Broadband scattering RCS acquisition method and system based on adaptive integral method and pseudo-spectral derivative method

Abstract

The invention discloses a broadband scattering RCS acquisition method and system based on an adaptive integral method and a pseudo-spectral derivative method, and mainly solves the problems of overlarge memory occupation, low calculation efficiency and unstable precision in the prior art. According to the implementation scheme, boundary conditions are applied to a composite electromagnetic target to obtain an EFIE-PMCHWT integral equation of an electromagnetic field, and discretization, Galerkin testing and fast Fourier transform are carried out on the EFIE-PMCHWT integral equation to obtain a near-field impedance matrix; selecting GLC interpolation sampling points at the center frequency based on a pseudo-spectral method to generate a pseudo-spectral derivative matrix, and performing linear combination on the pseudo-spectral derivative matrix by a near-field impedance matrix to obtain a high-order impedance matrix; setting a rectangular grid used for surrounding the composite target, projecting current and charges of the composite target to grid points, and expanding the current into Taylor series and expanding the frequency band of the current by using an asymptotic waveform technology; and the broadband electromagnetic scattering characteristic is calculated according to the frequency band and the moment coefficient. According to the method, memory occupation is reduced, calculation efficiency and precision are improved, and the method can be used for analyzing the broadband characteristic of the dielectric / metal composite object.

Description

Technical Field

[0001] The present invention belongs to the technical field of electromagnetic simulation, and in particular relates to a method and system for acquiring broadband scattering RCS, which can be used for rapid calculation and analysis of electromagnetic broadband scattering characteristics of composite targets. Background Art

[0002] Radar cross section (RCS) is a physical quantity that measures the intensity of the echo scattering generated by a target when illuminated by radar waves. It possesses the important electromagnetic properties of miniaturization, bandgap structure, and localized resonance. Antenna scattering often limits a system's stealth capabilities. In particular, radar detection and identification require calculation and analysis of the target's RCS, making it a critical factor in electronic device design. Antennas typically have both conductive and dielectric composite structures. Compared to purely conductive models, the interaction between the conductive and dielectric surfaces complicates analysis. Compared to perfect conductor problems, the mechanistic mechanisms of electromagnetic properties in composite materials are more complex, making the analysis and calculation more difficult. In most cases, both surface integral equations (SIEs) and volume integral equations (VIEs) can be used to solve electromagnetic problems in dielectric media. Efficient electric field and EFIE-PMCHWT integral equation methods can be used to solve more complex structures with various dielectric materials and certain arbitrarily shaped perfect electric conductors (PECs). However, to obtain the RCS over a frequency range using the MoM method, iterative calculations must be performed at each frequency within the desired range, a process that consumes significant computational time. In order to improve computational efficiency, various fast frequency sweeping methods have been studied, and techniques such as Chebyshev approximation, model-based parameter estimation (MBPE), and asymptotic waveform evaluation (AWE) have been reported. Among them, a combination of AIM and AWE has been developed to analyze the scattering of PECs, but the efie-based MoM can only calculate the conductors of perfect conductors, and both involve complex derivatives of the Green's function, which makes the calculation process complicated.

[0003] Patent application publication number CN 116484642A discloses a "Method for Obtaining Broadband RCS of Periodic Structures Based on CBFM and AWE." Its implementation steps include: 1) initializing parameters; 2) calculating the excitation vector for each subregion; 3) calculating the induced current in each subregion at each frequency corresponding to the wavenumber; and 4) obtaining the broadband RCS of the periodic structure. While this method addresses the high memory requirements and long computation time associated with traditional methods when dealing with large unknowns, it can lead to low matrix equation solution efficiency when the frequency band is too wide or when the scattering characteristics vary significantly with frequency.

[0004] Patent application publication number CN 115859613A discloses a "method for estimating the electromagnetic scattering characteristics of targets in heterogeneous media based on the PMCHWT integral equation." Its implementation steps include: modeling using FEKO software; introducing random variables related to the dielectric constant into the PMCHWT integral equation; expanding the impedance matrix, right-hand side vector, and current at the median of the random variables using a Taylor series; deriving the current moment vector expression through moment coefficient matching; then applying the pseudospectral method to the AWE to calculate the current moment vector of various orders; then, using the rational Padé approximation, combining Taylor series and Padé polynomials, calculating the current and radar cross section of targets in different media; and finally, obtaining the mean and variance of all RCS responses through multiple sampling. While this method has a larger convergence radius than the Taylor method and significantly improves efficiency compared to the Monte Carlo method, its sampling frequency and random variable generation method fail to account for practical application scenarios, resulting in excessive memory usage in wide-band or strongly coupled scenarios. Summary of the Invention

[0005] The purpose of the present invention is to address the deficiencies of the above-mentioned prior art and propose a broadband scattering RCS acquisition method and system based on an adaptive integration method and a pseudo-spectral derivative method to reduce memory usage, improve computational efficiency and improve accuracy.

[0006] The technical approach to achieving the objectives of the present invention is as follows: solving integral equations through AIM reduces the storage of the zero-order impedance matrix, thereby reducing memory usage; combining the adaptive integration method with the moment method to accelerate the solution of the integral equation, thereby improving computational efficiency; and effectively suppressing the divergence of the Taylor series through an approximation based on the Padé method, ensuring that broadband results are consistent with the direct scanning method, accurately predicting the scattering characteristics of PECs and dielectric composites, and thus improving accuracy.

[0007] According to the above ideas, the technical solution of the present invention includes:

[0008] 1. A broadband RCS acquisition method based on an adaptive integration method and a pseudo-spectral derivative method, comprising:

[0009] (1) A set of EFIE-PMCHWT integral equations for the electric and magnetic fields are obtained by applying boundary conditions to a three-dimensional mixed object consisting of a PEC and a lossless homogeneous medium under plane wave illumination;

[0010] (2) The set of integral equations is discretized using RWG basis functions and subjected to Galerkin test to obtain the EFIE-PMCHWT matrix; the interaction calculation of the matrix is ​​accelerated by fast Fourier transform FFT to obtain the near-field impedance matrix Z near and store;

[0011] (3) Based on the pseudo-spectral method PSDM, GLC interpolation sampling points are selected at the center frequency of the three-dimensional mixed object, i.e., the composite target, to generate the pseudo-spectral derivative matrix D, and according to the near-field impedance matrix Z near Perform linear combination to obtain the high-order impedance matrix Z;

[0012] (4) A rectangular grid is set up to surround the composite target, and the current and charge of the composite target are projected onto these grid points. The unknown current I is expanded into a Taylor series at the center frequency by combining the asymptotic waveform AWE technique, and its Taylor expansion coefficient moment m is calculated based on the high-order derivative matrix Z. The effective frequency band of the Taylor series of the unknown current I(k) is then approximately expanded near the center frequency by the Pad'e algorithm.

[0013] (5) According to the expanded frequency band and Taylor expansion coefficient moment m, the induced current coefficient corresponding to each frequency is calculated. Based on the current coefficient, the total scattered electric field E generated by the composite target in the far area is calculated to obtain the broadband electromagnetic scattering characteristics RCS of the composite target.

[0014] Furthermore, in (3), based on the pseudo-spectral method PSDM, GLC interpolation sampling points are selected at the center frequency of the composite target to generate the pseudo-spectral derivative matrix D and the high-order impedance matrix Z, which is implemented as follows:

[0015] (3a) Using the GLC interpolation formula, write the i-th order derivative Z of the matrix Z(k) (i) The matrix form of (k):

[0016] (3b) Z (i) (k) The first half of the matrix is ​​represented as matrix D, and the coefficient D of D is calculated based on the value of the i-th row and j-th column of the matrix ij

[0017] (3c) According to the near-field impedance matrix Z near Perform a linear combination of D and use its coefficient D ij The high-order impedance matrix Z is calculated.

[0018] 2. A broadband RCS acquisition system based on an adaptive integration method and a pseudo-spectral derivative method, comprising:

[0019] Target construction module, used to define the target surface boundary conditions and obtain the electromagnetic field integral equation;

[0020] Discretization processing module, used to process composite electromagnetic targets using rectangular grid discretization, and convert continuous electromagnetic field integral equations into discrete physical equations;

[0021] The equation group conversion module is used to convert the physical equations satisfied by the discretized composite electromagnetic target into a linear equation group;

[0022] The extended frequency band module is used to expand the effective frequency band of the Taylor series of the unknown current near the center frequency and obtain the target surface current coefficient from the solution of the linear equations;

[0023] The electromagnetic target RCS acquisition module is used to obtain the far-field scattering field E by integrating the target surface current coefficient to calculate the RCS of the composite target.

[0024] Compared with the prior art, the present invention has the following advantages:

[0025] First, the present invention obtains a set of EFIE-PMCHWT integral equations for the electric and magnetic fields by applying boundary conditions to a three-dimensional mixed object composed of a PEC and a lossless homogeneous medium under plane wave irradiation. Then, through discretization and Galerkin test, an EFIE-PMCHWT matrix is ​​obtained. The interaction calculation of the matrix is ​​then accelerated by fast Fourier transform (FFT) to obtain and store the near-field impedance moment. Compared with the existing technology, there is no need to store high-order derivative matrices, thereby reducing memory usage.

[0026] Secondly, the present invention is based on the pseudo-spectral method (PSDM) optimization and selects GLC interpolation sampling points at the center frequency of the three-dimensional mixed object, i.e., the composite target, thereby avoiding the direct calculation of high-order Green's function derivatives, simplifying the moment iteration process, and thus improving the computational efficiency.

[0027] Third, since the present invention adopts the Padé method to expand the effective frequency band of the Taylor series, it can effectively suppress the divergence of the high-order terms of the Taylor series, improve the stability of the calculated values, ensure high accuracy within a wider frequency band, and thus improve the accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 This is a flow chart of the broadband RCS acquisition method based on the adaptive integration method and pseudo-spectral derivative method of the present invention;

[0029] Figure 2 Schematic diagram of the structure of the composite target used in the method of the present invention;

[0030] Figure 3 This is a block diagram of the broadband RCS acquisition system based on the adaptive integration method and pseudo-spectral derivative method of the present invention;

[0031] Figure 4 Figure 3 is a simulation data diagram of obtaining the broadband RCS of a composite target using the method of the present invention, the existing EFIE-PMCHWT, and the traditional AWE method. DETAILED DESCRIPTION

[0032] To help those skilled in the art better understand the present invention, the following will provide a clear and complete description of the technical solutions in the embodiments of the present invention, in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0033] It should be noted that the step numbers in the specification and claims of the present invention are only for a clear description of the implementation scheme of the present invention and for ease of understanding, and the order of the step numbers is not limited.

[0034] Example 1: Broadband RCS Acquisition Method Based on Adaptive Integration Method and Pseudospectral Derivative Method

[0035] Reference Figure 1 The implementation steps of this example include the following:

[0036] Step 1: Target modeling and current definition to obtain the integral equation EFIE-PMCHWT.

[0037] 1.1) PEC and lossless uniform medium under plane wave irradiation are combined into a three-dimensional mixed object to obtain a composite electromagnetic target, such as Figure 2 As shown,

[0038] 1.2) define the dielectric part Ω1 of the composite electromagnetic target as characterized by the dielectric constant ε1 and the magnetic permeability μ1, and define the free space Ω0 of the composite object as characterized by the dielectric constant ε0 and the magnetic permeability μ0;

[0039] 1.3) According to the equivalence principle, the broadband RCS of a three-dimensional mixed object is divided into external equivalence and internal equivalence, where:

[0040] The external equivalent interface is composed of the surface S of the dielectric d and the surface S of the ideal conductor c composition;

[0041] The internal equivalent interface is composed of the dielectric surface S d and the interface S between PEC and dielectric cd composition;

[0042] 1.4) In S d The equivalent current J is introduced on the surface d and magnetic current M d , in S c The equivalent current J is introduced on the surface c , in the interface S cd The equivalent current J is introduced at cd According to the property that the tangential components of the electric and magnetic fields on the dielectric interface are continuous, S is determinedd The electric field current and magnetic field current on the opposite side are -J d and -M d ;

[0043] 1.5) Using the currents introduced in step 1.4) as boundary conditions on the conductor and dielectric surfaces, a set of integral equations EFIE-PMCHWT for the electric and magnetic fields of these currents are obtained:

[0044]

[0045] Among them, E1 sca (J c ,J d ,M d ) represents J c ,J d ,M d The scattered electric field generated by radiation into free space, J c represents the surface S of the ideal conductor part c The equivalent current on d Represents the surface S of the dielectric part d The equivalent current on d Indicates S d The magnetic current on the surface, the subscript "tan" indicates the tangential component, E inc represents the incident electric field generated by the plane wave, onS c Indicates that in S c On the surface;

[0046] E2 sca (J cd ,-J d ,-M d ) represents J cd , -J d , -M d The scattered electric field generated by radiation into the dielectric medium, J cd represents the interface between PEC and dielectric cd Equivalent current onS d Indicates that in S d On the surface;

[0047] H1 sca (J c ,J d ,M d ) represents J c ,J d ,M d The scattered magnetic field generated by radiation into free space, H inc represents the incident magnetic field generated by the plane wave;

[0048] H2 sca (Jcd ,-J d ,-M d ) represents J cd ,-J d ,-M d The scattered magnetic field generated by radiation into the dielectric medium, onS cd Indicates that in S cd On the surface.

[0049] Step 2: Discretize the integral equation EFIE-PMCHWT to obtain the EFIE-PMCHWT matrix.

[0050] 2.1) Use RWG basis function to analyze the J c ,J d ,J cd ,M d The current is discretized as follows:

[0051]

[0052] where f n is the RWG basis function, a n , b n , c n , d n J c ,J d ,J cd ,M d The coefficient of

[0053] 2.2) In the set of EFIE-PMCHWT equations, the RWG basis function f n As a test function, the test is carried out on the surface of the composite target, that is, on the surface of the three-dimensional mixed object, and the matrix formula of EFIE-PMCHWT is obtained:

[0054]

[0055] In the matrix equation, the subscripts d, c, and cd represent the dielectric surface, conductor surface, and interface between PEC and dielectric, respectively; η0 and η1 represent the free space wave impedance and dielectric wave impedance, respectively; P represents the impedance submatrix of the electric field integral operator; Q represents the impedance submatrix of the magnetic field integral operator; and b TE represents the excitation vector formed by the projection of the incident electric field, b TH represents the excitation vector consisting of the projection of the incident magnetic field.

[0056] 2.3) The elements of the two impedance sub-matrices P and Q in the above matrix are expressed as:

[0057]

[0058] in, represents the impedance submatrix of the electric field integration operator obtained by the inner product of the mth and nth RWG basis functions on two different surfaces ij of the hybrid object; the superscript a=0 and 1, i and j represent different surfaces of the hybrid object,

[0059] represents the impedance submatrix of the magnetic field integration operator of the inner product of the mth and nth RWG basis functions on two different surfaces ij of the hybrid object. The operator <> represents the inner product.

[0060] and are the mth and nth RWG basis functions on surfaces i and j respectively,

[0061] represents the electric field integration operator, represents the magnetic field integration operator,

[0062] Ω r Represents different media, Ω0 represents free space, and Ω1 represents the dielectric part;

[0063] 2.4) The two excitation vectors b in the above matrix TE and b TH Expressed as:

[0064]

[0065] in, represents the excitation vector formed by the projection of the m-th RWG basis function of surface i on the incident electric field,

[0066] represents the excitation vector formed by the projection of the m-th RWG basis function of surface i on the incident magnetic field,

[0067] represents the mth RWG basis function of surface i, E inc represents the incident electric field generated by the plane wave,

[0068] H inc represents the incident magnetic field generated by the plane wave;

[0069] Step 3: Use the AIM method to accelerate the calculation of the EFIE-PMCHWT matrix and obtain the near-field impedance matrix:

[0070] 3.1) For the desired frequency band k∈[k0-Δk,k0+Δk], at the wave number k corresponding to the given frequency f, replace the steps

[0071] The EFIE-PMCHWT matrix in 2.2) is abbreviated as:

[0072] Z(k)I(k)=V(k)

[0073] Where Z(k), I(k), and V(k) are the impedance matrix, excitation vector, and coefficient column vector, respectively, all of which are functions of the wave number k, k0 is the center frequency, and Δk represents half the bandwidth;

[0074] 3.2) Use the AIM method to obtain the near-field impedance matrix:

[0075] The AIM method is a fast algorithm for accelerating the calculation of electromagnetic field integral equations, which is used to reduce memory requirements and speed up matrix-vector multiplication in iterative solutions. This step is implemented as follows:

[0076] 3.2.1) Introduce the near-field threshold and divide the impedance matrix in step 3.1) into the near-field impedance matrix Z near (k) and the far-field interaction matrix Its representation is as follows:

[0077]

[0078] in is the inaccurate contribution of the near-field grid source that needs to be removed, is the matrix of the existing basis transformation, G(k) is the matrix of the existing Green function with Toeplitz property, The transpose of the matrix representing the basis transformation;

[0079] 3.2.2) Substitute the impedance matrix expression from step 3.2.1) into the matrix equation from step 3.1) and use the Fast Fourier Transform (FFT) to accelerate the interaction calculation of the matrix equation to obtain the following expression:

[0080]

[0081] Where Z(k) is the impedance matrix, is the inaccurate contribution of the near-field grid source that needs to be removed, I(k) is the excitation vector,

[0082] is the matrix of basis transformation, represents the transpose matrix of the basis transformation matrix, F and F-1 represent FFT and inverse FFT respectively, and G(k) is the matrix of Green's function with Toeplitz property;

[0083] 3.2.3) Solve the matrix equation in step 3.2.2) to obtain the near-field impedance matrix Z near .

[0084] Step 4: Generate high-order derivatives using the GLC interpolation pseudospectral method.

[0085] 4.1.1) The pseudo-spectral method PSDM is used to select the GLC interpolation sampling point at the center frequency of the composite target. The i-th order derivative Z of the matrix Z(k) is converted to (i) (k) is written in the following matrix form:

[0086]

[0087] Where N represents the number of sampling points, φ j (k) represents the GLC interpolation basis function in the frequency band [k0-Δk, k0+Δk], k j Indicates the wave number corresponding to the j-th GLC interpolation sampling point;

[0088] 4.1.2) Z (i) (k) The first half of the matrix It is represented as a matrix D, whose coefficient D ij According to the values ​​of the i-th row and j-th column of the matrix, the following calculations are made:

[0089]

[0090] in, represents the weight coefficient of the GLC interpolation point, Δk represents half of the bandwidth, k i represents the wave number corresponding to the jth GLC interpolation sampling point, k j Indicates the wave number corresponding to the j-th GLC interpolation sampling point;

[0091] 4.2) The first-order pseudo-spectral derivative matrix of the matrix Z(k) at each selected GLC interpolation point is expressed as:

[0092]

[0093] 4.3) According to the first-order pseudo-spectral derivative matrix at the sampling point, the following high-order derivative matrix Z is obtained (i) (k0)m q-i :

[0094]

[0095] Among them, k0 is the wave number corresponding to the center frequency f0, m q-i represents the moment coefficient of the qith order, k j Indicates the wave number corresponding to the j-th GLC interpolation sampling point;

[0096] 4.4) The high-order derivative matrix in step 4.3) is divided into two parts: near interaction and far interaction, and then the near-field impedance matrix Z is used to calculate the near-field impedance matrix Z. near The pseudo-spectral derivative matrix D is linearly combined to obtain the high-order impedance matrix Z, which is expressed as follows:

[0097]

[0098] Among them, Z near represents the near-field impedance matrix, Z far represents the far-field impedance matrix, m n-q represents the Taylor expansion coefficient moment of the nqth order, Represents the coefficient of the element in the N / 2th row and jth column of matrix D raised to the power of i.

[0099] Step 5: Perform broadband analysis using progressive waveform technology to obtain Taylor expansion coefficient moment m.

[0100] 5.1) Set up a rectangular grid to surround the composite target, project the current and charge of the composite target onto these grid points, that is, project the current and charge of the original RWG basis function in the x, y, and z directions onto these grid points, and construct a grid consisting of each (P+1) 3 A small rectangle composed of grid points is used to surround each RWG basis function; then the grid point current and charge on the small rectangle are used to construct an auxiliary basis function to replace the current and charge of the original RWG basis function, where P is the projection order;

[0101] 5.2) Expand the unknown current I at the center frequency f0 of the uniform plane incident wave into the following Taylor series:

[0102]

[0103] Among them, k0 is the wave number corresponding to the center frequency f0, m q is the Taylor expansion coefficient moment, Q is the truncation order of the Taylor series, and q is the order;

[0104] 5.3) Find the Taylor expansion coefficient moment m from the high-order derivative matrix Z q :

[0105]

[0106] Among them, k0 is the wave number corresponding to the center frequency f0, V (q) (k0) is the excitation vector of the q-order derivative of V(k) with respect to k at ko, where q represents the order;

[0107] 5.4) Approximately expand the effective frequency band of the step Taylor series near the center frequency using the Pad'e algorithm, and convert the Taylor series in step 5.2) into the following rational function:

[0108]

[0109] Among them, I n(k) represents the unknown current, Q = L + M, L represents the order of the numerator polynomial, M represents the order of the denominator polynomial, b n,j and a n,i represents two numerically distinct rational function coefficients, and m n,q represents the Taylor expansion coefficient moment, and Q is the truncation order of the Taylor series.

[0110] Step 6: Obtain the broadband RCS of the composite target.

[0111] 6.1) Based on the expanded frequency band and Taylor expansion coefficient moment m, we can obtain two different rational function coefficients b: n,j and a n,i :

[0112] 6.1.1) The rational function coefficient b is obtained by the following matrix calculation: n,j :

[0113]

[0114] Where m represents the Taylor expansion coefficient moment;

[0115] 6.1.2) According to b n,j Calculate the rational function coefficient a n,i , the formula is as follows:

[0116]

[0117] Among them, m n,i-j represents the Taylor expansion coefficient moment of the nth basis function at the ijth order;

[0118] 6.2) According to the rational function coefficient a n,i and b n,j , calculate the digital induction current coefficient I corresponding to each frequency by the following formula d :

[0119]

[0120] Among them, a d,l Represents the rational function polynomial P L The coefficient corresponding to the lth power of (k-k0) in (k-k0), l∈{0,1,2,...,L}, L is P L The maximum value of the exponent of (k-k0) in (k-k0);

[0121] b d,m Q M The coefficient corresponding to the mth power of (k-k0) in (k-k0), m∈{0,1,2,...,M}, M is Q MThe maximum value of the exponent of (k-k0) in (k-k0);

[0122] 6.3) According to the current coefficient I d Get the scattered electric field generated by the composite target area in the far area

[0123]

[0124] in, The unit vector of the field point position vector r′, i represents the imaginary unit symbol, × represents the cross multiplication operation, η represents the wave impedance in the air, S n is the area of ​​the outer surface of the composite target, I d (k) represents the induction current coefficient, f n (r) represents the nth characteristic basis function, r represents the field point vector in the nth characteristic function of the composite target, and G(r,r′) represents the Green’s function;

[0125] 6.4) According to the scattered electric field Calculate the broadband radar cross section RCS of the composite target at each frequency corresponding to the wave number in the frequency band f:

[0126]

[0127] in, represents the distance between the radar and the periodic structure, R represents the distance between the field point and the source point, represents the electric field of a uniform plane incident wave.

[0128] Example 2: Broadband RCS acquisition system based on adaptive integration method and pseudo-spectral derivative method

[0129] Reference Figure 3 This example includes a target construction module 1, a discretization processing module 2, an equation group conversion module 3, a frequency band extension module 4, and an electromagnetic target RCS acquisition module 5. Among them:

[0130] The construction module 1 is used to obtain a composite electromagnetic target using a three-dimensional mixed object composed of PEC and a lossless uniform medium under plane wave irradiation, define currents and apply boundary conditions to the composite electromagnetic target, obtain a set of EFIE-PMCHWT integral equations for electric and magnetic fields, and transmit them to the discretization processing module 2;

[0131] The discretization processing module 2 is used to discretize the composite electromagnetic target using basis functions and perform a Galerkin test on the composite electromagnetic target, convert the continuous electromagnetic field integral equation into a discrete physical equation, and transmit it to the equation group conversion module 3;

[0132] The equation group conversion module 3 is used to convert the discrete physical equations satisfied by the composite electromagnetic target into a linear equation group, that is, to accelerate the calculation of the EFIE-PMCHWT matrix using the AIM method and obtain the linear equation group using the GLC interpolation pseudo-spectral method, and transmit the linear equation group to the frequency band extension module 4;

[0133] The frequency band extension module 4 uses the Pad'e algorithm to approximately expand the effective frequency band of the Taylor series near the center frequency, converts the Taylor series of the unknown current I at the center frequency f0 in the uniform plane incident wave into a rational function, obtains the target surface current coefficient based on the rational function and the linear equation system, and transmits it to the electromagnetic target RCS acquisition module 5;

[0134] The electromagnetic target RCS acquisition module 5 obtains the far-field scattering field by integrating the surface current coefficient of the composite electromagnetic target, and then calculates the broadband RCS of the composite target based on the far-field scattering field.

[0135] It should be noted that the above-mentioned functional modules can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented using software, they can be implemented in whole or in part in the form of a program instruction product. The program instruction product includes one or a group of program instructions. When the program instructions are loaded and executed on a computer, the process or function is generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The program instructions can be stored in a computer-readable and writable storage medium, or transmitted from a computer-readable and writable storage medium to another computer-readable and writable storage medium.

[0136] The direct coupling or communication connection between the modules shown or discussed in this embodiment can be achieved through indirect coupling or communication connection of some interfaces, devices or modules. The various functional modules and submodules in this embodiment can be dynamically located in a processing component, or each module can exist physically separately, or two or more modules can be dynamically located in a processing component. When the above-mentioned dynamic components are implemented in the form of software functional modules and sold or used as independent products, they can also be stored in a computer-readable and writable storage medium. The storage medium can be a memory, a magnetic disk, an optical disk, etc.

[0137] The effects of the present invention can be further illustrated by the following simulation results:

[0138] 1. Simulation experiment conditions:

[0139] The simulation experiment hardware platform is: Intel i7-10700 CPU, main frequency is 2.9GHz, memory is 64GB. The software platform is: Windows 10 operating system

[0140] The composite electromagnetic target model used in the simulation experiment of the present invention is an airship object carrying a dielectric nose, and its structure is as follows: Figure 2 As shown, the relative dielectric constant and relative magnetic permeability ε of the dielectric head r =5.5, μr=1.0, the airship body is made of ideal conductor material, and the frequency band is 1.0-3.2GHz.

[0141] The length of the airship is 12 cm, the width is 4.3 cm, the height is 4.3 cm, and the circumference of the largest circle of the medium head is 9.4 cm.

[0142] 2. Simulation content and result analysis:

[0143] Simulation 1: Under the above simulation experimental conditions, the broadband radar cross section RCS of the composite electromagnetic target is simulated and obtained using the present invention, the existing EFIE-PMCHWT and AWE methods respectively. The results are as follows: Figure 4 shown.

[0144] from Figure 4 It can be seen that the broadband radar cross section (RCS) of the composite electromagnetic target obtained by the three methods is basically the same, but the calculation memory requirements and calculation time of the broadband radar cross section (RCS) obtained by different methods are different.

[0145] Simulation 2: Under the above simulation experimental conditions, the present invention, the existing EFIE-PMCHWT, and the traditional AWE methods are used to simulate the acquisition of the wideband radar cross section (RCS) of the composite electromagnetic target. The calculation memory and calculation time of each method in the process of obtaining the wideband radar cross section (RCS) of the composite electromagnetic target are statistically analyzed. The results are shown in Table 1:

[0146] Table 1 Comparison of simulation effects between the method of the present invention and the prior art

[0147] Calculation method Computing memory (MB) Calculation time (min) EFIE-PMCHWT 840 707.5 Traditional AWE 9240 133.4 The present invention 627 72.9

[0148] As can be seen from Table 1, the computational memory and computational time of the present invention are both smaller than those of the existing methods. Compared with the EFIE-PMCHWT method, the computational time of the present invention is shortened by 89.6%. Compared with the traditional AWE method, the computational memory of the present invention is reduced by 90.9%. This proves that the present invention can reduce the computational time and memory for acquiring the wideband radar cross section (RCS) of the target while maintaining accuracy.

Claims

1. A broadband RCS acquisition method based on adaptive integration method and pseudo-spectral derivative method, characterized in that: include: (1) A three-dimensional composite electromagnetic target consisting of a PEC and a lossless homogeneous medium under plane wave illumination is subjected to boundary conditions, and a set of EFIE-PMCHWT integral equations for the electric and magnetic fields are obtained; (2) The set of integral equations is discretized using RWG basis functions and subjected to Galerkin test to obtain the EFIE-PMCHWT matrix; the interaction calculation of the matrix is ​​accelerated by fast Fourier transform FFT to obtain the near-field impedance matrix Z near and store; (3) Based on the pseudo-spectral method PSDM, the GLC interpolation sampling points are selected at the center frequency of the composite electromagnetic target to generate the pseudo-spectral derivative matrix D, and the near-field impedance matrix Z is used to calculate the near Perform linear combination to obtain the high-order impedance matrix Z; (4) A rectangular grid is set up to surround the composite target, and the current and charge of the composite target are projected onto these grid points. The unknown current I is expanded into a Taylor series at the center frequency by combining the asymptotic waveform AWE technique, and its Taylor expansion coefficient moment m is calculated based on the high-order derivative matrix Z. The effective frequency band of the Taylor series of the unknown current I(k) is then approximately expanded near the center frequency by the Pad'e algorithm. (5) According to the expanded frequency band and moment coefficient m, the induced current coefficient corresponding to each frequency is calculated. Based on the current coefficient, the total scattered electric field E generated by the composite target in the far area is calculated to obtain the broadband electromagnetic scattering characteristics RCS of the composite electromagnetic target.

2. The method according to claim 1, characterized in that A set of EFIE-PMCHWT integral equations for the electric field and magnetic field are obtained in (1), which are expressed as follows: Among them, E1 sca (J c ,J d ,M d ) represents J c ,J d ,M d The scattered electric field generated by radiation into free space, J c represents the surface S of the ideal conductor part c The equivalent current on d Represents the surface S of the dielectric part d The equivalent current on d Indicates S d The magnetic current on the surface, the subscript "tan" indicates the tangential component, E inc represents the incident electric field generated by the plane wave, onS c Indicates that in S c On the surface; E2 sca (J cd ,-J d ,-M d ) represents J cd , -J d , -M d The scattered electric field generated by radiation into the dielectric medium, J cd represents the interface between PEC and dielectric cd Equivalent current onS d Indicates that in S d On the surface; H1 sca (J c ,J d ,M d ) represents J c ,J d ,M d The scattered magnetic field generated by radiation into free space, H inc represents the incident magnetic field generated by the plane wave; H2 sca (J cd ,-J d ,-M d ) represents J cd ,-J d ,-M d The scattered magnetic field generated by radiation into the dielectric medium, onS cd Indicates that in S cd On the surface.

3. The method according to any one of claims 1-2, characterized in that In (2), the set of integral equations is discretized using RWG basis functions and subjected to Galerkin test to obtain the EFIE-PMCHWT matrix, which includes: (2a) Use RWG basis functions to calculate J c ,J d ,J cd ,M d The current is discretized as follows: where f n is the RWG basis function, a n , b n , c n , d n J c ,J d ,J cd ,M d The coefficient of (2b) In the set of EFIE-PMCHWT equations described above, the RWG basis function f n As a test function, the matrix of EFIE-PMCHWT is obtained by testing on the composite target surface: In the matrix equation, the subscripts d, c, and cd represent the dielectric surface, conductor surface, and the interface between PEC and dielectric, respectively. η0 and η1 represent the free space wave impedance and dielectric wave impedance respectively, P represents the electric field integral operator impedance matrix, Q represents the magnetic field integral operator impedance matrix, b TE represents the excitation vector consisting of the projection of the incident electric field, b TH represents the excitation vector consisting of the projection of the incident magnetic field.

4. The method according to claim 1, wherein In (3), based on the pseudo-spectral method PSDM, GLC interpolation sampling points are selected at the center frequency of the composite target to generate the pseudo-spectral derivative matrix D, which is implemented as follows: (3a) Through the GLC interpolation formula, the i-order derivative Z of the matrix Z(k) is (i) (k) is written in the following matrix form: Among them, φ j (k) represents the GLC interpolation basis function in the frequency band [k0-Δk, k0+Δk], k j Indicates the wave number corresponding to the j-th GLC interpolation sampling point; (3b) Z (i) (k) The first half of the matrix It is represented as a matrix D, whose coefficient D ij According to the values ​​of the i-th row and j-th column of the matrix, the following calculations are made: in, represents the weight coefficient of the GLC interpolation point, Δk represents half of the bandwidth, k i represents the wave number corresponding to the jth GLC interpolation sampling point, k j Indicates the wave number corresponding to the j-th GLC interpolation sampling point.

5. The method according to claim 1, wherein: In (2), the interaction calculation of the matrix is ​​accelerated by fast Fourier transform FFT to obtain the near-field impedance matrix Z near , the formula is as follows: Where Z(k) is the impedance matrix, I(k) is the excitation vector, Λ is the matrix of the basis transformation, F and F-1 represent FFT and inverse FFT respectively, and G(k) is the matrix of the Green's function with Toeplitz property; In (3), according to the near-field impedance matrix Z near The pseudo-spectral derivative matrix D is linearly combined to obtain the high-order impedance matrix Z, which is expressed as follows: Among them, Z near represents the near-field impedance matrix, Z far represents the far-field impedance matrix, m n-q represents the moment coefficient of the nqth order, Represents the coefficient of the element in the N / 2th row and jth column of matrix D raised to the power of i.

6. The method according to claim 1, characterized in that The (4) sets a rectangular grid for surrounding the composite target, and projects the current and charge of the composite target onto these grid points, which is to project the current and charge of the original RWG basis function in the x, y, and z directions onto these grid points, and construct a grid consisting of each (P+1) 3 A small rectangle composed of grid points is used to surround each RWG basis function; then the grid point current and charge on the small rectangle are used to construct an auxiliary basis function to replace the current and charge of the original RWG basis function, where P is the projection order.

7. The method according to claim 1, characterized in that In (4), the unknown current I is expanded into a Taylor series at the center frequency by combining the asymptotic waveform AWE technology, and its Taylor expansion coefficient moment m is calculated according to the high-order derivative matrix Z. The implementation thereof includes: (4a) The unknown current I at the center frequency f0 in the uniform plane incident wave is expanded into the following Taylor series: Among them, k0 is the wave number corresponding to the center frequency f0, m q is the Taylor expansion coefficient moment, Q is the truncation order of the Taylor series; (4b) Find the moment coefficient m from the high-order derivative matrix Z q : Among them, k0 is the wave number corresponding to the center frequency f0, V (q) (k0) is the excitation vector of the qth order derivative of V(k) with respect to k at ko.

8. The method according to claim 1, characterized in that In (4), the effective frequency band of the Taylor series near the center frequency is approximately expanded by the Pad'e algorithm, and the Taylor series is converted into a rational function, which is as follows: Among them, I n (k) represents the unknown current, Q = L + M, represents the coefficient, k0 is the wave number corresponding to the center frequency f0, m n,q represents the Taylor expansion coefficient moment, and Q is the truncation order of the Taylor series.

9. The method according to claim 1, characterized in that In (5), the induced current coefficient I corresponding to each frequency is calculated based on the expanded frequency band and moment coefficient m. d , the total scattered electric field E generated by the composite target in the far area is calculated based on the current coefficient, and the broadband electromagnetic scattering characteristics RCS of the composite target are obtained. The calculation formulas are: (5a) According to the expanded frequency band and moment coefficient m, two rational coefficients b with different values ​​are obtained. n,j , a n,i : (5a1) The rational coefficient b is calculated by the following formula n,j : Wherein, L+M=Q, m represents the Taylor expansion coefficient moment. (5a2) According to b n,j The rational coefficient a is calculated by the following formula n,i : Among them, m n,i-j represents the Taylor expansion coefficient moment of the nth basis function at the ijth order; (5b) According to the rational coefficient function a n,i and b n,j , calculate the inductive current coefficient I by the following formula d : Among them, a d,l Represents the rational function polynomial P L The coefficient corresponding to the lth power of (k-k0) in (k-k0), l∈{0,1,2,...,L}, L is P L The maximum value of the exponent of (k-k0) in (k-k0); b d,m Q M The coefficient corresponding to the mth power of (k-k0) in (k-k0), m∈{0,1,2,...,M}, M is Q d,M The maximum value of the exponent of (k-k0) in (k-k0); (5c) Based on the current coefficient, the scattered electric field generated by the composite target area in the far area can be obtained To obtain the RCS of the composite target, the formula is as follows: in, represents the unit vector of the field point position vector r′, × represents the cross multiplication operation, η represents the wave impedance in the air, S n is the area of ​​the outer surface of the composite target, f n (r) represents the RWG basis function, represents the distance between the radar and the periodic structure taking the limit operation, R represents the distance between the field point and the source point, |·| 2 Represents the square operation.

10. A broadband RCS acquisition system based on adaptive integration method and pseudo-spectral derivative method, characterized in that: include: Target construction module, used to define the target surface boundary conditions and obtain the electromagnetic field integral equation; Discretization processing module, used to process composite electromagnetic targets using rectangular grid discretization, and convert continuous electromagnetic field integral equations into discrete physical equations; The equation group conversion module is used to convert the physical equations satisfied by the discretized composite electromagnetic target into a linear equation group; The extended frequency band module is used to expand the effective frequency band of the Taylor series of the unknown current near the center frequency and obtain the target surface current coefficient from the solution of the linear equations; The electromagnetic target RCS acquisition module is used to obtain the far-field scattering field E by integrating the target surface current coefficient to calculate the RCS of the composite target.

Images