- 學位論文
應用粒子群聚最佳法及動態差異演化法於時域重建金屬導體之影像
Image Reconstruction of Metallic Cylinders by Particle Swarm Optimization and Dynamic Differential Evolution
摘要
本論文研究自由空間中二維金屬導體柱體的電磁影像重建。此研究以有限時域差分法 (FDTD) 為基礎，利用最佳化方法於時域中重建自由空間中二維金屬導體柱體之特性參數。其中，對於描述形狀的方法，於正散射我們使用傅立葉函數展開(Fourier series expansion) ，並於逆散射中使用三次仿樣函數展開（cubic spline），另外，為了使柱體的形狀更為圓滑我們使用了次網格技術。 為了探究自由空間中未知形狀的金屬導體柱體，概念上吾人可向散射體發射電磁脈波，並量測其周圍的散射電磁波，再針對此量測散射電磁波分別以改良式粒子群聚法（MPSO）、動態差異形演化法（DDE）將逆散射問題轉化為求解最佳化問題。藉由量測而得的散射場以及計算而得的散射場數值互相比較，進而重建介電散射體的形狀函數與位置。 本論文探討上述兩種最佳化方法對於自由空間的二維金屬導體柱體逆散射問題的適用性。模擬結果顯示，即使最初的猜測值與實際散射體位置相距甚遠，此兩種最佳化方法皆可以成功地重建出柱體的位置與形狀。在此兩種最佳化方法收斂速度部份，動態差異型演化法與粒子群聚法可以大幅減少計算正散射次數並減少逆散射問題收斂時間，本研究模擬之數值結果中的金屬物體之電磁特性，可以得到良好的重建結果。
並列摘要
Microwave image problems of a two-dimensional metallic cylinder in free space based on the time-domain technique (finite difference time domain, FDTD)are investigated by modified particle swarm optimization (MPSO) and dynamic differential evolution (DDE).For the forward scattering the FDTD method is employed to calculate the scattered E fields, while for the inverse scattering modified modified particle swarm optimization (MPSO) and dynamic differential evolution (DDE) methods are utilized to determine the shape and location of the cylindrical scatterer with arbitrary cross section. The subgirdding technique is implemented for the FDTD code in order to model the shape of the cylinder more smoothly. In order to describe an unknown cylinder with arbitrary cross section more effectively during the course of searching, the closed cubic-spline expansion is adopted to represent the scatterer contour instead of the frequently used trigonometric series. The former is still used in the forward scattering part. In order to explore the unknown metallic cylinder in free space, an electromagnetic pulse can be conducted to illuminate the cylinder, for which the scattered E fields can then be measured. The inverse problem is then resolved by an optimization approach. The idea is to perform the image reconstruction by utilization of two optimization schemes to minimize the discrepancy between the measured and calculated scattered field data. Modified particle swarm optimization (MPSO) and dynamic differential evolution (DDE) are tested and employed to search the parameter space to determine the shape and location of the metallic cylinder. The suitability and efficiency of applying the above methods for microwave imaging of a 2D metallic cylinder are examined in this thesis. Numerical results show that even when the initial guesses are far away from the exact one, good reconstruction can be obtained by both these optimization methods. These optimization methods are tested by several numerical examples, and it is found that the performance of the MPSO and DDE are robust for reconstructing the metallic cylinder. Numerical results show that satisfactory reconstruction has been obtained.
參考文獻
延伸閱讀
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