Electromagnetic characteristics extraction method of target in inhomogeneous medium based on multi-dimensional uncertainty based on volume integral equation

Abstract

The present invention discloses a method for extracting electromagnetic characteristics of a multi-dimensional uncertain inhomogeneous dielectric target based on a volume integral equation. The method comprises the following steps: first, a model is established for the target using non-rational B-spline technology and ANSYS software. Then, several control points are used as random variables of the shape to control the target's slight deformation, and the dielectric constant change of the medium can be controlled by the random variable of the dielectric constant. Then, the random variables of the shape and dielectric constant are introduced into the volume integral equation through a perturbation method. Finally, the perturbation current is iteratively solved by sampling the change of the random variables multiple times, and the radar cross section of the target model after the slight change of the shape or dielectric constant is calculated, as well as the statistical mean and variance of all RCS responses. This method can take into account the impact of slight deformation of the target shape or slight jitter of the dielectric constant.

Description

Technical Field

[0001] The present invention belongs to the technical field of numerical calculation of target electromagnetic scattering characteristics, in particular to a method for extracting electromagnetic characteristics of a multi-dimensional uncertain inhomogeneous medium target based on a volume integral equation. Background Art

[0002] In general electromagnetic analysis problems, the target's geometric shape ideally remains unchanged, so the electromagnetic properties of a target with a defined shape are analyzed. However, due to factors such as manufacturing processes, the external environment, and human factors, uncertainties exist in the target's geometric shape and dielectric constant in real-world situations. To analyze the uncertainties in shape and dielectric constant, the derivative form of the volume integral equation (VSIE) is introduced. The volume integral equation can address the scattering characteristics of metal-dielectric hybrid structures. The volume integral equation acts on the dielectric region, while the surface integral equation acts on the metal region. This makes the volume integral equation applicable to any general metal-dielectric hybrid structure, without requiring a specific model. Furthermore, its application to dielectric problems can address inhomogeneous dielectric problems.

[0003] The most classic and widely used method for solving uncertain electromagnetic scattering problems is the Monte Carlo method (MC). This method, proposed in the mid-twentieth century, is a numerical computational technique that combines probability and statistics. The Monte Carlo method replaces uncertainty by generating random numbers, decomposing the uncertain problem into multiple deterministic problems. The statistical values of these problems are then calculated one by one to approximate the numerical solution. Therefore, for each different random number, the Monte Carlo method must recalculate the solution to the problem. Although the program is simple and easy to understand, it has a slow convergence rate and a long computation time.

[0004] In order to solve the shortcomings of the Monte Carlo method mentioned above, the perturbation method can sacrifice a little accuracy within an acceptable range to improve the calculation speed of uncertainty problems. From a mathematical point of view, the principle and essence of the perturbation method is the expansion approximation of the Taylor series. When the initial model to be solved has a relatively small change, and the electromagnetic scattering calculation law and characteristics of the model are known, the initial value obtained by the initial model can be used to add the perturbation value to approximate the electromagnetic scattering value of the model after the small perturbation. Compared with the Monte Carlo method, the perturbation method greatly reduces the calculation time and avoids the repeated modeling and solution process after each change in shape or dielectric constant. Based on the principle of the perturbation method and the volume integral equation, the present invention can realize rapid solution and analysis of the electromagnetic scattering characteristics of inhomogeneous medium targets with uncertain shape and uncertain dielectric constant. Summary of the Invention

[0005] The object of the present invention is to provide a method for extracting target electromagnetic characteristics based on uncertainty shape and dielectric constant of volume integral equation.

[0006] The technical solution to achieve the purpose of the present invention is: a method for extracting electromagnetic characteristics of a target in a multi-dimensional uncertain inhomogeneous medium based on a volume integral equation, the steps of which are as follows:

[0007] Step 1. Use NURBS modeling to make the target shape controlled by control points: Use NURBS modeling to make the target shape controlled by multiple control points, and combine the SWG basis function used in the volume integral equation with NURBS modeling, so that the coordinates of any point on the object surface can be expressed by the shape random variable α;

[0008] Step 2: Substitute the shape random variable α and the dielectric constant random variable ε r Introduced into the volume integral equation: the coordinates of any point on the target surface can be represented by the shape random variable α, and the dielectric constant of the medium in the target can be represented by the random variable ε r Indicates that the volume integral equation is related to the random variables α and ε r Combined; then calculate the derivative impedance matrix and the right side vector of the derivative, obtain the median current by solving the equation, and approximate the disturbance current by Taylor expansion;

[0009] Step 3. Each change in shape and dielectric constant is randomly generated within a certain range. Through each randomly generated change, the current of the model after the corresponding synchronous change is obtained. Finally, the current is solved by the matrix equation to obtain the RCS after the model change. After obtaining each RCS through the perturbation method, all RCS responses are statistically analyzed to obtain the electromagnetic scattering characteristics of the target with uncertain shape and uncertain dielectric constant. The statistical mean and variance of the RCS response are calculated and compared with the statistical mean and variance of the Monte Carlo method.

[0010] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the method for extracting electromagnetic characteristics of a target in a multi-dimensional uncertain inhomogeneous medium based on a volume integral equation is implemented.

[0011] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the above-mentioned method for extracting electromagnetic characteristics of a multi-dimensional uncertain inhomogeneous medium target based on a volume integral equation.

[0012] Compared with the existing technology, the present invention has the following significant advantages: (1) By combining NURBS surfaces with SWG basis functions, independent control points can be used to control each surface, thereby controlling the overall shape of the object and introducing random variables into the volume integral equation; (2) Based on the principle of the perturbation method, the uncertainty of the shape and the uncertainty of the dielectric constant are combined with the volume integral equation. Only the electromagnetic scattering of the initial median model needs to be calculated. The changed model can be superimposed and analyzed using the formula of the perturbation method, which greatly reduces the calculation time. In addition, this method can simultaneously handle the multi-dimensional uncertainty problem of the shape and dielectric constant; (3) The volume integral equation can handle the uncertainty problem of inhomogeneous media. By combining the uncertainty of the shape and the uncertainty of the dielectric constant with the volume integral equation, the uncertainty problem of inhomogeneous media can be handled. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 It is a schematic diagram of RWG basis function.

[0014] Figure 2 It is a schematic diagram of SWG basis function.

[0015] Figure 3 It is a cube model diagram.

[0016] Figure 4 This is a comparison chart of the RCS statistical results (mean and variance) of the dielectric cube model with an uncertain shape.

[0017] Figure 5 It is a diagram of a cylindrical model.

[0018] Figure 6 This is a comparison chart of the RCS statistical results (mean and variance) of a dielectric cylinder model with uncertain shape and uncertain dielectric constant.

[0019] Figure 7 It is a multi-media prism model diagram.

[0020] Figure 8 This is a comparison chart of the RCS statistical results (mean and variance) of the inhomogeneous medium prism model with uncertain shape and uncertain dielectric constant.

[0021] Tables 1 to 3 compare the memory and computation time of this method with the Monte Carlo method. DETAILED DESCRIPTION

[0022] The present invention discloses a method for extracting electromagnetic characteristics of a multidimensional uncertainty inhomogeneous medium target based on a volume integral equation. The method comprises the following steps: first, a model is established on the target using non-uniform rational B-spline (NURBS) technology and ANSYS software, and then several control points are used as random variables of the shape to control the target's slight deformation, and the dielectric constant change of the medium can be controlled by the random variable of the dielectric constant. Then, the random variables of the shape and dielectric constant are introduced into the volume integral equation (VSIE) by a perturbation method. Finally, the variation of the random variables is sampled multiple times, and the perturbation current is iteratively solved each time. The radar cross section (RCS) of the target model after the shape or dielectric constant is slightly changed, as well as the statistical mean and variance of all RCS responses, are calculated. This method can take into account the impact of slight deformation of the target shape or slight jitter of the dielectric constant.

[0023] The present invention is further described in detail below with reference to the accompanying drawings.

[0024] Step 1: Model the NURBS surface. The definition of the NURBS surface requires the use of B-spline basis functions. The surface of a three-dimensional target can be approximated by multiple NURBS surfaces. The shape of a NURBS surface can be controlled by multiple control points through a two-variable piecewise rational function. The coordinates of any point on the surface can be expressed by the coordinates of the control points on the NURBS surface. The coordinate expression of any point on the NURBS surface is written as:

[0025]

[0026] Where U and V represent the number of control points in the u and v directions respectively. p and q are the corresponding orders. ij =[P ijx ,P ijy ,P ijz ] represent the coordinates of the control point in the x, y, and z directions respectively. ij is the corresponding weight. N i,p (u) is the node vector U=[u0,u1,...,u n+k+1 ] According to the Cox-DeBoor recursive formula, the p-order canonical B-spline basis function is obtained. Similarly, N j,q (v) is the node vector V = [v0,v1,...,v n+k+1 ]The q-order canonical B-spline basis function is obtained according to the Cox-DeBoor recursive formula.

[0027] The target shape can then be represented by a NURBS surface, where each coordinate point on the surface is related to the coordinates of the control point, i.e., the shape random variable α. Based on the meshing model established with the NURBS surface, the model is meshed using SWG basis functions in ANSYS software to obtain the meshing model required for the volume integral equation.

[0028] Step 2: Substitute the shape random variable α and the dielectric constant random variable ε r Introduced into the volume integral equation: the coordinates of any point on the target surface can be represented by the shape random variable α, and the dielectric constant of the medium in the target can be represented by the random variable ε r Indicates that the volume integral equation is related to the random variables α and ε r Then calculate the derivative impedance matrix and the right side vector of the derivative, and obtain the median current by solving the equation and the Taylor expansion approximation to obtain the disturbance current. The details are as follows:

[0029] First, the matrix equation formed by introducing the shape random variable α into the volume integral equation is as follows:

[0030]

[0031] D n , I n and is the current coefficient on the body and surface and the right-hand side vector with random variables, and its impedance matrix is given by Z DD (α), Z DM (α), Z MD (α), Z MM (α) is composed of four parts, and the specific expression of the impedance matrix is:

[0032]

[0033]

[0034] Where ω is the angular frequency, μ is equal to 4π×10 -7 H / m, ε0 is equal to ε(r′) is the dielectric constant of the medium, Ω m is the basis function The total boundary surface of the corresponding tetrahedron, n is Ω m is the external normal vector of , and G(r,r′) is the free space Green’s function.

[0035] f v (r), f s (r) are SWG basis functions and RWG basis functions respectively. The basis functions of RWG are as follows: Figure 1 Its mathematical expression is as follows, where r represents and For any observation point in and and Represents the upper triangle and the lower triangle The free vertices corresponding to the common edge are the other two points except the two end points of the common edge. n is the length of the common side, is the area of the triangle.

[0036]

[0037] SWG basis functions such as Figure 2 As shown; the SWG basis function is defined in a similar way to the RWG basis function, using two tetrahedrons with common faces to replace the triangle pairs with common edges. Its mathematical expression is as follows, where a n is the area of the public surface, is the volume of the tetrahedron, The definition is similar to that in the RWG basis function.

[0038]

[0039] K in the formula n 、 It is a quantity related to the dielectric constant and its expression is as follows:

[0040]

[0041] Similarly, the vector on the right can also be expressed by the shape random variable α, expressed as volume integral and surface integral respectively. After introducing the random variable, the expression is as follows:

[0042]

[0043] So we obtain the surface integral equation with the shape random variable α.

[0044] Similarly, we will use the random variable ε of the dielectric constant r Introduced into the volume integral equation, the volume integral equation formed is as follows:

[0045]

[0046] For the impedance matrix of dielectric constant, only Z DD , Z DM The two terms are related to the dielectric constant of the medium, so they are combined with the random variable ε r Combined with the above, the vector on the right is also independent of the dielectric constant. DD (ε r ), Z DM(ε r ) is represented as follows:

[0047]

[0048] In order to solve the multi-dimensional uncertainty problem, the shape random variable α and the dielectric constant random variable ε can be simultaneously r Introduced into the volume integral equation, we get α and ε r The volume integral equation of two variables is as follows:

[0049]

[0050] Z DD (α,ε r ), Z DM (α,ε r ) is as follows:

[0051]

[0052] Through this formula, the disturbance current can be calculated when the shape and dielectric parameters change simultaneously.

[0053] Next, we need to construct the derivative impedance matrix and the right-hand side vector of the surface integral equation. Let α c To determine the size of the random variable when the model is running, Δα is the maximum value of the random variable change, α i For the interval [α c -Δα,α c +Δα], where i = 1,…n, n represents the number of random variables; for the uncertainty of the target shape, the random variable α i These are the coordinates of the control points on the target.

[0054] According to the perturbation method theory, the matrix equation is c The first-order Taylor series expansion is as follows:

[0055]

[0056] Δα i is the change of the i-th random variable, n is the number of random variables, and the disturbance current is obtained by simplifying and discarding the high-order terms From the formula, we can see that we only need to find the derivative matrix and the right side vector of the derivative The perturbation current can be obtained. For each changed model, its current can be obtained by multiplying the perturbation current and the change of the random variable. The derivative impedance matrix expression of the surface integral equation is as follows, which also consists of four parts:

[0057]

[0058]

[0059] The vector expression on the right side of the derivative of the surface integral equation is as follows:

[0060]

[0061] For the dielectric constant, consistent with the shape change, let ε c To determine the size of the random variable in the model, Δε r is the maximum value of the random variable change, ε r For the interval [ε c -Δε r ,ε c +Δε r ], for any value within the target dielectric constant, the random variable ε r This is the dielectric constant of the target change.

[0062] According to the perturbation method theory, the matrix equation is r Use the first-order Taylor series expansion at , because the vector on the right is independent of the dielectric constant, so the expression is as follows:

[0063]

[0064] Δε r is the change of the random variable, and m is the number of media whose dielectric constant changes. By simplifying and discarding the high-order terms, the perturbation current is obtained From the formula, we can see that we only need to find the derivative matrix The disturbance current can be obtained. For each changed model, its current can be obtained by multiplying the disturbance current and the change of the random variable; the derivative impedance matrix expression of the surface integral equation is as follows:

[0065]

[0066] In order to solve the multi-dimensional uncertainty problem of simultaneous changes in shape and dielectric constant, random variations α and ε are introduced simultaneously. r The volume integral equation is derived. That is, additional solution is obtained and The other processes are the same as solving the derivative impedance matrix of the shape and dielectric constant separately. r After obtaining the derivative impedance matrix of the volume integral equation, the Taylor formula can be used to solve the electromagnetic scattering characteristics problem with multi-dimensional uncertainty.

[0067] When the direction, frequency of the incident wave and the shape and size of the target are determined, for each different random variation Δα i and Δεr , simply finding the impedance matrix of the first median, the right-hand side vector, the derivative of the impedance matrix, and the derivative of the right-hand side vector allows the perturbation current to be obtained using Taylor's formula. Therefore, the current variation caused by the multidimensional uncertainty of the target shape and dielectric constant can be approximately represented by the product of the perturbation current and the change in the random variable.

[0068] Step 3: Calculate the model current after the corresponding control point changes synchronously using each randomly generated change. Finally, solve the matrix equation to obtain the RCS after the model changes. After obtaining each RCS using the perturbation method, perform a statistical analysis of all RCS responses to determine the electromagnetic scattering characteristics of a target with an uncertain shape and dielectric constant. Calculate the statistical mean and variance of the RCS response and compare them with the statistical mean and variance of the Monte Carlo method.

[0069] The technical solution of the present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0070] Example 1

[0071] This embodiment performs electromagnetic scattering calculations on a dielectric cube with an uncertain shape. This embodiment is implemented on a computing platform with an Intel(R) Core(TM) i7-7700K CPU @ 3.6GHz and 8GB of memory. The dielectric cube model is as follows: Figure 3 As shown, the cube has a side length of 0.5m and a dielectric constant ε r =(2,0). By using the NURBS surface modeling method, the cube model can be constructed using 6 NURBS surfaces and controlled by 8 control points. The cube range is [-0.05m, 0.05m], which is determined by Figure 3 The Z coordinates of the four control points shown are controlled. Therefore, we only need to set the Z coordinates of the four control points as random variables. The plane wave incident frequency is 300 MHz and the direction is θ = 0°. Where θ is the pitch angle, is the azimuth. The observation angle is θ=0~180°, Using the same incident wave setting, the Monte Carlo method with 1000 sampling times is compared with the method of the present invention. The statistical change results of RCS are as follows: Figure 4 As shown in Figure 1, the two curves agree well. The comparison of the computation time and memory usage of the two methods is shown in Table 1.

[0072] Table 1

[0073]

[0074] As can be seen from Table 1, the memory required by the method of the present invention is larger than that required by the Monte Carlo method, but the calculation time is much shorter than the Monte Carlo method with 1000 samples. This shows that the method of the present invention has the advantage of faster calculation speed than the Monte Carlo method.

[0075] Example 2

[0076] This example performs electromagnetic scattering calculations on a dielectric cylinder model with an uncertain shape and an uncertain dielectric constant. The dielectric cylinder is 0.5 m high, 0.1 m in radius, and the dielectric constant of the medium is ε r =(2,0). The control points on the NURBS surface are distributed as follows Figure 5 As shown in the figure, the z coordinate of the control point is used as a random variable to control the height of the dielectric cylinder, and the range of variation is [-0.05m, 0.05m]. At the same time, the dielectric constant of the cylinder varies in the range of [-0.1, 0.1]. The incident wave and observation angle settings are consistent with Example 1. Similarly, the RCS statistical results of the method of the present invention are compared with the Monte Carlo method with 1000 sampling times. The comparison results are shown as follows: Figure 6 As shown, the two curves agree well, indicating that the method of the present invention is also very applicable to models with uncertain shapes and uncertain media. Table 2 shows the memory and time comparison of the two methods.

[0077] Table 2

[0078]

[0079] As can be seen from Table 2, the memory required by the method of the present invention is larger than that required by the Monte Carlo method, but the calculation time is much shorter than the Monte Carlo method with 1000 samples. This shows that the method of the present invention has the advantage of faster calculation speed than the Monte Carlo method.

[0080] Example 3: This example performs electromagnetic scattering calculations on a multi-medium pyramid model with uncertain shapes and uncertain dielectric constants. The pyramid is divided into three types of media: Figure 7 As shown in the figure, the bottom length of the first part is 0.3m, the top length is 0.2m, and the height is 0.2m. The dielectric constant of medium 1 is ε1=(3,0). The bottom length of the second part is 0.4m, the top length is 0.3m, and the height is 0.2m. The dielectric constant of medium 2 is ε2=(2,0). The bottom length of the third part is 0.5m, the top length is 0.4m, and the height is 0.2m. The dielectric constant of medium 3 is ε3=(1.5,0). The distribution of the control points on the NURBS surface is shown as follows. Figure 7As shown in the figure, the z coordinates of the four control points are used as random variables to control the height of the dielectric prism, with a range of [-0.05m, 0.05m]. At the same time, the dielectric constant of the first part is changed, with a range of [-0.1, 0.1]. The incident wave and observation angle settings are consistent with those in Example 1. Similarly, the RCS statistical results of the method of the present invention are compared with the Monte Carlo method with 1000 sampling times. The comparison results are shown in the figure. Figure 8 As shown, it can be seen that the two curves agree well, which shows that the method of the present invention is also very applicable to multimedia models with uncertain shapes. Table 3 shows the memory and time comparison of the two methods.

[0081] Table 3

[0082]

[0083] Table 3 also shows that the method of the present invention has an advantage of faster calculation speed than the Monte Carlo method.

[0084] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A method for extracting electromagnetic characteristics of a target in a multi-dimensional uncertain inhomogeneous medium based on a volume integral equation, comprising the following steps: Step 1. Using NURBS modeling to make the target shape controlled by control points: Using NURBS modeling to make the target shape controlled by multiple control points, and combining the SWG basis function used in the volume integral equation with NURBS modeling, the coordinates of any point on the object surface are represented by the shape random variable α; Step 2: Substitute the shape random variable α and the dielectric constant random variable ε r Introduced into the volume integral equation: the coordinates of any point on the target surface are represented by the shape random variable α, and the dielectric constant of the medium in the target is represented by the random variable ε r Indicates that the volume integral equation is related to the random variables α and ε r Combined; then calculate the derivative impedance matrix and the right side vector of the derivative, obtain the median current by solving the equation, and approximate the disturbance current by Taylor expansion; the details are as follows: First, the matrix equation formed by introducing the shape random variable α into the volume integral equation is as follows: D n , I n and is the current coefficient on the body and surface and the right-hand side vector with random variables, and its impedance matrix is given by Z DD (α), Z DM (α), Z MD (α), Z MM (α) is composed of four parts, and the specific expression of the impedance matrix is: Where ω is the angular frequency, ε(r′) is the dielectric constant of the medium, Ω m is the basis function The total boundary surface of the corresponding tetrahedron, n is Ω m The external normal vector of , G(r,r′) is the free space Green’s function; f v (r), f s (r) are SWG basis function and RWG basis function respectively, and their mathematical expressions are as follows, where r represents and For any observation point in and and Represents the upper triangle and the lower triangle The free vertices corresponding to the common edge are the other two points except the two end points of the common edge; n is the length of the common side, is the area of the triangle; The SWG basis function is defined in a similar way to the RWG basis function, replacing the triangle pair with common edges with two tetrahedrons with common faces; its mathematical expression is as follows, where a n is the area of the public surface, is the volume of the tetrahedron, The definition is similar to that in the RWG basis function; K in the formula n 、 It is a quantity related to the dielectric constant and its expression is as follows: Similarly, the vector on the right can be represented by the shape random variable α, which can be expressed as volume integral and surface integral respectively. After introducing the random variable, the expression is as follows: Obtain the volume integral equation with the shape random variable α; The random variable ε of the dielectric constant r Introduced into the volume integral equation, the volume integral equation formed is as follows: For the impedance matrix of dielectric constant, only Z DD , Z DM The two terms are related to the dielectric constant of the medium, so they are combined with the random variable ε r Combined with the above, the vector on the right is also independent of the dielectric constant; Z DD (ε r ), Z DM (ε r ) is represented as follows: At the same time, the shape random variable α and the dielectric constant random variable ε r Introduced into the volume integral equation, we get α and ε r The volume integral equation of two variables is as follows: Z DD (α,ε r ), Z DM (α,ε r ) is as follows: By using the above formula, the disturbance current when the shape and dielectric parameters change simultaneously is calculated; Next, construct the derivative impedance matrix and the right side vector of the surface integral equation; let α c To determine the size of the random variable when the model is running, Δα is the maximum value of the random variable change, α i For the interval [α c -Δα,α c +Δα], where i = 1,…n, n represents the number of random variables; for the uncertainty of the target shape, the random variable α i That is the coordinates of the control point on the target; According to the perturbation method theory, the matrix equation is c The first-order Taylor series expansion is as follows: Δα i is the change of the i-th random variable, n is the number of random variables, and the disturbance current is obtained by simplifying and discarding the high-order terms From the formula, we can see that we only need to find the derivative matrix and the right side vector of the derivative The disturbance current can be obtained. For each changed model, the current can be obtained by multiplying the disturbance current and the change of the random variable. The derivative impedance matrix expression of the surface integral equation is as follows, which also consists of four parts: composition: The vector expression on the right side of the derivative of the surface integral equation is as follows: For the dielectric constant, consistent with the shape change, let ε c To determine the size of the random variable in the model, Δε r is the maximum value of the random variable change, ε r For the interval [ε c -Δε r ,ε c +Δε r ], for any value within the target dielectric constant, the random variable ε r That is the dielectric constant of the target change; According to the perturbation method theory, the matrix equation is r Use the first-order Taylor series expansion at , because the vector on the right is independent of the dielectric constant, so the expression is as follows: Δε r is the change of the random variable, m is the number of media whose dielectric constant changes; by simplifying and discarding the high-order terms, the perturbation current is obtained From the formula, we can see that we only need to find the derivative matrix The disturbance current can be obtained. For each changed model, its current can be obtained by multiplying the disturbance current and the change of the random variable; the derivative impedance matrix expression of the surface integral equation is as follows: For the simultaneous introduction of random variations α and ε r The volume integral equation is derived; that is, additional solution is obtained and The rest of the process is the same as solving the derivative impedance matrix of the shape and dielectric constant separately; The random variation α and ε are introduced simultaneously r After obtaining the derivative impedance matrix of the volume integral equation, Taylor's formula is used to solve the electromagnetic scattering characteristics problem with multi-dimensional uncertainty. When the direction, frequency of the incident wave and the shape and size of the target are determined, for each different random variation Δα i and Δε r , it is only necessary to find the impedance matrix of the first median, the right-hand side vector, the derivative of the impedance matrix, and the derivative of the right-hand side vector, and the perturbation current can be obtained through Taylor's formula. Therefore, the change in current caused by the multidimensional uncertainty of the target shape and dielectric constant can be approximately expressed by the product of the perturbation current and the change in the random variable. Step 3: Each time the change in shape and dielectric constant is randomly generated within a certain range, the current of the model corresponding to the synchronous change is obtained through each randomly generated change. Finally, the current is solved by the matrix equation to obtain the RCS of the model after the change; After obtaining each RCS through the perturbation method, a statistical analysis is performed on all RCS responses to obtain the electromagnetic scattering characteristics of a target with uncertain shape and dielectric constant. The statistical mean and variance of the RCS responses are calculated and compared with the statistical mean and variance of the Monte Carlo method.

2. The method for extracting electromagnetic characteristics of a target in a multi-dimensional uncertain inhomogeneous medium based on a volume integral equation according to claim 1 is characterized in that: As described in step 1, the target shape is controlled by the control points through NURBS modeling, and the SWG basis function used in the volume integral equation is combined with the NURBS modeling, so that the coordinates of any point on the object surface are represented by the shape random variable α. The terms related to the triangle coordinates in the volume integral equation are combined with the shape random variable α, as follows: Step 1: Model the NURBS surface. The definition of the NURBS surface requires the use of B-spline basis functions. The surface of a three-dimensional target can be approximated by multiple NURBS surfaces. The shape of a NURBS surface can be controlled by multiple control points through a two-variable piecewise rational function. The coordinates of any point on the surface are represented by the coordinates of the control points on the NURBS surface. The coordinate expression of any point on the NURBS surface is written as: Among them, U and V represent the number of control points in the u and v directions respectively; p and q are the corresponding orders; P ij =[P ijx ,P ijy ,P ijz ] represent the coordinates of the control point in the x, y, and z directions respectively; w ij is the corresponding weight; N i,p (u) is the node vector U=[u0,u1,...,u n+k+1 ]According to the Cox-DeBoor recursive formula, the p-order canonical B-spline basis function, N j,q (v) is the node vector V = [v0,v1,...,v n+k+1 ] The q-order canonical B-spline basis function is obtained according to the Cox-DeBoor recursive formula; the target shape is represented by a NURBS surface, and each coordinate point on the surface is related to the coordinate of the control point, that is, the shape random variable α; based on the segmentation model established by the NURBS surface, the model is segmented using the SWG basis function through the ANSYS software to obtain the segmentation model required for the volume integral equation.

3. The method for extracting electromagnetic characteristics of a target in a multi-dimensional uncertain inhomogeneous medium based on a volume integral equation according to claim 1 is characterized in that: μ in free space is equal to 4π×10 -7 H / m, ε0 is equal to 4. An electronic 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 method for extracting electromagnetic characteristics of a multi-dimensional uncertain inhomogeneous medium target based on a volume integral equation as described in any one of claims 1 to 3 is implemented.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the method for extracting electromagnetic characteristics of a target in a multi-dimensional uncertain inhomogeneous medium based on a volume integral equation as described in any one of claims 1 to 3 is implemented.

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