一种灵活高效的电磁散射宽角度扫描算法

doi:10.12263/DZXB.20210241

摘要/Abstract

摘要：

基于骨架结构元（骨元）技术，提出一种灵活高效的电磁散射宽角度扫描算法.与已有骨元扫角算法不同，本文提出的算法对扫描角度抽样没有任何限制.算法将所有角度抽样对应的右端项向量空间用一组骨元向量来表达，通过求解一个超定方程得到任意角度抽样对应的右端项向量.对超定方程的求解进行了分析，研究了超定方程的求解精度与开销问题.讨论了超定方程引入对骨元扫角的影响.通过超低散射目标和电大复杂目标的雷达散射截面数值仿真结果，验证了所提算法的精确性和高效性.

关键词: 电磁散射, 角度扫描, 骨元化

Abstract:

Based on previously developed angular sweeping grounding on skeletonization, a flexible and efficient wide angular sweeping algorithm is proposed. Different from the previous skeletonization-based angular sweeping methods, the proposed one removes the limitation on how to select the incident samples. Taking the skeleton right-hand sides(RHSs) as the basis vectors which can uniquely and accurately represent the vector space of the whole RHS space, the RHS of an arbitrary incident can be obtained by solving an overdetermined system. The accuracy and the cost of solving the overdetermined system is analyzed. The impact of the overdetermined system on the angular sweeping is discussed. Numerical experiments are carried out to show the performance of the proposed method to solve the overdetermined system. Radar cross section(RCS) computations on ultra-low scattering targets and electrically large complex targets validate the performance of the proposed angular sweeping algorithm.

Key words: electromagnetic scattering, angular sweeping, skeletonization

中图分类号:

O441.4

薛博文, 顾思卓, 潘小敏, 等. 一种灵活高效的电磁散射宽角度扫描算法[J]. 电子学报, 2022, 50(10): 2329-2335.

Bo-wen XUE, Si-zhuo GU, Xiao-min PAN, et al. Wide Angular Sweeping of Electromagnetic Scattering Based on Skeletonization[J]. Acta Electronica Sinica, 2022, 50(10): 2329-2335.

图/表 10

图1 无人机模型示意图

图2 通过求解超定方程得到线性组合系数后利用该系数恢复得到的右端项与原有右端项的误差

图3 远场计算的误差

图4 RCS计算的计算结果

表1 低秩分解误差对远场计算的影响

低秩分解阈值	远场平均误差
$1.0 × 10 - 2$	$5.5 × 10 - 1$
$1.0 × 10 - 3$	$2.2 × 10 - 2$
$1.0 × 10 - 4$	$7.9 × 10 - 3$

表1 低秩分解误差对远场计算的影响

低秩分解阈值	远场平均误差
$1.0 × 10 - 2$	$5.5 × 10 - 1$
$1.0 × 10 - 3$	$2.2 × 10 - 2$
$1.0 × 10 - 4$	$7.9 × 10 - 3$

表 2 无人机模型计算时的计算资源

矩量法计算资源
		进入迭代前计算资源	求解单个右端项(GMRES)
峰值内存/MB		229.4	10.4
时间/s		27.5	14.1
求解超定方程所需计算资源(最小二乘法)
峰值内存/MB		2.7
时间/s	阶段一	$1.6 × 10 - 2$
时间/s	阶段二	$3.3 × 10 - 4$

表 2 无人机模型计算时的计算资源

矩量法计算资源
		进入迭代前计算资源	求解单个右端项(GMRES)
峰值内存/MB		229.4	10.4
时间/s		27.5	14.1
求解超定方程所需计算资源(最小二乘法)
峰值内存/MB		2.7
时间/s	阶段一	$1.6 × 10 - 2$
时间/s	阶段二	$3.3 × 10 - 4$

图5 贴片天线阵列模型单站VV极化RCS结果

图6 无人机模型单站VV极化RCS结果

表3 天线阵列模型计算时的计算资源

矩量法计算资源
		进入迭代前计算资源	求解单个右端项(GMRES)
峰值内存/MB		4 300.84	169.6
时间/s		5 310.7	8.4
求解超定方程所需计算资源(最小二乘法)
峰值内存/MB		4.7
时间/s	阶段一	$2.7 × 10 - 2$
时间/s	阶段二	$1.3 × 10 - 4$

表3 天线阵列模型计算时的计算资源

矩量法计算资源
		进入迭代前计算资源	求解单个右端项(GMRES)
峰值内存/MB		4 300.84	169.6
时间/s		5 310.7	8.4
求解超定方程所需计算资源(最小二乘法)
峰值内存/MB		4.7
时间/s	阶段一	$2.7 × 10 - 2$
时间/s	阶段二	$1.3 × 10 - 4$

表4 无人机模型计算时的计算资源

矩量法计算资源
		进入迭代前计算资源	求解单个右端项(GMRES)
峰值内存/MB		21 811.2	1 128.5
时间/s		13 334.9	1 448.5
求解超定方程所需计算资源(最小二乘法)
峰值内存/MB		3 558.3
时间/s	阶段一	4.5
时间/s	阶段二	$1.4 × 10 - 1$

表4 无人机模型计算时的计算资源

矩量法计算资源
		进入迭代前计算资源	求解单个右端项(GMRES)
峰值内存/MB		21 811.2	1 128.5
时间/s		13 334.9	1 448.5
求解超定方程所需计算资源(最小二乘法)
峰值内存/MB		3 558.3
时间/s	阶段一	4.5
时间/s	阶段二	$1.4 × 10 - 1$

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