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系統識別號 U0002-0507201121243400
中文論文名稱 時域中重建二維非均勻介質柱體之研究
英文論文名稱 Time Domain Inverse Scattering of 2-D Inhomogeneous Dielectric Cylinders
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 99
學期 2
出版年 100
研究生中文姓名 陳紹仁
研究生英文姓名 Shoa-Jen Chen
學號 698450110
學位類別 碩士
語文別 中文
第二語文別 英文
口試日期 2011-06-15
論文頁數 51頁
口試委員 指導教授-丘建青
委員-李慶烈
委員-黃中信
委員-錢威
委員-林丁丙
中文關鍵字 有限時域差分法  時域逆散射  動態差異演化法 
英文關鍵字 Time Domain Inverse scattering  Finite Difference Time Domain  Dynamic Differential Evolution 
學科別分類 學科別應用科學電機及電子
中文摘要 本論文研究埋藏於半空間中二維非均勻介質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埋藏於半空間中二維非均勻介質柱體之特性參數。
為了探究埋藏於半空間中未知的非均勻介質柱體,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介電參數。
本論文探討以動態差異演化法對於半空間下的二維非均勻介質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,此最佳化方法皆可以成功地重建出柱體的介電參數。動態差異型演化法可以大幅減少計算正散射次數,並且減少逆散射問題收斂時間。
英文摘要 This paper presents the studies of microwave image reconstructions that are approached based on the time-domain technique (finite difference time domain, FDTD) and optimization method for 2-D inhomogeneous dielectric cylinders. The dielectric cylinder is buried in half-space media. For the forward scattering the FDTD method is employed to calculate the scattered E fields, while for the inverse scattering Dynamic Differential Evolution (DDE) is utilized to determine the permittivity of the cylindrical scatterer with arbitrary cross section.
In order to explore the unknown dielectric cylinder in half-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 Dynamic Differential Evolution to minimize the discrepancy between the measured and calculated scattered field data. Dynamic Differential Evolution is tested and employed to search the parameter space to determine the permittivity of the dielectric cylinder.
The suitability and efficiency of applying DDE for microwave imaging of 2D dielectric cylinders are examined in this dissertation. Numerical results show that even when the initial guesses are far away from the exact one, good reconstruction can be obtained by Dynamic Differential Evolution. However, the DDE can reduce the convergent speed in terms of the number of the objective function calls.
論文目次 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……………………………………6
1.3 各章內容簡述……………………………………6
第二章 時域有限差分法…………………………………7
2.1 馬克斯威爾方程式………………………………7
2.2 馬克斯威爾方程式於FDTD方法中差分離散現…10
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………10
2.2.2 FDTD更新方程式………………………………12
2.3 數值色散現象與Courant穩定準則……………13
2.4 吸收邊界條件
(Absorbing Boundary Conditions)……………15
2.5 動態差異型演化法
(Dynamic Differential Evolution)……………16
第三章 埋藏於半空間中二維均勻介質柱體影像重建…22
3.1 模擬環境與相關參數設定………………………22
3.2 目標函數與最佳化方法搜尋參數………………23
3.3 數值模擬結果……………………………………24
第四章 結論………………………………………………41
參考文獻........................................42
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.............................................................11
圖2.3 動態差異型進化法中突變的示意圖.................................................18
圖2.4 動態差異型演化策略法流程圖.........................................................21
圖3.1 埋藏於半空間中任意形狀非均勻介質柱體模擬環境示意圖.........23
圖3.2 重建例子一之原始結構示意圖………............................................26
圖3.3 重建例子一示意圖.............................................................................26
圖3.4 不同亂數重建例子一示意圖.............................................................27
圖3.5 不同亂數重建例子一示意圖.............................................................27
圖3.6 加入高斯雜訊後重建例子一示意圖.................................................28
圖3.7 重建例子二之原始結構示意圖……….............................................30
圖3.8 重建例子二示意圖.............................................................................30
圖3.9 不同亂數重建例子二示意圖.............................................................31
圖3.10 不同亂數重建例子二示意圖.............................................................31
圖3.11 加入高斯雜訊後重建例子二示意圖.................................................32
圖3.12 重建例子三之原始結構示意圖……….............................................34
圖3.13 重建例子三示意圖...........................................................................34
圖3.14 不同亂數重建例子三示意圖...........................................................35
圖3.15 不同亂數重建例子三示意圖...........................................................35
圖3.16 加入高斯雜訊後重建例子三示意圖...............................................36
圖3.17 重建例子四之原始結構示意圖………...........................................38
圖3.18 重建例子四示意圖...........................................................................38
圖3.19 不同亂數重建例子四示意圖...........................................................39
圖3.20 不同亂數重建例子四示意圖...........................................................39
圖3.21 加入高斯雜訊後重重建例子四示意圖...........................................40

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