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研究生:陳岳呈
研究生(外文):Yueh-Cheng Chen
論文名稱:利用TE入射波重建掩埋完全導體之影像
論文名稱(外文):Image Reconstruction of a Buried PerfectlyConducting Cylinder Illuminated by Transverse Electric Waves
指導教授:丘建青
指導教授(外文):Chien-Ching Chiu
學位類別:碩士
校院名稱:淡江大學
系所名稱:電機工程學系碩士班
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2005
畢業學年度:93
語文別:中文
論文頁數:58
中文關鍵詞:完全導體遺傳演算法半空間TE極化電磁波
外文關鍵詞:Electromagnetic imagingTransverse electric (TE)Half-space structurePerfect ConductorSteady-state genetic algorithm
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本論文之目的在於研究利用遺傳演算法對完全導體的影像重建問題。針對不同平面波入射的情況,就完全導體的逆散射問題進行探討。
首先探討完全導體掩埋在半空間介質中的逆散射,將一個未知形狀、未知材質的二維完全導體掩埋在半空間介質中,吾人在第一層以TE極化電磁波照射掩埋於第二層的物體,並於第一層量得其散射場。吾人將利用接收到的散射場及適當的邊界條件,導出一組非線性積分方程式,再利用動差法將此積分方程式化為矩陣形式,把成像問題化成一個求最佳化問題。再引用遺傳演算法將逆散射問題轉成求解最佳化的問題。
遺傳演算法是一種模擬自然界生物進化的搜尋法則,利用簡單的位元複製、交配及突變,可完成搜尋的程序。不論初始的猜測值為何,遺傳演算法總會收斂到整體的極值(global extreme),而非只收斂於局部極值,藉此可重建物體的形狀函數及導電率。所以在數值模擬中,即使初始的猜測值與實際值相去甚遠,我們仍可求得精準的數值解,成功的重建出物體形狀函數與導電率。而以微分為基礎求取極值的方法(calculus-based method),常會陷入區域極值(local extreme)的陷阱裡。最後將電磁成像的結果與原先假設者做比較,藉以驗證並改進電磁成像理論。
The paper presents a computational approach to the image reconstruction of a perfectly conductor cylinder illuminated by transverse electric (TE) waves. A perfectly conducting cylinder of unknown shape buried in one half-space and scatters the incident wave from another half-space where the scattered field is recorded. 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. The steady state genetic algorithm is then employed to find out the global extreme solution of the cost function. Numerical results demonstrated that, even when the initial guess is far away from the exact one, good reconstruction can be obtained. In such a case, the gradient-based methods often get trapped in a local extreme. In addition, the effect of different noise on the reconstruction is investigated.
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 ………………………………………… 7
1.3 各章內容簡述 ………………………………………… 7
第二章 掩埋在半空間中完全導體之正散射 …………………. 9
2.1節 半空間結構之Green''s Function …………………. 9
2.2節 正散射之理論推導 …………………………………………11
2.3節 數值方法 …………………………………………………. 15
第三章 基因演算法則 …………..……………………………..20
3.1節 前言 …………………………………………………………20
3.2節 基因演算法之基本概念 ………………………………… 20
3.3節 介紹基因演算法則中的運算方式 ……………………… 24
3.4節 基因法則在逆散射的應用 …………………………………31
第四章 數值模擬 ……………………………………………… 34
4.1節 模擬結果 …………………………………………………. 34
4.2節 結論 …………………………………………………………36
第五章 結論與展望 …………………………………………… .37
附錄一 加快週期性格林函數收斂的方法 ………………………. 49
參考文獻 …………………………………………………………….53

圖目錄
圖2.1 求解格林函數之結構圖…………………………………18
圖2.2 掩埋在半空間結構中之完全導體示意圖………………19
圖3.1 基因法則流程……………………………………………31
圖4.1(a) 例子1中形狀函數為7個變數的還原情形。實線代表真的形狀函數,其他類型的線條則代表不同基因世代所計算出來的形狀函數。……………………………………40
圖4.1(b) 例子1中形狀函數為7個變數在不同基因世代中形狀函數偏差量的變化情形。…………………………………41
圖4.1(c) 例子1中形狀函數相對雜訊位準變化情形。…………42
圖4.2(a) 例子2中形狀函數為7個變數的還原情形。實線代表真的形狀函數,其他類型的線條則代表不同基因世代所計算出來的形狀函數。……………………………………43
圖4.2(b) 例子2中形狀函數為7個變數在不同基因世代中形狀函數偏差量的變化情形。…………………………………44
圖4.2(c) 例子2中形狀函數相對雜訊位準變化情形。…………45
圖4.3(a) 例子3中形狀函數為7個變數在不同基因世代中形狀函數偏差量的變化情形。…………………………………46
圖4.3(b) 例子3中形狀函數為7個變數的還原情形。實線代表真的形狀函數,其他類型的線條則代表不同基因世代所計算出來的形狀函數。……………………………………47
圖4.3(c) 例子2中形狀函數相對雜訊位準變化情形。…………48

表目錄
表3.1  基因演算法相關名詞解釋與中英對照表………………22
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