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系統識別號 U0002-1801201421282500
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
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。  
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
第四章 結論 82
參考文獻 84

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2.7應用APSO及其衍生算法於搜尋Quadric函數之收斂測試 28
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
圖3.1二維完全導體在 平面上的示意圖
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(
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)
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)
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)

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)
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)
圖3.7(a) 例子二 f=0.03+cos3(θ)的適應值曲線變化圖(
圖3.7 (b) 例子二 f=0.03+cos3(θ)的適應值曲線變化圖(
圖3.7 (c) 例子二 f=0.03+cos3(θ)的適應值曲線變化圖(
圖3.8 (a) 例子二 f=0.03+cos3(θ)的形狀錯誤率曲線變化圖(
圖3.8 (b) 例子二 f=0.03+cos3(θ)的形狀錯誤率曲線變化圖(
圖3.8 (c) 例子二 f=0.03+cos3(θ)的形狀錯誤率曲線變化圖(
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)
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)
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)

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