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中文論文名稱 結合直交表與隨機搜尋法於逆散射問題的應用研究
英文論文名稱 Investigation of orthogonal array combined with random search method in the application of the inverse scattering problem
校院名稱 淡江大學
系所名稱(中) 電機工程學系碩士班
系所名稱(英) Department of Electrical Engineering
學年度 102
學期 1
出版年 103
研究生中文姓名 翁黃偉
研究生英文姓名 Huang-Wei Wong
學號 600440290
學位類別 碩士
語文別 中文
口試日期 2014-01-07
論文頁數 92頁
口試委員 指導教授-李慶烈
委員-丘建青
委員-張知難
中文關鍵字 直交表  動差法  平滑變化機制  非同步粒子群聚法 
英文關鍵字 Orthogonal array  Method of Moments  Smooth variation  Synchronous Particle Swarm Optimization 
學科別分類 學科別應用科學電機及電子
中文摘要 本論文研究存在於自由空間中二維金屬導體的頻域電磁逆散射問題。在正散射的分析部分,本研究以動差法(Method of Moments, MoM)為基礎,至於逆散射則被轉換為最佳化問題以進行求解,吾人使用非同步粒子群聚法(APSO)、非同步粒子群聚法結合平滑變化機制(APSO+Smoothvary)以及非同步粒子群聚法結合直交表和平滑變化機制(OA+APSO+Smoothvary)所求的解做比較。  
  本論文先探討非同步粒子群聚法、非同步粒子群聚法結合平滑變化機制與非同步粒子群聚法結合直交表和平滑變化機制在不同學習因子的情況下,以九種具不同特性之測試函數予以測試,維度方面皆設定為10維。每個測試函數最佳的學習因子和成功率不盡相同,經過實驗結果可以發現學習因子c1=2.8和c2=1.3是一組普遍通用的學習因子,在引進平滑變化機制之後,讓成功率大幅提昇之外,在收斂深度方面來的更深。
另外,直交表因為具有均勻分布的特性,將其結合並應用在逆散射問題時,可展現出其優越性,例如在初始最佳物種、收斂深度和圖形重建方面,皆有明顯的改善。為此,我們可看到針對二維金屬導體的逆散射問題,結合直交表及/或平滑變化機制之後皆可以有良好的改善。
英文摘要 This thesis studies the electromagnetic inverse scattering problem in frequency domain for a two-dimensional inhomogeneous dielectric cylinder located in free space. The analysis of forward scattering part is based on the Method of Moments (MoM) , while the inverse scattering part is tackled by transforming the problem into an optimization one, of which the asynchronous particle swarm optimization(APSO) is chosen. The reconstructed results by APSO are compared with those obtained by APSO plus certain kind of smooth variation for the control parameter and/or associated with the orthogonal array (OA).

At first, the convergence speed and results for nine benchmarked functions (with dimension 10) are tested as the control parameters are varied for the algorithm of APSO. It is found that not only the best values of the control parameters are different for each function, but also the best success rates are. Nevertheless, we do find one set of the learning factor, c1=2.8 and c2=1, that is suitable for all benchmarked functions tested in general. Then the introduction of certain kind of smooth variation for the control parameters is tested during the course of searching procedure. It is found that the mechanism of smooth variation for the control parameters can increase the success rate significantly in addition to the convergence depth.
Finally, since the orthogonal array exhibits the characteristic of uniform appearance for each level of the experimental parameters, it do reveal its superiority as combined and applied for the inverse scattering problem. For examples, the initial best particle, convergence depth and reconstructed results can be significant improved. It is concluded that for the inverse scattering problem of a two-dimensional metallic conductor, the inclusion of orthogonal array and the mechanism of smooth variation of the control parameters is a helpful technique.
論文目次 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 8
1.3 各章內容簡述 8
第二章 最佳化演算法 10
2.1直交表 10
2.2非同步粒子群聚最佳化法 12
2.3平滑變化機制 17
2.4最佳化方法測試 17
第三章 頻域自由空間中二維金屬導體影像重建 61
3.1自由空間理論推導與數值方法 61
3.2數值模擬結果 65
3.3以非同步粒子群聚法重建自由空間中二維金屬柱體影像
65
3.4非同步粒子群聚法重建自由空間中二維金屬柱體影像之討論
81
第四章 結論 82
參考文獻 84

















圖目錄
圖2.1改良式粒子群聚法流程圖 14
圖2.2二維問題空間中,PSO的邊界條件示意圖 16
圖2.3學習因子C1和C2的平滑變化示意圖 18
圖2.4九種驗證函數的圖形 18
圖2.5應用APSO及其衍生算法於搜尋SPHERE函數之收斂測試 26
圖2.6應用APSO及其衍生算法於搜尋AXIS PARALLEL HYPER-ELLIPSOID函數之收斂測試 27
圖2.7應用APSO及其衍生算法於搜尋Quadric函數之收斂測試 28
圖2.8應用APSO及其衍生算法於搜尋Griewank函數之收斂測試
29
圖2.9應用APSO及其衍生算法(p=16)於搜尋Rosenbrock函數之收斂測試
30
圖2.10應用APSO及其衍生算法(P=64)於搜尋ROSENBROCK函數之收斂測試
31
圖2.11應用APSO及其衍生算法於搜尋Ackley函數之收斂測試
32
圖2.12應用APSO及其衍生算法於搜尋Generalized Schwefel’s Problem函數之收斂測試
33
圖2.13應用APSO及其衍生算法於搜尋RASTRIGIN函數之收斂測試
34
圖2.14應用APSO及其衍生算法於搜尋Weierstrass函數之收斂測試
36
圖2.15應用APSO及其衍生算法於多種驗證函數之混合比較
38
圖3.1二維完全導體在 平面上的示意圖
64
圖3.2 (a) 例子一 f=0.03的適應值曲線變化圖(
使用APSO) 67
圖3.2 (b) 例子一 f=0.03的適應值曲線變化圖(
使用APSO+smoothvary)
68
圖3.2 (c) 例子一 f=0.03的適應值曲線變化圖(
使用APSO+smoothvary+OA) 68
圖3.3 (a) 例子一 f=0.03的形狀錯誤率曲線變化圖(使用APSO)
68
圖3.3 (b) 例子一 f=0.03的形狀錯誤率曲線變化圖(使用APSO+smoothvary)
69
圖3.3 (c) 例子一 f=0.03的形狀錯誤率曲線變化圖(使用APSO+smoothvary+OA)
69

圖3.4例子一 f=0.03的兩條最佳適應值曲線之比較圖(分別使用apso+smoothvary和apso+smoothvary+OA)
70
圖3.5例子一 f=0.03的兩條形狀錯誤率曲線之比較圖(分別使用apso+smoothvary和apso+smoothvary+OA)
70
圖3.6針對例子一f=0.03,在c1=2.8to0.1下的影像重建圖(分別使用apso+smoothvary和apso+smoothvary+oa)
71
圖3.7(a) 例子二 f=0.03+cos3(θ)的適應值曲線變化圖(
使用APSO)
75
圖3.7 (b) 例子二 f=0.03+cos3(θ)的適應值曲線變化圖(
使用APSO+smoothvary)
75
圖3.7 (c) 例子二 f=0.03+cos3(θ)的適應值曲線變化圖(
使用APSO+smoothvary+oa)
75
圖3.8 (a) 例子二 f=0.03+cos3(θ)的形狀錯誤率曲線變化圖(
使用APSO)
76
圖3.8 (b) 例子二 f=0.03+cos3(θ)的形狀錯誤率曲線變化圖(
使用APSO+smoothvary)
76
圖3.8 (c) 例子二 f=0.03+cos3(θ)的形狀錯誤率曲線變化圖(
使用APSO+smoothvary+oa)
76
圖3.9例子二 f=0.03+cos3(θ)的兩條適應值收斂最快曲線之比較圖(分別使用apso+smoothvary和apso+smoothvary+OA)
77
圖3.10例子二 f=0.03+cos3(θ)的兩條形狀錯誤率曲線之比較圖—在 c1=2.8to0.1的情況下(分別使用apso+smoothvary和apso+smoothvary+oa)
77
圖3.11針對例子二f=0.03+cos3θ,在c1=2.8to0.1下的影像重建圖(分別使用apso+smoothvary和apso+smoothvary+oa)
78
圖3.12形狀誤差率隨雜訊位準的變化模擬 78
圖3.13針對例子三,分別使用apso、apso+smoothvary和apso+smoothvary+oa三種方法的適應值曲線之比較圖 81
圖3.14針對例子三,分別使用apso、apso+smoothvary和apso+smoothvary+oa三種方法的形狀錯誤率曲線之比較圖 80
圖3.15針對例子三,在c1=2.7下的影像重建圖(使用apso) 80
圖3.16針對例子三,在c1= c1=2.8to0.1下的影像重建圖(使用apso+smoothvary) 80
圖3.17針對例子三,在c1= c1=2.8to0.1下的影像重建圖(使用apso+smoothvary+oa) 81



表目錄
表2.1 田口直交表OA(18,5,3,2) 11
表2.2 九種驗證函數列表 19
表2.3 FTN1到FTN9的收斂速度排名列表(當C1值改變) 58
表2.4 FTN1到FTN9的成功率排名列表(當C1值改變) 59
表2.5 C1=2.8TO0.1(APSO+SMOOTH VARY and/or OA)和C1=2.8(APSO)的收斂速度和成功率比較表(FTN1~FTN9)
59





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