CN115510690A - Novel electromagnetic characteristic calculation method of electrically uncertain outline metal target based on AWE technology - Google Patents

Novel electromagnetic characteristic calculation method of electrically uncertain outline metal target based on AWE technology Download PDF

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CN115510690A
CN115510690A CN202211381204.5A CN202211381204A CN115510690A CN 115510690 A CN115510690 A CN 115510690A CN 202211381204 A CN202211381204 A CN 202211381204A CN 115510690 A CN115510690 A CN 115510690A
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何姿
赵敏
栾宇哲
丁大志
樊振宏
顾鹏飞
孙永志
李由
国少卿
孙胜
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Nanjing University of Science and Technology
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Abstract

The invention discloses a novel electromagnetic characteristic calculation method of an electrically large uncertain outline metal target based on an AWE (active surface energy) technology, which comprises the steps of firstly establishing a model according to FEKO (software engineering task) software and a NURBS (non-Uniform rational B-spline) technology, and defining all control point coordinates of the outline of the target as an outline vector; introducing a random variable to change the shape of the target; then introducing the shape vector into a mixed field integral equation, and developing an expression of a current moment vector by expanding an impedance matrix, a right vector and a current into a Taylor series form; applying a pseudo-spectrum method to AWE, respectively calculating a product of a matrix derivative and a moment vector and a derivative of a right vector, and further calculating a current moment vector; calculating the current after each model change through a simultaneous Taylor series and a Pasteur polynomial; and finally calculating the radar scattering sectional area by combining the current and the coordinate information after the model change. The method can greatly shorten the calculation time and quickly calculate the scattering characteristic of the electrically large metal target after deformation.

Description

Novel electromagnetic characteristic calculation method of uncertain electrical configuration metal target based on AWE technology
Technical Field
The invention belongs to the technical field of target electromagnetic scattering characteristic numerical value calculation, and particularly relates to a novel electromagnetic characteristic calculation method of an electrically uncertain outline metal target based on an AWE (active wavelet transform) technology.
Background
The electromagnetic scattering calculation principle of the metal target based on the mixed field integral equation is that the surface of the target is split into a plurality of triangles, wherein the splitting precision is set to be less than one tenth of the incident wavelength. The RWG basis functions are introduced to represent an upper triangle and a lower triangle, and the continuity of current between the two adjacent triangles is guaranteed. The method can calculate the metal target in any shape and has strong applicability. Compared with other high-frequency approximation methods, the numerical method based on the moment method has higher calculation precision. When the combination coefficient of the mixed field integral equation is set to be 1, the mixed field integral equation is converted into an electric field integral equation, and because the impedance matrix of the mixed field integral equation is a full-rank matrix, the calculation time is slow, but the calculation accuracy is high; when the combination coefficient is set to be 0, the magnetic field integral equation is converted, and the integral equation is a main diagonal dominant matrix, so that the calculation time is short, but the calculation accuracy is limited. Therefore, both the calculation accuracy and the calculation speed can be taken into consideration by reasonably setting the combination coefficient in the mixed field integral equation. In addition, the mixed field integral equation can also avoid the internal resonance problem. The non-cooperative metal model is one of important targets monitored by the current radar, and the calculation of the electromagnetic scattering property of the non-cooperative metal target with uncertain appearance information is the key point of the research of the invention based on a mixed field integral equation.
When the target shape contains uncertain factors, the electromagnetic scattering property of the calculation model can be repeatedly calculated by using a Monte Carlo (MC) method, and the calculation method is specifically characterized in that a group of random variables are introduced into the shape parameters, and the uncertain problems are converted into the confirmed problems for calculation. And further carrying out statistical analysis on the radar scattering cross section obtained by repeated calculation, and finally obtaining the mean value and the variance. The Monte Carlo method has high calculation result precision by calculating the scattering characteristics of the models one by one, but the calculation is time-consuming, and the calculation efficiency is seriously influenced. Aiming at the defects of the MC method, the traditional Perturbation method (Perturbation method) based on Taylor series expansion can improve the calculation efficiency by sacrificing partial precision. The method is characterized in that a matrix equation is expanded into a Taylor series, and the final current is expressed in the form of the sum of the initial solution of an original model and the change current. However, the convergence radius of the method is small, and derivation by adopting a formula is complex. When the number of control points that change increases, the time increases accordingly.
Disclosure of Invention
The invention aims to provide a novel electromagnetic characteristic calculation method of an electrically large uncertain outline metal target based on an AWE (active wavelet transform) technology.
The technical solution for realizing the purpose of the invention is as follows: in a first aspect, the invention provides a novel electromagnetic property calculation method of an electrically large uncertain outline metal target based on an AWE technology, which comprises the following steps:
step 1, realizing modeling of a non-cooperative metal target by utilizing FEKO software and NURBS modeling technology: establishing a model with controllable target appearance according to the NURBS technology; combining all the control point coordinates into a row vector, and defining the row vector as an appearance vector;
step 2, establishing a mixed field integral equation related to the shape vector: respectively expanding an impedance matrix, a right vector and current of the shape vector into Taylor series, and deducing an expression of a current moment vector; then determining the variation range of the introduced shape vector, constructing a D matrix in a pseudo-spectrum method, and calculating the vector multiplication of the derivative of each order matrix and the derivative of the right vector to further obtain the current moment vector of each order; establishing an equation of the Taylor series and the Pad polynomial, deducing the relation between a current moment vector and a vector coefficient of the Pad polynomial, and further calculating the vector coefficient; obtaining the current after the model changes once according to the vector coefficient and the random variation of the shape vector;
step 3, calculating to obtain the RCS after the model changes once according to the coordinate information and the corresponding current after the model changes; according to the set sampling times, calculating the RCS of the model after each change by using an AWE-based perturbation method; and carrying out statistical analysis on the RCS sampled for multiple times to obtain the electromagnetic scattering characteristic of the non-cooperative metal target with the uncertain shape.
In a second aspect, the present invention provides a computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements the steps of the method of the first aspect when executing the program.
In a third aspect, the invention provides a computer-readable storage medium, on which a computer program is stored, which program, when being executed by a processor, is adapted to carry out the steps of the method according to the first aspect.
In a fourth aspect, the invention provides a computer program product comprising a computer program, characterized in that the computer program, when executed by a processor, implements the steps of the method according to the first aspect.
Compared with the prior art, the invention has the advantages that: (1) Compared with the traditional method of directly carrying out formula derivation on the shape vector, the derivative of the right vector multiplied by the matrix vector is calculated by using a pseudo-spectrum method, so that the complex formula derivation is avoided, the thought is clear, and the program is simple and convenient to implement; (2) Compared with the traditional Taylor method, the improved AWE perturbation method utilizes the Pade approximation, and the convergence radius is wider; for the condition that a plurality of control points change simultaneously, the method has shorter calculation time and smaller memory. (3) Compared with the traditional Monte Carlo method, the method greatly shortens the calculation time.
Drawings
FIG. 1 shows the sum of θ angles in a three-dimensional coordinate system
Figure BDA0003928403090000021
Angle schematic.
Fig. 2 is a schematic size diagram of a metal cube model.
FIG. 3 is a schematic diagram of a metal cube model control point setting.
FIG. 4 is a comparison (mean) of RCS statistics when the uncertain outline metal cube model changes one point by one coordinate.
Fig. 5 is a statistical comparison graph (mean variance) of RCS when the uncertain outline metal cube model changes multiple points and multiple coordinates.
FIG. 6 is a schematic diagram showing the dimensions of a metallic electrically large rectangular parallelepiped model.
Fig. 7 is a schematic diagram of the control point setting of the metal electrical large-size rectangular parallelepiped model.
FIG. 8 is a comparison graph of RCS statistics (mean variance) when an electrically large cuboid of an indeterminate profile metal is changed by a plurality of points.
Detailed Description
The invention provides a novel electromagnetic characteristic calculation method of an electrically large uncertain outline metal target based on an AWE (active surface energy) technology. By introducing a random variable into the shape vector, the aim of changing the target shape is fulfilled. Unlike the application of the AWE technique to scalar domains such as frequency, angle, etc., the present invention generalizes the AWE technique to the vector domain, i.e., the shape vector. The shape vector is then introduced into a mixed Field Integral Equation (CFIE), and an expression for the current moment vector is derived by developing the impedance matrix, the right vector, and the current into the form of a taylor series. And applying a pseudo-spectrum method to the AWE, and respectively calculating the product of the matrix derivative and the moment vector and the derivative of the right vector so as to calculate the current moment vector. And calculating the current after each model change through a simultaneous Taylor series and a Pasteur polynomial. The convergence radius is also further enlarged compared to the conventional taylor method. And finally calculating the Radar scattering Cross Section (RCS) by combining the current and the coordinate information after the model change. After multiple sampling, the mean and variance of the RCS were statistically analyzed. Because the interpolation idea is adopted in the derivation process of the shape vector, the addition theorem is still satisfied. The AWE-based perturbation method can be combined with fast multipole (MLFMA) acceleration to calculate the scattering properties of the electrical large model. Compared with a Monte Carlo (MC) method, the method can greatly shorten the calculation time. By the method, the scattering characteristic of the deformed electrically large metal target can be calculated quickly and efficiently.
The present invention is described in further detail below with reference to the attached drawing figures.
A novel electromagnetic characteristic calculation method of an electrically large uncertain outline metal target based on an AWE technology comprises the following steps:
step 1, establishing a model with controllable target appearance according to NURBS technology. All control point coordinates are combined into a row vector, defined as an outline vector, denoted by α. Specifically, α can be unfolded as [ α [ ] 1 ,α 2 ,α 3 ,...,α n-2 ,α n-1 ,α n ]Here, n is the number of model control points multiplied by 3. Wherein alpha is 1 ,α 2 ,α 3 Representing x, y and z coordinates of the control point #1, wherein the control point #1 is a first coordinate point in the NURBS modeling file; an initial target model is established through FEKO software, and a random variable delta alpha is not introduced at the moment. And importing the model into rhinoceros software for reconstruction, wherein the reconstruction comprises two processes of resetting the coordinates of the control points and establishing a curved surface, and finally obtaining the coordinates of each control point and different control points which form the curved surface. Alpha (alpha) ("alpha") 0 Appearance vector, alpha, representing the original model s Representing any element in the outline vector, i.e. any coordinate of any point.
The target profile is flexibly changed by introducing a random variable delta alpha to the profile vector alpha. Specifically, Δ α is a range of variation, Δ α = [ Δ α = [ [ Δ α ] 1 ,Δα 2 ,Δα 3 ,...,Δα n-2 ,Δα n-1 ,Δα n ]. In the object model containing α + Δ α, according toAnd (3) setting subdivision sizes in the u and v directions for each surface of the wavelength of the radio-electromagnetic wave, and carrying out surface subdivision on the model by using the RWG basis function. Where the subdivision size is typically set to less than one tenth of the wavelength. This results in a subdivision model that can be calculated in the mixed field integral equation. And (3) dividing the target surface into a plurality of triangles by a NURBS technology, and establishing a mixed field integral equation based on the RWG basis function.
Step 2, establishing a mixed field integral equation related to the appearance vector alpha: and respectively expanding the impedance matrix, the right vector and the current of the outline vector into a Taylor series, and deriving an expression of a current moment vector. And then determining the variation range of the introduced shape vector, constructing a D matrix by using a pseudo-spectrum method, and calculating the derivative vector multiplication of each order of matrix and the derivative of the right vector so as to obtain each order of current moment vector. And establishing an equation of the Taylor series and the Pasteur polynomial, deriving the relation between the current moment vector and the vector coefficient of the Pasteur polynomial, and further calculating the vector coefficient. Unlike the monte carlo method, this process needs to be performed only once. And obtaining the current after the model changes once according to the vector coefficient and the random variable quantity of the shape vector. The method comprises the following specific steps:
firstly, establishing a matrix equation of a metal target CFIE containing a random variable alpha:
Z(α)·I(α)＝b(α) (23)
where Z (α) is the impedance matrix of the mixed-field integral equation, I (α) is the surface current, and b (α) is the right vector. The hybrid field integral equation can be expressed as a combination of an electric field integral equation and a magnetic field integral equation. Wherein the impedance matrix can be further represented as:
Z(α)＝α c ·Z EFIE (α)+(1-α c )·Z MFIE (α) (24)
α c the value of the combination coefficient is between 0 and 1; z is a linear or branched member EFIE (. Alpha.) and Z MFIE And (alpha) is an impedance matrix in an electric field integral equation and an impedance matrix in a magnetic field integral equation respectively.
The right vector in the mixed-field integral equation can be expressed as:
b(α)＝b EIFE (α)+b MFIE (α) (25)
wherein, b EIFE (α) is the right vector in the electric field integral equation, b MFIE And (α) is the right vector in the magnetic field integral equation.
Further, the mixed field matrix equation can be expressed as follows:
[α c ·Z EFIE (α)+(1-α c )·Z MFIE (α)]·I(α)＝b EIFE (α)+b MFIE (α)(26)
according to the progressive waveform estimation theory, the impedance matrix and the right vector of the mixed field integral equation are expanded into a form of Taylor series,
Figure BDA0003928403090000051
Figure BDA0003928403090000052
Figure BDA0003928403090000053
random variation introduced for the s-th element in the shape vector; k is the order of derivation of the appearance vector, and L and M are the highest orders of the numerator and denominator in the Pasteur polynomial, respectively.
Similarly, the current is expressed as the product of the current moment vector and the shape change:
Figure BDA0003928403090000054
by matching the variation of each order in the mixed field integral equation, the current moment vector is obtained as follows:
m 0 ＝Z -1 (α 0 )·b(α 0 ) (30)
Figure BDA0003928403090000055
equations for the Pade's approximation polynomial and Taylor series with respect to current are established as follows:
Figure BDA0003928403090000056
further, a i And b j The expression of (c) is as follows:
Figure BDA0003928403090000057
Figure BDA0003928403090000058
according to the Chebyshev-Gauss-Lobatto (GLC) interpolation method, in [ alpha ] 0 -Δα,α 0 +Δα]Within the range, N +1 interpolation nodes are determined, each node being represented as alpha j The expression is as follows:
Figure BDA0003928403090000059
and constructing a D matrix according to a pseudo-spectrum method, and calculating a first derivative expression of a right vector as follows:
Figure BDA0003928403090000061
wherein the dimensions of the D matrix are (N + 1) × (N + 1), b (α) j ) The dimension of the one-dimensional right vector is the number of model unknowns, namely N. [ b (α) j )]J = -N/2., N/2 is a two-dimensional matrix of (N + 1) × N. Wherein the D matrix may represent the following:
Figure BDA0003928403090000062
Figure BDA0003928403090000063
Figure BDA0003928403090000064
Figure BDA0003928403090000065
Figure BDA0003928403090000066
in particular, when the right vector first derivative is known, its second derivative can be calculated by:
[b (2) (α j )]＝D·[b (1) (α j )]＝D·D·[b(α j )] (42)
by analogy, the nth derivative b of the right vector can be obtained (n) (α 0 )：
Figure BDA0003928403090000071
Similarly, for the matrix derivative Z (k) (α 0 ) The calculation of (c) can also be given with reference to the right vector. But the present invention does not directly calculate Z (k) (α 0 ) The reasons are two:
first, calculating the derivative of the impedance matrix directly using the D matrix requires constructing the dimension as (N + 1) × N 2 A prior matrix of [ Z (alpha) ] j )]J = -N/2. For models with larger unknowns, the computational complexity and the consumption of memory resources will increase linearly.
Secondly, when the calculation of the fast multipole (MLFMA) acceleration electric large-size model is applied, the impedance matrix of the far field part is difficult to obtain, and difficulty is brought to the acquisition of the prior matrix.
Thus, by calculating the value under each interpolated vectorThe product of the impedance matrix and the moment vector replaces the direct calculation of the impedance matrix. Wherein Z (. Alpha.) is -N/2 )m n-i The dimensionality is N, the dimensionality of the reconstructed prior matrix is (N + 1) N, the memory consumption is greatly reduced, and the calculation complexity is also obviously reduced. Similarly, the derivative Z of the product of the impedance matrix derivative and the moment vector (k) (α 0 )m n-i The following can also be obtained by D matrix calculation:
Figure BDA0003928403090000072
unlike the application of pseudospectral methods in scalar domains like frequency, angle, etc., pseudospectral methods are applied to the shape vector α of the vector domain such that the derivative of the matrix vector multiplication contains the coordinate information of all control points. Further calculate the current moment vector m of each order n According to the current moment vector m n Coefficient vector a in polynomial approximation with Pade i And b j The surface current of the model after random sampling variation each time is calculated.
Step 3, calculating to obtain the RCS after the model is changed once according to the coordinate information after the model is changed and the corresponding current; and according to the set sampling times, calculating the RCS after each change of the model by using an AWE-based perturbation method. And carrying out statistical analysis on the RCS sampled for multiple times to obtain the electromagnetic scattering property of the non-cooperative metal target with the uncertain shape. Because the pseudo-spectrum method and the interpolation idea are adopted in the derivation process of the shape vector, the addition theorem is still satisfied. The fast multipole (MLFMA) technique can be used to accelerate the calculation of the scattering properties of the electrical large model. And (3) verifying the effectiveness of the AWE-based perturbation method by taking the statistical mean and variance of the Monte Carlo method as reference values.
Firstly, a model is reestablished according to a random variable introduced during current calculation, and the time consumption of the process is negligible; and calculating the radar scattering cross section (RCS) after the model is changed once by using the surface current and the re-established model shape information. The Monte Carlo method needs to perform the operation of filling an impedance matrix and matrix inversion every time of modeling, and the time consumption is huge. The method only needs to calculate the coefficient vector in the Pasteur polynomial once, and can obtain the current after the model change by introducing different random variables.
Secondly, calculating the electromagnetic scattering property of the deterministic target after each model random change. And finally, solving the mean value E (RCS) and the variance sigma (RCS) of RCS response obtained by multiple sampling to obtain the electromagnetic scattering characteristic of the non-cooperative metal target with the uncertain outline.
Example 1
In the embodiment, electromagnetic scattering calculation of a cubic model with an uncertain metal appearance is carried out, and the embodiment is realized on a calculation platform with Inter (R) Core (TM) i9-10850K CPU @3.6GHz and 16GB internal memory. The different coordinate directions in example 1 are shown in fig. 1. The metal cube model is shown in fig. 2 as having a side length of 2 meters. The cubic model consists of 8 control points, for a total of 6 NURBS faces, as shown in fig. 3. The incident wave frequency is 300MHz, and λ =1m is the wavelength of the incident wave.
(1) When the X coordinate of the #4 control point is changed, the change range of the coordinate is [ -0.6 λ,0.6 λ]The electromagnetic wave is horizontally incident, namely theta = -90 degrees,
Figure BDA0003928403090000081
scattering angle of
Figure BDA0003928403090000082
Theta = -90 to +90 degrees. Under the same incidence and scattering angles, the calculation was performed by the taylor method and the monte carlo method, respectively. The sampling times of the three methods are set to be 1000 times. The mean value of RCS is shown in FIG. 4, for example, the method provided by the invention can be matched with Monte Carlo, and the Taylor method is shifted, which shows that the improved AWE-based perturbation method can effectively enlarge the convergence radius compared with the traditional Taylor method.
(2) The X coordinates and the Z coordinates of the #2 control point and the #4 control point are changed simultaneously, and the change range of the coordinates is [ -0.6 lambda, 0.6 lambda]Electromagnetic waves are normally incident, i.e. θ =0 °,
Figure BDA0003928403090000083
scattering angle of
Figure BDA0003928403090000084
θ =0 ° to 180 °. Mean and variance ratio of RCS for example, as shown in fig. 5, the taylor method is significantly shifted, which shows that the improved accuracy of the AWE-based perturbation method is better than the conventional taylor method for a plurality of points and directions. A comparison of time and memory consumption is given in table 1.
TABLE 1
Figure BDA0003928403090000085
Figure BDA0003928403090000091
When one point and one coordinate are changed, the method occupies less memory and is shorter than the Monte Carlo in time compared with the traditional Taylor method; when a plurality of points and a plurality of coordinates are changed, compared with the traditional Taylor method and the Monte Carlo method, the method has more advantages in calculation time and memory consumption.
Example 2
This example performed an electromagnetic scattering calculation for an electrically large-sized rectangular solid model of an indeterminate shape of metal. The different coordinate directions in example 2 are shown in fig. 1. The metal cube model is shown in fig. 6, the length and width of the rectangular solid are both 0.8 meter, and the height is 12 meters. The cuboid model is composed of 8 control points controlled by a total of 6 NURBS surfaces, and a schematic diagram of the control points is shown in fig. 7. The electromagnetic wave is incident perpendicularly, i.e. theta =0 deg.,
Figure BDA0003928403090000092
the incident wave frequency is 300MHz, and λ =1m is the wavelength of the incident wave. When changing the Z coordinates of the control points #3, #4, #6 and #8, the coordinate change range is [ -0.4 λ,0.4 λ]Scattering angle of
Figure BDA0003928403090000093
Theta = -90 degrees to 90 degrees. Respectively with modifications of AThe WE method, the modified AWE + MLMFA method, the monte carlo method. Wherein, the number of the rapid multipole layers is 5. The sampling times of the three methods are set to 1000 times. Mean comparison of RCS as shown in fig. 8, both the AWE method and the AWE + MLFMA method were found to be compatible with the monte carlo method. The improved AWE-based perturbation method provided by the invention can be used in combination with a fast multipole method, so that the calculation speed is obviously improved while the precision is ensured. A comparison of time and memory consumption is given in table 2.
TABLE 2
Figure BDA0003928403090000094
As can be seen from table 2, the memory is reduced by 4 times after the method proposed in the present invention is combined with fast multipole. Compared with the Monte Carlo method, the method has the advantages that the sampling time is 1000 times, and the speed is improved by 5.5 times. The method has the advantage of high calculation speed of the Bimonte Carlo while ensuring the precision.

Claims (8)

1. A novel electromagnetic characteristic calculation method of an electrically uncertain outline metal target based on an AWE technology is characterized by comprising the following steps:
step 1, realizing modeling of a non-cooperative metal target by utilizing FEKO software and NURBS modeling technology: establishing a model with controllable target appearance according to the NURBS technology; combining all the control point coordinates into a row vector, and defining the row vector as an appearance vector;
step 2, establishing a mixed field integral equation related to the shape vector: respectively expanding an impedance matrix, a right vector and current of the shape vector into Taylor series, and deducing an expression of a current moment vector; then determining the variation range of the introduced shape vector, constructing a D matrix in a pseudo-spectral method, and calculating the derivative vector multiplication of each order of matrix and the derivative of a right vector to further obtain each order of current moment vector; establishing an equation of the Taylor series and the Pasteur polynomial, deriving the relation between a current moment vector and a vector coefficient of the Pasteur polynomial, and further calculating the vector coefficient; obtaining the current after the model changes once according to the vector coefficient and the random variable quantity of the shape vector;
step 3, calculating to obtain the RCS after the model is changed once according to the coordinate information after the model is changed and the corresponding current; according to the set sampling times, calculating the RCS of the model after each change by using an AWE-based perturbation method; and carrying out statistical analysis on the RCS sampled for multiple times to obtain the electromagnetic scattering property of the non-cooperative metal target with the uncertain shape.
2. A novel method of calculating electromagnetic properties of electrically indeterminate profile metal targets based on AWE technique as claimed in claim 1, characterized by the fact that in step 1 the model of controllable target profile is established according to NURBS technique; combining all control point coordinates of the model into a row vector, defining the row vector as an appearance vector and expressing the appearance vector by alpha; alpha is developed into [ alpha ] 1 ,α 2 ,α 3 ,...,α n-2 ,α n-1 ,α n ]Wherein α is 1 ,α 2 ,α 3 X, y, z coordinates representing a first coordinate point in the NURBS modeling file;
firstly, establishing an initial target model through FEKO software, wherein a random variable delta alpha is not introduced at the moment; guiding the model into rhinoceros software for reconstruction, wherein the reconstruction comprises two processes of resetting the coordinates of the control points and establishing a curved surface, and finally obtaining the coordinates of each control point and different control points which form the curved surface; alpha is alpha 0 Appearance vector, alpha, representing the original model s An arbitrary coordinate representing an arbitrary element, i.e., an arbitrary point, in the outline vector; ,
the target appearance is flexibly changed by introducing a random variable delta alpha into the appearance vector alpha; Δ α is a range of variation, Δ α = [ ] 1 ,Δα 2 ,Δα 3 ,...,Δα n-2 ,Δα n-1 ,Δα n ](ii) a In a target model containing alpha + delta alpha, according to the wavelength of incident electromagnetic waves, subdivision sizes in the u and v directions are respectively set for each surface, and the model is subjected to surface subdivision by using RWG basis functions; and (3) dividing the target surface into a plurality of triangles by a NURBS technology, and establishing a mixed field integral equation based on the RWG basis function.
3. The novel method of calculating electromagnetic properties of electrically indeterminate profile metal targets based on AWE technique according to claim 2, characterized in that the subdivision size is set to less than one tenth of the wavelength.
4. The AWE technology-based novel electromagnetic property calculation method for electrically uncertain contoured metal targets of claim 2, characterized in that step 2 establishes a mixed field integral equation about a contour vector α: respectively expanding an impedance matrix, a right vector and current of the shape vector into Taylor series, and deducing an expression of a current moment vector; then determining the variation range of the introduced shape vector, constructing a D matrix by using a pseudo-spectrum method, and calculating the derivative vector multiplication of each order matrix and the derivative of the right vector so as to obtain each order current moment vector; establishing an equation of the Taylor series and the Pasteur polynomial, deriving the relation between a current moment vector and a vector coefficient of the Pasteur polynomial, and further calculating the vector coefficient; obtaining the current after the model changes once according to the vector coefficient and the random variable quantity of the shape vector; the method comprises the following specific steps:
firstly, establishing a matrix equation of a metal target CFIE containing a random variable alpha:
Z(α)·I(α)＝b(α) (1)
wherein Z (alpha) is an impedance matrix of a mixed field integral equation, I (alpha) is a surface current, and b (alpha) is a right vector; the mixed field integral equation is expressed in a combination form of an electric field integral equation and a magnetic field integral equation; wherein the impedance matrix is represented as:
Z(α)＝α c ·Z EFIE (α)+(1-α c )·Z MFIE (α) (2)
α c the value of the combination coefficient is between 0 and 1; z EFIE (. Alpha.) and Z MFIE (alpha) is an impedance matrix in an electric field integral equation and an impedance matrix in a magnetic field integral equation respectively;
the right vector in the mixed field integral equation is represented as:
b(α)＝b EIFE (α)+b MFIE (α) (3)
wherein，b EIFE (α) is the right vector in the electric field integral equation, b MFIE (α) is the right vector in the magnetic field integral equation;
the mixed field matrix equation is expressed as follows:
[α c ·Z EFIE (α)+(1-α c )·Z MFIE (α)]·I(α)＝b EIFE (α)+b MFIE (α) (4)
according to the progressive waveform estimation theory, the impedance matrix and the right vector of the mixed field integral equation are expanded into the form of Taylor series:
Figure FDA0003928403080000021
Figure FDA0003928403080000022
Figure FDA0003928403080000023
random variation introduced for the s-th element in the shape vector; k is the order of derivation of the appearance vector, and L and M are respectively the highest order of the numerator and the denominator in the Pasteur polynomial;
the current is expressed as the product of the current moment vector and the shape variation:
Figure FDA0003928403080000031
by matching the variable quantity of each order in the mixed field integral equation, the current moment vector is obtained as follows:
m 0 ＝Z -1 (α 0 )·b(α 0 ) (8)
Figure FDA0003928403080000032
equations for the Pade's approximation polynomial and Taylor series with respect to current are established as follows:
Figure FDA0003928403080000033
a i and b j The expression of (a) is as follows:
Figure FDA0003928403080000034
Figure FDA0003928403080000035
according to the Chebyshev-Gauss-Lobatto interpolation method, in alpha 0 -Δα,α 0 +Δα]Within the range, N +1 interpolation nodes are determined, each node being represented as alpha j The expression is as follows:
Figure FDA0003928403080000036
and constructing a D matrix according to a pseudo-spectrum method, and calculating a first derivative expression of a right vector as follows:
Figure FDA0003928403080000037
wherein the dimensions of the D matrix are (N + 1) × (N + 1), b (α) j ) The dimension of the one-dimensional right vector is the number of model unknowns, namely N; [ b (. Alpha.) ] j )]Is a two-dimensional matrix of (N + 1) × N, j = -N/2, ·, N/2;
wherein the D matrix is represented as follows:
Figure FDA0003928403080000041
Figure FDA0003928403080000042
Figure FDA0003928403080000043
Figure FDA0003928403080000044
Figure FDA0003928403080000045
when the right vector first derivative is known, its second derivative is calculated by:
[b (2) (α j )]＝D·[b (1) (α j )]＝D·D·[b(α j )] (20)
obtaining the nth derivative b of the right vector (n) (α 0 )：
Figure FDA0003928403080000046
Calculating the product of an impedance matrix and a moment vector under each interpolation vector instead of directly calculating the impedance matrix; wherein Z (. Alpha.) is -N/2 )m n-i The dimension is N, the reconstructed prior matrix dimension is (N + 1) N, and the derivative Z of the product of the impedance matrix derivative and the moment vector (k) (α 0 )m n-i The calculation of the D matrix obtains:
Figure FDA0003928403080000051
applying pseudo-spectral method to shape vector alpha of vector fieldMaking the derivative of the matrix vector product contain the coordinate information of all control points; further calculate the moment vector m of each current order n According to the current moment vector m n Coefficient vector a in polynomial approximation with Pade i And b j And (4) calculating the surface current of the model after randomly sampling the variable quantity every time.
5. The AWE technology-based novel electromagnetic property calculation method for the metal target with the uncertain electrical configuration according to claim 4, wherein RCS after the model is changed once is calculated in the step 3 according to the coordinate information and the corresponding current after the model is changed; according to the set sampling times, calculating the RCS of the model after each change by using an AWE-based perturbation method; carrying out statistical analysis on RCS sampled for multiple times to obtain the electromagnetic scattering property of the non-cooperative metal target with uncertain appearance; the method comprises the following specific steps:
reestablishing the model according to a random variable introduced during current calculation, and further calculating the radar scattering sectional area after the model changes once by utilizing the surface current and the reestablished model shape information;
calculating the electromagnetic scattering characteristic of the deterministic target after each model random change;
and (4) solving the mean value and the variance of RCS response obtained by multiple sampling to obtain the electromagnetic scattering characteristic of the non-cooperative metal target with the uncertain shape.
6. A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the steps of the method of any of claims 1-5 are implemented when the program is executed by the processor.
7. A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the steps of the method of any one of claims 1 to 5.
8. A computer program product comprising a computer program, characterized in that the computer program realizes the steps of the method of any one of claims 1-5 when executed by a processor.
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117436273A (en) * 2023-11-14 2024-01-23 南京理工大学 Novel electromagnetic characteristic calculation method of electric large uncertain shape metal target based on Maehly approximation

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117436273A (en) * 2023-11-14 2024-01-23 南京理工大学 Novel electromagnetic characteristic calculation method of electric large uncertain shape metal target based on Maehly approximation

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