本論文探討改良式粒子群聚法則應用於掩埋二維雙導體之逆散射問題。針對物體照射極化波之情況，在半空間中雙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，並在演算法中使用改良式粒子群聚法重建埋藏雙導體之形狀。
     利用傅立葉級數展開描述物體形狀及適當的選取演算法中的參數形式，同時結合所求的散射公式，可得到每一代所計算之散射場值，並利用這些散射場值的相關資訊，將電磁成像問體轉換為最佳化問題，藉由改良式粒子群聚最佳化演算法進行重建，求得埋藏導體之形狀。
       因此，在數值模擬顯示中，即使最初的猜測值與實際相差甚遠，以及兩個導體之間多成散射效應非常嚴重，依然可求得準確的數值解，成功的重建出物體的形狀函數，當量測的散射場值中有雜訊存在時，透過數值模擬仍可得到良好的重建結果。

This paper presents an inverse scattering problem for recovering the shape of multiple conducting cylinders with the immersed targets in a half space by Asynchronous particle swarm optimization (APSO). 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 sat of nonlinear integral equation is derived and the imaging problem is reformulated into optimization problem.
    The Asynchronous particle swarm optimization algorithm is employed to find out the global extreme solution of the object function. Numerical results demonstrate even when the initial guesses are far away from the exact shapes, and then the multiple scattered fields between two conductors are serious the good reconstruction can be obtained. 
In addition, the effect of Gaussian noise on the reconstruction result is investigated and through the numerical simulation shows that we can still get good results of reconstructions.

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……………………...……………………...9
1.3節	各章內容簡述……………………………………………..9
第二章	多導體在半空間中的逆散射理論…………………………11
   2.1節  正散射的理論公式推導…………..……..……...……….11 2.2節  數值方法………………………………………………….15
2.2.1節	動差法於積分方程式的應用……………………….15
2.2.2節	非同步粒子群聚最佳化法…………………….……17
2.3		最佳化方法測試…………………………………………..22
第三章	數值模擬結果…………………………………………..……38
    3.1節  Fourier series描述重建的形狀之數值模擬……………..38
第四章	結論…………………………………………………………..58
附錄一  計算格林函數的方法………………………………………..60
參考文獻………………………………………………………………..63
 

圖目錄
圖2-1  二維雙導體在半空間的示意圖………………………………15
圖2-2  改良式粒子群聚法流程圖……………………………………20
圖 2-3  二維問題中，不同邊界條件示意圖….……………………...22
圖 2-4  測試函數函數圖形…………………………….…….…….....24
圖 2-5  Sphere使用非同步粒子群聚法之收斂情況……….……….28
圖 2-6  Axis parallel hyper-ellipsoid使用非同步粒子群聚法之
    收斂情況………………………………………………………29
圖 2-7 Quadric使用非同步粒子群聚法之收斂情況…………………30
圖 2-8 Griewank 使用非同步粒子群聚法之收斂情況………………31
圖 2-9 Rosebrock使用非同步粒子群聚法法之收斂情………………32
圖 2-10 Ackley使用非同步粒子群聚法之收斂情況…………………33
圖 2-11 Generalized Schwefel’s Problem使用非同步粒子群聚法之收
斂情況…………………………………………………………34
圖 2-12 Rastrigin使用非同步粒子群聚法之收斂情況……………35
圖 2-13 Weierstrass使用非同步粒子群聚法之收斂情況……………36
圖 3-1(a)  例子1雙導體在半空間的形狀函數的重建情形。實線代表實際的形狀函數，星狀線(*)代表第1世代猜測的形狀，虛線(-x-)代表最後所重建之圖形。……………………..41

圖 3-1(b)  例子1物體在基因演算法中每個世代重建的DR值的變化情形………………………………………………………..42
圖 3-1(c)  Function calls 與參數相對誤差變化趨勢圖……..………43
圖 3-1(d) 例子1雙導體在半空間兩物體距離小為一波長形狀函數的
  重建情形。實線代表實際的形狀函數，星狀線(*)代表第1 
  世代猜測的形狀，虛線(-x-)代表最後所重建之圖形。….44
圖 3-1(e) 兩物體小於一個波長時Function calls與參數相對誤差之變
         化趨勢………………………………………………………45
圖 3-2(a)  例子2雙導體在半空間的形狀函數的重建情形。實線代表實際的形狀函數，星狀線(*)代表第1世代猜測的形狀，虛線(-x-)代表最後所重建之圖形。……………………..47

圖 3-2(b)  例子2物體在基因演算法中每個世代重建的DR值的變化情形………………………………………………………..48
圖 3-2(c)  Function calls 與參數相對誤差變化趨勢圖……..………49
圖 3-2(d) 例子2雙導體在半空間兩物體距離小為一波長形狀函數的
  重建情形。實線代表實際的形狀函數，星狀線(*)代表第1 
  世代猜測的形狀，虛線(-x-)代表最後所重建之圖形。….50
圖 3-2(e) 兩物體小於一個波長時Function calls與參數相對誤差之變
         化趨勢………………………………………………………51
圖 3-3(a)  例子3雙導體在半空間的形狀函數的重建情形。實線代表實際的形狀函數，星狀線(*)代表第1世代猜測的形狀，虛線(-x-)代表最後所重建之圖形。……………………..53

圖 3-3(b)  例子3物體在基因演算法中每個世代重建的DR值的變化情形………………………………………………………..51
圖 3-3(c)  Function calls 與參數相對誤差變化趨勢圖……..………55
圖 3-3(d) 例子3雙導體在半空間兩物體距離小為一波長形狀函數的
  重建情形。實線代表實際的形狀函數，星狀線(*)代表第1 
  世代猜測的形狀，虛線(-x-)代表最後所重建之圖形。….56
圖 3-3(e) 兩物體小於一個波長時Function calls與參數相對誤差之變
         化趨勢………………………………………………………57                                                         
 
表目錄
表 2-1  測試函數(benchmark functions)表………….……………...23
表2-2利用非同步粒子群聚法測試九種測試函數的結果…………37

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