本論文使用自我適應之動態差異型演化法應用於TE極化波照射穿牆導體之逆散射問題。針對物體照射TE (Transverse Electric) 極化波在穿牆導體的逆散射進行探討。在此使用傅立葉級數展開及描述物體的形狀，利用在導體表面的邊界條件及在物體外部量測的散射場，可推導出非線性積分方程式。將散射場積分方程式透過動差法求得散射場相關資訊，藉由此散射場相關資訊與自我適應之動態差異型演化法，將逆散射問題轉化為求解最佳化問題，重建出穿牆導體之形狀。
     對於自我適應之動態差異型演化法，在數值模擬顯示中，即使最初的猜測值與實際散射體的形狀相差甚遠，我們仍可求得不錯的形狀函數，成功的重建出物體的形狀。而且在數值模擬顯示中，量測的散射場即使加入高斯分布雜訊的存在，依然可以得到良好的重建結果，研究證實其有良好的抗雜訊能力。

This thesis presents an inverse scattering problem for recovering the shape of Through-Wall conducting cylinders behind the wall by self-adaptive dynamic differential evolution (SADDE). The Through-Wall conducting cylinders of unknown  shapes are behind the wall and illuminated by the transverse electric (TE) plane wave from another space.
   Based on the boundary condition and the measured scattered field, the nonlinear integral equation is derived and the imaging problem is reformulated into optimization problem. The self-adaptive dynamic differential evolution is employed to find out the global extreme solution of the object function. Numerical results show that the shape of the conductors can be well reconstructed.

第一章	簡介	1
1.1  研究動機與相關文獻	1
1.2  本研究之貢獻	10
1.3  各章內容簡述	11
第二章	穿牆導體的逆散射理論	12
2.1  正散射的理論公式推導	12 
    2.2  數值方法	20
2.2.1  動差法於積分方程式的應用	20
第三章	隨機式全域最佳化演算法	22
    3.1  自我適應之動態差異型演化法	22
第四章	數值分析及模擬結果	30
    4.1  自我適應之動態差異型演化法在逆散射的應用	30
    4.2  環境模擬介紹	31
    4-3  自我適應之動態差異型演化法重建穿牆導體影像	32
第五章	結論	41
參考文獻	43

圖目錄
圖 2-1  穿牆導體的示意圖	18
圖 2-2  源(Line Source)在第三層的二維示意圖	19
圖 3-1  自我適應之動態差異型演化法流程圖	23
圖 3-2  自我適應之動態差異型進化法中突變方法一的示意圖	25
圖 3-3  自我適應之動態差異型進化法中突變方法二的示意圖	26
圖 3-4  自我適應之動態差異型進化法中的交配向量於一個二維目
        標函數等位線圖描述的示意圖	28
圖 4-1  SADDE重建例子一柱體形狀的情形	33
圖 4-2  SADDE重建例子一柱體的形狀參數相對誤差變化趨勢圖	34
圖 4-3  SADDE重建例子一柱體DR值隨相對雜訊位準變化的情形	34
圖 4-4  SADDE重建例子二柱體形狀函數的情形	36
圖 4-5  SADDE重建例子二柱體的形狀參數相對誤差變化趨勢圖	36
圖 4-6  SADDE重建例子二柱體DR值隨相對雜訊位準變化的情形	37
圖 4-7  SADDE重建例子三柱體形狀的情形	39
圖 4-8  SADDE重建例子三柱體的形狀參數相對誤差變化趨勢圖	39
圖 4-9  SADDE重建例子三柱體DR值隨相對雜訊位準變化的情形	40

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