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系統識別號 U0002-1306200700450200
中文論文名稱 利用基因法則及TE極化波照射重建部份掩埋完全導體之研究
英文論文名稱 Electromagnetic Transverse Electric Wave Inverse Scattering of a Partially Immersed Conductor by the Steady-State Genetic Algorithm
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 95
學期 2
出版年 96
研究生中文姓名 蔡佳昌
研究生英文姓名 Chia-Chang Tsai
學號 694350124
學位類別 碩士
語文別 中文
口試日期 2007-06-06
論文頁數 84頁
口試委員 指導教授-丘建青
委員-李慶烈
委員-林丁丙
委員-余金郎
委員-陳富強
委員-丘建青
中文關鍵字 穩態基因演算法  完全導體  動差法  部分掩埋  TE極化波 
英文關鍵字 Steady-State Genetic Algorithm  Perfect conductor  Moment Method  Partially immersed  TE wave 
學科別分類 學科別應用科學電機及電子
中文摘要 本論文探討基因法則應用於二維物體之逆散射問題。我們針對物體照射TE極化波的情況下,就在兩半空間中完全導體的逆散射進行探討。

對於完全導體而言,電磁波在完全導體表面之總電場的切線分量為零。因此我們利用完全導體表面電流的概念,可導出一組非線性績分方程式,利用該方程式,我們可以從中得到該物體的散射場資訊。此一步驟為正散射問題。對於逆散射部份,我們引進了基因法則(Genetic Algorithm)。利用基因法則時,我們適當的選取參數,同時結合所求的正散射公式,由此即可求出散射場的相關資料,藉以求得此二維物體的形狀函數。

不論初始值的猜測值如何,基因法則總會收斂至整體的極值(global extreme),因此,在數值模擬顯示中,即時最初的猜測值與實際值相距甚遠,最終我們依然可求得準確的數值解,成功的重建物體形狀函數。而在數值模擬顯示中,量測的散射場即使加入高斯分佈的雜訊,依然可以得到良好的重建結果,研究證實其有良好的抗雜訊能力。
英文摘要 In this paper, we present a computational approach to the imaging of a partially immersed perfectly conducting cylinder by the steady-state genetic algorithm. A conducting cylinder of unknown shape scatters the incident transverse electric (TE) wave in free space while the scattered field is recorded outside. Based on the boundary condition and the measured scattered field, a set of nonlinear integral equations is derived and the imaging problem is reformulated into an optimization problem. An improved steady-state genetic algorithm is employed to search for the global extreme solution. Numerical results demonstrate that, even when the initial guess is far away from the exact one, good reconstruction can be obtained.
論文目次 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………………………………………… 7
1.3節 各章內容簡述………………………………………… 7

第二章 部分掩埋完全導體之正散射………………………… 9
2.1節 兩半空間之Green’s Function 推導……………… 9
2.1.1 線電流位於上半平面之Green’s function……… 9
2.1.2 線電流位於下半平面之Green’s function……… 10
2.2節 正散射之理論推導 ………………………………… 11
2.3節 數值方法……………………………………………… 17

第三章 基因演算法則………………………………………… 23
3.1節 前言…………………………………………………… 23
3.2節 基因演算法之基本概念……………………………… 23
3.3節 介紹基因演算法則中的運算方式…………………… 27
3.4節 基因法則在逆散射的應用…………………………… 34
3.5節 任意形狀函數圖形及三次方仿樣函數的描述……… 35

第四章 數值模擬……………………………………………… 41
4.1節 模擬環境介紹………………………………………… 41
4.2節 使用傅立葉級數描述物體之模擬結果……………… 41
4.3節 使用三次方仿樣函數描述物體之模擬結果………… 43
4.4節 高參數情況下重建物體之分析……………………… 45
4.5節 結論…………………………………………………… 47

第五章 結論與展望…………………………………………… 48

附錄一 計算格林函數的方法………………………………… 70
附錄二 三次方仿樣函數數學推導…………………………… 76
參考文獻…………………………………………………………… 79


圖目錄
圖2.1(a) 當線電流位於上半平面時之結構圖…………………… 19
圖2.1(b) 當線電流位於下半平面時之結構圖…………………… 20
圖2.2(a) 當a > 0時,部份掩埋在半空間結構中之完全導體示意圖… 21
圖2.2(b) 當a ≦ 0時,部份掩埋在半空間結構中之完全導體示意圖… 22
圖3.1 基因法則流程圖……………………………………………… 39
圖3.2 利用三次方仿樣函數描述任意形狀結構示意圖…………… 40
圖4.1(a) 例子一 利用傅立葉級數重建兩辦物體還原結果……… 51
圖4.1(b) 例子一 兩辦物體每代物體函數偏差量………………… 52
圖4.1(c) 例子一 兩辦物體在不同雜訊大小下的形狀偏差量…… 53
圖4.2(a) 例子二 利用傅立葉級數重建三辦物體還原結果……… 54
圖4.2(b) 例子二 三辦物體每代物體函數偏差量………………… 55
圖4.3(a) 例子三 利用傅立葉級數重建不對稱複雜物體還原結果……… 56
圖4.3(b) 例子三 不對稱複雜物體每代物體函數偏差量………… 57
圖4.4(a) 例子四 利用三次方仿樣函數複雜物體還原結果……… 58
圖4.4(b) 例子四 每代物體函數偏差量…………………………… 59
圖4.4(c) 例子四 加入不同雜訊大小時物體還原情形…………… 60
圖4.5(a) 例子五 利用三次方仿樣函數及傅立葉級數重建例子二圖形還原結果比較圖……… 61
圖4.5(b) 例子五 傅立葉級數與三次方仿樣函數重建例子二之雜訊比較圖…………………… 62
圖4.6(a) 例子六 利用三次方仿樣函數及傅立葉級數重建例子三圖形還原結果比較圖……… 63
圖4.6(b) 例子六 傅立葉級數與三次方仿樣函數重建例子三之雜訊比較圖…………………… 64
圖4.7 例子七 利用7、15及19個傅立葉級數參數數重建例子四 由三次方仿樣函數所描述之複雜物體……………… 65
圖4.8(a) 例子八 利用13、17及21個三次方仿樣函數參數重建例子一由傅立葉級數描述兩辦物體之重建結果 …… 66
圖4.8(b) 例子八 利用13、17及21個傅立葉級數參數重建例子一由傅立葉級數描述兩辦物體之重建結果 ………… 67
圖4.9(a) 例子九 利用三次方仿樣函數重建正方形導體之重建情形……… 68
圖4.9(b) 例子九 在不同參數數量情況下之適應值與重建偏差量比較圖… 69


表目錄
表3.1 基因演算法相關名詞解釋與中英對照表………………25


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