Cubic-spline expansion for a two-dimensional periodic conductor in free space
Cubic-spline expansion for a two-dimensional periodic conductor in free space
复制标题
DOI：
10.3233/jae-2006-780
复制
发表时间：
2006
影响因子：
0.6
通讯作者：
W. Chien;Chung-Hsin Huang;C. Chiu
中科院分区：
文献类型：
--
作者：
W. Chien;Chung-Hsin Huang;C. Chiu
本文提出了一种二维周期导体成像的计算方法。对形状描述的三次样条法和三角级数法进行了比较。在自由空间中放置一个形状未知的周期性导体圆柱，在圆柱外部记录散射场。基于边界条件和记录的散射场，导出了一组非线性积分方程，将成像问题转化为一个优化问题。采用遗传算法求解目标函数的全局极值解。结果表明，用三次样条函数描述的形状可以重建。在这种情况下，傅里叶级数展开将失败。即使初始值与精确值相差甚远，样条展开和遗传算法也能避免局部极值，收敛到全局极值解。数值结果表明，用样条函数方法描述形状比用傅里叶级数描述形状好得多。此外，高斯噪声对重建的影响进行了研究。
This paper presents a computational approach to the imaging of a two-dimensional periodic conductor. Both cubic-spline method and trigonometric series for shape description are used and compared. A periodic conducting cylinder with unknown shape in free space and the scattered field is recorded outside. Based on the boundary condition and the recorded scattered field, a set of nonlinear integral equations is derived and the imaging problem is reformulated into an optimization problem. The genetic algorithm is employed to find out the global extreme solution of the object function. It is found that the shape described by cubic-spline can be reconstructed. In such a case, Fourier series expansion will fail. Even when the initial guess is far away from the exact one, the cubic-spline expansion and genetic algorithm can avoid the local extreme and converge to a global extreme solution. Numerical results are given to show that the shape description by using cubic-spline method is much better than that by the Fourier series. In addition, the effect of Gaussian noise on the reconstruction is investigated.