目标时域EM散射特性数值计算方法与实验研究
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摘要
目标瞬态电磁响应的获取对于电磁脉冲激励研究、高分辨雷达技术、目标识别技术等具有重要意义,本文以精确获取金属目标的瞬态/宽带电磁散射特征为目的,研究了基于时域积分方程的瞬态电磁散射数值计算方法和实验测量技术。深入探讨了制约时域积分方程算法广泛应用的一些问题;详细分析了微波暗室条件下目标时域电磁散射测量技术和数据处理方法。在此基础上,提出了更为稳定的时域积分方程数值算法;实现了用于电大尺寸目标散射计算的快速算法;并获取了多组复杂金属目标在暗室条件下的高精度散射测量数据。
论文首先回顾了金属目标时域电磁散射问题中积分方程(电场积分方程(EFIE)、磁场积分方程(MFIE)以及混合积分方程(CFIE))的建立方法,以及基本MOT(Marching-On-In-Time)技术的时间递推求解过程;给出了目标表面建模剖分的方法,设计制造了几种缩比目标模型;分析了MOT算法中的奇异性积分、后时不稳定的原因以及计算量缩减等问题,并提出了可行性解决方案。
其次,针对时域积分方程求解目标电磁散射时的后时不稳定问题,研究了基于加权Laguerre多项式展开的MOT技术变形算法MOO(Marching-On-In-Order)算法以及采用隐式步进方案的隐式算法(IMPT)思想在电磁散射求解中的应用。分别通过对Hertz矢量展开系数的误差逼近和全域基函数加权Laguerre多项式的时频振荡特性分析,提出了MOO算法中Laguerre展开阶数的判定方法和利用频谱信息改善MOO算法低能区域振荡性的方法;推导了不同差分形式的磁场积分方程隐式算法求解式,与电场积分方程相结合建立了九种形式的混合积分方程,通过实际应用分析比较了它们的性能;此外,通过对电场积分方程进行微分,去除掉电标位中对电流展开系数的时间积分项,提出了一种基于二阶差分的电场积分方程隐式算法(SOD-IMPT);解决了适用于任意封闭或开放表面散射体散射计算的后时发散振荡问题,并且使得算法的执行效率得以大幅度提高。
然后,针对电大尺寸目标快速计算的计算量缩减问题,将时域平面波(PWTD)技术成功应用于采用混合积分方程的IMPT算法进行目标的电磁散射计算。分析了PWTD+MOT的快速算法思想,并将两层PWTD(TLPWTD)和多层PWTD(MLPWTD)技术成功应用于本文提出的基于二阶差分的电场积分方程隐式算法的加速运算,使得时域积分方程方法解决电大尺寸目标电磁散射问题的能力进一步增强。
最后,研究了暗室瞬态电磁测量系统的工作原理以及测量方法。给出了如何从测量数据中消除杂波、噪声从而获取有效数据的处理方法,采用本实验室的暗室测量系统对几种复杂金属目标的瞬态电磁散射特性进行了测量,获取了几种典型目标模型的瞬态/宽带测量数据,并与数值计算得到的数据进行比较,相互验证了有效性。
The recently developments in the areas of high resolution radar technology, electromagnetic pulse simulation studies, and target identification techniques related problems where the transient response plays major role. In order to obtain the wide-band electromagnetic scattering characteristics of arbitrary shaped conducting structures, a computation method which based on the Time-Domain-Integral-Equation (TDIE) and measurement method in transient electromagnetic scattering laboratory for electromagnetic scattering were investigated in this thesis. As two important reasons which restrict the the progress of the TDIE arithmetic, the late-time instabilites and large quantity of computation of TDIE method were studied deeply. Measurement theory and technique in a shielded anechoic chamber were researched, stable methods based on TDIE were developed, the fast analysis for electrically large structures were implemented successfully, and accurate wide-band scattering data for some complex shaped targets were measured.
Firstly, the derivations of time domain EFIE, MFIE and CFIE for transient electromagnetic scattering from arbritrary shaped perfect electrically conducting bodies and Marching-On-In-Time(MOT) method for solving TDIE were reviewed, modeling and partitioning method for scatterers were presented, and some scale model radar targets are designed and manufactured. Some questions in MOT method including integral singularity, late-time-instabilites and computation complexity were analized, and some feasible schemes were advised.
Secondly, aiming at the late-time-instabilites of the MOT, two improved algorithms, named marching on in order(MOO) algorithm which based on the weighed Laguerre polynomials and implicit method(IMPT) which based on implicit time recursion, were investigated for electromagnetic scattering. We proposed a new method to detemine the orders of the weighted Laguerre polynomial which are needed in the time variable expansion through approaching the temporal coefficients of the Hertz vector. And we also proposed an approach to reduce the oscillations which emerged in low energy region according to the Fourier transforms relation between frequency responses and time responses and oscillation character of laguerre polynomial in time and frequency domain, respectively. Implicit expressions were deduced from magnetic field integral equation using different kinds of finite differences, and nine kinds of integral equations were obtained through combine electric field integral equation with magnetic field integral equation with different kinds of finite differences, comparisons of performance with different kinds of differences were presented through simulation for different targets by using different kinds of incident pulse. A stable and accelerated procedure for EFIE was developed, the procedure employs implicit method in conjunction with a time averaging scheme to solve EFIE with the second order time derivatives, it has the superior stability and great efficiency for electromagnetic scattering compution for arbitrary surface of a closed or open PEC body.
Thirdly, in order to reduce the computational complexity for the electrically large structures, the plane-wave-time-domain(PWTD) method was used to enhanced MOT algorithm by associated PWTD with IMPT method using CFIE, and both the two level PWTD(TLPWTD) and multilevel PWTD(MLPWTD) methods were used to enhanced MOT algorithm by associated them with second-order-time-derivatives IMPT method using EFIE which was proposed by the author in this thesis. It farther enhanced the ability to solve the electromagnetic scattering from arbitrary closed or open PEC surface of the electrically large structures using TDIE.
At last, a system for measurement of ultra-wideband impulse scattering responses from scale models of radar targets in time domain is described. The method of acquisition of the scattering signal, and signal processing technique for measurement data are investigated in detail. Three scatterers, including a PEC sphere, a missile scale-model and a plane scale-model, are measured using this system. Compared the measured data with the numerical data, the result shows a good agreement.
论文首先回顾了金属目标时域电磁散射问题中积分方程(电场积分方程(EFIE)、磁场积分方程(MFIE)以及混合积分方程(CFIE))的建立方法,以及基本MOT(Marching-On-In-Time)技术的时间递推求解过程;给出了目标表面建模剖分的方法,设计制造了几种缩比目标模型;分析了MOT算法中的奇异性积分、后时不稳定的原因以及计算量缩减等问题,并提出了可行性解决方案。
其次,针对时域积分方程求解目标电磁散射时的后时不稳定问题,研究了基于加权Laguerre多项式展开的MOT技术变形算法MOO(Marching-On-In-Order)算法以及采用隐式步进方案的隐式算法(IMPT)思想在电磁散射求解中的应用。分别通过对Hertz矢量展开系数的误差逼近和全域基函数加权Laguerre多项式的时频振荡特性分析,提出了MOO算法中Laguerre展开阶数的判定方法和利用频谱信息改善MOO算法低能区域振荡性的方法;推导了不同差分形式的磁场积分方程隐式算法求解式,与电场积分方程相结合建立了九种形式的混合积分方程,通过实际应用分析比较了它们的性能;此外,通过对电场积分方程进行微分,去除掉电标位中对电流展开系数的时间积分项,提出了一种基于二阶差分的电场积分方程隐式算法(SOD-IMPT);解决了适用于任意封闭或开放表面散射体散射计算的后时发散振荡问题,并且使得算法的执行效率得以大幅度提高。
然后,针对电大尺寸目标快速计算的计算量缩减问题,将时域平面波(PWTD)技术成功应用于采用混合积分方程的IMPT算法进行目标的电磁散射计算。分析了PWTD+MOT的快速算法思想,并将两层PWTD(TLPWTD)和多层PWTD(MLPWTD)技术成功应用于本文提出的基于二阶差分的电场积分方程隐式算法的加速运算,使得时域积分方程方法解决电大尺寸目标电磁散射问题的能力进一步增强。
最后,研究了暗室瞬态电磁测量系统的工作原理以及测量方法。给出了如何从测量数据中消除杂波、噪声从而获取有效数据的处理方法,采用本实验室的暗室测量系统对几种复杂金属目标的瞬态电磁散射特性进行了测量,获取了几种典型目标模型的瞬态/宽带测量数据,并与数值计算得到的数据进行比较,相互验证了有效性。
The recently developments in the areas of high resolution radar technology, electromagnetic pulse simulation studies, and target identification techniques related problems where the transient response plays major role. In order to obtain the wide-band electromagnetic scattering characteristics of arbitrary shaped conducting structures, a computation method which based on the Time-Domain-Integral-Equation (TDIE) and measurement method in transient electromagnetic scattering laboratory for electromagnetic scattering were investigated in this thesis. As two important reasons which restrict the the progress of the TDIE arithmetic, the late-time instabilites and large quantity of computation of TDIE method were studied deeply. Measurement theory and technique in a shielded anechoic chamber were researched, stable methods based on TDIE were developed, the fast analysis for electrically large structures were implemented successfully, and accurate wide-band scattering data for some complex shaped targets were measured.
Firstly, the derivations of time domain EFIE, MFIE and CFIE for transient electromagnetic scattering from arbritrary shaped perfect electrically conducting bodies and Marching-On-In-Time(MOT) method for solving TDIE were reviewed, modeling and partitioning method for scatterers were presented, and some scale model radar targets are designed and manufactured. Some questions in MOT method including integral singularity, late-time-instabilites and computation complexity were analized, and some feasible schemes were advised.
Secondly, aiming at the late-time-instabilites of the MOT, two improved algorithms, named marching on in order(MOO) algorithm which based on the weighed Laguerre polynomials and implicit method(IMPT) which based on implicit time recursion, were investigated for electromagnetic scattering. We proposed a new method to detemine the orders of the weighted Laguerre polynomial which are needed in the time variable expansion through approaching the temporal coefficients of the Hertz vector. And we also proposed an approach to reduce the oscillations which emerged in low energy region according to the Fourier transforms relation between frequency responses and time responses and oscillation character of laguerre polynomial in time and frequency domain, respectively. Implicit expressions were deduced from magnetic field integral equation using different kinds of finite differences, and nine kinds of integral equations were obtained through combine electric field integral equation with magnetic field integral equation with different kinds of finite differences, comparisons of performance with different kinds of differences were presented through simulation for different targets by using different kinds of incident pulse. A stable and accelerated procedure for EFIE was developed, the procedure employs implicit method in conjunction with a time averaging scheme to solve EFIE with the second order time derivatives, it has the superior stability and great efficiency for electromagnetic scattering compution for arbitrary surface of a closed or open PEC body.
Thirdly, in order to reduce the computational complexity for the electrically large structures, the plane-wave-time-domain(PWTD) method was used to enhanced MOT algorithm by associated PWTD with IMPT method using CFIE, and both the two level PWTD(TLPWTD) and multilevel PWTD(MLPWTD) methods were used to enhanced MOT algorithm by associated them with second-order-time-derivatives IMPT method using EFIE which was proposed by the author in this thesis. It farther enhanced the ability to solve the electromagnetic scattering from arbitrary closed or open PEC surface of the electrically large structures using TDIE.
At last, a system for measurement of ultra-wideband impulse scattering responses from scale models of radar targets in time domain is described. The method of acquisition of the scattering signal, and signal processing technique for measurement data are investigated in detail. Three scatterers, including a PEC sphere, a missile scale-model and a plane scale-model, are measured using this system. Compared the measured data with the numerical data, the result shows a good agreement.
引文
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