A novel electromagnetic characteristics calculation method for metallic targets with uncertain shapes based on AWE technology

Abstract

This invention discloses a novel electromagnetic characteristic calculation method for electrically large, uncertain metal targets based on AWE technology. First, a model is established using FEKO software and NURBS technology, with the coordinates of all control points of the target's shape defined as shape vectors. Random variables are introduced to change the target's shape. The shape vector is then introduced into the hybrid field integral equation. By expanding the impedance matrix, right-hand side vector, and current into Taylor series form, an expression for the current moment vector is derived. A pseudospectral method is applied to AWE to calculate the product of the matrix derivative and the moment vector, as well as the derivative of the right-hand side vector, to further calculate the current moment vector. The current after each model change is calculated by combining the Taylor series and Padé polynomials. Finally, the radar cross-section is calculated by combining the current and the coordinate information after the model change. This method significantly reduces calculation time and rapidly calculates the scattering characteristics of electrically large metal targets after deformation.

Description

Technical Field

[0001] The present invention belongs to the technical field of numerical calculation of electromagnetic scattering characteristics of targets, and in particular to a novel electromagnetic characteristic calculation method of an electrically large uncertain shape metal target based on AWE technology. Background Art

[0002] The principle of calculating electromagnetic scattering from metal targets based on the hybrid field integral equation is to divide the target surface into several triangles, with the segmentation accuracy set to less than one-tenth of the incident wavelength. The RWG basis function is introduced to represent the upper and lower triangles, ensuring current continuity between adjacent triangles. This method can calculate metal targets of arbitrary shapes and has strong applicability. Compared with other high-frequency approximation methods, the numerical method based on the method of moments has higher computational accuracy. When the combination coefficient of the hybrid field integral equation is set to 1, it is converted to an electric field integral equation. Due to its full-rank impedance matrix, the calculation time is slow, but the computational accuracy is high. When the combination coefficient is set to 0, it is converted to a magnetic field integral equation. In this case, the integral equation is a main diagonally dominant matrix, which has a fast computational time but limited computational accuracy. Therefore, by properly setting the combination coefficient in the hybrid field integral equation, both computational accuracy and speed can be achieved. In addition, the hybrid field integral equation can also avoid internal resonance problems. Non-cooperative metal models are one of the important targets of current radar monitoring. The focus of this study is to calculate the electromagnetic scattering characteristics of non-cooperative metal targets with uncertain shape information based on the hybrid field integral equation.

[0003] When the target's shape contains uncertainties, the Monte Carlo (MC) method can be used to repeatedly calculate the model's electromagnetic scattering characteristics. Specifically, this method introduces a set of random variables into the shape parameters, transforming the uncertain problem into a deterministic one for calculation. The resulting radar cross-section is then statistically analyzed to determine its mean and variance. While the Monte Carlo method calculates the model's scattering characteristics one by one, resulting in highly accurate results, it is extremely time-consuming, significantly impacting computational efficiency. To address the shortcomings of the MC method, the traditional perturbation method based on Taylor series expansion can improve computational efficiency at the expense of some accuracy. Specifically, the matrix equation is expanded into a Taylor series, with the final current expressed as the sum of the initial solution of the original model and the changed current. However, this method has a small convergence radius and complex formula derivation. The computation time also increases as the number of control points to be changed increases. Summary of the Invention

[0004] The purpose of the present invention is to provide a new electromagnetic characteristic calculation method for a metallic target with an electrically large uncertain shape based on AWE technology.

[0005] The technical solution to achieve the purpose of the present invention is as follows: First, the present invention provides a new electromagnetic characteristic calculation method for a metallic target with an electrically large uncertain shape based on AWE technology, the steps of which are as follows:

[0006] Step 1: Use FEKO software and NURBS modeling technology to model the non-cooperative metal target: Use NURBS technology to establish a model with controllable target shape; combine the coordinates of all control points into a row vector, which is defined as the shape vector;

[0007] Step 2: Establish a hybrid field integral equation for the shape vector: Expand the impedance matrix, right-hand side vector, and current of the shape vector into Taylor series to derive the expression of the current moment vector. Then, determine the variation range of the introduced shape vector, construct the D matrix in the pseudo-spectral method, calculate the product of the matrix derivative vectors of each order and the derivative of the right-hand side vector, and then obtain the current moment vectors of each order. Establish an equation for the Taylor series and the Padé polynomial, derive the relationship between the current moment vector and the Padé polynomial vector coefficients, and then calculate the vector coefficients. Based on the random variation of the vector coefficients and the shape vector, obtain the current after the model changes once.

[0008] Step 3. Calculate the RCS after the model changes once based on the coordinate information and corresponding current after the model changes. Calculate the RCS after each model change using the AWE-based perturbation method based on the set number of sampling times. Perform statistical analysis on the RCS sampled multiple times to obtain the electromagnetic scattering characteristics of the uncertain shape non-cooperative metal target.

[0009] In a second aspect, the present invention provides a computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the method described in the first aspect when executing the program.

[0010] In a third aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the program, when executed by a processor, implements the steps of the method described in the first aspect.

[0011] In a fourth aspect, the present invention provides a computer program product, comprising 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.

[0012] Compared with the existing technology, the advantages of the present invention are as follows: (1) Compared with the traditional method of directly deriving the formula of the shape vector, the pseudo-spectral method is used to calculate the derivative of the right-hand vector and the matrix-vector multiplication, which avoids the complex formula derivation, has a clear idea, and is easy to implement; (2) Compared with the traditional Taylor method, the improved AWE perturbation method uses the Padé approximation and has a wider convergence radius; for the case where multiple control points change simultaneously, this method has a shorter calculation time and smaller memory. (3) Compared with the traditional Monte Carlo method, the calculation time is greatly shortened. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 is the angle θ in the three-dimensional coordinate system and Angle diagram.

[0014] Figure 2 Schematic diagram of the metal cube model size.

[0015] Figure 3 Schematic diagram of the control point settings for the metal cube model.

[0016] Figure 4 RCS statistical comparison chart (mean) when changing one coordinate of one point for the uncertain shape metal cube model.

[0017] Figure 5 RCS statistical comparison chart (mean variance) when changing multiple points and multiple coordinates for the uncertain shape metal cube model.

[0018] Figure 6 This is a schematic diagram of the dimensions of the metal electrical large-size rectangular model.

[0019] Figure 7 Schematic diagram of control point settings for the metal electrically large rectangular block model.

[0020] Figure 8 This is a statistical comparison chart (mean variance) of the RCS when multiple points of a large-sized metallic cuboid with uncertain shape are changed. DETAILED DESCRIPTION

[0021] This paper proposes a novel electromagnetic property calculation method for metallic targets with electrically large uncertain shapes based on AWE technology. First, a model is established using FEKO software and non-uniform rational B-spline (NURBS) technology. The coordinates of all control points of the target shape are defined as shape vectors. By introducing random variables into this shape vector, the target shape can be modified. Unlike applying AWE technology to scalar domains such as frequency and angle, this paper extends AWE technology to the vector domain, namely, the shape vector. The shape vector is then introduced into the combined field integral equation (CFIE). By expanding the impedance matrix, right-hand side vector, and current into a Taylor series, an expression for the current moment vector is derived. A pseudospectral method is applied to AWE, and the product of the matrix derivative and the moment vector, as well as the derivative of the right-hand side vector, is calculated to calculate the current moment vector. The current after each model change is calculated by combining the Taylor series and the Padé polynomials. Compared to the traditional Taylor method, the convergence radius is also further extended. Finally, the radar cross section (RCS) is calculated by combining the coordinate information after the current and the model change. After multiple sampling, the mean and variance of the RCS are statistically analyzed. Since the interpolation idea is adopted in the derivation 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 electrically large metal targets after deformation.

[0022] The present invention is further described in detail below with reference to the accompanying drawings.

[0023] A new electromagnetic characteristic calculation method for metallic targets with uncertain shapes based on AWE technology is proposed. The steps are as follows:

[0024] Step 1: Use NURBS technology to build a model with controllable target shape. Combine all control point coordinates into a row vector, defined as the shape vector, represented by α. Specifically, α can be expanded into [α1, α2, α3, ..., α n-2 ,α n-1 ,α n], where n is the number of model control points multiplied by 3. Among them, α1, α2, α3 represent the x, y, z coordinates of control point #1, and control point #1 is the first coordinate point in the NURBS modeling file. The initial target model is first established using FEKO software, and the random variable Δα is not introduced at this time. The model is imported into Rhino software for reconstruction, which includes resetting the coordinates of the control points and establishing the surface. Finally, the coordinates of the control points that constitute the surface and the different control points are obtained. α0 represents the shape vector of the original model, α s Represents any element in the shape vector, that is, any coordinate of any point.

[0025] By introducing random variables Δα into the shape vector α, the target shape can be flexibly changed. Specifically, Δα is the range of the change, Δα=[Δα1,Δα2,Δα3,...,Δα n-2 ,Δα n-1 ,Δα n In a target model containing α+Δα, the subdivision size in the u and v directions is set for each surface according to the wavelength of the incident electromagnetic wave, and the model is subdivided using the RWG basis function. The subdivision size is usually set to less than one tenth of the wavelength. This results in a subdivision model that can be calculated in the hybrid field integral equation. The target surface is subdivided into several triangles using NURBS technology, and the hybrid field integral equation is established based on the RWG basis function.

[0026] Step 2. Establish a mixed field integral equation about the shape vector α: expand the impedance matrix, right-hand side vector and current about the shape vector into Taylor series respectively, and derive the expression of the current moment vector. Then determine the variation range of the introduced shape vector, construct the D matrix using the pseudo-spectral method, calculate the product of the matrix derivative vector of each order and the derivative of the right-hand side vector, and then obtain the current moment vector of each order. Establish the equation of Taylor series and Padé polynomial, derive the relationship between the current moment vector and the Padé polynomial vector coefficient, and then calculate the vector coefficient. Unlike the Monte Carlo method, this process only needs to be executed once. According to the random change of the vector coefficient and the shape vector, the current after the model changes once is obtained. Specifically as follows:

[0027] First, the matrix equation of the metal target CFIE containing the random variable α is established:

[0028] Z(α)·I(α)=b(α) (23)

[0029] Where Z(α) is the impedance matrix of the hybrid field integral equation, I(α) is the surface current, and b(α) is the right-hand side vector. The hybrid field integral equation can be expressed as a combination of the electric field integral equation and the magnetic field integral equation. The impedance matrix can be further expressed as:

[0030] Z(α)=αc ·Z EFIE (α)+(1-α c )·Z MFIE (α) (24)

[0031] α c is the combination coefficient, which ranges from 0 to 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.

[0032] The right-hand side vector in the mixed field integral equation can be expressed as:

[0033] b(α)=b EIFE (α)+b MFIE (α) (25)

[0034] Among them, b EIFE (α) is the right-hand side vector in the electric field integral equation, b MFIE (α) is the right-hand side vector in the magnetic field integral equation.

[0035] Furthermore, the mixed field matrix equation can be expressed as follows:

[0036] [α c ·Z EFIE (α)+(1-α c )·Z MFIE (α)]·I(α)=b EIFE (α)+b MFIE (α)(26)

[0037] According to the theory of asymptotic waveform estimation, the impedance matrix and right-hand side vector of the hybrid field integral equation are expanded into the form of Taylor series.

[0038]

[0039]

[0040] is the random variation introduced by the sth element in the shape vector; k is the order of the derivative of the shape vector, L and M are the highest orders of the numerator and denominator in the Padé polynomial, respectively.

[0041] Similarly, the current is expressed as the product of the current moment vector and the shape change:

[0042]

[0043] By matching the various order variables in the hybrid field integral equation, the current moment vector is obtained as follows:

[0044] m0=Z-1 (α0)·b(α0) (30)

[0045]

[0046] The equations for the Padé approximation polynomial and Taylor series regarding the current are established as follows:

[0047]

[0048] Furthermore, a i and b j The expression is as follows:

[0049]

[0050]

[0051] According to the Chebyshev–Gauss–Lobatto (GLC) interpolation method, N+1 interpolation nodes are determined in the range [α0-Δα,α0+Δα], each node is represented by α j , which is expressed as follows:

[0052]

[0053] According to the pseudo-spectral method, the D matrix is ​​constructed and the first-order derivative expression of the right-hand vector is calculated as follows:

[0054]

[0055] The dimension of the D matrix is ​​(N+1)*(N+1), b(α j ) is a one-dimensional right-hand side vector when any vector is a vector, and its dimension is the number of unknown quantities in the model, that is, N. j )], j = -N / 2, ..., N / 2 is a two-dimensional matrix of (N+1)*N. The D matrix can be expressed as follows:

[0056]

[0057]

[0058]

[0059]

[0060]

[0061] In particular, when the first-order derivative of the right-hand side vector is known, its second-order derivative can be calculated as follows:

[0062] [b (2) (αj )]=D·[b (1) (α j )]=D·D·[b(α j )] (42)

[0063] By analogy, we can get the nth order derivative b of the vector on the right (n) (α0):

[0064]

[0065] Similarly, for the matrix derivative Z (k) The calculation of (α0) can also be given in the form of the right vector. However, the present invention does not directly calculate Z (k) (α0), for two reasons:

[0066] First, directly using the D matrix to calculate the derivative of the impedance matrix requires constructing a matrix with a dimension of (N+1)*N 2 The prior matrix, [Z(α j )], j = -N / 2, ..., N / 2. For models with large unknowns, the computational complexity and memory resource consumption will increase linearly.

[0067] Secondly, when applying the fast multipole method (MLFMA) to accelerate the calculation of electrically large-scale models, the impedance matrix of the far-field part is difficult to obtain, which makes it difficult to obtain the prior matrix.

[0068] Therefore, the impedance matrix is ​​calculated by multiplying the impedance matrix and the moment vector under each interpolation vector instead of directly calculating the impedance matrix. -N / 2 )m n-i The dimension is N, and the dimension of the reconstructed prior matrix is ​​(N+1)*N, which greatly reduces the memory consumption and the computational complexity. Similarly, the derivative of the impedance matrix derivative and the moment-vector product Z is (k) (α0)m n-i It can also be calculated by D matrix:

[0069]

[0070] Different from the application of pseudo-spectral method in scalar domains such as frequency and angle, the pseudo-spectral 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 the current moment vector m of each order is calculated. n , according to the current moment vector m n The coefficient vector a in the Padé approximation polynomial i and b j The relationship between is used to calculate the surface current of the model after each random sampling change.

[0071] Step 3: Based on the model's changed coordinate information and the corresponding current, calculate the RCS after each model change. Based on the set number of sampling times, use the AWE-based perturbation method to calculate the RCS after each model change. Statistical analysis of the multiple RCS samples reveals the electromagnetic scattering characteristics of non-cooperative metal targets with uncertain shapes. Because the pseudospectral method and interpolation concepts are used in the derivation of the shape vector, the addition theorem is still satisfied. Therefore, the fast multipole method (MLFMA) can be used to accelerate the calculation of the scattering characteristics of large electric models. The statistical mean and variance of the Monte Carlo method are used as reference values ​​to verify the effectiveness of the AWE-based perturbation method.

[0072] First, the model is rebuilt based on the random variables introduced when calculating the current, a process that consumes negligible time. The surface current and the rebuilt model's shape information are then used to calculate the radar cross-section (RCS) after the model has been modified. The Monte Carlo method requires significant time to fill in the impedance matrix and perform matrix inversion operations for each modeling step. The present invention only requires calculating the coefficient vector of the Padé polynomial once, and by introducing different random variables, the current after the model modification can be obtained.

[0073] Secondly, the electromagnetic scattering characteristics of the deterministic target after each random change of the model are calculated. Finally, the mean E(RCS) and variance σ(RCS) of the RCS responses obtained from multiple samplings are calculated to obtain the electromagnetic scattering characteristics of the non-cooperative metal target with uncertain shape.

[0074] Example 1

[0075] This embodiment performs electromagnetic scattering calculations on a metal cube model with an uncertain shape. This embodiment is implemented on a computing platform with an Intel(R) Core(TM) i9-10850K CPU @ 3.6GHz and 16GB of memory. Figure 1 The metal cube model is shown as Figure 2 As shown, the side length is 2 meters. The cube model is controlled by 8 control points and consists of 6 NURBS faces. Figure 3 As shown in Figure 2, the incident wave frequency is 300 MHz, and λ = 1 m is the wavelength of the incident wave.

[0076] (1) When the X coordinate of control point #4 is changed, the range of the coordinate change is [-0.6λ, 0.6λ], and the electromagnetic wave is horizontally incident, that is, θ = -90°, The scattering angle is θ=-90°~+90°. Under the same incident and scattering angles, Taylor method and Monte Carlo method are used for calculation respectively. The sampling times of the three methods are all set to 1000 times. The mean value of RCS is compared with Figure 4As shown in the figure, the method proposed in the present invention can be consistent with Monte Carlo, while the Taylor method has a deviation, which shows that the improved AWE-based perturbation method can effectively expand the convergence radius compared with the traditional Taylor method.

[0077] (2) Simultaneously change the X and Z coordinates of control points #2 and #4. The range of the coordinate change is [-0.6λ, 0.6λ]. The electromagnetic wave is incident vertically, that is, θ = 0°. The scattering angle is θ=0°~180°. The mean and variance of RCS are compared as follows Figure 5 As shown in Figure 1, the Taylor method has a significant deviation, indicating that the improved AWE-based perturbation method is more accurate than the traditional Taylor method when changing multiple points and multiple directions. Table 1 shows a comparison of time and memory consumption.

[0078] Table 1

[0079]

[0080]

[0081] Table 1 shows that when changing one point and one coordinate, this method takes up less memory than the traditional Taylor method and takes less time than the Monte Carlo method. When changing multiple points and multiple coordinates, this method has more advantages in both computing time and memory consumption compared to the traditional Taylor method and Monte Carlo method.

[0082] Example 2

[0083] This embodiment performs electromagnetic scattering calculations on a large rectangular parallelepiped model of metal with uncertain shape. Figure 1 The metal cube model is shown as Figure 6 As shown in the figure, 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 control point diagram is as follows: Figure 7 As shown. The electromagnetic wave is incident vertically, that is, θ=0°, The frequency of the incident wave is 300MHz, and λ=1m is the wavelength of the incident wave. When the Z coordinates of control points #3, #4, #6, and #8 are changed, the range of the coordinate change 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 calculations. The number of fast multipole layers is 5. The sampling times of the three methods are all set to 1000. The mean value of RCS is compared as follows: Figure 8As shown in Figure 2, both the AWE method and the AWE+MLFMA method are found to be consistent with the Monte Carlo method. This demonstrates that the improved AWE-based perturbation method proposed in this paper can be used in conjunction with the fast multipole method to significantly improve computational speed while maintaining accuracy. Table 2 shows a comparison of time and memory consumption.

[0084] Table 2

[0085]

[0086] As shown in Table 2, the method proposed in this invention, combined with fast multipole analysis, reduces memory usage by a factor of four. Compared to the Monte Carlo method, which samples 1,000 times, the speed is increased by a factor of 5.5. This demonstrates the advantage of the method proposed in this invention over Monte Carlo in terms of computational speed while maintaining accuracy.

Claims

1. A new electromagnetic characteristic calculation method for metallic targets with uncertain shapes based on AWE technology, characterized by: The steps include: Step 1: Use FEKO software and NURBS modeling technology to model the non-cooperative metal target: Use NURBS technology to establish a model with controllable target shape; combine the coordinates of all control points into a row vector, which is defined as the shape vector; Step 2: Establish a hybrid field integral equation for the shape vector: Expand the impedance matrix, right-hand side vector, and current of the shape vector into Taylor series to derive the expression of the current moment vector. Then, determine the variation range of the introduced shape vector, construct the D matrix in the pseudo-spectral method, calculate the product of the matrix derivative vectors of each order and the derivative of the right-hand side vector, and then obtain the current moment vectors of each order. Establish the equation of the Taylor series and the Padé polynomial, derive the relationship between the current moment vector and the Padé polynomial vector coefficients, and then calculate the vector coefficients. Based on the random variation of the vector coefficients and the shape vector, obtain the current after the model changes once. The details are as follows: First, the matrix equation of the metal target CFIE containing the random variable α is established: Z(α)·I(α)=b(α) (1) Where Z(α) is the impedance matrix of the hybrid field integral equation, I(α) is the surface current, and b(α) is the right-hand side vector. The hybrid field integral equation is expressed as a combination of the electric field integral equation and the magnetic field integral equation. The impedance matrix is ​​expressed as: Z(a)=a c ·Z EFIE (a)+(1-a c )·Z MFIE (a) (2) α c is the combination coefficient, which ranges from 0 to 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-hand side vector in the mixed field integral equation is expressed as: b(a)=b EIFE (a)+b MFIE (a) (3) Among them, b EIFE (α) is the right-hand side vector in the electric field integral equation, b MFIE (α) is the right-hand side vector in the magnetic field integral equation; The mixed field matrix equation is expressed as follows: [a c ·Z EFIE (a)+(1-a c )·Z MFIE (a)]·I(a)=b EIFE (a)+b MFIE (a) (4) According to the asymptotic waveform estimation theory, the impedance matrix and right-hand side vector of the hybrid field integral equation are expanded into the form of Taylor series: is the random variation introduced by the sth element in the shape vector; k is the order of the derivative of the shape vector, L and M are the highest orders of the numerator and denominator in the Padé polynomial respectively; α0 represents the shape vector of the original model; α s Represents any element in the shape vector, that is, any coordinate of any point; The current is expressed as the product of the current moment vector and the shape change: By matching the various order variables in the hybrid field integral equation, the current moment vector is obtained as follows: m0=Z -1 (α0)·b(α0) (8) The equations for the Padé approximation polynomial and Taylor series regarding the current are established as follows: a i and b j The expression is as follows: According to the Chebyshev–Gauss–Lobatto interpolation method, N+1 interpolation nodes are determined in the range [α0-Δα,α0+Δα], each node is represented by α j , which is expressed as follows: According to the pseudo-spectral method, the D matrix is ​​constructed and the first-order derivative expression of the right-hand vector is calculated as follows: The dimension of the D matrix is ​​(N+1)*(N+1), b(α j ) is a one-dimensional right-hand side vector when any vector, and its dimension is the number of unknown quantities in the model, that is, for A two-dimensional matrix, j = -N / 2, ..., N / 2; where the D matrix is ​​expressed as follows: When the first-order derivative of the right-hand side vector is known, its second-order derivative is calculated as follows: [b (2) (a j )]=D·[b (1) (a j )]=D·D·[b(α j )] (20) Get the nth derivative b of the right vector (n) (α0): The impedance matrix is ​​calculated by multiplying the impedance matrix and the moment vector under each interpolation vector instead of directly calculating the impedance matrix; where Z(α -N / 2 )m n-i The dimension is The dimension of the reconstructed prior matrix is The derivative of the impedance matrix and the derivative of the moment-vector product Z (k) (α0)m n-i Calculated by D matrix: The pseudo-spectral 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 the current moment vector m of each order is calculated. n , according to the current moment vector m n The coefficient vector a in the Padé approximation polynomial i and b j The relationship between the surface current of the model after each random sampling change is calculated; Step 3. Calculate the RCS after the model changes once based on the coordinate information and corresponding current after the model changes. Calculate the RCS after each model change using the AWE-based perturbation method based on the set number of sampling times. Perform statistical analysis on the RCS sampled multiple times to obtain the electromagnetic scattering characteristics of the uncertain shape non-cooperative metal target.

2. The novel electromagnetic characteristic calculation method of a metal target with an electrically large uncertain shape based on AWE technology according to claim 1 is characterized in that: As described in step 1, a model with controllable target shape is established based on NURBS technology; the coordinates of all control points of the model are combined into a row vector, which is defined as the shape vector and represented by α; α is expanded into [α1, α2, α3, ..., α n-2 ,α n-1 ,α n ], where α1, α2, and α3 represent the x, y, and z coordinates of the first coordinate point in the NURBS modeling file; First, the initial target model is established using FEKO software, without introducing the random variable Δα. This model is then imported into Rhino software for reconstruction, which involves resetting the coordinates of the control points and establishing the surface. Ultimately, the coordinates of the control points that make up the surface and the coordinates of the different control points are obtained. The target shape can be flexibly changed by introducing a random variable Δα into the shape vector α; Δα is the range of the variation, Δα=[Δα1,Δα2,Δα3,...,Δα n-2 ,Δα n-1 ,Δα n ]; In the target model containing α+Δα, the subdivision size in the u and v directions is set for each surface according to the wavelength of the incident electromagnetic wave, and the model is subdivided using the RWG basis function; the target surface is subdivided into several triangles using the NURBS technology, and the mixed field integral equation is established based on the RWG basis function.

3. The novel electromagnetic characteristic calculation method of a metal target with an electrically large uncertain shape based on AWE technology according to claim 2 is characterized in that: The segmentation size is set to be smaller than one tenth of the wavelength.

4. The novel electromagnetic characteristic calculation method of a metal target with an electrically large uncertain shape based on AWE technology according to claim 1 is characterized in that: In step 3, the RCS after the model changes once is calculated based on the coordinate information and the corresponding current after the model changes. The RCS after each model change is calculated using the AWE-based perturbation method according to the set number of sampling times. The RCS of multiple samplings is statistically analyzed to obtain the electromagnetic scattering characteristics of the uncertain shape non-cooperative metal target. Specifically: The model is re-established based on the random variables introduced when calculating the current, and the radar cross-section after the model is changed once is calculated using the surface current and the re-established model shape information; Calculate the electromagnetic scattering characteristics of the deterministic target after each random change of the model; The mean and variance of the RCS responses obtained from multiple samplings are calculated to obtain the electromagnetic scattering characteristics of non-cooperative metal targets with uncertain shapes.

5. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the steps of the method according to any one of claims 1 to 4 are implemented.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method according to any one of claims 1 to 4 are implemented.

7. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 4 are implemented.

Images