本論文探討非平坦介質表面進行重建的問題，吾人利用掩埋物體法進行重建，即將非平坦部分之介質視為一連串之物體，埋藏於平坦之半空間中，計算出這些掩埋物體之介電常數，就可以重建出非平坦介質表面之形狀，吾人利用積分方程式及量到的散射場，將逆散射問題轉化成最佳化問題，搭配自我適應之動態差異型演化法來處理大量未知數的電磁成像問題。本論文將會以非平坦介質表面為主軸，探討在此環境下，給予不同的初始條件，使用自我適應之動態差異型演化法(SADDE)重建，測試其對非平坦介質表面的搜尋速度及強建性。
    將非平坦介質表面視為一連串之物體掩埋於平坦之半空間中，一組為凸起之物體，另一組為凹陷之物體，並分別對兩組物體進行重建，首先推導其數學式，利用等效電流導出兩組物體的積分方程式，並使用動差法將其轉為矩陣，交由電腦計算散射場，並進行數值模擬。
    最後利用自我適應之動態差異性演化法重建出非平坦介質之表面，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，成功的重建出表面區域的介電常數。另外模擬結果亦顯示無論在低於5%雜訊的情況下，吾人都可重建出近似的結果

This thesis presents the reconstruction of rough surface ,we use the buried object approach to reconstruct the shape and dielectric constant of the rough surface. The rough surface is regarded as a series of objects buried in the flat half space which located alternately on both sides of a plan on interface between two half space .By calculating the dielectric constant of these buried objects, we can reconstruct the shape of rough surface use through the application of the integral equations and the measured scattered field, the inverse scattering problem is transformed into an optimization problem and solved by self-adaptive dynamic differential evolution(SADDE) which can process a lot of unknowns for the electromagnetic imaging problems. The thesis tests the search speed for SADDE by different initial guesses for the rough surface.                                       
    The rough surface is regarded as a series of objects buried on the both sides of the flat half space. A group of convex objects, and a group of concave objects are to be reconstructed. The mathematical formula for the equivalent current is derived by applying two integral equations, then the moment method is employed to solve these equations by computer.
    By using the SADDE to reconstruct the rough surface, numerical results show that the SADDE converges to the overall extreme value (global extreme) regardless of the initial guess. Even if the initial guess is far away from the actual value, SADDE can get the correct shape and the dielectric constant of the rough surface. Simulation results also show that when the noise in less than 5%, we can also reconstruct the similar result.

目錄
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	10
第二章  非平坦介質表面在半空間中的正散射理論	12
2.1  Green's Function(格林函數)推導	12
2.1.1  前言                              12
2.1.2  線電流位於上半平面之Green's Function 13
2.1.3  線電流位於下半平面之Green's Function 13 
2.2  正散射的理論公式推導 14  
2.3  數值方法	19
第三章  自我適應之動態差異型演化法在逆散射的應用	22
3.1  自我適應之動態差異型演化法 22
3.2  整數型自我適應之動態差異型演化法 31
3.3  子空間演算法 32
第四章  數值分析及模擬結果	37
第五章  結論	58
參考文獻	60

















圖目錄
圖2-1-1  線電流源位於區域1時的示意圖	17
圖2-1-2  線電流源位於區域2時的示意圖	17
圖2-2-1  二維非平坦介質表面在半空間的示意圖	18
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演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演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演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4-1-1  物體切格數同為2X2之正方形原始型狀	39
圖4-1-2  以SADDE搭配CSI重建物體同為2X2之情形	40
圖4-1-3  以SADDE搭配SOM重建物體同為2X2之情形	40
圖4-1-4  物體同為2X2不同分佈之原始型狀	41
圖4-1-5  SADDE搭配CSI重建物體同為2X2不同分佈之情形	42
圖4-1-6  SADDE搭配SOM重建物體同為2X2不同分佈之情形	42
圖4-1-7  以SADDE搭配CSI重建物體加入雜訊之情形(A)~(E) 43
圖4-1-8  以SADDE搭配SOM重建物體加入雜訊之情形(A)~(E) 44
圖4-1-9  無雜訊錯誤率和迭代次數之比較圖 45
圖4-1-10  雜訊和錯誤率之比較圖 45
圖4-2-1  物體切格數上為2X2下為3X3之原始型狀	47
圖4-2-2  以SADDE搭配CSI重建物體上為2X2下為3X3之情形	48
圖4-2-3  以SADDE搭配SOM重建物體上為2X2下為3X3之情形	48
圖4-2-4  物體切格數上為2X2下為3X3不同分佈之原始型狀	49
圖4-2-5  SADDE搭配CSI重建物體上為2X2下為3X3不同分佈之情形 50
圖4-2-6  SADDE搭配SOM重建物體上為2X2下為3X3不同分佈之情形 50
圖4-2-7  以SADDE搭配CSI重建物體加入雜訊之情形(A)~(E) 51
圖4-2-8  以SADDE搭配SOM重建物體加入雜訊之情形(A)~(E) 52
圖4-2-9  無雜訊錯誤率和迭代次數之比較圖 53
圖4-2-10  雜訊和錯誤率之比較圖 53
圖4-3-1  物體切格數上為4X4下為3X3之型狀	55
圖4-3-2  以SADDE搭配CSI重建物體上為4X4下為3X3之情形	56
圖4-3-3  以SADDE搭配SOM重建物體上為4X4下為3X3之情形	56
圖4-3-4  無雜訊錯誤率和迭代次數之比較圖 57

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