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    Title: 利用基因演算法重建埋藏多導體之影像
    Other Titles: Image reconstruction of buried multiple conductors using genetic algorithm
    Authors: 呂鴻政;Lu, Hung-cheng
    Contributors: 淡江大學電機工程學系碩士班
    賴友仁;Lai, Eugene;丘建青;Chiu, Chien-cChing
    Keywords: 逆問題;半空間;穩定型基因演算法;橫磁平面波;多重散射場;Inverse problem;Half-space;Steady-state genetic algorithm;Transverse magnetic plane wave;Multiple scattered fields
    Date: 2007
    Issue Date: 2010-01-11 06:59:08 (UTC+8)
    Abstract: 本論文呈現一個在半空間中多導體形狀重建的逆散射問題之研究。在第一區分別由三個不同方向發射TM平面波照射埋藏的雙導體。經由在導體表面的邊界條件及在物體外部量測到的散射電場,我們可以推導出一組非線性的積分方程式,之後,這些散射場積分方程式透過動差法求得散射電場相關資訊,將電磁成像問題轉化為最佳化的問題。在這裡我們選擇使用傅立葉級數(Fourier series)展開及描述物體的形狀,並在逆演算法中利用改良型基因演算法(Steady state genetic algorithm)重建埋藏雙導體的形狀。只要適當的選取參數,並結合所求的散射公式,可以得到每一個世代所計算的散射場值。跟以往以微分為基礎求取極值的梯度法比較下,更容易找到全域最小值,而不易陷入區域最小值的陷阱。在模擬的結果中,不管初始的猜測值如何,改良型基因演算法總是能收斂至全域極值,甚至,初始猜測的形狀函數跟實際形狀函數相差甚鉅,以及兩個導體之間多重散射效應是非常嚴重的,依然可以很精準的重建其形狀,並且得到精確的數值解。另外,在本研究中即使加入高斯雜訊,我們可看到重建的結果是非常良好的,在雜訊準位為0.01以下時錯誤率在3%,由此可證明其雜訊容忍能力是相當好的。在本研究中,兩個導體埋藏的深度大約為八倍的波長,甚至物體的埋藏深度不同,其形狀還原的效果非常好,除此,埋藏較深的物體形狀的重建效果比另一個物體差。由此可知,埋藏越深的物體較不易得到散射場的資訊。
    This paper presents an inverse scattering problem for recovering the shapes of multiple conducting cylinders with the immersed targets in a half space by genetic algorithm. Two separate perfect-conducting cylinders of unknown shapes are buried in one half space and illuminated by the transverse magnetic (TM) plane wave from the other half space. Based on the boundary condition and the measured scattered field, a set of nonlinear integral equations are derived, and the electromagnetic imaging problem is reformulated into an optimization problem. The improved steady state genetic algorithm is used to find out the global extreme solution. Numerical results are given to demonstrate the performance of the inverse algorithm. Good reconstruction can be obtained even when the initial guesses are far different from the exact shapes, and then the multiple scattered fields between two conductors are huge. In addition, the effect of Gaussian noise on reconstruction results is investigated. We find that the effect of noise is negligible for the normalized standard deviation below 0.01.
    Appears in Collections:[電機工程學系暨研究所] 學位論文

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