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中文論文名稱 應用粒子群聚最佳法及動態差異演化法於時域重建金屬導體之影像
英文論文名稱 Image Reconstruction of Metallic Cylinders by Particle Swarm Optimization and Dynamic Differential Evolution
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 98
學期 2
出版年 99
研究生中文姓名 張婉玲
研究生英文姓名 Wan-Ling Chang
學號 697450301
學位類別 碩士
語文別 中文
口試日期 2010-06-07
論文頁數 82頁
口試委員 指導教授-丘建青
中文關鍵字 粒子群聚最佳法  動態差異演化法  微波成像  有限時域差分法 
英文關鍵字 Particle Swarm Optimization  Dynamic Differential Evolution  Time Domain Inverse Scattering  Finite Difference Time Domain 
學科別分類 學科別應用科學電機及電子
中文摘要 本論文研究自由空間中二維金屬導體柱體的電磁影像重建。此研究以有限時域差分法 (FDTD) 為基礎,利用最佳化方法於時域中重建自由空間中二維金屬導體柱體之特性參數。其中,對於描述形狀的方法,於正散射我們使用傅立葉函數展開(Fourier series expansion) ,並於逆散射中使用三次仿樣函數展開(cubic spline),另外,為了使柱體的形狀更為圓滑我們使用了次網格技術。
為了探究自由空間中未知形狀的金屬導體柱體,概念上吾人可向散射體發射電磁脈波,並量測其周圍的散射電磁波,再針對此量測散射電磁波分別以改良式粒子群聚法(MPSO)、動態差異形演化法(DDE)將逆散射問題轉化為求解最佳化問題。藉由量測而得的散射場以及計算而得的散射場數值互相比較,進而重建介電散射體的形狀函數與位置。
本論文探討上述兩種最佳化方法對於自由空間的二維金屬導體柱體逆散射問題的適用性。模擬結果顯示,即使最初的猜測值與實際散射體位置相距甚遠,此兩種最佳化方法皆可以成功地重建出柱體的位置與形狀。在此兩種最佳化方法收斂速度部份,動態差異型演化法與粒子群聚法可以大幅減少計算正散射次數並減少逆散射問題收斂時間,本研究模擬之數值結果中的金屬物體之電磁特性,可以得到良好的重建結果。
英文摘要 Microwave image problems of a two-dimensional metallic cylinder in free space based on the time-domain technique (finite difference time domain, FDTD)are investigated by modified particle swarm optimization (MPSO) and dynamic differential evolution (DDE).For the forward scattering the FDTD method is employed to calculate the scattered E fields, while for the inverse scattering modified modified particle swarm optimization (MPSO) and dynamic differential evolution (DDE) methods are utilized to determine the shape and location of the cylindrical scatterer with arbitrary cross section. The subgirdding technique is implemented for the FDTD code in order to model the shape of the cylinder more smoothly. In order to describe an unknown cylinder with arbitrary cross section more effectively during the course of searching, the closed cubic-spline expansion is adopted to represent the scatterer contour instead of the frequently used trigonometric series. The former is still used in the forward scattering part.
In order to explore the unknown metallic cylinder in free space, an electromagnetic pulse can be conducted to illuminate the cylinder, for which the scattered E fields can then be measured. The inverse problem is then resolved by an optimization approach. The idea is to perform the image reconstruction by utilization of two optimization schemes to minimize the discrepancy between the measured and calculated scattered field data. Modified particle swarm optimization (MPSO) and dynamic differential evolution (DDE) are tested and employed to search the parameter space to determine the shape and location of the metallic cylinder.
The suitability and efficiency of applying the above methods for microwave imaging of a 2D metallic cylinder are examined in this thesis. Numerical results show that even when the initial guesses are far away from the exact one, good reconstruction can be obtained by both these optimization methods. These optimization methods are tested by several numerical examples, and it is found that the performance of the MPSO and DDE are robust for reconstructing the metallic cylinder. Numerical results show that satisfactory reconstruction has been obtained.

論文目次 目錄
中文摘要 ………………………………………………………………Ⅰ
英文摘要 ………………………………………………………………Ⅲ
第一章 簡介 P1
1.1 研究動機與相關文獻 P1
1.2 本研究之貢獻 P7
1.3 各章內容簡述 P7
第二章 時域有限差分法 P8
2.1 馬克斯威爾方程式 P8
2.2 馬克斯威爾方程式於FDTD方法中差分離散實現 P11
2.2.1 Yee單胞(Yee cell)的空間解析方法與蛙跳式(leap-frog)時間步進計算方法 P11
2.2.2 FDTD更新方程式 P12
2.3 數值色散現象與Courant穩定準則 P13
2-4 吸收邊界條件(Absorbing Boundary Conditions) P15
2-5 次網格方法(subgrid FDTD) P16
第三章 改良式粒子群聚法與動態差異型演化法 P20
3.1改良式粒子群聚最佳化法(Modified Particle Swarm Optimization)... P20
3.2動態差異型演化法(Dynamic Differential Evolution) P28
第四章 數值模擬結果 P38
4.1模擬環境與相關參數設定 P38
4.1.1模擬環境配置與參數設定 P38
4.1.2 散射體形狀描述方法 P40
4.1.3 目標函數與最佳化方法搜尋參數 P42
4.2最佳化方法重建自由空間中二維金屬導體柱體影像 P43
4.2.1 以改良式粒子群聚法重建自由空間中二維金屬導體柱體 P44
4.2.2 以動態差異型演化法重建自由空間中二維金屬導體柱體 P54
4.2.3 最佳化方法重建自由空間中二維金屬導體柱體收斂速度及柱體影像 P64
第五章 結論 P70
參考文獻 P72
圖目錄
圖2.1 FDTD中二維Yee單胞於TMz模態(左)與TEz模態(右)表示圖。 11
圖2.2 FDTD中電磁場計算時序圖。 12
圖2.3 次網格結構示意圖。 18
圖2.4 次網格與大網格的電磁場更新動作時序圖。 19
圖2.5 次網格方法流程圖。 19
圖3.1 粒子群聚法流程圖。 21
圖3.2 粒子群聚法中於二維目標函數等位線圖。 23
圖3.3 二維問題中,三種不同邊界條件示意圖。 與 表示更新後的粒子位置與速度。 25
圖3.4 改良式粒子群聚法流程圖。 27
圖3.5 差異型演化法流程圖。 29
圖3.6 差異型進化法中突變方法一的示意圖。 31
圖3.7 差異型進化法中突變方法二的示意圖。 32
圖3.8 差異型進化法中突變方法三的示意圖。 32
圖3.9 差異型進化法中交配向量結構示意圖。 34
圖3.10 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。 35
圖3.11 動態差異型演化策略法流程圖。 37
圖4.1 自由空間中任意形狀金屬導體柱體模擬環境示意圖 39
圖4.2 入射電場波形與頻譜分佈。(a)入射電場時域波形,(b) 入射電場頻譜分佈。 39
圖4.3 三次仿樣函數描述任意形狀散射體示意圖 41
圖4.4 MPSO重建例子一柱體形狀函數的情形,實線代表真正的形狀函數,其他類型的線條則代表不同的世代中所計算出的形狀函數。 45
圖4.5 MPSO重建例子一柱體的特性參數過程中目標函數隨代數變化圖。 46
圖4.6 MPSO重建例子一柱體的特性參數過程中相對誤差變化趨勢圖。 46
圖4.7 MPSO重建例子一柱體特性參數隨相對雜訊位準變化的情形。 47
圖4.8 MPSO重建例子二柱體形狀的情形,實線代表真正的形狀函數,其他線條類型代表不同的世代中所計算出的形狀函數。 48
圖4.9 MPSO重建例子二柱體的特性參數過程中目標函數隨代數變化圖..............................................49
圖4.10 MPSO重建例子二柱體的特性參數過程中相對誤差變化趨勢圖。 49
圖4.11 MPSO重建例子二柱體特性參數隨相對雜訊位準變化的情形。 50
圖4.12 MPSO重建例子三柱體形狀的情形,實線代表真正的形狀函數,其他線條類型代表不同的世代中所計算出的形狀函數。 51
圖4.13 MPSO重建例子三柱體的特性參數過程中目標函數隨代數變化圖…………………………………………………………52
圖4.14 MPSO重建例子三柱體的特性參數過程中相對誤差變化趨勢圖。 52
圖4.15 MPSO重建例子三柱體特性參數隨相對雜訊位準變化的情形。 53
圖4.16 MPSO重建例子二之柱體影像隨機取5次的目標函數與function calls比較圖 53
圖4.17 DDE重建例子一柱體形狀函數的情形,實線代表真正的形狀函數,其他類型的線條則代表不同的世代中所計算出的形狀函數。 55
圖4.18 DDE重建例子一柱體的特性參數過程中目標函數隨代數變化圖。 56
圖4.19 DDE重建例子一柱體的特性參數過程中相對誤差變化趨勢圖。 56
圖4.20 DDE重建例子一柱體特性參數隨相對雜訊位準變化的情形。 57
圖4.21 DDE重建例子二柱體形狀的情形,實線代表真正的形狀函數,其他線條類型代表不同的世代中所計算出的形狀函數。 58
圖4.22 DDE重建例子二柱體的特性參數過程中目標函數隨代數變化圖 59
圖4.23 DDE重建例子二柱體的特性參數過程中相對誤差變化趨勢圖。 59
圖4.24 DDE重建例子二柱體特性參數隨相對雜訊位準變化的情形。 60
圖4.25 DDE重建例子三柱體形狀的情形,實線代表真正的形狀函數,其他線條類型代表不同的世代中所計算出的形狀函數。 61
圖4.26 DDE重建例子三柱體的特性參數過程中目標函數隨代數變化圖…………………………………………………………..62
圖4.27 DDE重建例子三柱體的特性參數過程中相對誤差變化趨勢圖。 62
圖4.28 DDE重建例子三柱體特性參數隨相對雜訊位準變化的情形。 63
圖4.29 DDE重建例子二之柱體影像隨機取5次的目標函數與function calls比較圖 63
圖4.30 兩種最佳化方法重建葫蘆形影像的目標函數與function calls比較。(a) Linear scale (b) Log scale 65
圖4.31 兩種最佳化方法重建三凹形柱體影像的目標函數與function calls比較。(a) Linear scale (b) Log scale 66
圖4.32 兩種最佳化方法重建四凹形影像的目標函數與function calls比較。(a) Linear scale (b) Log scale 67
圖4.33 兩種最佳化方法重建葫蘆形柱體影像的形狀比較 68
圖4.34 兩種最佳化方法重建三凹形柱體影像的形狀比較 69
圖4.35 兩種最佳化方法重建四凹形柱體影像的形狀比較 69



表目錄

表4.1 最佳化方法重建自由空間中金屬導體散射體相關錯誤率表…….69










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