本論文比較自我適應之動態差異型演化法和非同步粒子群聚法應用於半空間二維非完全導體之逆散射問題。針對物體照射TM(Transverse Magnetic)極化波之情況，在半空間非完全導體的逆散射進行探討。利用在導體表面的邊界條件及在物體外部量測的散射電場，可推導出一組非線性積分方程，將散射場積分方程式透過動差法求得散射電場相關資訊。在此使用傅立葉極數展開及描述物體的形狀，並在演算法中使用自我適應之動態差異型演化法和非同步粒子群聚法重建半空間非完全導體之形狀和導電率進行比較。
     不論初始的猜測值如何，自我適應之動態差異性演化法總會收歛到整體的極值(global extreme)，因此在數值模擬顯示中，即使最初的猜測值遠大於實際值，我們仍可求得準確的數值解，成功的重建出物體的形狀函數、導電率。而且在數值模擬顯示中，量測的散射場即使加入均勻分佈的雜訊存在，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。我們也發現，在非完全導體中，形狀函數的收斂速度總是優於導電率。因此可知形狀函數對散射場之貢獻大於導電率，導電率對散射場的貢獻次之。利用上述新型最佳化演算法提供更準確形狀函數的重建，使導電率的重建能更準確。

This paper presents an inverse scattering problem for recovering the shape of an imperfectly conducting cylinder buried in a half space by self-adaptive dynamic differential evolution (SADDE). The imperfectly conducting cylinder of unknown conductivity and 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 equation is derived and the imaging problem is reformulated into optimization problem. The particle swarm optimization algorithm is employed to find out the global extreme solution of the object function. Numerical results show that the conductivity and the shape of the conductor are 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	非完全導體在半空間中的逆散射理論	13
2.1  正散射的理論公式推導	13 
2.2  數值方法	17
2.2.1  動差法於積分方程式的應用	17
第三章	隨機式全域最佳化演算法	20
    3.1  自我適應之動態差異型演化法	20
    3.2  粒子群聚最佳化法	27
第四章	數值分析及模擬結果	33
    4.1  自我適應之動態差異型演化法在逆散射的應用	33
    4.2  環境模擬介紹	34
    4-3  自我適應之動態差異型演化法重建半空間中非完全導體柱體影像	36
第五章	結論	48
附錄一  計算格林函數的方法	50
參考文獻	53

圖目錄
圖 2-1  二維非完全導體在半空間的示意圖	17
圖 3-1  自我適應之動態差異型演化法流程圖	21
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	23
圖 3-2  自我適應之動態差異型進化法中突變方法二的示意圖	24
圖 3-3  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	26
圖 3-5  粒子群聚法流程圖	29
圖 3-6  粒子群聚法中於二維目標函數等位線圖	30
圖 3-7  二維問題中，三種不同邊界條件示意圖	32
圖 4-1  SADDE重建例子一柱體形狀的情形	37
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	38
圖 4-3  SADDE重建例子一柱體的形狀錯誤率比較圖	38
圖 4-4  SADDE和PSO重建例子二柱體形狀的情形	40
圖 4-5  SADDE和PSO重建例子二柱體的形狀錯誤率比較圖	40
圖 4-6  SADDE和PSO重建例子三柱體形狀的情形	42
圖 4-7  SADDE和PSO重建例子二柱體的形狀錯誤率比較圖	42
圖 4-8  SADDE和PSO重建例子三柱體形狀的情形	45
圖 4-9  SADDE和PSO重建例子四柱體的形狀錯誤率比較圖	45
圖4-10  PSO重建例子二形狀參數相對誤差變化趨勢圖	46
圖4-11  PSO重建例子三形狀參數相對誤差變化趨勢圖	46
圖4-12  PSO重建例子四形狀參數相對誤差變化趨勢圖	47

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