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    Title: 二維導體逆散射問題之最佳化研究
    Other Titles: The optimization of inverse problems for two-dimensional conductors
    Authors: 錢威;Chien, Wei
    Contributors: 淡江大學電機工程學系博士班
    丘建青;Chiu, Chien-ching
    Keywords: 基因法則;三次方仿樣函數;傅立葉級數;Genetic Algorithm;Cubic Spline;Fourier series
    Date: 2006
    Issue Date: 2010-01-11 07:10:34 (UTC+8)
    Abstract: 本論文就柱型導體逆散射問題做了三個面向的探討。
    第一個部分,考慮在不同環境下一個未知形狀及表面可變導電係數
    的非完全導體,對於非完全導體之邊界條件,可藉由表面阻抗的概念配
    合導體表面感應電流的觀念,可導出非線性積分方程式,繼而利用動差
    法求得正散射公式。利用正散射公式,我們可以得到散射場的相關資料。
    對於逆散射部分,我們引進了基因法則(genetic algorithm)。利用基因
    法則時,我們適當地選取參數形式,同時結合所求的散射公式,由此即
    可求出散射場的相關資料,藉以求得柱體的形狀函數與導電係數。
    第二個部分,藉由傳統的Fourier series 以及cubic-spline 描述
    物體外觀形狀,探討在基因法則下,對於不同環境逆散射問題的形狀重
    建的適用性,實驗顯示,利用Fourier series 描述複雜形狀往往造成無
    法得到收斂解,cubic-spline 的描述方式則可在較少的變數個數,獲得
    良好的形狀描述結果。
    第三個部分,藉由使用改良的基因法則(NU-SSGA)與傳統GA 比較,
    NU-SSGA 可藉由大幅減少計算正散射的次數,獲取遠優於傳統GA 的效
    能,以往利用全域解演算法解逆散射問題最令人詬病的收斂時間,實驗
    結果顯示,利用NU-SSGA 求解可獲得大幅改善。
    The thesis presents three related aspects of computational approach to
    the imaging of a conducting cylinder. In the first one, an imperfect
    conducting cylinder of unknown shape and variable conductivity is
    considered. Two different cases of inverse problem in free space and half
    space have done respectively. In the second one, cubic-spline method and
    trigonometric series for shape description are used and compared in several
    different situations (half space, partially immersed, slab medium, and
    periodic conductor in free space). In the third one, the inverse scattering
    problem is addressed to discuss the CPU time for reconstructing a perfectly
    conducting cylinder for two different cases (half space and slab medium). It
    is solved by the improved Steady State Genetic Algorithm (SSGA) and
    Simple Genetic Algorithm (SGA) and the consuming time in finding out the
    global extreme solution of the objective function is compared. Based on the
    boundary conditions and the measured scattered field, a set of nonlinear
    integral equations is derived and the imaging problem is reformulated into an
    III
    optimization problem. In the first one, the genetic algorithm is employed to
    find out the global extreme solution of the objective function. Numerical
    results demonstrate that, even when the initial guess is far away from the
    exact one, a good reconstruction has been obtained. In the second one, the
    shape of the scatterer described by using cubic-spline method can be
    reconstructed. In such case, Fourier series expansion will fail. Numerical
    results show that the shape description by using cubic-spline method is much
    better than that Fourier series. In the third one, it is found that the searching
    ability of SSGA is much powerful than that of the SGA. The consuming time
    for converging to a global extreme solution by using SSGA is much less than
    that SGA. Numerical results show that the image reconstruction problem by
    using SSGA is much better than by SGA in time consuming.
    Appears in Collections:[Graduate Institute & Department of Electrical Engineering] Thesis

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