Cubic-Spline Expansion with GA for a Partially Immersed Conducting Cylinder

摘要

This paper presents a computational approach to the imaging of a partially immersed conducting cylinder. Both cubic-spline method and trigonometric series for shape description are used and compared. 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 Fourier series can be reconstructed by cubic-spline. In the opposite case, the shape described by cubic-spline and reconstructed by 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.