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系統識別號 U0002-1707201209583800
中文論文名稱 使用隨機式最佳化法於二維散射體之逆散射研究
英文論文名稱 Application of Stochastic Optimization Methods to the Inverse Scattering of 2-D scatterers
校院名稱 淡江大學
系所名稱(中) 電機工程學系博士班
系所名稱(英) Department of Electrical Engineering
學年度 100
學期 2
出版年 101
研究生中文姓名 孫積賢
研究生英文姓名 Chi-Hsien Sun
學號 897440029
學位類別 博士
語文別 中文
口試日期 2012-06-19
論文頁數 192頁
口試委員 指導教授-丘建青
委員-鄭士康
委員-林丁丙
委員-張道治
委員-郭仁財
委員-方文賢
委員-唐震寰
委員-李慶烈
中文關鍵字 逆散射  微波成像  時域有限差分法  演化計算 
英文關鍵字 Inverse Scattering  Finite Difference Time Domain (FDTD)  Moment Method (MoM)  Green’s Function  Dynamic Differential Evolution (DDE)  Self-Adaptive Dynamic Differential Evolution (SADDE)  Particle Swarm Optimization (PSO)  Asynchronous Particle Swarm Optimization (APSO) 
學科別分類
中文摘要 本論文提出一種新型隨機式最佳化演算法應用於高維度測試函數與二維逆散射問題。本論文的貢獻有兩點,第一點將隨機式最佳化演算法在九種不同特性之測試函數進行測試,結果發現,將”最佳”概念引進隨機式最佳化演算法容易陷入區域極値,而加入”自我適應”的概念之後,參數可以選取到較佳的數值,可以大幅度改善動態差異形演化法的搜尋能力與提升演算法的強健性。
第二個貢獻在研究埋藏於自由空間、半空間與三層空間二維散射體的電磁影像重建。此研究分別以有限時域差分法 (FDTD) 與動差法(MoM)為基礎,利用最佳化方法於時域重建埋藏於不同空間中二維散射體之特性參數。。
為了探究埋藏於不同空間中未知形狀的二維散射體,概念上吾人可向散射體發射電磁脈波/平面波,並量測其周圍的散射場,再針對此散射場分別以粒子群聚法(PSO)、非同步粒子群聚法(APSO)、動態差異形演化法(DDE)與自我適應之動態差異形演化法(SADDE)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,進而重建散射體的形狀函數。
本論文探討上述多種最佳化方法對於不同環境下的二維散射體之逆散射問題,並且引用統計的數據來分析判斷各種演算法的好壞。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,此四種最佳化方法幾乎可以成功地重建出柱體的形狀,其中以自我適應之動態差異形演化法(SADDE)在執行三十次程式後,透過統計數據所得到之平均錯誤率、標準差值與收斂速度上,皆優於其他種隨機式全域演算法。
英文摘要 This dissertation presents a new stochastic optimization algorithm for high dimensional test functions and two-dimensional inverse scattering problem. There are two contributions of this dissertation, the first point of the stochastic optimization algorithms are tested in nine different benchmark functions and found that the idea of approaching the “Best” during the course of optimization procedure are easy to fail into local optimal solution. However, the algorithm of SADDE is a self-adaptive version of DDE, which is processed of self-adaptibility and the ability of approaching the “Best”. Based on the self-adaptive concept, it can improve the robustness of the algorithm.
The second point is presented the studies of some stochastic optimization methods for the shape reconstruction and permittivity distribution of two-dimensional scatterers. The scatterers are located in free space, or embedded in a three-layered material medium, respectively. In time domain, Finite-difference time-domain (FDTD) technique is employed for electromagnetic analyses for both the forward and inverse scattering problems, while the reconstruction problem is transformed into optimization one during the course of inverse scattering.
The idea is to perform the image reconstruction by utilization of some optimization scheme to minimize the discrepancy between the measured and calculated scattered field data. Four optimization schemes are tested and employed to search the parameter space to determine the shape, location and permittivity of the two-dimensional scatterers. They are asynchronous particle swarm optimization (APSO), particle swarm optimization (PSO), dynamic differential evolution (DDE) and self-adaptive dynamic differential evolution (SADDE).
The suitability and efficiency of applying the above methods for microwave imaging of two-dimensional scatterers are examined in this dissertation. The statistical performances of these algorithms are compared. The results show that SADDE outperforms PSO, APSO and DDE in terms of the ability of exploring the optima. However, these results are considered to be indicative and do not generally apply to all optimization problems in electromagnetics.
論文目次 目錄
中文摘要 ………………………………………………………………………………III
英文摘要 ………………………………………………………………………………IV
第一章 簡介 1
1.1逆散射原理、應用與文獻回顧 1
1.2 本研究之貢獻 12
1.3 各章內容簡述 13
第二章 正散射理論推導 14
2.1 馬克斯威爾方程式 14
2.1馬克斯威爾方程式於FDTD方法中差分離散實現 17
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 17
2.2.2 FDTD更新方程式 18
2.3 數值色散現象與Courant穩定準則 19
2.4 吸收邊界條件(Absorbing Boundary Conditions) 21
2.5 次網格方法(subgrid FDTD) 22
2.6頻域半空間正散射的理論公式推導 22
第三章 隨機式全域最佳化演算法 30
3.1 差異型演化法(Differential Evolution) 27
3.2 動態差異型演化法(Dynamic Differential Evolution) 37
3.3自我適應之差異型演化法/自我適應之動態差異型演化法(Self-Adaptive Differential Evolutio/Self-Adaptive Dynamic Differential Evolution) 38
3.4 粒子群聚最佳化法(Particle Swarm Optimization) 40
3.5 非同步粒子群聚最佳化法(Asynchronous Particle Swarm Optimization) 45
3.6最佳化方法測試 49
第四章 自由空間中二維金屬導體影像重建 103
4.1模擬環境與相關參數設定 103
4.1.1模擬環境配置與參數設定 103
4.1.2 散射體形狀描述方法 105
4.1.3 目標函數與最佳化方法搜尋參數 107
4.1最佳化方法重建自由空間中二維金屬導體影像 105
4.2.1以粒子群聚法、非同步粒子群聚法、差異形演化法、自我適應之差異形演化法、動態差異形演化法與自我適應之動態差異形演化法重建自由空間中二維金屬導體 109
4.2.2最佳化方法重建自由空間中二維金屬導體討論 127
第五章 埋藏於三層空間中二維金屬柱體影像重建 130
5.1模擬環境與相關參數設定 130
5.1.1模擬環境配置與參數設定 130
5.1.2 散射體形狀描述方法 132
5.1.3 目標函數與最佳化方法搜尋參數 132
5.2最佳化方法重建埋藏於三層空間中二維金屬柱體影像 133
5.2.1以粒子群聚法、非同步粒子群聚法、動態差異型演化法與自我適應之動態差異形演化法重建三層空間中二維金屬柱體影像 134
5.2.2最佳化方法重建三層空間中二維金屬導體討論 149
第六章 頻域半空間二為金屬導體影像重建 152
6.1理論公式推導與數值方法 152
6.1.1正散射的理論公式推導 152
6.1.2動差法於積分方程式的應用 153
6.2數值結果討論 154
6.2.1以粒子群聚法、非同步粒子群聚法、動態差異型演化法與自我適應之動態差異形演化法重建三層空間中二維金屬柱體影像 155
6.2.2最佳化方法重建半空間中二維金屬導體討論 168
第七章 結論 173
附錄一 中英文對照 174
參考文獻 176
Publication of C. H. Sun 189




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 18
圖2.2 FDTD中電磁場計算時序圖 18
圖2.3 次網格結構示意圖 23
圖2.4 次網格與大網格的電磁場更新動作時序圖。 25
圖2.5 次網格方法流程圖 26
圖2.6二維導體在半空間的示意圖 26
圖3.1 差異型演化法流程圖 31
圖3.2差異型進化法中突變方法一的示意圖 33
圖3.3 差異型進化法中突變方法二的示意圖 34
圖3.4 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3.5 粒子群聚法流程圖 42
圖3.6 粒子群聚法中於二維目標函數等位線圖 43
圖3.7 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 45
圖3.8 非同步粒子群聚法流程圖 48
圖3.9 測試函數函數圖形 50
圖3.10利用自我適應之動態差異形演算法於不同族群大小在10-D測試函數收斂特性比較 54
圖3.11利用動態差異形演算法於不同族群大小在10-D測試函數收斂特性比較 56
圖3.12利用差異形演算法於不同族群大小在10-D測試函數收斂特性比較 58
圖3.13利用非同步粒子群聚法於不同族群大小在10-D測試函數收斂特性比較 60
圖3.14利用自我適應之動態差異形演算法之收斂情況 63
圖3.15利用動態差異形演算法之收斂情況 72
圖3.16利用差異形演算法之收斂情況 81
圖3.17利用非同步粒子群聚法之收斂情況 90
圖4.1自由空間中任意形狀金屬導體模擬環境示意圖 103
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。 104
圖4.3 三次仿樣函數描述任意形狀散射體示意圖 106
圖4.4(a) 使用粒子群聚法重建的形狀圖。 111
圖4.4 (b) 使用非同步粒子群聚法重建的形狀圖 112
圖4.4 (c) 使用差異形演化法重建的形狀圖 112
圖4.4 (d) 使用自我適應之差異形演化法重建的形狀圖 113
圖4.4 (e) 使用動態差異形演化法重建的形狀圖 113
圖4.4(f) 使用自我適應之動態差異形演化法重建的形狀圖 114
圖4.5 六種最佳化方法重建例子一柱體影像的目標函數與function calls比較 114
圖4.6 六種最佳化方法重建例子一柱體影像之形狀錯誤率比較 115
圖4.7(a)使用粒子群聚法重建的形狀圖 117
圖4.7(b)使用非同步粒子群聚法重建的形狀圖 118
圖4.7(c)使用差異形演化法重建的形狀圖 118
圖4.7(d)使用差異形演化法重建的形狀圖 119
圖4.7(e)使用動態差異形演化法重建的形狀圖 119
圖4.7(f)使用自我適應之動態差異形演化法重建的形狀圖 120
圖4.8 六種最佳化方法重建例子二柱體影像的目標函數與function calls比較。 120
圖4.9 六種最佳化方法重建例子二柱體影像之形狀錯誤率比較 121
圖4.10 使用六種演算法重建例子二柱體特性參數隨相對雜訊位準變化的情形 122
圖4.11(a) 原始正解的金屬形狀圖 123
圖4.11(b) 使用粒子群聚法重建的形狀圖 124
圖4.11(c)使用非同步粒子群聚法重建的形狀圖 124
圖4.11(d)差異形演化法重建的形狀圖 125
圖4.11(e) 自我適應之差異形演化法重建的形狀圖 125
圖4.11(f) 動態差異形演化法重建的形狀圖 126
圖4.11(g) 自我適應之動態差異形演化法重建的形狀圖 126
圖5.1埋藏於三層空間中任意形狀金屬導體模擬環境示意圖 130
圖5.2 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。 131
圖5.3(a) 粒子群聚法重建的形狀圖 135
圖5.3(b) 非同步粒子群聚法重建的形狀圖 135
圖5.3(c) 動態差異形演化法重建的形狀圖 136
圖5.3(d) 自我適應之動態差異形演化法重建的形狀圖 136
圖5.4四種隨機式最佳化之目標函數與function calls比較圖 137
圖5.5四種最佳化方法重建例子一之形狀函數相對誤差變化趨勢圖 137
圖5.6(a) 粒子群聚法重建的形狀圖 134
圖5.6(b) 非同步粒子群聚法重建的形狀圖 139
圖5.6(c) 動態差異形演化法重建的形狀圖 140
圖5.6(d) 自我適應之動態差異形演化法重建的形狀圖 141
圖5.7 四種隨機式最佳化之目標函數與function calls比較 141
圖5.8四種最佳化方法重建例子一之形狀函數相對誤差變化趨勢圖 142
圖5.9(a)粒子群聚法重建的形狀圖 144
圖5.9(b)非同步粒子群聚法重建的形狀圖 145
圖5.9(c)動態差異形演化法重建的形狀圖 145
圖5.9(c)自我適應之動態差異形演化法重建的形狀圖 146
圖5.10 四種隨機式最佳化之價值函數與function calls比較 146
圖5.11四種最佳化方法重建例子一之形狀函數相對誤差變化趨勢圖 147
圖5.12 使用四種演算法重建例子三柱體特性參數隨相對雜訊位準變化的情形 148
圖6.1 (a) 為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演算法所計算出的形狀函數 154
圖6.1 (b) 為重建例子一柱體形狀函數情形之放大圖,實線代表真正的形狀函數,其他類型的線條則代表不同演算法所計算出的形狀函數 155
圖6.2四種最佳化方法重建例子一之形狀函數相對誤差變化趨勢圖 156
圖6.3 四種隨機式最佳化之價值函數與function calls比較圖 156
圖6.4 (a) 為重建例子二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演算法所計算出的形狀函數 158
圖6.4 (b)為重建例子一柱體形狀函數情形之放大圖,實線代表真正的形狀函數,其他類型的線條則代表不同演算法所計算出的形狀函數 159
圖6.5四種最佳化方法重建例子二之形狀函數相對誤差變化趨勢圖 160
圖6.6 四種隨機式最佳化之價值函數與function calls比較圖 160
圖6.7 使用四種演算法重建例子二柱體特性參數隨相對雜訊位準變化的情形 161
圖6.8 (a) 為重建例子三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演算法所計算出的形狀函數 163
圖6.8 (b)為重建例子三柱體形狀函數情形之放大圖,實線代表真正的形狀函數,其他類型的線條則代表不同演算法所計算出的形狀函數 163
圖6.9四種最佳化方法重建例子三之形狀函數相對誤差變化趨勢圖 164
圖6.10 四種隨機式最佳化之價值函數與function calls比較圖 164


表目錄
表1.1逆散射問題研究的發展歷史:首次發表者、年代與其使用方法 8
表3.1 測試函數(benchmark functions)表 49
表3.2 利用自我適應之動態差異形演化法測試九種測試函數的結果 99
表3.3 利用動態差異形演化法測試九種測試函數的結果 100
表3.4 利用差異形演化法測試九種測試函數的結果 101
表3.5利用非同步粒子群聚法測試九種測試函數的結果 102
表4.1六種演算法於例子一之目標函數與function calls統計數據分析. 115
表4.2六種演算法於例子一之形狀函數相對誤差率統計數據分析. 116
表4.3六種演算法於例子二之目標函數與function calls統計數據分析. 121
表4.4六種演算法於例子二之形狀函數相對誤差率統計數據分析. 122
表4.5五種最佳化方法重建自由空間中二維金屬導體成功率表(以目標函數為基準). 128
表4.6五種最佳化方法重建自由空間中二維金屬導體成功率表(以形狀錯誤率為基準). 129
表4.7四種最佳化方法計算所需之時間(單位:秒) 129
表5.1四種演算法於例子一之目標函數與function calls統計數據分析 138
表5.2四種演算法於例子一之形狀函數相對誤差率統計數據分析 138
表5.3四種演算法於例子二之目標函數與function calls統計數據分析 142
表5.4四種演算法於例子二之形狀函數相對誤差率統計數據分析 142
表5.5四種演算法於例子三之目標函數與function calls統計數據分析 147
表5.6四種演算法於例子三之形狀函數相對誤差率統計數據分析 148
表5.7四種最佳化方法重建三層空間中二維金屬導體成功率表(以目標函數為基準) 151
表5.8四種最佳化方法重建三層空間中二維金屬導體成功率表(以形狀錯誤率為基準) 151
表5.9四種最佳化方法計算所需之時間(單位:秒) 151
表6.1四種演算法於例子一之目標函數與function calls統計數據分析 159
表6.2四種演算法於例子一之形狀函數相對誤差率統計數據分析 159
表6.3四種演算法於例子二之目標函數與function calls統計數據分析 163
表6.4四種演算法於例子二之形狀函數相對誤差率統計數據分析 163
表6.5四種演算法於例子三之目標函數與function calls統計數據分析 167
表6.6四種演算法於例子三之形狀函數相對誤差率統計數據分析 167
表6.7四種最佳化方法重建半空間中二維金屬導體成功率表(以目標函數為基準) 170
表6.8四種最佳化方法重建半空間中二維金屬導體成功率表 170
表6.9四種最佳化方法計算所需之時間(單位:秒) 170
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