本論文探討自我適應之動態差異型演化法則應用於半空間二維週期性導體之逆散射問題。針對物體照射TM(Transverse Magnetic)極化波之情況，在半空間中週期性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重建半空間週期性導體之形狀。
     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週期大小、形狀函數。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，在週期性導體中，週期大小的收斂速度總是優於形狀函數。因此可知週期大小對散射場之貢獻最大，形狀函數對散射場的貢獻次之。

This paper presents an inverse scattering problem for recovering the shape of periodic perfectly conducting cylinders buried in a half space by self-adaptive dynamic differential evolution (SADDE). The periodic perfect conducting cylinders of unknown periodic length 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 periodic length and the shape of the conductor are well reconstructed.

目錄
第一章	簡介……………………………………………………………1
1.1節	研究動機與相關文獻…………………………………1
1.2節	本研究之貢獻………………………………………10
1.3節	各章內容簡述…………………………………………11
第二章	週期性導體在半空間中的逆散射理論……………………13
2.1節   正散射的理論公式推導……………………………13 
2.2節   數值方法…………………………………………………17
2.2.1節	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…………………………………19
3.1節   自我適應之動態差異型演化法……………………19
第四章	數值分析及模擬結果………………………………………27
4.1節   自我適應之動態差異型演化法在逆散射的應用……27
4.2節   環境模擬介紹..………………………………………28
4-3節   自我適應之動態差異型演化法重建半空間中二維週期性導體柱體影像…30
第五章	結論…………………………………………………………45
附錄一   計算格林函數的方法………………………………………47
參考文獻………………………………………………………………50

圖目錄
圖2-1  二維週期性導體在半空間的示意圖…………………………15
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的示意圖…………23
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…………………………25
圖4-1  SADDE重建例子一柱體形狀函數的情形……………………31
圖4-2  SADDE重建例子一柱體的特性參數相對誤差變化趨勢圖…32
圖4-3  SADDE重建例子一柱體特性參數隨相對雜訊位準變化的情形………………………33
圖4-4  SADDE重建之例子一的價值函數與function calls比較…34
圖4-5  SADDE重建例子二柱體形狀的情形…………………………36
圖4-6  SADDE重建例子二柱體的特性參數相對誤差變化趨勢圖…37
圖4-7  SADDE重建例子二柱體特性參數隨相對雜訊位準變化的情形………………………38
圖4-8  SADDE重建之例子二的價值函數與function calls比較…39
圖4-9  SADDE重建例子三柱體形狀的情形………………………41
圖4-10  SADDE重建例子三柱體的特性參數相對誤差變化趨勢圖……………………………42
圖4-11  SADDE重建例子三柱體特性參數隨相對雜訊位準變化的情形……………………43
圖4-12  SADDE重建之例子三的價值函數與function calls比較……………………44

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