overlapping region, so that the obtained electromagnetic flow is more approximate to the actual electromagnetic flow.
The method selects the midpoint of the central connecting line of every two subregions, continuously divides a plurality of subregions by taking the midpoint as the sphere center, and the newly formed subregions are partially overlapped with the original subregions, so that the selection of the subregion size has a considerable influence on the calculation amount and the convergence. The larger the overlap between regions, the more computation increases for each region, but the better the convergence of the overall problem iteration solution, and the correspondingly fewer the number of iterations needed, and vice versa. Therefore, the influence of the two is comprehensively considered in the actual solving process, and the optimal size of the overlapping area is selected.
The invention adopts the concept of 'divide and conquer', and greatly improves the analysis capability of the moment method on the electric large-size targets. And decomposing the object to be solved into a plurality of small sub-problems, wherein each sub-region extends a part of buffer area to the adjacent region to form a new iteration region, and solving each sub-region by adopting a line 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, computer resources are ensured to meet the maximum subarea. The overlapping area decomposition utilizes the buffer area to enable the current obtained by solving to approach to the real current distribution, so that the algorithm thought 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 following description will briefly explain the drawings needed in the embodiments of the present application, and it is obvious that the drawings described below are only some embodiments of the present application, and that other drawings can be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a flowchart of a foil cloud scattering rapid 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 strip cloud scattering computing system provided by 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 an algorithm provided by an embodiment of the present 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 discrete schematic diagram of an electronic marker provided by an embodiment of the present invention.
Fig. 7 is a schematic illustration of a split of a foil strip provided by an embodiment of the present invention.
Fig. 8 is a block diagram of foil cloud partition provided by an embodiment of the present invention.
Fig. 9 is a schematic diagram of inter-subarea coupling region definition according to an embodiment of the present invention.
Fig. 10 is a schematic diagram of a foil strip cloud partition numbering rule according to an embodiment of the present invention.
Fig. 11 is a schematic diagram of impedance matrix element supplementation provided in an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the following examples in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
Aiming at the problems in the prior art, the invention provides a foil strip cloud scattering rapid 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 cloud scattering rapid calculation method based on impedance matrix blocking provided by the invention comprises the following steps:
s101: the specific steps of calculating the RCS of the foil cloud by combining the line moment method are used for calculating the RCS of the single foil and the multiple foil strips, and comparing the RCS with the calculation result of the moment method by using the RWG basis function to verify the correctness of the line moment method.
S102: and compared with the calculation result of the line moment method by the moment method of the RWG basis function, the number of split units of the foil strip by the line moment method is greatly reduced while the accuracy is ensured.
S103: for the geometrically discontinuous electromagnetic target of the foil cloud, the foil cloud is divided into a plurality of sub-areas according to actual conditions, as the sub-areas are geometrically disconnected with each other, the problem of continuity of current does not exist between the areas, the current matrix of each sub-area is calculated in parallel in a blocking manner, and then the current matrix of the whole area is obtained.
S104: error compensation, dividing the target into n sub-regions according to the original problem geometry. Each sub-region extends to a part of the adjacent sub-region to form an overlapping region, so that the obtained electromagnetic flow is more approximate to the actual electromagnetic flow.
The method for rapidly calculating the foil cloud scattering based on the impedance matrix block provided by the invention can be implemented by other steps by one of ordinary skill in the art, and the method for rapidly calculating the foil cloud scattering based on the impedance matrix block provided by the invention of fig. 1 is only one specific embodiment.
As shown in fig. 2, the foil cloud scattering computing system provided by the present invention includes:
the first result comparison module 1 is used for calculating the RCS of the single foil strip and the multiple foil strips by combining the specific steps of calculating the RCS of the foil strip cloud by a line moment method, comparing the RCS with the calculation result of the moment method by using RWG (random wave generator) basis functions, and verifying the correctness of the line moment method;
The second result comparison module 2 is used for comparing the calculated result of the moment method of the RWG basis function with the calculated result of the line moment method;
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-areas according to actual conditions, wherein the sub-areas are geometrically disconnected, so that the problem of current continuity does not exist between the areas, the current matrix of each sub-area is calculated in parallel in a blocking manner, and the current matrix of the whole area is obtained;
the error compensation module 4 is configured to divide the target into n sub-regions according to the geometry of the original problem. Each sub-region extends to a part of the adjacent sub-region to form an overlapping region, so that the obtained electromagnetic flow is more approximate to the actual electromagnetic flow.
The technical scheme of the invention is further described below with reference to the accompanying drawings.
The foil cloud scattering rapid calculation method based on impedance matrix partitioning uses a line moment method theory to perform preliminary calculation on the radar scattering cross section of the foil cloud cluster; comparing the calculation result with the calculation result of the moment method of the RWG basis function, and when the result is accurate, greatly reducing the number of split units of the foil strip by the line moment method, primarily improving the calculation speed of the cloud scattering characteristics of the foil strip and obtaining the calculation result more quickly; for the geometrically discontinuous electromagnetic target of the foil cloud, dividing the geometrically discontinuous electromagnetic target into a plurality of sub-areas according to actual conditions, and calculating the current matrix of each sub-area in parallel in a blocking manner so as to further calculate the current matrix of the whole area, thereby obtaining the electromagnetic scattering characteristic of the foil cloud and realizing further acceleration of solving; and performing error compensation, further considering the coupling effect of partial foil strips between every two adjacent spherical areas, so that the obtained electromagnetic flow is more approximate to the actual electromagnetic flow, and balancing the calculated amount and the convergence of the result.
The method aims to solve the problem of acceleration calculation of the problem of electromagnetic scattering (radar cross section) of foil cloud clusters. Preliminarily calculating the radar cross section of the foil cloud cluster by using a line moment method theory; then, comparing the calculation result with the calculation result of the moment method of the RWG basis function, and obtaining the calculation result faster by primarily improving the calculation speed of the cloud scattering characteristics of the foil strips due to the fact that the number of split units of the foil strips is greatly reduced by the line moment method while the result is accurate; then dividing the geometrically discontinuous electromagnetic target of the foil cloud into a plurality of sub-areas according to actual conditions, and calculating the current matrix of each sub-area in parallel in blocks so as to calculate the current matrix of the whole area, thereby obtaining the electromagnetic scattering characteristic of the foil cloud and realizing further acceleration of solving; 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 more approximate to the actual electromagnetic flow, and the calculated amount and the convergence of the result are balanced.
The foil cloud scattering rapid calculation method based on the impedance matrix blocking method comprises the following steps:
the first step, the specific step of calculating the RCS of the foil strip cloud by combining the line moment method is to calculate the RCS of single and multiple foil strips, and the accuracy of the line moment method is verified by comparing the RCS with the calculation result of the moment method by using the RWG basis function.
Line moment method basic theory:
(1) Moment method basic principle
It is assumed that the field to be solved problem can be described by the following operator equations:
L(f)＝g(1)
where L represents one of a differential or an integral linear operator. g represents a known function source and f represents a response function. The response function f is linearly spread out in the domain of L with N functions as:
in the formula an Representing unknown scalar coefficients to be solved for, f n Called the basis function. The sum of infinite terms is performed in the above equation, but only finite terms can be summed in the actual solving process. Substituting the above formula into the formula, the linear characteristic of the application operator L can be obtained:
then selecting a proper function { w ] in the value range of L 1 ,w 2 ,…w m As a test function, and taking the inner product for both sides of the above, we get:
where m=1, 2,3 … N, this linear system of equations can be written as a matrix of:
[l mn ][a n ]＝[g m ](5)
in the formula ：
let us assume an impedance matrix l mn ]Is non-singular, [ a ] n ]The following equation can be used to determine:
[a n ]＝[l mn ] -1 [g m ](9)
will solve for a n Substituting the formula to obtain f.
In summary, the core factor affecting the accuracy of the moment method calculation is the basis function f n Sum weight function w n If f and g are defined in the same space, f can be taken n ＝w n Commonly referred to as the gamma method.
wherein fn and wn Must be linearly independent. Influence f n and wn The selected factors are as follows:
(1) calculating the difficulty level of matrix elements;
(2) calculation accuracy to be solved:
(3) good state matrix [ l ] mn ] -1 Availability of (3);
(4) the rate of matrix convergence.
(2) The method is applied to a line moment method of foil strips, and the moment method is used for calculating the scattering characteristics of the foil strips by solving a delay bit integral formula, namely firstly dividing grids of a scattering body, and then converting the integral formula into a matrix formula [ V ] = [ Z ] [ I ] by using a discrete integral formula, so that the current on the surface of the scattering body is obtained. Other useful parameters, such as field pattern, input impedance, RCS, etc., can be calculated by corresponding formulas as long as the current distribution is known.
Suppose that field E is applied to a known i Under the influence of (a) the charge density sigma and the current density on the conductor S
The equation of (2) can be obtained by the following method. Sigma and +.>
Generated scattered field E s And uses the boundary on SThe conditions, the formulas are summarized as follows:
for thin wires, the following approximation is made: 1. it is assumed that the current flows only in the wire shaft direction. 2. The current and charge density can be approximated as the line current
And sigma on the wire axis. 3. The boundary conditions are only used on the axial component of the wire surface electric field.
Thus, the above formula becomes:
where l is the variable along the wire axis and R is the distance from the source point on the wire axis to the field point on the wire surface.
For the equation above, the integration may be approximated as a summation by dividing the wire into N segments. 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 there are
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
N of the expression representationThe equation is a pair with terminals +.>
The voltage applied to each port is approximately E i ·Δl n . Thus, a matrix is defined:
[V]＝[Z][I] (24)
for [ Z ] solving, it can be obtained by substituting and simplifying the arrangement, and the other method is to directly obtain [ Z ] by using two isolated elements.
Has the same form, expressed as:
the bonding to formula is obtainable:
wherein ：
therefore, the [ Z ] matrix can be obtained.
Then [ I ] can be obtained]＝[Y][V]Wherein [ Y ]]The matrix is composed of Z]Inversion of the matrix, thisA process corresponds to taking the pulse function as a basis function of both current and charge, with point matching as a weight function. After the current is obtained on each segment of the foil strip, it can be considered as N current elements 
The far-zone magnetic sagittal position is:
after obtaining the far-field magnetic sagittal position, the relation between the far-field electric field and the magnetic sagittal position is used for:
thereby obtaining the far-field electric field, and considering the polarization form of the receiver
Radar cross-section can be obtained:
and secondly, comparing a moment method of the RWG basis function with a calculation result of a line moment method, and greatly reducing the number of split units of the foil strip by the line moment method while ensuring the accuracy. The impulse basis function is utilized to divide the foil strips, the number of unknown quantities can be reduced to a great extent while the calculation accuracy is ensured, the scale of the equation is reduced, and therefore the calculation speed of the cloud scattering characteristics of the foil strips is improved, and the calculation result is obtained more quickly.
Third, for the complex electrical problem of the foil cloud, when solving the matrix equation [ Z ] [ I ] = [ V ] by using the line moment method, considerable storage and long calculation time will be required. For the geometrically discontinuous electromagnetic target of the foil cloud, the foil cloud is divided into a plurality of sub-areas according to actual conditions, as the sub-areas are geometrically disconnected with each other, the problem of continuity of current does not exist between the areas, the current matrix of each sub-area is calculated in parallel in a blocking manner, and then the current matrix of the whole area is obtained.
Specifically, with the thin metal wire structure of the foil strips, as the spacing of the foil strips increases, the coupling effect becomes weaker, which is negligible already when the spacing is 3-4 λ (λ is the incident wavelength), so that when the spacing between the foil strips is larger (greater than 4 λ), the coupling effect between the foil strips can be ignored. Therefore, a cloud of foil strips of volume V can be divided into several spherical subregions of diameter 4λ until all foil strips are covered. Thus, the currents on the foil strips in the spherical subareas can be calculated in parallel respectively, and further the current distribution on the overall foil strip cloud can be obtained, so that the electromagnetic scattering characteristics of the foil strip cloud can be obtained, and further acceleration of solving is realized.
And fourthly, performing error compensation on the previous step. The result obtained by carrying out the integral solution on the problem by the partition parallel calculation solution and directly adopting a line 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-region extends to a part of the adjacent sub-region to form an overlapping region, so that the obtained electromagnetic flow is more approximate to the actual electromagnetic flow.
Specifically, the midpoint of the central connecting line of every two sub-areas is selected, a plurality of sub-areas are continuously divided by taking the midpoint as the sphere center, the newly formed sub-areas are partially overlapped with the original sub-areas, and the selection of the sizes of the sub-areas has a considerable influence on the calculation amount and the convergence. The larger the overlap between regions, the more computation increases for each region, but the better the convergence of the overall problem iteration solution, and the correspondingly fewer the number of iterations needed, and vice versa. Therefore, the influence of the two is comprehensively considered in the actual solving process, and the optimal size of the overlapping area is selected.
The basic block diagram of the algorithm of the present invention is shown in fig. 3.
(1) Firstly, uniformly distributed foil cloud is established in a cube range with a volume of V, the spatial distribution and orientation information of the foil cloud are read, and the reading format of data is as shown in table 1:
wherein the serial number is the serial number of each foil strip, the (x, y, z) is the coordinate of the central point of the foil strip, the unit is meter,
is the orientation of the foil strip in radians.
Table 1 foil cloud data storage format table
Next, each foil strip is segmented (10 segments are taken as an example), and all foil strip segmentation information numbers are stored in a table, wherein the table comprises an upper endpoint coordinate, a lower endpoint coordinate and a center coordinate of each small segment and a corresponding foil strip serial number, as shown in table 2.
Table 2 table of data storage formats for upper and lower endpoints and center points of foil cloud segments
(2) Substituting data into a line moment theory for calculation according to the spatial distribution and orientation information of the foil cloud: the construction of an integral equation, the discrete and optional processes of the integral equation, the calculation of matrix elements and the calculation of a radiation far field are respectively carried out, and the specific steps are as follows:
(1) construction of integral equation
For a thin metal wire of radius a and axial length l in the uniform media space, as shown in fig. 4; the electromagnetic field generated by the electromagnetic field satisfies the following conditions:
wherein ：
wherein ,
and
The field points ∈ ->
An electric field, a magnetic vector position and an electric target position; if the radius and length of the thin wire satisfy a < lambda, a < l, it can be considered that: 1. the wire has only axial current, and the current in the circumferential direction on the surface of the wire and the current on the two end surfaces of the wire can be ignored; 2. the current being only in the axial direction->
Flow, can use line current +.>
Instead of the bulk current density, the charge bulk density ρ may be replaced by the charge linear density σ;3. the current distribution is only dependent on the length of the wire and not on the radius.
From the assumption, the expression for magnetic and electrical signposts can be approximated as:
wherein ：
for the field point of the wire surface, according to the boundary conditions:
The method comprises the following steps:
(2) integral equation dispersion
The line moment method uses a pulse basis function to discretize the integral equation. The thin metal wire is divided into N segments as shown in FIG. 5, and the length of the nth small segment is denoted as Deltal n ，
Represents the distance between n and n+1, < >>
Representing the distance between n and n-1.
The unknown current density on the metal filament can be expressed as:
wherein ,
is the pulse basis function, I (n) is the expansion coefficient;
The expression is:
in the formula ,
the axial unit vector of the wire on the nth section is expressed, and the direction points to the end point from the starting point of the wire. Magnetic vector position
The discrete to N partitions with the pulse basis function is:
because the basis function is a pulse basis function, the conducting wire has the charge density sigma at the junction of the line segment, 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 marker
Can be calculated from the charge density sigma (n + ) (n=0, 1,2,) N, due to
And I (0) =i (n+1) =0, the electrical index is discretized into n+1 partitions:
wherein
(3) Selection process
The weight function of the selection is
According to the formula, there are:
in the formula ：
wherein ：
substituting the formula and formula into the formula:
the above 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:
(4) Calculation of matrix elements, for the line moment method, the key to calculate the impedance matrix elements is to calculate the electric sign bit generated at the m point by the unit charge on the n-th segment:
in calculating electrical benchmarks
When the integration interval is selected to be Deltal n + Or Deltal n - Corresponding to the two halves of the wire. Thus the electric sign bit can be replaced by the sum of the integrals on the two halves>
in the formula ,
represents n - Integration result onto n half-segment, +.>
Represents n to n + Integration results over the half-segments. For the following
The calculation of (2) can be divided into a far zone and a near zone, but the calculation amount is increased, and the method is not suitable for a scene with a particularly large number of subdivision units. A first partThe general calculation method is as follows:
assuming that the split units are sufficiently large and each unit is sufficiently small in length, then
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,
(5) calculation of the far field of radiation
The radiation field expression of the current element in the maximum radiation direction is as follows:
according to the reciprocity definition:
an expression for the radiation field can be derived:
simplifying and obtaining:
so there are:
and according to the far zone approximation, there are all the amplitudes and phases
wherein
Is the vector from the origin of coordinates to the center of the nth segment of the wire, and substitutes +. >
The method can obtain:
the field generated by the antenna in the far zone can be seen as a spherical wave, i.e. with a transverse electric field E θ and Eφ Does not contain radial electric field E r If extract
and
Then can obtain E respectively θ and Eφ The total field expression can be written as:
(3) And comparing the result obtained in the steps with the calculation result of the moment method and the line moment method of the RWG basis function, and greatly reducing the number of split units of the line moment method on the foil strip while ensuring the precision. The impulse basis function is utilized to divide the foil strips, the number of unknown quantities can be reduced to a great extent while the calculation accuracy is ensured, the scale of the equation is reduced, and therefore the calculation speed of the cloud scattering characteristics of the foil strips is improved, and the calculation result is 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 induction current on the common edges of the triangles is calculated, and finally, a calculation result is obtained according to the expression of the far-field RCS. The RWG basis function is a modified pulse basis function, which is defined on two adjacent triangular surface elements, and is a surface element pair, and the definition formula is:
when the RWG basis function is used for calculating the scattering characteristics of the three-dimensional target, the three-dimensional target is required to be split by using a small triangle, then the current distribution of each surface element is calculated, and finally the scattering field information is obtained. However, for thin line models such as foil strips, a large number of subdivision blocks are required to ensure a good fit to the geometric model when using triangular surface elements for subdivision, and therefore the RWG basis functions are not suitable for calculating the scattering properties of the foil strips.
Because the induction current of the foil strip is distributed along the length direction due to the special model of the foil strip slender metal wire, the pulse basis function which is difficult to solve the three-dimensional target is generally suitable for the foil strip, and the current on the foil strip can be better split by using the pulse basis function, and the current distribution on the foil strip can be accurately described only by splitting the foil strip into a plurality of sections along the length direction.
FIG. 7 shows the distinction between splitting foil strips with RWG basis functions and pulse basis functions, for a foil strip applied at 3GHz radar frequency, 0.05m long and 0.001m in diameter, a large number of splitting units are required to fit the fine line structure of the foil strip when the RWG basis functions are used, and the foil strip is split into 468 small triangles, so that calculation can be well completed; however, for the subdivision of the pulse basis function, the current distribution of the foil strip can be described by only about 20 subdivision units. Therefore, the impulse basis function is utilized to split the foil strips, the number of unknown quantities can be reduced to a great extent while the calculation accuracy is ensured, the scale of the equation is reduced, the calculation speed of the foil strip cloud scattering characteristics is improved, and the calculation result is obtained more quickly.
(4) For foil strips, which are thin metal wire structures, the coupling effect becomes weaker as the spacing between the foil strips increases, which is negligible already at a spacing of 3-4 λ (λ being the incident wavelength), so that the coupling effect between the foil strips can be ignored when the spacing between the foil strips is larger (greater than 4 λ). Therefore, as shown in FIG. 8, a square foil cloud with a volume V can be divided into a plurality of square subregions with a side length of 4λ until all foil strips are covered, the partitioned foil cloud data are stored in the form of Table 3 and then substituted into an impedance element calculation formula, wherein the form of an impedance matrix equation is shown as the formula, and Z is as follows 11 ,Z 22 ,…,Z nn Is the impedance element in each partition. In this way, the currents on the foil strips in these cube sub-areas 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 characteristic of the foil cloud can be obtained, and further acceleration of solving is realized.
Table 3 foil cloud data partition mark storage format table
| Foil serial number | x | y | | Area code | |
| 1 | |||||
| 2 | |||||
| …… | …… | …… | …… | …… |
[Z 11 ][I 1 ]＝[V 1 ],[Z 22 ][I 2 ]＝[V 2 ],…,[Z nn ][I n ]＝[V n ] (71)
(5) The error compensation is performed. The result obtained by carrying out the integral solution on the problem by the partition parallel calculation solution and directly adopting a line 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-region and the adjacent sub-regions form a coupling region, so that the obtained electromagnetic flow is more approximate to the actual electromagnetic flow.
Specifically, the midpoint of the central connecting line of every two sub-areas is selected, a plurality of sub-areas are continuously divided by taking the midpoint as the center, the newly formed sub-areas can be partially overlapped with the original sub-areas, and the selection of the sizes of the sub-areas has a considerable influence on the calculation amount and the convergence. The larger the overlap between regions, the more computation increases for each region, but the better the convergence of the overall problem iteration solution, and the correspondingly fewer the number of iterations needed, and vice versa. Therefore, the influence of the two is comprehensively considered in the actual solving process, and the optimal size of the overlapping area is selected. The spherical region with the diameter of 4λ is now selected as the mutual coupling region of two adjacent cube subregions, as shown in fig. 9, which is the case of the regions in one cross-sectional view, and there is a coupling region between the regions (1) and (2), the regions (1) and (3), the regions (2) and (4), and the regions (3) and (4). After the coupling area is divided, renumbering each sub-area divided in the previous step, wherein the numbering rule is as follows: the sub-area where a certain vertex of the cube is located is taken as a number (1) area, the vertex is taken as a sphere center, and the radius is gradually increased to form each concentric sphere to be intersected with each sub-area, as shown in fig. 10. Numbering the subsequent subareas according to the sequence of the intersection, numbering the subareas according to rules of up-down, left-right, front-back and front-back if a sphere is intersected with a plurality of subareas at the same time, and then storing the foil cloud data partition marks in the table 3 again.
The center of the sphere of the coupling area is taken as the center, foil strips and corresponding foil strip serial numbers in the coupling area are screened out, and the total impedance matrix is newly supplemented, wherein the effect after supplementation is shown in fig. 11, and the dotted line part is the filling of new matrix elements which is performed by taking the coupling between the (1) area and the (2) area, the (1) area and the (3) area, the (2) area and the (4) area into consideration. And solving the supplemented matrix equation, wherein the solved electromagnetic flow is more approximate to the real electromagnetic flow.
The technical effects of the present invention will be described in detail with reference to simulation examples.
1. Simulation conditions: the simulation uses different numbers of foil clouds uniformly distributed in the cube, and parameters are shown in table 4, wherein the parameters comprise the volume size of the cube, the frequency of incident plane waves, the incidence angle, the number of foil clouds and the like.
Table 4 simulation Condition list
2. Comparison of simulation results
The single-station RCS calculation results before and after acceleration by the line moment method are compared, as shown in table 5:
table 5 comparison of calculated results
According to the comparison of the results, the error of the calculated result before and after acceleration is within 10%, and the solving time is obviously shortened, so that the calculation efficiency of the simple type general mass foil cloud is obviously improved.
The foregoing is merely illustrative of specific embodiments of the present invention, and the scope of the invention is not limited thereto, but any modifications, equivalents, improvements and alternatives falling within the spirit and principles of the present invention will be apparent to those skilled in the art within the scope of the present invention.
Claims (7)
1. The foil cloud scattering rapid calculation method based on the impedance matrix blocks is characterized by comprising the following steps of:
calculating RCS of single and multiple foil strips by combining specific steps of calculating RCS of foil strip cloud by a line moment method theory, comparing with calculation results of a moment method by RWG basis functions, and verifying correctness of the line moment method;
comparing the split quantity of the foil strips by a moment method of the RWG basis function with a line moment method, and verifying the improvement of the calculation efficiency of the line moment method;
for the geometrically discontinuous electromagnetic target of the foil cloud, dividing the foil cloud into a plurality of sub-areas according to actual conditions, wherein the sub-areas are geometrically disconnected, the problem of continuity of current does not exist between the areas, and the current matrix of each sub-area is calculated in parallel in a blocking manner to obtain the current matrix of the whole area;
Error compensation, dividing a target into n sub-areas, wherein each sub-area extends to a part of adjacent sub-areas to form an overlapping area, so that the obtained electromagnetic flow is more approximate to the actual electromagnetic flow;
calculating the scattering characteristics of foil strips by a moment method based on the impedance matrix block foil strip cloud scattering rapid calculation method, namely firstly dividing grids of a scattering body by a delay bit integral formula, and converting the integral formula into a matrix formula [ V ] = [ Z ] [ I ] by a discrete integral formula to obtain the current of the surface of the scattering body, wherein [ Z ] is an impedance matrix, [ I ] is a current matrix, [ V ] is a voltage matrix;
at a known applied field E i Under the influence of (a) the charge density sigma and the current density on the conductor S
The equation of (2) can be obtained by expressing sigma and ++by the integration of the delay bits>
Generated scattered field E s And using the boundary conditions on S, the formula is generalized as follows:
wherein ,
is the magnetic vector position, R is the distance between the field point and the source, and for thin wires, the following approximation is made: assuming that the current flows only in the wire shaft direction; the current and charge density can be approximated as line current +.>
Sigma on the wire spool; the boundary conditions are used only on the axial component of the wire surface electric field;
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 shaft to a field point on the surface of the wire;
for the equation, we use dividing the wire into N segments, approximating the integral to sum, I and q are constants on each segment, and approximating the derivative with finite difference using finite difference method, we further develop the above equation as:
also, there are
and
Defining a matrix:
[V]＝[Z][I]；
for [ Z ]]Solving can be to
Substituted into->
Simplifying the arrangement to obtain Z]Another method is to directly find [ Z ] by using two isolated elements]；
bonding of
To->
The formula can be obtained:
wherein ：
obtaining a [ Z ] matrix;
obtain [ I ]]＝[Y][V]Wherein [ Y ]]The matrix is composed of Z]Inverting the matrix to obtain the current on each segment of the foil strip, and treating the current as N current elements
The far-zone magnetic sagittal position is:
after obtaining the far-field magnetic sagittal position, the relation between the far-field electric field and the magnetic sagittal position is used for:
obtaining the far-field electric field and considering the polarization form of the receiver
Radar cross-section can be obtained:
2. the impedance matrix block-based foil cloud scattering rapid calculation method of claim 1, wherein the impedance matrix block-based foil cloud scattering rapid calculation method uses a pulse basis function to split foil strips by comparing a moment method of RWG basis functions with a line moment method.
3. The quick calculation method of foil cloud scattering based on impedance matrix blocking according to claim 1, wherein when a matrix equation [ Z ] [ I ] = [ V ] is solved by a line moment method for complex electricity of foil cloud, the geometrically discontinuous electromagnetic target of the foil cloud is divided into a plurality of subareas according to actual conditions, and as the subareas are geometrically disconnected, no problem of current continuity exists between the subareas, the current matrix of each subarea is calculated in parallel in a blocking manner, and the current matrix of the whole area is obtained.
4. The method for rapidly calculating cloud scattering of foil strips based on impedance matrix partitioning according to claim 3, wherein for the foil strip of this fine metal wire structure, a cloud of foil strips with a volume V is divided into a number of spherical subregions with a diameter of 4λ until all foil strips are covered; and respectively calculating the currents on all foil strips in the spherical subareas in parallel to obtain the current distribution on the overall foil strip cloud, obtain the electromagnetic scattering characteristics of the foil strip cloud, and realize the acceleration of solving.
5. The rapid calculation method of foil cloud scattering based on impedance matrix partitioning according to claim 1, wherein the error compensation of the rapid calculation method of foil cloud scattering based on impedance matrix partitioning divides a target into n sub-areas according to the original geometric structure of the problem, and each sub-area extends to a part of adjacent sub-areas to form an overlapping area, so that the obtained electromagnetic flow is more approximate to the real electromagnetic flow.
6. The rapid calculation method of foil cloud scattering based on impedance matrix blocking according to claim 5, wherein a midpoint of a central line 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 subregion size has influence on calculation amount and convergence; the larger the overlap between regions, the more computation for each region increases, the better the convergence of the overall problem iteration solution, and the correspondingly fewer the number of iterations needed, and vice versa.
7. A substantial amount foil cloud cluster radar cross section calculation system, characterized in that the substantial amount foil cloud cluster radar cross section calculation system is used for realizing the foil cloud scattering rapid calculation method based on impedance matrix blocking according to any one of claims 1 to 6.
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