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

A New Calculation Method for Electromagnetic Properties of Uncertain Shape Metal Targets Based on AWE Technology Download PDF

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

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

Description

基于AWE技术的电大不确定外形金属目标的新型电磁特性计 算方法A new type of electromagnetic characteristic meter for metal targets with uncertain shape based on AWE technology calculation method

技术领域technical field

本发明属于目标电磁散射特性数值计算技术领域,尤其是一种基于AWE技术的电大不确定外形金属目标的新型电磁特性计算方法。The invention belongs to the technical field of numerical calculation of target electromagnetic scattering characteristics, in particular to a novel electromagnetic characteristic calculation method of a metal target with an electrically large and uncertain shape based on AWE technology.

背景技术Background technique

基于混合场积分方程的金属目标的电磁散射计算原理是目标表面剖分成若干个三角形,其中剖分精度设置为小于入射波长的十分之一。引入RWG基函数表示上下两个三角形,保证相邻两个三角形之间的电流连续性。该方法能够计算任意形状的金属目标,适用性较强。相较于其他高频近似方法,基于矩量法的数值方法具有较高的计算精度。当混合场积分方程的组合系数设为1时,转换为电场积分方程,由于其阻抗矩阵为满秩矩阵,计算时间慢,但是计算精度高;当组合系数设为0时,转换为磁场积分方程,此时积分方程为主对角占优矩阵,计算时间快,但是计算精度受限。因此,通过合理设置混合场积分方程中的组合系数能够兼顾计算精度和计算速度。另外,混合场积分方程亦能够避免内谐振问题。非合作金属模型是当前雷达监测的重要目标之一,基于混合场积分方程,计算外形信息不确定的非合作金属目标的电磁散射特性是本发明研究的重点。The calculation principle of electromagnetic scattering of metal targets based on the mixed field integral equation is that the target surface is divided into several triangles, and the division precision is set to be less than one-tenth of the incident wavelength. The RWG basis function is introduced to represent the upper and lower triangles to ensure the continuity of current between two adjacent triangles. This method can calculate metal targets of any shape, and has strong applicability. Compared with other high-frequency approximation methods, the numerical method based on the method of moments has higher calculation accuracy. When the combination coefficient of the mixed field integral equation is set to 1, it is converted to the electric field integral equation. Since its impedance matrix is a full-rank matrix, the calculation time is slow, but the calculation accuracy is high; when the combination coefficient is set to 0, it is converted to the magnetic field integral equation , at this time the integral equation is the main diagonal dominant matrix, the calculation time is fast, but the calculation accuracy is limited. Therefore, by reasonably setting the combination coefficient in the integral equation of the mixed field, both the calculation accuracy and the calculation speed can be considered. In addition, the mixed field integral equation can also avoid the internal resonance problem. The non-cooperative metal model is one of the important targets of current radar monitoring. Based on the mixed field integral equation, the calculation of the electromagnetic scattering characteristics of the non-cooperative metal target with uncertain shape information is the focus of this invention.

当目标外形含有不确定因素时,使用蒙特卡洛(Monte Carlo,MC)方法能够重复多次的计算模型的电磁散射特性,具体表现为对外形参数引入一组随机变量,将不确定问题转换为确定问题进行计算。进而对重复多次计算得到的雷达散射截面积进行统计分析,最终得到均值和方差。蒙特卡洛方法通过逐一计算模型的散射特性方法,计算结果精度高,但是计算极为耗时,严重影响了计算效率。针对MC方法的弊端,传统的基于泰勒级数展开的扰动法(Perturbation method)能够通过牺牲部分精度的方式提高计算效率。具体表现为将矩阵方程展开为泰勒级数,最终的电流表示为原始模型的初解和变化电流之和的形式。但是该方法的收敛半径较小,采用公式求导复杂。当发生改变的控制点增多时,时间也会相应增加。When the shape of the target contains uncertain factors, the Monte Carlo (MC) method can be used to repeatedly calculate the electromagnetic scattering characteristics of the model. The specific performance is to introduce a set of random variables into the shape parameters, and convert the uncertain problem into Determine the problem to calculate. Then, the radar cross-sectional area obtained by repeating the calculation is statistically analyzed, and finally the mean value and variance are obtained. The Monte Carlo method calculates the scattering characteristics of the model one by one, and the calculation results have high accuracy, but the calculation is extremely time-consuming, which seriously affects the calculation efficiency. In view of the disadvantages of the MC method, the traditional perturbation method based on Taylor series expansion can improve the computational efficiency by sacrificing part of the precision. Specifically, the matrix equation is expanded into a Taylor series, and the final current is expressed as the sum of the initial solution of the original model and the changing current. However, the convergence radius of this method is small, and the derivation by formula is complicated. When more control points are changed, the time will increase accordingly.

发明内容Contents of the invention

本发明的目的在于提供一种基于AWE技术的电大不确定外形金属目标的新型电磁特性计算方法。The purpose of the present invention is to provide a new method for calculating the electromagnetic characteristics of a metal target with an electrically large and uncertain shape based on AWE technology.

实现本发明目的的技术解决方案为:第一方面,本发明提供一种基于AWE技术的电大不确定外形金属目标的新型电磁特性计算方法,步骤如下:The technical solution to realize the object of the present invention is: first aspect, the present invention provides a kind of novel electromagnetic characteristic calculation method based on the AWE technology of the metal object of electric large uncertain appearance, and the steps are as follows:

步骤1、利用FEKO软件和NURBS建模技术实现非合作金属目标的建模:根据NURBS技术建立目标外形可控的模型;将所有控制点坐标组合成一个行向量,定义为外形矢量;Step 1. Use FEKO software and NURBS modeling technology to realize the modeling of non-cooperative metal targets: establish a model with controllable target shape according to NURBS technology; combine all control point coordinates into a row vector, which is defined as a shape vector;

步骤2、建立关于外形矢量的混合场积分方程:分别将关于外形矢量的阻抗矩阵、右边向量和电流展开为泰勒级数,推导出电流矩矢量的表达式;然后确定引入的外形矢量的变化范围,构造伪谱法中的D矩阵,计算各阶矩阵导数矢量乘和右边向量的导数,进而得到各阶电流矩矢量;建立泰勒级数和帕德多项式的等式,推导出电流矩矢量与帕德多项式向量系数的关系,并进而计算出向量系数;根据向量系数和外形矢量的随机变化量,得到模型变化一次后的电流;Step 2. Establish the mixed field integral equation about the shape vector: respectively expand the impedance matrix, the right vector and the current about the shape vector into Taylor series, and derive the expression of the current moment vector; then determine the variation range of the introduced shape vector , construct the D matrix in the pseudospectral method, calculate the matrix derivative vector of each order and the derivative of the right vector, and then obtain the current moment vector of each order; establish the Taylor series and Padre polynomial equation, deduce the current moment vector and Pa The relationship between the polynomial vector coefficients, and then calculate the vector coefficients; according to the vector coefficients and the random variation of the shape vector, the current after the model changes once is obtained;

步骤3、根据模型改变后的坐标信息和对应的电流,计算得到模型变化一次后的RCS;根据设定的采样次数,利用基于AWE的扰动法计算出模型每一次变化后的RCS;对采样多次的RCS进行统计分析,得到不确定外形非合作金属目标的电磁散射特性。Step 3. According to the coordinate information after the model change and the corresponding current, calculate the RCS after the model changes once; according to the set sampling times, use the AWE-based perturbation method to calculate the RCS after each model change; Statistical analysis is performed on the second RCS, and the electromagnetic scattering characteristics of non-cooperative metal targets with uncertain shapes are obtained.

第二方面,本发明提供一种计算机设备,包括存储器、处理器及存储在存储器上并可在处理器上运行的计算机程序,其特征在于,所述处理器执行所述程序时实现第一方面所述的方法的步骤。In a second aspect, the present invention provides a computer device, including a memory, a processor, and a computer program stored on the memory and operable on the processor, wherein the first aspect is realized when the processor executes the program The steps of the method.

第三方面,本发明提供一种计算机可读存储介质,其上存储有计算机程序,其特征在于,该程序被处理器执行时实现第一方面所述的方法的步骤。In a third aspect, the present invention provides a computer-readable storage medium on which a computer program is stored, wherein the program implements the steps of the method described in the first aspect when the program is executed by a processor.

第四方面,本发明提供一种计算机程序产品,包括计算机程序,其特征在于,该计算机程序被处理器执行时实现第一方面所述的方法的步骤。In a fourth aspect, the present invention provides a computer program product, including a computer program, characterized in that, when the computer program is executed by a processor, the steps of the method described in the first aspect are implemented.

本发明与现有技术相比,其优点为:(1)相较于传统的直接对外形矢量进行公式求导,使用伪谱法计算右边向量和矩阵矢量乘的导数,避免了复杂的公式求导,思路清晰,且程序实现简便;(2)相较于传统泰勒方法,改进的AWE扰动法利用了帕德近似,收敛半径更宽;对于多个控制点同时变化的情况,该方法计算时间更短,内存更小。(3)相较于传统蒙塔卡罗方法,大大缩短了计算时间。Compared with the prior art, the present invention has the following advantages: (1) Compared with the traditional method of directly deriving the formula for the shape vector, the pseudo-spectral method is used to calculate the derivative of the right vector and matrix-vector multiplication, which avoids complicated formula derivation (2) Compared with the traditional Taylor method, the improved AWE perturbation method uses the Padé approximation, and the convergence radius is wider; for the situation where multiple control points change at the same time, the calculation time of this method Shorter and less memory. (3) Compared with the traditional Monte Carlo method, the calculation time is greatly shortened.

附图说明Description of drawings

图1为三维坐标系中θ角和

Figure BDA0003928403090000021
角示意图。Figure 1 shows the θ angle and
Figure BDA0003928403090000021
angle diagram.

图2为金属立方体模型尺寸示意图。Figure 2 is a schematic diagram of the size of the metal cube model.

图3为金属立方体模型控制点设置示意图。Figure 3 is a schematic diagram of the control point setting of the metal cube model.

图4为不确定外形金属立方体模型改变一个点一个坐标时的RCS统计对比图(均值)。Fig. 4 is a statistical comparison chart (mean value) of RCS when one point and one coordinate are changed for the metal cube model with uncertain shape.

图5为不确定外形金属立方体模型改变多个点多个坐标时的RCS统计对比图(均值方差)。Fig. 5 is a statistical comparison chart (mean variance) of RCS when multiple coordinates of multiple points are changed for the metal cube model with uncertain shape.

图6为金属电大尺寸长方体模型尺寸示意图。Fig. 6 is a schematic diagram of the size of the metal electric large-size cuboid model.

图7为金属电大尺寸长方体模型控制点设置示意图。Fig. 7 is a schematic diagram of setting control points of the metal electric large-size cuboid model.

图8为不确定外形金属电大尺寸长方体改变多个点时的RCS统计对比图(均值方差)。Fig. 8 is a statistical comparison chart (mean value variance) of RCS when a metal electric large-size cuboid with an uncertain shape changes multiple points.

具体实施方式detailed description

本发明提出一种基于AWE技术的电大不确定外形金属目标的新型电磁特性计算方法,首先根据FEKO软件和非均匀有理B样条(Non-uniform Rational B-spline,NURBS)技术建立模型,将目标外形的所有控制点坐标定义为外形矢量。通过对该外形矢量引入随机变量,实现改变目标外形的目的。不同于将AWE技术应用于频率、角度等标量域,本发明将AWE技术推广至矢量域,即外形矢量。然后将外形矢量引入到混合场积分方程(Combined FieldIntegral Equation,CFIE)中,通过把阻抗矩阵、右边向量和电流展开为泰勒级数的形式,推导出电流矩矢量的表达式。将伪谱法应用至AWE中,分别计算出矩阵导数与矩矢量的乘积,以及右边向量的导数,进而计算出电流矩矢量。通过联立泰勒级数和帕德多项式,计算出每次模型变化后的电流。相较于传统泰勒方法,收敛半径也被进一步扩大。最终结合电流和模型变化后的坐标信息计算雷达散射截面积(Radar Cross Section,RCS)。多次采样后,统计分析RCS的均值和方差。由于在对外形矢量的求导过程中,采用了插值思想,加法定理依旧满足。所以基于AWE的扰动法能够结合快速多极子(MLFMA)加速计算电大模型的散射特性。相较于蒙特卡洛(Monte Carlo,MC)方法,本发明能够大大缩短计算时间。通过此方法能够快速高效的计算电大金属目标发生形变后的散射特性。The present invention proposes a new type of calculation method for electromagnetic characteristics of metal objects with large and uncertain shapes based on AWE technology. All control point coordinates of the shape are defined as shape vectors. By introducing random variables into the shape vector, the purpose of changing the shape of the target is achieved. Different from applying AWE technology to scalar domains such as frequency and angle, the present invention extends AWE technology to vector domain, namely shape vector. Then the shape vector is introduced into the combined field integral equation (Combined Field Integral Equation, CFIE), and the expression of the current moment vector is derived by expanding the impedance matrix, the right vector and the current into the form of Taylor series. Applying the pseudospectral method to AWE, the product of the matrix derivative and the moment vector and the derivative of the right vector are calculated respectively, and then the current moment vector is calculated. The current after each model change is calculated by combining Taylor series and Padé polynomials. Compared with the traditional Taylor method, the convergence radius is further expanded. Finally, the Radar Cross Section (RCS) is calculated by combining the coordinate information of the current and the model change. After multiple sampling, the mean and variance of RCS were statistically analyzed. Since the interpolation idea is adopted in the derivation process of the shape vector, the addition theorem is still satisfied. Therefore, the perturbation method based on AWE can be combined with the fast multipole (MLFMA) to accelerate the calculation of the scattering characteristics of the electrically large model. Compared with the Monte Carlo (MC) method, the present invention can greatly shorten the calculation time. This method can quickly and efficiently calculate the scattering characteristics of the deformed electrically large metal target.

下面结合附图对本发明作进一步详细描述。The present invention will be described in further detail below in conjunction with the accompanying drawings.

一种基于AWE技术的电大不确定外形金属目标的新型电磁特性计算方法,步骤如下:A new calculation method for electromagnetic properties of metal targets with uncertain shapes based on AWE technology, the steps are as follows:

步骤1、根据NURBS技术建立目标外形可控的模型。将所有控制点坐标组合成一个行向量,定义为外形矢量,用α表示。具体地,α可展开为[α123,...,αn-2n-1n],此处n取值为模型控制点的个数乘以3。其中,α123代表#1号控制点的x,y,z坐标,,#1号控制点为NURBS建模文件中的第一个坐标点;先通过FEKO软件建立初始目标模型,此时未引入随机变量Δα。将该模型导入犀牛软件中重建,包括重新设置控制点的坐标和建立曲面两个过程,最终得到构成曲面的各控制点以及不同控制点的坐标。α0表示原始模型的外形矢量,αs表示外形矢量中的任意元素,即任意点的任意坐标。Step 1. Establish a controllable model of the target shape according to NURBS technology. Combine all control point coordinates into a row vector, defined as the shape vector, denoted by α. Specifically, α can be expanded to [α 123 ,...,α n-2n-1n ], where n is the number of model control points multiplied by 3 . Among them, α 1 , α 2 , α 3 represent the x, y, and z coordinates of #1 control point, and #1 control point is the first coordinate point in the NURBS modeling file; first establish the initial target through FEKO software model, no random variable Δα is introduced at this time. Import the model into Rhino software for reconstruction, including resetting the coordinates of the control points and establishing the surface, and finally obtain the coordinates of each control point and different control points that constitute the surface. α 0 represents the shape vector of the original model, and α s represents any element in the shape vector, that is, any coordinate of any point.

通过给外形矢量α引入随机变量Δα来灵活的改变目标外形。具体的,Δα为变化量的范围,Δα=[Δα1,Δα2,Δα3,...,Δαn-2,Δαn-1,Δαn]。在含有α+Δα的目标模型中,根据入射电磁波的波长,对每个面分别设置u,v方向的剖分尺寸,使用RWG基函数对模型进行面剖分。其中剖分尺寸通常设置为小于波长的十分之一。由此,得到能够在混合场积分方程中计算的剖分模型。通过NURBS技术将目标表面剖分成若干个三角形,基于RWG基函数建立混合场积分方程。By introducing a random variable Δα to the shape vector α, the target shape can be changed flexibly. Specifically, Δα is the range of variation, Δα=[Δα 1 , Δα 2 , Δα 3 , . . . , Δα n-2 , Δα n-1 , Δα n ]. In the target model containing α+Δα, according to the wavelength of the incident electromagnetic wave, the subdivision dimensions in the u and v directions are set for each surface, and the RWG basis function is used to subdivide the model. The subdivision size is usually set to be less than one-tenth of the wavelength. From this, a subdivision model that can be calculated in the mixed field integral equation is obtained. The target surface is divided into several triangles by NURBS technology, and the mixed field integral equation is established based on the RWG basis function.

步骤2、建立关于外形矢量α的混合场积分方程:分别将关于外形矢量的阻抗矩阵、右边向量和电流展开为泰勒级数,推导出电流矩矢量的表达式。然后确定引入的外形矢量的变化范围,利用伪谱法构造D矩阵,计算各阶矩阵导数矢量乘和右边向量的导数,进而得到各阶电流矩矢量。建立泰勒级数和帕德多项式的等式,推导出电流矩矢量与帕德多项式向量系数的关系,并进而计算出向量系数。不同于蒙特卡洛方法,该过程只需执行一次。根据向量系数和外形矢量的随机变化量,得到模型变化一次后的电流。具体如下:Step 2. Establish the mixed field integral equation about the shape vector α: respectively expand the impedance matrix, the right vector and the current about the shape vector into Taylor series, and derive the expression of the current moment vector. Then determine the variation range of the introduced shape vector, use the pseudo-spectral method to construct the D matrix, calculate the matrix derivative vector of each order and the derivative of the right vector, and then obtain the current moment vector of each order. Establish the equation of Taylor series and Padé polynomial, deduce the relationship between the current moment vector and the vector coefficient of Padé polynomial, and then calculate the vector coefficient. Unlike Monte Carlo methods, this procedure only needs to be performed once. According to the vector coefficient and the random variation of the shape vector, the current after the model changes once is obtained. details as follows:

首先建立含有随机变量α的金属目标CFIE的矩阵方程:Firstly, the matrix equation of metal target CFIE with random variable α is established:

Z(α)·I(α)=b(α) (23)Z(α)·I(α)=b(α) (23)

其中Z(α)为混合场积分方程的阻抗矩阵,I(α)为表面电流,b(α)为右边向量。混合场积分方程可表示为电场积分方程和磁场积分方程的组合形式。其中阻抗矩阵可进一步表示为:Where Z(α) is the impedance matrix of the mixed field integral equation, I(α) is the surface current, and b(α) is the right vector. The mixed field integral equation can be expressed as a combined form of electric field integral equation and magnetic field integral equation. The impedance matrix can be further expressed as:

Z(α)=αc·ZEFIE(α)+(1-αc)·ZMFIE(α) (24)Z(α)=α c Z EFIE (α)+(1-α c ) Z MFIE (α) (24)

αc为组合系数,其取值为0到1之间;ZEFIE(α)和ZMFIE(α)分别为电场积分方程中的阻抗矩阵,磁场积分方程中的阻抗矩阵。α c is the combination coefficient, and its value is between 0 and 1; Z EFIE (α) and Z MFIE (α) are the impedance matrix in the electric field integral equation and the impedance matrix in the magnetic field integral equation, respectively.

混合场积分方程中右边向量可表示为:The right vector in the mixed field integral equation can be expressed as:

b(α)=bEIFE(α)+bMFIE(α) (25)b(α)=b EIFE (α)+b MFIE (α) (25)

其中,bEIFE(α)为电场积分方程中的右边向量,bMFIE(α)为磁场积分方程中的右边向量。Among them, b EIFE (α) is the right vector in the electric field integral equation, and b MFIE (α) is the right vector in the magnetic field integral equation.

进一步的,混合场矩阵方程可表示如下:Further, the mixed field matrix equation can be expressed as follows:

c·ZEFIE(α)+(1-αc)·ZMFIE(α)]·I(α)=bEIFE(α)+bMFIE(α)(26)c ·Z EFIE (α)+(1-α c )·Z MFIE (α)]·I(α)=b EIFE (α)+b MFIE (α)(26)

根据渐进波形估计理论,将混合场积分方程的阻抗矩阵和右边向量展开为泰勒级数的形式,According to the theory of asymptotic waveform estimation, the impedance matrix and the right vector of the mixed field integral equation are expanded into the form of Taylor series,

Figure BDA0003928403090000051
Figure BDA0003928403090000051

Figure BDA0003928403090000052
Figure BDA0003928403090000052

Figure BDA0003928403090000053
为外形矢量中第s个元素引入的随机变化量;k为对外形矢量求导的阶次,L和M分别为帕德多项式中分子、分母的最高阶次。
Figure BDA0003928403090000053
is the random variation introduced by the sth element in the shape vector; k is the order of the derivative of the shape vector, and L and M are the highest order of the numerator and denominator in the Padé polynomial, respectively.

类似的,电流表示为电流矩矢量和外形变化量乘积的形式:Similarly, the current is expressed as the product of the current moment vector and the shape change:

Figure BDA0003928403090000054
Figure BDA0003928403090000054

通过匹配混合场积分方程中各阶变化量,得到电流矩矢量如下:By matching the changes of each order in the mixed field integral equation, the current moment vector is obtained as follows:

m0=Z-10)·b(α0) (30)m 0 =Z -10 )·b(α 0 ) (30)

Figure BDA0003928403090000055
Figure BDA0003928403090000055

建立帕德近似多项式和泰勒级数关于电流的等式如下:Establish the Padé approximation polynomial and the Taylor series equation for the current as follows:

Figure BDA0003928403090000056
Figure BDA0003928403090000056

进一步的,ai和bj的表达式如下:Further, the expressions of a i and b j are as follows:

Figure BDA0003928403090000057
Figure BDA0003928403090000057

Figure BDA0003928403090000058
Figure BDA0003928403090000058

根据Chebyshev–Gauss–Lobatto(GLC)插值方法,在[α0-Δα,α0+Δα]范围内,确定N+1个插值节点,每个节点表示为αj,其表达式如下:According to the Chebyshev–Gauss–Lobatto (GLC) interpolation method, within the range of [α 0 -Δα,α 0 +Δα], determine N+1 interpolation nodes, each node is denoted as α j , and its expression is as follows:

Figure BDA0003928403090000059
Figure BDA0003928403090000059

根据伪谱法构造D矩阵,计算右边向量的一阶导数表达式如下:Construct the D matrix according to the pseudo-spectral method, and calculate the first-order derivative expression of the right vector as follows:

Figure BDA0003928403090000061
Figure BDA0003928403090000061

其中D矩阵的维度为(N+1)*(N+1),b(αj)为任一向量时的一维右边向量,其维度为模型未知量的个数,即N。[b(αj)],j=-N/2,...,N/2为(N+1)*N的二维矩阵。其中,D矩阵可表示如下:The dimension of the D matrix is (N+1)*(N+1), b(α j ) is a one-dimensional right vector when any vector is used, and its dimension is the number of model unknowns, namely N. [b(α j )], j=-N/2,..., N/2 is a two-dimensional matrix of (N+1)*N. Among them, the D matrix can be expressed as follows:

Figure BDA0003928403090000062
Figure BDA0003928403090000062

Figure BDA0003928403090000063
Figure BDA0003928403090000063

Figure BDA0003928403090000064
Figure BDA0003928403090000064

Figure BDA0003928403090000065
Figure BDA0003928403090000065

Figure BDA0003928403090000066
Figure BDA0003928403090000066

特别地,在已知右边向量一阶导数时,其二阶导数可通过下式计算:In particular, when the first derivative of the right vector is known, its second derivative can be calculated by the following formula:

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

以此类推,可得到右边向量的n阶导数b(n)0):By analogy, the nth order derivative b (n)0 ) of the right vector can be obtained:

Figure BDA0003928403090000071
Figure BDA0003928403090000071

同理,对于矩阵导数Z(k)0)的计算也可参照右边向量的形式给出。但是本发明并未直接计算Z(k)0),原因有二:Similarly, the calculation of the matrix derivative Z (k)0 ) can also be given in the form of the right vector. But the present invention does not directly calculate Z (k)0 ), there are two reasons:

其一,直接利用D矩阵计算阻抗矩阵的导数,需要构造维度为(N+1)*N2的先验矩阵,[Z(αj)],j=-N/2,...,N/2。对于未知量较大的模型,其计算复杂度和对内存资源的消耗将是线性增加的。First, to directly use the D matrix to calculate the derivative of the impedance matrix, it is necessary to construct a prior matrix with a dimension of (N+1)*N 2 , [Z(α j )], j=-N/2,...,N /2. For models with large unknowns, the computational complexity and consumption of memory resources will increase linearly.

其二,应用快速多极子(MLFMA)加速电大尺寸模型的计算时,远场部分的阻抗矩阵难以获得,给先验矩阵的获取带来困难。Second, when the fast multipole (MLFMA) is used to accelerate the calculation of the electrically large-scale model, it is difficult to obtain the impedance matrix of the far-field part, which brings difficulties to the acquisition of the prior matrix.

因此,通过计算各插值矢量下的阻抗矩阵与矩矢量的乘积代替直接计算阻抗矩阵。其中Z(α-N/2)mn-i维度为N,重新构造的先验矩阵维度为(N+1)*N,大大降低了内存消耗,计算复杂度也明显降低。类似地,阻抗矩阵导数与矩矢量乘积的导数Z(k)0)mn-i也可以通过D矩阵计算得到:Therefore, instead of directly calculating the impedance matrix, the product of the impedance matrix and the moment vector under each interpolation vector is calculated. Among them, the dimension of Z(α -N/2 )m ni is N, and the dimension of the reconstructed prior matrix is (N+1)*N, which greatly reduces memory consumption and computational complexity. Similarly, the derivative Z (k)0 )m ni of the product of the impedance matrix derivative and the moment vector can also be calculated by the D matrix:

Figure BDA0003928403090000072
Figure BDA0003928403090000072

不同于伪谱法在频率、角度等标量域中的应用,将伪谱法应用于矢量域的外形矢量α,使得矩阵矢量乘的导数包含所有控制点的坐标信息。进而计算出各阶电流矩矢量mn,根据电流矩矢量mn与帕德近似多项式中系数向量ai和bj的关系式,计算出每次随机采样变化量后模型的表面电流。Different from the application of the pseudospectral method in the scalar domain such as frequency and angle, the pseudospectral method is applied to the shape vector α in the vector domain, so that the derivative of the matrix-vector multiplication contains the coordinate information of all control points. Then calculate the current moment vector m n of each order, and calculate the surface current of the model after each random sampling variation according to the relationship between the current moment vector m n and the coefficient vectors a i and b j in the Padé approximation polynomial.

步骤3、根据模型改变后的坐标信息和对应的电流,计算得到模型变化一次后的RCS;根据设定的采样次数,利用基于AWE的扰动法计算出模型每一次变化后的RCS。对采样多次的RCS进行统计分析,得到不确定外形非合作金属目标的电磁散射特性。由于在对外形矢量的求导过程中,采用了伪谱法和插值思想,加法定理依旧满足。所以快速多极子(MLFMA)技术能够用来加速计算电大模型的散射特性。将蒙特卡洛方法的统计均值和方差作为参考值,验证基于AWE的扰动法的有效性。Step 3. According to the coordinate information after the model change and the corresponding current, calculate the RCS after the model changes once; according to the set sampling times, use the AWE-based perturbation method to calculate the RCS after each model change. Statistical analysis is carried out on the RCS sampled many times, and the electromagnetic scattering characteristics of non-cooperative metal targets with uncertain shapes are obtained. Since the pseudospectral method and interpolation idea are used in the derivation process of the shape vector, the addition theorem is still satisfied. So the fast multipole (MLFMA) technique can be used to speed up the calculation of the scattering properties of the electrically large model. The statistical mean and variance of the Monte Carlo method are used as reference values to verify the effectiveness of the perturbation method based on AWE.

首先根据计算电流时引入的随机变量重新建立模型,该过程耗时可忽略不计;进而利用表面电流和重新建立的模型外形信息计算模型变化一次后的雷达散射截面积(RCS)。蒙特卡洛方法每次建模都要执行填充阻抗矩阵,矩阵求逆的操作,耗时巨大。本发明只需要计算一次帕德多项式中的系数向量,通过引入不同的随机变量即可获得模型变化后的电流。Firstly, the model is rebuilt according to the random variables introduced when calculating the current, which takes negligible time; then, the radar cross section (RCS) after one change of the model is calculated by using the surface current and the rebuilt model shape information. The Monte Carlo method needs to perform the operations of filling the impedance matrix and inverting the matrix every time it is modeled, which takes a lot of time. The present invention only needs to calculate the coefficient vector in the Padé polynomial once, and the current after the model change can be obtained by introducing different random variables.

其次,计算出每次模型随机改变后的确定性目标的电磁散射特性。最后对多次采样得到的RCS响应求均值E(RCS)和方差σ(RCS),得到具有不确定外形非合作金属目标电磁散射特性。Second, calculate the electromagnetic scattering characteristics of the deterministic target after each random change of the model. Finally, the mean value E(RCS) and variance σ(RCS) of the RCS responses obtained by multiple sampling are calculated to obtain the electromagnetic scattering characteristics of non-cooperative metal targets with uncertain shapes.

实施例1Example 1

本实施例进行了对金属不确定外形的立方体模型的电磁散射计算,本实施例在Inter(R)Core(TM)i9-10850K CPU@3.6GHz,内存为16GB的计算平台上实现。实施例1中的不同坐标方向如图1所示。金属立方体模型如图2所示,边长为2米。立方体模型由8个控制点控制,共有6个NURBS面构成,如图3所示。入射波频率为300MHz,λ=1m为入射波的波长。In this embodiment, the electromagnetic scattering calculation of a cube model with an uncertain metal shape is carried out. This embodiment is implemented on a computing platform with an Inter(R)Core(TM)i9-10850K CPU@3.6GHz and a memory of 16GB. The different coordinate directions in Embodiment 1 are shown in FIG. 1 . The metal cube model is shown in Figure 2, with a side length of 2 meters. The cube model is controlled by 8 control points and consists of 6 NURBS surfaces, as shown in Figure 3. The frequency of the incident wave is 300MHz, and λ=1m is the wavelength of the incident wave.

(1)当变化#4号控制点的X坐标,坐标的变化范围为[-0.6λ,0.6λ],电磁波水平入射,即θ=-90°,

Figure BDA0003928403090000081
散射角为
Figure BDA0003928403090000082
θ=-90°~+90°。在相同的入射和散射角度下,分别用泰勒方法、蒙特卡洛方法进行计算。其中,三种方法的采样次数均设为1000次。RCS的均值对比如图4所示,本发明提出的方法能够和蒙特卡洛吻合,而泰勒方法发生了偏移,说明改进的基于AWE的扰动法相较于传统泰勒方法能够有效扩大收敛半径。(1) When changing the X coordinate of control point #4, the coordinate range is [-0.6λ, 0.6λ], and the electromagnetic wave is incident horizontally, that is, θ=-90°,
Figure BDA0003928403090000081
The scattering angle is
Figure BDA0003928403090000082
θ=-90°~+90°. Under the same incident and scattering angles, Taylor method and Monte Carlo method were used to calculate. Among them, the sampling times of the three methods are all set to 1000 times. The mean comparison of RCS is shown in Figure 4. The method proposed by the present invention can be consistent with Monte Carlo, while the Taylor method has shifted, indicating that the improved AWE-based perturbation method can effectively expand the convergence radius compared with the traditional Taylor method.

(2)同时变化#2号控制点、#4号控制点的X坐标、Z坐标,坐标的变化范围为[-0.6λ,0.6λ],电磁波垂直入射,即θ=0°,

Figure BDA0003928403090000083
散射角为
Figure BDA0003928403090000084
θ=0°~180°。RCS的均值和方差对比如图5所示,泰勒方法发生了明显偏移,说明针对变化多个点,多个方向时,改进的基于AWE的扰动法精度优于传统泰勒方法。表1中给出了时间和内存消耗的对比。(2) Simultaneously change the X coordinates and Z coordinates of #2 control point and #4 control point, the coordinate range is [-0.6λ, 0.6λ], the electromagnetic wave is vertically incident, that is, θ=0°,
Figure BDA0003928403090000083
The scattering angle is
Figure BDA0003928403090000084
θ=0°~180°. The comparison of the mean and variance of RCS is shown in Figure 5. The Taylor method has shifted significantly, indicating that the improved AWE-based perturbation method is more accurate than the traditional Taylor method when changing multiple points and directions. A comparison of time and memory consumption is given in Table 1.

表1Table 1

Figure BDA0003928403090000085
Figure BDA0003928403090000085

Figure BDA0003928403090000091
Figure BDA0003928403090000091

由表1能够体现变化一个点一个坐标时,本方法比传统泰勒方法的内存占用更少,时间上比蒙特卡洛更短;变化多个点多个坐标时,相较于传统泰勒方法和蒙特卡洛方法,本方法在计算时间和内存消耗上都更有优势。It can be seen from Table 1 that when changing one point and one coordinate, this method occupies less memory than the traditional Taylor method, and the time is shorter than Monte Carlo; when changing multiple points and multiple coordinates, compared with the traditional Taylor method and Monte Carlo Carlo's method, this method has more advantages in computing time and memory consumption.

实施例2Example 2

本实施例进行了对金属不确定外形的电大尺寸长方体模型的电磁散射计算。实施例2中的不同坐标方向如图1所示。金属立方体模型如图6所示,长方体长度和宽度均为0.8米,高度为12米。长方体模型由8个控制点控制,共有6个NURBS面构成,控制点示意图如图7所示。电磁波垂直入射,即θ=0°,

Figure BDA0003928403090000092
入射波频率为300MHz,λ=1m为入射波的波长。当变化#3号、#4号、#6号、#8号控制点的Z坐标,坐标的变化范围为[-0.4λ,0.4λ],散射角为
Figure BDA0003928403090000093
θ=-90°~90°。分别用改进的AWE方法、改进的AWE+MLMFA方法、蒙特卡洛方法进行计算。其中,快速多极子层数为5层。三种方法的采样次数均设为1000次。RCS的均值对比如图8所示,发现AWE方法和AWE+MLFMA方法均能够和蒙特卡洛方法吻合。说明本发明提出的改进的基于AWE的扰动法能够与快速多极子方法联合使用,在保证精度的同时,明显提高计算速度。表2中给出了时间和内存消耗的对比。In this embodiment, the calculation of electromagnetic scattering is performed on an electrically large-sized cuboid model of an uncertain metal shape. The different coordinate directions in Embodiment 2 are shown in FIG. 1 . The metal cube model is shown in Figure 6. The length and width of the cuboid are both 0.8 meters and the height is 12 meters. The cuboid model is controlled by 8 control points and consists of 6 NURBS surfaces. The schematic diagram of the control points is shown in Figure 7. The electromagnetic wave is vertically incident, that is, θ=0°,
Figure BDA0003928403090000092
The frequency of the incident wave is 300MHz, and λ=1m is the wavelength of the incident wave. When changing the Z coordinates of #3, #4, #6, and #8 control points, the coordinate range is [-0.4λ, 0.4λ], and the scattering angle is
Figure BDA0003928403090000093
θ=-90°~90°. The improved AWE method, the improved AWE+MLMFA method and the Monte Carlo method are used for calculation respectively. Among them, the number of fast multipole layers is 5 layers. The sampling times of the three methods are all set to 1000 times. The mean comparison of RCS is shown in Figure 8, and it is found that both the AWE method and the AWE+MLFMA method can be consistent with the Monte Carlo method. It shows that the improved AWE-based perturbation method proposed by the present invention can be used in conjunction with the fast multipole method, and the calculation speed is obviously improved while ensuring the accuracy. A comparison of time and memory consumption is given in Table 2.

表2Table 2

Figure BDA0003928403090000094
Figure BDA0003928403090000094

由表2中可以看出,本发明中提出的方法结合快速多极子之后,内存较之前减少了4倍。相较于蒙特卡洛方法采样1000次,速度提升了5.5倍。说明本发明方法在保证精度的同时,比蒙特卡洛计算速度快的优点。It can be seen from Table 2 that after the method proposed in the present invention is combined with the fast multipole, the memory is reduced by 4 times compared with before. Compared with the Monte Carlo method sampling 1000 times, the speed is increased by 5.5 times. It illustrates that the method of the present invention has the advantage of faster calculation speed than Monte Carlo while ensuring accuracy.

Claims (8)

1. A novel electromagnetic characteristic calculation method of an electrically uncertain outline metal target based on an AWE technology is characterized by comprising the following steps:
step 1, realizing modeling of a non-cooperative metal target by utilizing FEKO software and NURBS modeling technology: establishing a model with controllable target appearance according to the NURBS technology; combining all the control point coordinates into a row vector, and defining the row vector as an appearance vector;
step 2, establishing a mixed field integral equation related to the shape vector: respectively expanding an impedance matrix, a right vector and current of the shape vector into Taylor series, and deducing an expression of a current moment vector; then determining the variation range of the introduced shape vector, constructing a D matrix in a pseudo-spectral method, and calculating the derivative vector multiplication of each order of matrix and the derivative of a right vector to further obtain each order of current moment vector; establishing an equation of the Taylor series and the Pasteur polynomial, deriving the relation between a current moment vector and a vector coefficient of the Pasteur polynomial, and further calculating the vector coefficient; obtaining the current after the model changes once according to the vector coefficient and the random variable quantity of the shape vector;
step 3, calculating to obtain the RCS after the model is changed once according to the coordinate information after the model is changed and the corresponding current; according to the set sampling times, calculating the RCS of the model after each change by using an AWE-based perturbation method; and carrying out statistical analysis on the RCS sampled for multiple times to obtain the electromagnetic scattering property of the non-cooperative metal target with the uncertain shape.
2. A novel method of calculating electromagnetic properties of electrically indeterminate profile metal targets based on AWE technique as claimed in claim 1, characterized by the fact that in step 1 the model of controllable target profile is established according to NURBS technique; combining all control point coordinates of the model into a row vector, defining the row vector as an appearance vector and expressing the appearance vector by alpha; alpha is developed into [ alpha ] 123 ,...,α n-2n-1n ]Wherein α is 123 X, y, z coordinates representing a first coordinate point in the NURBS modeling file;
firstly, establishing an initial target model through FEKO software, wherein a random variable delta alpha is not introduced at the moment; guiding the model into rhinoceros software for reconstruction, wherein the reconstruction comprises two processes of resetting the coordinates of the control points and establishing a curved surface, and finally obtaining the coordinates of each control point and different control points which form the curved surface; alpha is alpha 0 Appearance vector, alpha, representing the original model s An arbitrary coordinate representing an arbitrary element, i.e., an arbitrary point, in the outline vector; ,
the target appearance is flexibly changed by introducing a random variable delta alpha into the appearance vector alpha; Δ α is a range of variation, Δ α = [ ] 1 ,Δα 2 ,Δα 3 ,...,Δα n-2 ,Δα n-1 ,Δα n ](ii) a In a target model containing alpha + delta alpha, according to the wavelength of incident electromagnetic waves, subdivision sizes in the u and v directions are respectively set for each surface, and the model is subjected to surface subdivision by using RWG basis functions; and (3) dividing the target surface into a plurality of triangles by a NURBS technology, and establishing a mixed field integral equation based on the RWG basis function.
3. The novel method of calculating electromagnetic properties of electrically indeterminate profile metal targets based on AWE technique according to claim 2, characterized in that the subdivision size is set to less than one tenth of the wavelength.
4. The AWE technology-based novel electromagnetic property calculation method for electrically uncertain contoured metal targets of claim 2, characterized in that step 2 establishes a mixed field integral equation about a contour vector α: respectively expanding an impedance matrix, a right vector and current of the shape vector into Taylor series, and deducing an expression of a current moment vector; then determining the variation range of the introduced shape vector, constructing a D matrix by using a pseudo-spectrum method, and calculating the derivative vector multiplication of each order matrix and the derivative of the right vector so as to obtain each order current moment vector; establishing an equation of the Taylor series and the Pasteur polynomial, deriving the relation between a current moment vector and a vector coefficient of the Pasteur polynomial, and further calculating the vector coefficient; obtaining the current after the model changes once according to the vector coefficient and the random variable quantity of the shape vector; the method comprises the following specific steps:
firstly, establishing a matrix equation of a metal target CFIE containing a random variable alpha:
Z(α)·I(α)=b(α) (1)
wherein Z (alpha) is an impedance matrix of a mixed field integral equation, I (alpha) is a surface current, and b (alpha) is a right vector; the mixed field integral equation is expressed in a combination form of an electric field integral equation and a magnetic field integral equation; wherein the impedance matrix is represented as:
Z(α)=α c ·Z EFIE (α)+(1-α c )·Z MFIE (α) (2)
α c the value of the combination coefficient is between 0 and 1; z EFIE (. Alpha.) and Z MFIE (alpha) is an impedance matrix in an electric field integral equation and an impedance matrix in a magnetic field integral equation respectively;
the right vector in the mixed field integral equation is represented as:
b(α)=b EIFE (α)+b MFIE (α) (3)
wherein,b EIFE (α) is the right vector in the electric field integral equation, b MFIE (α) is the right vector in the magnetic field integral equation;
the mixed field matrix equation is expressed as follows:
c ·Z EFIE (α)+(1-α c )·Z MFIE (α)]·I(α)=b EIFE (α)+b MFIE (α) (4)
according to the progressive waveform estimation theory, the impedance matrix and the right vector of the mixed field integral equation are expanded into the form of Taylor series:
Figure FDA0003928403080000021
Figure FDA0003928403080000022
Figure FDA0003928403080000023
random variation introduced for the s-th element in the shape vector; k is the order of derivation of the appearance vector, and L and M are respectively the highest order of the numerator and the denominator in the Pasteur polynomial;
the current is expressed as the product of the current moment vector and the shape variation:
Figure FDA0003928403080000031
by matching the variable quantity of each order in the mixed field integral equation, the current moment vector is obtained as follows:
m 0 =Z -10 )·b(α 0 ) (8)
Figure FDA0003928403080000032
equations for the Pade's approximation polynomial and Taylor series with respect to current are established as follows:
Figure FDA0003928403080000033
a i and b j The expression of (a) is as follows:
Figure FDA0003928403080000034
Figure FDA0003928403080000035
according to the Chebyshev-Gauss-Lobatto interpolation method, in alpha 0 -Δα,α 0 +Δα]Within the range, N +1 interpolation nodes are determined, each node being represented as alpha j The expression is as follows:
Figure FDA0003928403080000036
and constructing a D matrix according to a pseudo-spectrum method, and calculating a first derivative expression of a right vector as follows:
Figure FDA0003928403080000037
wherein the dimensions of the D matrix are (N + 1) × (N + 1), b (α) j ) The dimension of the one-dimensional right vector is the number of model unknowns, namely N; [ b (. Alpha.) ] j )]Is a two-dimensional matrix of (N + 1) × N, j = -N/2, ·, N/2;
wherein the D matrix is represented as follows:
Figure FDA0003928403080000041
Figure FDA0003928403080000042
Figure FDA0003928403080000043
Figure FDA0003928403080000044
Figure FDA0003928403080000045
when the right vector first derivative is known, its second derivative is calculated by:
[b (2)j )]=D·[b (1)j )]=D·D·[b(α j )] (20)
obtaining the nth derivative b of the right vector (n)0 ):
Figure FDA0003928403080000046
Calculating the product of an impedance matrix and a moment vector under each interpolation vector instead of directly calculating the impedance matrix; wherein Z (. Alpha.) is -N/2 )m n-i The dimension is N, the reconstructed prior matrix dimension is (N + 1) N, and the derivative Z of the product of the impedance matrix derivative and the moment vector (k)0 )m n-i The calculation of the D matrix obtains:
Figure FDA0003928403080000051
applying pseudo-spectral method to shape vector alpha of vector fieldMaking the derivative of the matrix vector product contain the coordinate information of all control points; further calculate the moment vector m of each current order n According to the current moment vector m n Coefficient vector a in polynomial approximation with Pade i And b j And (4) calculating the surface current of the model after randomly sampling the variable quantity every time.
5. The AWE technology-based novel electromagnetic property calculation method for the metal target with the uncertain electrical configuration according to claim 4, wherein RCS after the model is changed once is calculated in the step 3 according to the coordinate information and the corresponding current after the model is changed; according to the set sampling times, calculating the RCS of the model after each change by using an AWE-based perturbation method; carrying out statistical analysis on RCS sampled for multiple times to obtain the electromagnetic scattering property of the non-cooperative metal target with uncertain appearance; the method comprises the following specific steps:
reestablishing the model according to a random variable introduced during current calculation, and further calculating the radar scattering sectional area after the model changes once by utilizing the surface current and the reestablished model shape information;
calculating the electromagnetic scattering characteristic of the deterministic target after each model random change;
and (4) solving the mean value and the variance of RCS response obtained by multiple sampling to obtain the electromagnetic scattering characteristic of the non-cooperative metal target with the uncertain shape.
6. A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the steps of the method of any of claims 1-5 are implemented when the program is executed by the processor.
7. A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the steps of the method of any one of claims 1 to 5.
8. A computer program product comprising a computer program, characterized in that the computer program realizes the steps of the method of any one of claims 1-5 when executed by a processor.
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117436273A (en) * 2023-11-14 2024-01-23 南京理工大学 A new method for calculating electromagnetic properties of metal targets with electrically large uncertain shapes based on Maehly approximation

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117436273A (en) * 2023-11-14 2024-01-23 南京理工大学 A new method for calculating electromagnetic properties of metal targets with electrically large uncertain shapes based on Maehly approximation

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