改进特征基函数法及其在电磁散射中的应用
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摘要
目标的电磁散射是雷达探测、地质勘测、遥感观测等的信息来源,电磁散射特性的定量分析是这些应用系统设计、运行的主要依据,特别在军事目标的特性分析、识别及设计中尤为重要。而军事目标往往是一些电大尺寸或结构复杂的目标,因此如何获得一种精确、高效分析电大复杂目标电磁散射问题的方法一直是计算电磁学的一个研究热点。本文在此背景下对矩量法的一个分支——特征基函数法进行了研究。本文紧紧围绕提高计算效率和节省内存这两个关键技术,研究特征基函数法的加速技术以及特征基函数法在目标宽带特性分析中的应用。本文对特征基函数法的研究主要分为两个部分,第一部分是对特征基函数法的改进以及加速技术进行研究；第二部分是特征基函数法应用的拓展,主要介绍了将特征基函数法应用到目标宽带电磁散射特性分析中。
在第一部分中,首先提出了一种加快特征基函数构造以及缩减矩阵构造的方法——快速偶极子法。快速偶极子法通过转换,将远组矩阵向量积转换成聚集—转移—发散的模式,大大减少了计算量,降低了内存消耗。其次,针对传统快速偶极子法存在的不足,提出了一种改进的快速偶极子法,并将改进的快速偶极子法与特征基函数法结合,进一步提高了计算精度和计算效率。最后,针对基于奇异值分解的特征基函数法在构造特征基函数时,需要设置足够多的入射波激励,生成的特征基函数个数较多,特征基函数构造时间长的缺点,提出一种改进的特征基函数法,该方法减少入射波激励个数,对于每个平面波激励,求出每个子域的主要特征基函数后,充分考虑子域间的耦合效应,求出每个子域的次要特征基函数,最后将该子域的特征基函数经过奇异值分解,得到一组与激励无关的最小完备特征基函数。由于改进后的特征基函数法考虑到子域间的耦合作用,可以大大减少入射平面波激励的个数,从而减少特征基函数的个数,减少特征基函数构造时间；另外,应用自适应交叉近似算法加快求解次要特征基函数以及缩减矩阵的矩阵向量积运算,提高了计算效率
在第二部分中,主要研究特征基函数法在目标宽带电磁散射特性分析中的应用。针对超宽带特征基函数法在计算目标宽带RCS时,在低频率点计算精度差的缺点,对传统超宽带特征基函数进行改进,提出一种通用特征基函数构造方案,该方法通过考虑子域间的耦合效应,求出次要特征基函数,改进后的超宽带特征基函数包含更多的电流信息特征,解决了传统方法在低频点计算精度差的缺点。最后,提出一种模型参数估计技术结合通用特征基函数法的方法,避免了对每个频率点RCS的计算,通过少量采样点的计算结果来拟合整个宽带RCS曲线,提高了计算了效率
The electromagnetic scattering of target is the information source of radar detection, geological surveying, and remote sensing. Analysis of electromagnetic scattering characteristics of these applications is the main basis for the design, operation, especially important in the characteristics analysis, identification of military objectives. The military objectives are usually some of the electrically large or complex targets. So how to obtain an accurate and efficient method for analyzing electromagnetic scattering problems is becoming a hot topic in computional electromagnetics. In this dissertation, we focused on the characteristic basis function method, which is one branch of method of moments, to reduce the memory requirements, enhance the computational efficiency in accelerating the characteristic basis function method and analyzing the wideband electromagnetic characteristics. The research of the characteristic basis function method in this dissertation divided into two parts, the first part is the improvement of the characteristic basis function method and acceleration technology. The second part is to expand the application of the characteristic basis function method to analysis of the wideband characteristics of targets.
In the first part, the fast dipole method was presented to accelerate the matrix-vector products in the construction of characteristic basis functions and the calculation of the reduced matrix. The fast dipole method transforms the matrix-vector products of the far groups into aggregation-translation-disaggregation form naturally, so it can cut down the computational complexity and memory requirement. And then, an improved fast dipole method combined with the characteristic basis function method was presented to improve the computation accuracy and the efficiency of the conventional method. At last, we focus on the singular value decomposition-characteristic basis function method (SVD-CBFM), which should be set adequate plane waves in each sub-block to construct characteristic basis functions, thus increasing the number of characteristic basis functions and causing higher time consumption in singular value decomposition. An improved SVD-CBFM is presented. This approach reduces the number of plane waves and fully considers the mutual coupling effects among sub-blocks to obtain the secondary level characteristic basis function. Therefore, the total number of characteristic basis functions and the time required by singular value decomposition are significantly reduced. And also, the adaptive cross approximation algorithm is also used to accelerate the matrix-vector products in the construction of secondary level characteristic basis functions and vector-matrix-vector products in the calculation of the reduced matrix.
In the second part, the characteristic basis function method applied into the analysis of the wideband electromagnetic scattering of the target was studied. Because the traditional ultra-wideband characteristic basis function method has the poor accuracy at the lower frequency points, so an improved ultra-wideband characteristic basis functions named general characteristic basis functions was presented. The general characteristic basis functions fully considers the mutual coupling effects among sub-blocks to obtain the secondary level characteristic basis functions, so it can improve the accuracy at the lower frequency points because the general characteristic basis functions contain more information of the current. Finally, a combination of general characteristic basis function method and model based parameter estimation technology was presented to reduce the frequency points, which only needs a small number of sampling points to fit the entire broadband RCS curve, so it can improve the computational efficiency.
在第一部分中,首先提出了一种加快特征基函数构造以及缩减矩阵构造的方法——快速偶极子法。快速偶极子法通过转换,将远组矩阵向量积转换成聚集—转移—发散的模式,大大减少了计算量,降低了内存消耗。其次,针对传统快速偶极子法存在的不足,提出了一种改进的快速偶极子法,并将改进的快速偶极子法与特征基函数法结合,进一步提高了计算精度和计算效率。最后,针对基于奇异值分解的特征基函数法在构造特征基函数时,需要设置足够多的入射波激励,生成的特征基函数个数较多,特征基函数构造时间长的缺点,提出一种改进的特征基函数法,该方法减少入射波激励个数,对于每个平面波激励,求出每个子域的主要特征基函数后,充分考虑子域间的耦合效应,求出每个子域的次要特征基函数,最后将该子域的特征基函数经过奇异值分解,得到一组与激励无关的最小完备特征基函数。由于改进后的特征基函数法考虑到子域间的耦合作用,可以大大减少入射平面波激励的个数,从而减少特征基函数的个数,减少特征基函数构造时间；另外,应用自适应交叉近似算法加快求解次要特征基函数以及缩减矩阵的矩阵向量积运算,提高了计算效率
在第二部分中,主要研究特征基函数法在目标宽带电磁散射特性分析中的应用。针对超宽带特征基函数法在计算目标宽带RCS时,在低频率点计算精度差的缺点,对传统超宽带特征基函数进行改进,提出一种通用特征基函数构造方案,该方法通过考虑子域间的耦合效应,求出次要特征基函数,改进后的超宽带特征基函数包含更多的电流信息特征,解决了传统方法在低频点计算精度差的缺点。最后,提出一种模型参数估计技术结合通用特征基函数法的方法,避免了对每个频率点RCS的计算,通过少量采样点的计算结果来拟合整个宽带RCS曲线,提高了计算了效率
The electromagnetic scattering of target is the information source of radar detection, geological surveying, and remote sensing. Analysis of electromagnetic scattering characteristics of these applications is the main basis for the design, operation, especially important in the characteristics analysis, identification of military objectives. The military objectives are usually some of the electrically large or complex targets. So how to obtain an accurate and efficient method for analyzing electromagnetic scattering problems is becoming a hot topic in computional electromagnetics. In this dissertation, we focused on the characteristic basis function method, which is one branch of method of moments, to reduce the memory requirements, enhance the computational efficiency in accelerating the characteristic basis function method and analyzing the wideband electromagnetic characteristics. The research of the characteristic basis function method in this dissertation divided into two parts, the first part is the improvement of the characteristic basis function method and acceleration technology. The second part is to expand the application of the characteristic basis function method to analysis of the wideband characteristics of targets.
In the first part, the fast dipole method was presented to accelerate the matrix-vector products in the construction of characteristic basis functions and the calculation of the reduced matrix. The fast dipole method transforms the matrix-vector products of the far groups into aggregation-translation-disaggregation form naturally, so it can cut down the computational complexity and memory requirement. And then, an improved fast dipole method combined with the characteristic basis function method was presented to improve the computation accuracy and the efficiency of the conventional method. At last, we focus on the singular value decomposition-characteristic basis function method (SVD-CBFM), which should be set adequate plane waves in each sub-block to construct characteristic basis functions, thus increasing the number of characteristic basis functions and causing higher time consumption in singular value decomposition. An improved SVD-CBFM is presented. This approach reduces the number of plane waves and fully considers the mutual coupling effects among sub-blocks to obtain the secondary level characteristic basis function. Therefore, the total number of characteristic basis functions and the time required by singular value decomposition are significantly reduced. And also, the adaptive cross approximation algorithm is also used to accelerate the matrix-vector products in the construction of secondary level characteristic basis functions and vector-matrix-vector products in the calculation of the reduced matrix.
In the second part, the characteristic basis function method applied into the analysis of the wideband electromagnetic scattering of the target was studied. Because the traditional ultra-wideband characteristic basis function method has the poor accuracy at the lower frequency points, so an improved ultra-wideband characteristic basis functions named general characteristic basis functions was presented. The general characteristic basis functions fully considers the mutual coupling effects among sub-blocks to obtain the secondary level characteristic basis functions, so it can improve the accuracy at the lower frequency points because the general characteristic basis functions contain more information of the current. Finally, a combination of general characteristic basis function method and model based parameter estimation technology was presented to reduce the frequency points, which only needs a small number of sampling points to fit the entire broadband RCS curve, so it can improve the computational efficiency.
引文
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