CN115510690A - A New Calculation Method for Electromagnetic Properties of Uncertain Shape Metal Targets Based on AWE Technology - Google Patents

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

A new type of electromagnetic characteristic meter for metal targets with uncertain shape based on AWE technology calculation method

technical field

The invention belongs to the technical field of numerical calculation of target electromagnetic scattering characteristics, in particular to a novel electromagnetic characteristic calculation method of a metal target with an electrically large and uncertain shape based on AWE technology.

Background technique

The calculation principle of electromagnetic scattering of metal targets based on the mixed field integral equation is that the target surface is divided into several triangles, and the division precision is set to be less than one-tenth of the incident wavelength. The RWG basis function is introduced to represent the upper and lower triangles to ensure the continuity of current between two adjacent triangles. This method can calculate metal targets of any shape, and has strong applicability. Compared with other high-frequency approximation methods, the numerical method based on the method of moments has higher calculation accuracy. When the combination coefficient of the mixed field integral equation is set to 1, it is converted to the electric field integral equation. Since its impedance matrix is a full-rank matrix, the calculation time is slow, but the calculation accuracy is high; when the combination coefficient is set to 0, it is converted to the magnetic field integral equation , at this time the integral equation is the main diagonal dominant matrix, the calculation time is fast, but the calculation accuracy is limited. Therefore, by reasonably setting the combination coefficient in the integral equation of the mixed field, both the calculation accuracy and the calculation speed can be considered. In addition, the mixed field integral equation can also avoid the internal resonance problem. The non-cooperative metal model is one of the important targets of current radar monitoring. Based on the mixed field integral equation, the calculation of the electromagnetic scattering characteristics of the non-cooperative metal target with uncertain shape information is the focus of this invention.

When the shape of the target contains uncertain factors, the Monte Carlo (MC) method can be used to repeatedly calculate the electromagnetic scattering characteristics of the model. The specific performance is to introduce a set of random variables into the shape parameters, and convert the uncertain problem into Determine the problem to calculate. Then, the radar cross-sectional area obtained by repeating the calculation is statistically analyzed, and finally the mean value and variance are obtained. The Monte Carlo method calculates the scattering characteristics of the model one by one, and the calculation results have high accuracy, but the calculation is extremely time-consuming, which seriously affects the calculation efficiency. In view of the disadvantages of the MC method, the traditional perturbation method based on Taylor series expansion can improve the computational efficiency by sacrificing part of the precision. Specifically, the matrix equation is expanded into a Taylor series, and the final current is expressed as the sum of the initial solution of the original model and the changing current. However, the convergence radius of this method is small, and the derivation by formula is complicated. When more control points are changed, the time will increase accordingly.

Contents of the invention

The purpose of the present invention is to provide a new method for calculating the electromagnetic characteristics of a metal target with an electrically large and uncertain shape based on AWE technology.

The technical solution to realize the object of the present invention is: first aspect, the present invention provides a kind of novel electromagnetic characteristic calculation method based on the AWE technology of the metal object of electric large uncertain appearance, and the steps are as follows:

Step 1. Use FEKO software and NURBS modeling technology to realize the modeling of non-cooperative metal targets: establish a model with controllable target shape according to NURBS technology; combine all control point coordinates into a row vector, which is defined as a shape vector;

Step 2. Establish the mixed field integral equation about the shape vector: respectively expand the impedance matrix, the right vector and the current about the shape vector into Taylor series, and derive the expression of the current moment vector; then determine the variation range of the introduced shape vector , construct the D matrix in the pseudospectral method, calculate the matrix derivative vector of each order and the derivative of the right vector, and then obtain the current moment vector of each order; establish the Taylor series and Padre polynomial equation, deduce the current moment vector and Pa The relationship between the polynomial vector coefficients, and then calculate the vector coefficients; according to the vector coefficients and the random variation of the shape vector, the current after the model changes once is obtained;

Step 3. According to the coordinate information after the model change and the corresponding current, calculate the RCS after the model changes once; according to the set sampling times, use the AWE-based perturbation method to calculate the RCS after each model change; Statistical analysis is performed on the second RCS, and the electromagnetic scattering characteristics of non-cooperative metal targets with uncertain shapes are obtained.

In a second aspect, the present invention provides a computer device, including a memory, a processor, and a computer program stored on the memory and operable on the processor, wherein the first aspect is realized when the processor executes the program The steps of the method.

In a third aspect, the present invention provides a computer-readable storage medium on which a computer program is stored, wherein the program implements the steps of the method described in the first aspect when the program is executed by a processor.

In a fourth aspect, the present invention provides a computer program product, including a computer program, characterized in that, when the computer program is executed by a processor, the steps of the method described in the first aspect are implemented.

Compared with the prior art, the present invention has the following advantages: (1) Compared with the traditional method of directly deriving the formula for the shape vector, the pseudo-spectral method is used to calculate the derivative of the right vector and matrix-vector multiplication, which avoids complicated formula derivation (2) Compared with the traditional Taylor method, the improved AWE perturbation method uses the Padé approximation, and the convergence radius is wider; for the situation where multiple control points change at the same time, the calculation time of this method Shorter and less memory. (3) Compared with the traditional Monte Carlo method, the calculation time is greatly shortened.

Description of drawings

角示意图。Figure 1 shows the θ angle and

angle diagram.

Figure 2 is a schematic diagram of the size of the metal cube model.

Figure 3 is a schematic diagram of the control point setting of the metal cube model.

Fig. 4 is a statistical comparison chart (mean value) of RCS when one point and one coordinate are changed for the metal cube model with uncertain shape.

Fig. 5 is a statistical comparison chart (mean variance) of RCS when multiple coordinates of multiple points are changed for the metal cube model with uncertain shape.

Fig. 6 is a schematic diagram of the size of the metal electric large-size cuboid model.

Fig. 7 is a schematic diagram of setting control points of the metal electric large-size cuboid model.

Fig. 8 is a statistical comparison chart (mean value variance) of RCS when a metal electric large-size cuboid with an uncertain shape changes multiple points.

detailed description

The present invention proposes a new type of calculation method for electromagnetic characteristics of metal objects with large and uncertain shapes based on AWE technology. All control point coordinates of the shape are defined as shape vectors. By introducing random variables into the shape vector, the purpose of changing the shape of the target is achieved. Different from applying AWE technology to scalar domains such as frequency and angle, the present invention extends AWE technology to vector domain, namely shape vector. Then the shape vector is introduced into the combined field integral equation (Combined Field Integral Equation, CFIE), and the expression of the current moment vector is derived by expanding the impedance matrix, the right vector and the current into the form of Taylor series. Applying the pseudospectral method to AWE, the product of the matrix derivative and the moment vector and the derivative of the right vector are calculated respectively, and then the current moment vector is calculated. The current after each model change is calculated by combining Taylor series and Padé polynomials. Compared with the traditional Taylor method, the convergence radius is further expanded. Finally, the Radar Cross Section (RCS) is calculated by combining the coordinate information of the current and the model change. After multiple sampling, the mean and variance of RCS were statistically analyzed. Since the interpolation idea is adopted in the derivation process of the shape vector, the addition theorem is still satisfied. Therefore, the perturbation method based on AWE can be combined with the fast multipole (MLFMA) to accelerate the calculation of the scattering characteristics of the electrically large model. Compared with the Monte Carlo (MC) method, the present invention can greatly shorten the calculation time. This method can quickly and efficiently calculate the scattering characteristics of the deformed electrically large metal target.

The present invention will be described in further detail below in conjunction with the accompanying drawings.

A new calculation method for electromagnetic properties of metal targets with uncertain shapes based on AWE technology, the steps are as follows:

Step 1. Establish a controllable model of the target shape according to NURBS technology. Combine all control point coordinates into a row vector, defined as the shape vector, denoted by α. Specifically, α can be expanded to [α ₁ ,α ₂ ,α ₃ ,...,α _n-2 ,α _n-1 ,α _n ], where n is the number of model control points multiplied by 3 . Among them, α ₁ , α ₂ , α ₃ represent the x, y, and z coordinates of #1 control point, and #1 control point is the first coordinate point in the NURBS modeling file; first establish the initial target through FEKO software model, no random variable Δα is introduced at this time. Import the model into Rhino software for reconstruction, including resetting the coordinates of the control points and establishing the surface, and finally obtain the coordinates of each control point and different control points that constitute the surface. α ₀ represents the shape vector of the original model, and α _s represents any element in the shape vector, that is, any coordinate of any point.

By introducing a random variable Δα to the shape vector α, the target shape can be changed flexibly. Specifically, Δα is the range of variation, Δα=[Δα ₁ , Δα ₂ , Δα ₃ , . . . , Δα _n-2 , Δα _n-1 , Δα _n ]. In the target model containing α+Δα, according to the wavelength of the incident electromagnetic wave, the subdivision dimensions in the u and v directions are set for each surface, and the RWG basis function is used to subdivide the model. The subdivision size is usually set to be less than one-tenth of the wavelength. From this, a subdivision model that can be calculated in the mixed field integral equation is obtained. The target surface is divided into several triangles by NURBS technology, and the mixed field integral equation is established based on the RWG basis function.

Step 2. Establish the mixed field integral equation about the shape vector α: respectively expand the impedance matrix, the right vector and the current about the shape vector into Taylor series, and derive the expression of the current moment vector. Then determine the variation range of the introduced shape vector, use the pseudo-spectral method to construct the D matrix, calculate the matrix derivative vector of each order and the derivative of the right vector, and then obtain the current moment vector of each order. Establish the equation of Taylor series and Padé polynomial, deduce the relationship between the current moment vector and the vector coefficient of Padé polynomial, and then calculate the vector coefficient. Unlike Monte Carlo methods, this procedure only needs to be performed once. According to the vector coefficient and the random variation of the shape vector, the current after the model changes once is obtained. details as follows:

Firstly, the matrix equation of metal target CFIE with random variable α is established:

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 mixed field integral equation can be expressed as a combined form of electric field integral equation and magnetic field integral equation. The impedance matrix can be further expressed as:

Z(α)=α _c Z _EFIE (α)+(1-α _c ) Z _MFIE (α) (24)

α _c is the combination coefficient, and its value is between 0 and 1; Z _EFIE (α) and Z _MFIE (α) are the impedance matrix in the electric field integral equation and the impedance matrix in the 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)

Among them, b _EIFE (α) is the right vector in the electric field integral equation, and b _MFIE (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 theory of asymptotic waveform estimation, the impedance matrix and the right vector of the mixed field integral equation are expanded into the form of Taylor series,

为外形矢量中第s个元素引入的随机变化量；k为对外形矢量求导的阶次，L和M分别为帕德多项式中分子、分母的最高阶次。

is the random variation introduced by the sth element in the shape vector; k is the order of the derivative of the shape vector, and L and M are the highest order of the numerator and denominator in the Padé polynomial, respectively.

Similarly, the current is expressed as the product of the current moment vector and the shape change:

By matching the changes 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)

Establish the Padé approximation polynomial and the Taylor series equation for the current as follows:

Further, the expressions of a _i and b _j are as follows:

According to the Chebyshev–Gauss–Lobatto (GLC) interpolation method, within the range of [α ₀ -Δα,α ₀ +Δα], determine N+1 interpolation nodes, each node is denoted as α _j , and its expression is as follows:

Construct the D matrix according to the pseudo-spectral method, and calculate the first-order derivative expression of the right vector as follows:

The dimension of the D matrix is (N+1)*(N+1), b(α _j ) is a one-dimensional right vector when any vector is used, and its dimension 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. Among them, the D matrix can be expressed as follows:

In particular, when the first derivative of the right vector is known, its second derivative can be calculated by the following formula:

[b ⁽²⁾ (α _j )]=D·[b ⁽¹⁾ (α _j )]=D·D·[b(α _j )] (42)

By analogy, the nth order derivative b ⁽ⁿ⁾ (α ₀ ) of the right vector can be obtained:

Similarly, the calculation of the matrix derivative Z ^(k) (α ₀ ) can also be given in the form of the right vector. But the present invention does not directly calculate Z ^(k) (α ₀ ), there are two reasons:

First, to directly use the D matrix to calculate the derivative of the impedance matrix, it is necessary to construct a prior matrix with a dimension of (N+1)*N ² , [Z(α _j )], j=-N/2,...,N /2. For models with large unknowns, the computational complexity and consumption of memory resources will increase linearly.

Second, when the fast multipole (MLFMA) is used to accelerate the calculation of the electrically large-scale model, it is difficult to obtain the impedance matrix of the far-field part, which brings difficulties to the acquisition of the prior matrix.

Therefore, instead of directly calculating the impedance matrix, the product of the impedance matrix and the moment vector under each interpolation vector is calculated. Among them, the dimension of Z(α _-N/2 )m _ni is N, and the dimension of the reconstructed prior matrix is (N+1)*N, which greatly reduces memory consumption and computational complexity. Similarly, the derivative Z ^(k) (α ₀ )m _ni of the product of the impedance matrix derivative and the moment vector can also be calculated by the D matrix:

Different from the application of the pseudospectral method in the scalar domain such as frequency and angle, the pseudospectral method is applied to the shape vector α in the vector domain, so that the derivative of the matrix-vector multiplication contains the coordinate information of all control points. Then calculate the current moment vector m _n of each order, and calculate the surface current of the model after each random sampling variation according to the relationship between the current moment vector m _n and the coefficient vectors a _i and b _j in the Padé approximation polynomial.

Step 3. According to the coordinate information after the model change and the corresponding current, calculate the RCS after the model changes once; according to the set sampling times, use the AWE-based perturbation method to calculate the RCS after each model change. Statistical analysis is carried out on the RCS sampled many times, and the electromagnetic scattering characteristics of non-cooperative metal targets with uncertain shapes are obtained. Since the pseudospectral method and interpolation idea are used in the derivation process of the shape vector, the addition theorem is still satisfied. So the fast multipole (MLFMA) technique can be used to speed up the calculation of the scattering properties of the electrically large model. The statistical mean and variance of the Monte Carlo method are used as reference values to verify the effectiveness of the perturbation method based on AWE.

Firstly, the model is rebuilt according to the random variables introduced when calculating the current, which takes negligible time; then, the radar cross section (RCS) after one change of the model is calculated by using the surface current and the rebuilt model shape information. The Monte Carlo method needs to perform the operations of filling the impedance matrix and inverting the matrix every time it is modeled, which takes a lot of time. The present invention only needs to calculate the coefficient vector in the Padé polynomial once, and the current after the model change can be obtained by introducing different random variables.

Second, calculate the electromagnetic scattering characteristics of the deterministic target after each random change of the model. Finally, the mean value E(RCS) and variance σ(RCS) of the RCS responses obtained by multiple sampling are calculated to obtain the electromagnetic scattering characteristics of non-cooperative metal targets with uncertain shapes.

Example 1

In this embodiment, the electromagnetic scattering calculation of a cube model with an uncertain metal shape is carried out. This embodiment is implemented on a computing platform with an Inter(R)Core(TM)i9-10850K CPU@3.6GHz and a memory of 16GB. The different coordinate directions in Embodiment 1 are shown in FIG. 1 . The metal cube model is shown in Figure 2, with a side length of 2 meters. The cube model is controlled by 8 control points and consists of 6 NURBS surfaces, as shown in Figure 3. The frequency of the incident wave is 300MHz, and λ=1m is the wavelength of the incident wave.

散射角为

θ＝-90°～+90°。在相同的入射和散射角度下，分别用泰勒方法、蒙特卡洛方法进行计算。其中，三种方法的采样次数均设为1000次。RCS的均值对比如图4所示，本发明提出的方法能够和蒙特卡洛吻合，而泰勒方法发生了偏移，说明改进的基于AWE的扰动法相较于传统泰勒方法能够有效扩大收敛半径。(1) When changing the X coordinate of control point #4, the coordinate range is [-0.6λ, 0.6λ], and the electromagnetic wave is incident horizontally, that is, θ=-90°,

The scattering angle is

θ=-90°～+90°. Under the same incident and scattering angles, Taylor method and Monte Carlo method were used to calculate. Among them, the sampling times of the three methods are all set to 1000 times. The mean comparison of RCS is shown in Figure 4. The method proposed by the present invention can be consistent with Monte Carlo, while the Taylor method has shifted, indicating that the improved AWE-based perturbation method can effectively expand the convergence radius compared with the traditional Taylor method.

散射角为

θ＝0°～180°。RCS的均值和方差对比如图5所示，泰勒方法发生了明显偏移，说明针对变化多个点，多个方向时，改进的基于AWE的扰动法精度优于传统泰勒方法。表1中给出了时间和内存消耗的对比。(2) Simultaneously change the X coordinates and Z coordinates of #2 control point and #4 control point, the coordinate range is [-0.6λ, 0.6λ], the electromagnetic wave is vertically incident, that is, θ=0°,

The scattering angle is

θ=0°～180°. The comparison of the mean and variance of RCS is shown in Figure 5. The Taylor method has shifted significantly, indicating that the improved AWE-based perturbation method is more accurate than the traditional Taylor method when changing multiple points and directions. A comparison of time and memory consumption is given in Table 1.

Table 1

It can be seen from Table 1 that when changing one point and one coordinate, this method occupies less memory than the traditional Taylor method, and the time is shorter than Monte Carlo; when changing multiple points and multiple coordinates, compared with the traditional Taylor method and Monte Carlo Carlo's method, this method has more advantages in computing time and memory consumption.

Example 2

入射波频率为300MHz，λ＝1m为入射波的波长。当变化#3号、#4号、#6号、#8号控制点的Z坐标，坐标的变化范围为[-0.4λ,0.4λ]，散射角为

θ＝-90°～90°。分别用改进的AWE方法、改进的AWE+MLMFA方法、蒙特卡洛方法进行计算。其中，快速多极子层数为5层。三种方法的采样次数均设为1000次。RCS的均值对比如图8所示，发现AWE方法和AWE+MLFMA方法均能够和蒙特卡洛方法吻合。说明本发明提出的改进的基于AWE的扰动法能够与快速多极子方法联合使用，在保证精度的同时，明显提高计算速度。表2中给出了时间和内存消耗的对比。In this embodiment, the calculation of electromagnetic scattering is performed on an electrically large-sized cuboid model of an uncertain metal shape. The different coordinate directions in Embodiment 2 are shown in FIG. 1 . The metal cube model is shown in Figure 6. The length and width of the cuboid are both 0.8 meters and the height is 12 meters. The cuboid model is controlled by 8 control points and consists of 6 NURBS surfaces. The schematic diagram of the control points is shown in Figure 7. The electromagnetic wave is vertically incident, that is, θ=0°,

The frequency of the incident wave is 300MHz, and λ=1m is the wavelength of the incident wave. When changing the Z coordinates of #3, #4, #6, and #8 control points, the coordinate range is [-0.4λ, 0.4λ], and the scattering angle is

θ=-90°～90°. The improved AWE method, the improved AWE+MLMFA method and the Monte Carlo method are used for calculation respectively. Among them, the number of fast multipole layers is 5 layers. The sampling times of the three methods are all set to 1000 times. The mean comparison of RCS is shown in Figure 8, and it is found that both the AWE method and the AWE+MLFMA method can be consistent with the Monte Carlo method. It shows that the improved AWE-based perturbation method proposed by the present invention can be used in conjunction with the fast multipole method, and the calculation speed is obviously improved while ensuring the accuracy. A comparison of time and memory consumption is given in Table 2.

Table 2

It can be seen from Table 2 that after the method proposed in the present invention is combined with the fast multipole, the memory is reduced by 4 times compared with before. Compared with the Monte Carlo method sampling 1000 times, the speed is increased by 5.5 times. It illustrates that the method of the present invention has the advantage of faster calculation speed than Monte Carlo while ensuring accuracy.

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:

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:

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)

equations for the Pade's approximation polynomial and Taylor series with respect to current are established as follows:

a _i and b _j The expression of (a) is as follows:

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:

and constructing a D matrix according to a pseudo-spectrum method, and calculating a first derivative expression of a right vector as follows:

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:

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 )：

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:

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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