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系統識別號 U0002-2506200923574200
中文論文名稱 利用粒子群聚最佳化演算法重建埋藏完全導體之影像
英文論文名稱 Image Reconstruction of a Buried Conductor by the Particle Swarm Optimization
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 97
學期 2
出版年 98
研究生中文姓名 范裕昇
研究生英文姓名 Yu-Sheng Fan
學號 696440253
學位類別 碩士
語文別 中文
口試日期 2009-06-19
論文頁數 53頁
口試委員 指導教授-丘建青
委員-丘建青
委員-李慶烈
委員-林丁丙
委員-錢威
委員-林俊華
中文關鍵字 逆散射  半空間  粒子群聚最佳化演算法 
英文關鍵字 Inverse scattering problem  Half space  Particle Swarm Optimization 
學科別分類 學科別應用科學電機及電子
中文摘要 本論文呈現利用粒子群聚最佳化演算法重建半空間中埋藏完全導體的逆散射問題。在第一區分別由三個不同方向發射之TM平面波照射埋藏於第二區中之導體。經由在導體表面之邊界條件及在第一區所量測到的散射電場,我們可推導出一組非線性積分方程式。接著,透過動差法我們可求得正散射公式。利用正散射公式,我們可以得到散射電場的相關資訊。在這裡我們選擇使用傅立葉級數(Fourier series)展開及描述物體的形狀,並在逆演算法中利用粒子群聚最佳化演算法(Particle Swarm Optimization)和改良式粒子群聚最佳化法(Modified particle swarm optimization)來進行埋藏導體之模擬重建,重建埋藏導體的形狀。
PSO的基本演算模式如下:先以均勻分佈,隨機產生初始粒子群,每一個粒子都是一個求解問題的候選解,粒子群會參考個體的最佳經驗,以及群體的最佳經驗,選擇修正的方式,經過不斷的修正之後,粒子群會漸漸接近最佳解。
透過傅立葉級數(Fourier series)展開描述物體形狀及適當的選取演算法中的參數形式,同時結合所求的散射公式,我們可以得到每一代所計算的散射場值,並利用這些散射場值的相關資訊,將電磁成像問題轉化為最佳化問題,藉由粒子群聚最佳化演算法進行重建,求得埋藏導體之形狀。
在模擬的結果中我們可以發現,不論是利用粒子群聚最佳化法或改良式粒子群聚最佳化法來進行重建,不管初始的猜測值如何,粒子群聚最佳化演算法總是能收斂至整體的極值,即使初始猜測的形狀函數與實際形狀函數相距甚遠,我們仍可求得準確的數值解,成功的重建出物體形狀,而當量測的散射場值中有雜訊存在時,透過數值模擬仍顯示,我們依然可以得到良好的重建結果。
英文摘要 This paper presents an inverse scattering problem for recovering the shape ofconducting cylinders in a half space by Particle Swarm Optimization. A perfect-conducting cylinder of unknown shape is buried in one half space and illuminated by the transverse magnetic (TM) plane wave from the other space. Based on the boundary condition and the measured scattered field, a set of nonlinear integral equations are derived, and the electromagnetic imaging problem is reformulated into an optimization problem. Here we choose Fourier series to describe the shape of object. The particle swarm optimization and the modified particle swarm optimization are used to find out the global extreme solution.
The basic process of PSO is as follows: firsta population of individuals defined as random guesses at the problem solutions is initialized. These individuals are candidate solutions, also known as the particles. The particles iteratively evaluate the fitness of the particles and remember the location where they had their best success. The particle's best solution is called the pbest and that of the best particle in the swarm, called gbest. Movements through the search space are guided by these successes and after generations,the PSO can find the best solution according to the best solution experience.
Numerical results are given to demonstrate the performance of the inverse algorithm. Good reconstruction can be obtained even when the initial guess is far different from the exact shape. In addition, the effect of Guassian noise on reconstruction results is investigated and through the numerical simulation shows that we can still get good results of reconstruction.
論文目次 目錄
中文摘要................................................III
英文摘要................................................IV
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......................................5
1.3節 各章內容簡述......................................5
第二章 完全導體之逆散射問題.............................6
2.1節 理論公式推導與數值方法............................6
2.1.1節 正散射的理論公式推導............................6
2.1.2節 動差法於積分方程式的應用........................10
2.2節 粒子群聚最佳化法(Particle Swarm Optimization).....11
2.3節 改良式粒子群聚最佳化法(Modified Particle Swarm Optimization)...........................................17
第三章 數值模擬結果.....................................21
3.1節 粒子群聚最佳化法重建之模擬數值結果................21
3.2節 改良式粒子群聚最佳化法重建之模擬數值結果..........32
第四章 結論.............................................43
附錄一 計算半空間格林函數的方法.........................45
參考文獻................................................48

圖目錄
圖2-1 二維導體在半空間的示意圖..........................7
圖2-2 粒子群聚最佳化法流程圖............................13
圖2-3 粒子群聚法中位置與速度更新示意圖..................14
圖2-4 在粒子群聚最佳化法中,三種不同邊界條件之示意圖....16
圖2-5 改良式粒子群聚法流程圖............................20
圖3-1埋藏在半空間之二維導體在 平面上的示意圖............22
圖3-2(a) 例子1完全導體在半空間中形狀函數的重建情形......24
圖3-2(b) 例子1物體在粒子群聚最佳化法中每個世代重建的目標函數值之變化情形..........................................25
圖3-2(c) 例子1物體在粒子群聚最佳化法中每個世代重建的DR值之變化情形................................................25
圖3-2(d) 例子1物體針對不同雜訊準位重建時之DR值變化情形..26
圖3-3(a) 例子2完全導體在半空間中形狀函數的重建情形......27
圖3-3(b) 例子2物體在粒子群聚最佳化法中每個世代重建的目標函數值之變化情形..........................................28
圖3-3(c) 例子2物體在粒子群聚最佳化法中每個世代重建的DR值之變化情形................................................28
圖3-3(d) 例子2物體針對不同雜訊準位重建時之DR值變化情形..29
圖3-4(a) 例子3完全導體在半空間中形狀函數的重建情形......30
圖3-4(b) 例子3物體在粒子群聚最佳化法中每個世代重建的目標函數值之變化情形..........................................31
圖3-4(c) 例子3物體在粒子群聚最佳化法中每個世代重建的DR值之變化情形................................................31
圖3-4(d) 例子3物體針對不同雜訊準位重建時之DR值變化情形..32
圖3-5(a) 例子1完全導體在半空間中形狀函數的重建情形......34
圖3-5(b) 例子1物體在改良式粒子群聚最佳化法中每個世代重建的目標函數值之變化情形....................................35
圖3-5(c) 例子1物體在改良式粒子群聚最佳化法中每個世代重建的DR值之變化情形..........................................35
圖3-5(d) 例子1物體針對不同雜訊準位重建時之DR值變化情形..36
圖3-6(a) 例子2完全導體在半空間中形狀函數的重建情形......37
圖3-6(b) 例子2物體在改良式粒子群聚最佳化法中每個世代重建的目標函數值之變化情形....................................38
圖3-6(c) 例子2物體在改良式粒子群聚最佳化法中每個世代重建的DR值之變化情形..........................................38
圖3-6(d) 例子2物體針對不同雜訊準位重建時之DR值變化情形..39
圖3-7(a) 例子3完全導體在半空間中形狀函數的重建情形(原始圖).....................................................40
圖3-7(b) 例子3完全導體在半空間中形狀函數的重建情形(放大圖).....................................................41
圖3-7(c) 例子3物體在改良式粒子群聚最佳化法中每個世代重建的目標函數值之變化情形....................................41
圖3-7(d) 例子3物體在改良式粒子群聚最佳化法中每個世代重建的DR值之變化情形..........................................42
圖3-7(e) 例子3物體針對不同雜訊準位重建時之DR值變化情形..42


參考文獻 參考文獻
[1]Manuel Benedetti, Massimo Donelli, Anna Martini, Matteo Pastorino, Andrea Rosani, and Andrea Massa “An innovative microwave-imaging technique for nondestructive evaluation: applications to civil structures monitoring and biological bodies inspection,” IEEE Transactions on Instrumentation and Measurement, vol. 55, no. 6, Dec 2006, pp. 1878-1884.
[2]Tony Huang, and Ananda Sanagavarapu “A Microparticle swarm optimizer for the reconstruction of microwave images,” IEEE Transactions on Antennas and Propagation, vol. 55, no. 3, Mar 2007, pp. 568-576.
[3]A. G. Ramm, “Uniqueness result for inverse problem of geophysics: I,” Inverse Problems., vol. 6, Aug. 1990, pp. 635-641.
[4]S. Caorsi, M. Donelli, D. Franceschini, and A. Massa, “A new methodology based on an iterative multiscaling for microwave imaging,” IEEE Transactions on Microwave Theory and Techniques, vol. 51,no. 4, Apr. 2003, pp. 1162-1173.
[5]R. M. Lewis, “Physical optics inverse diffraction,” IEEE Trans. Antennas Propagat., vol. AP-17, 1969, pp. 308-314.
[6]N. N. Bojarski, “A survey of the physical optics inverse scattering identity,” IEEE Trans. Antennas Propagat., vol. 30, Sept. 1982, pp. 980-989.
[7]M. A. Slaney, A. C. Kak, and L. E. Larsen, “Limitations of imaging with first-order diffraction tomography,” IEEE Trans. Microwave Theory Tech., vol. MTT-32, Aug. 1984, pp. 860-874.
[8]J. B. Keller, “Accuracy and validity of Born and Rytov approximations,” J. Opt. Soc. Amer., vol. 59, 1969, pp. 1003-1004.
[9]K. P. Bube and R. Burridge, “The one-dimensional inverse problem of reflection seismology,” SIAM Rev., vol. 25 no. 4, 1983, pp. 497-559.
[10]J. Sylvester, “On the layer stripping approach to a 1-D inverse problem,” in Inverse Problems in Wave Propagation, G. Chavent et al., Eds. New York: Springer-Verlag, 1997, pp. 453-462.
[11]F. Santosa and H. Schwetlick, “The inversion of acoustical impedance profile by methods of characteristics,” Wave Motion, vol. 4, 1982, pp. 99-1101.
[12]T. M. Habashy, “ A generalized Gel’fand-Levitan-Marchenko integral equation, ” Inverse Problems, vol. 7, 1991, pp. 703-711.
[13]R. F. Harrington, Field Computation by Moment Methods. New York, Macmillan, 1968.
[14]Hung-Yi Li, ”Solution of inverse blackbody radiation problem with conjugate gradient method,” IEEE Trans. Antennas Propagate., vol. 53, issue 5, May. 2005, pp.1840-1842.
[15]A. Roger, “Newton-Kantorovitch algorithm applied to an electromagnetic inverse problem,” IEEE Trans. Antennas Propagate., vol. AP-29, Mar. 1981, pp.232-238.
[16]C. C. Chiu and Y. M. Kiang, “Electromagnetic imaging for an imperfectly conducting cylinder,” IEEE Trans. Microwave Theory Tech., vol. 39, Sept. 1991, pp. 1631- 1639.
[17]A. Kirsch, R. Kress, P. Monk and A. Zinn, “Two methods for solving the inverse acoustic scattering problem,” Inverse Problems., vol. 4, Aug. 1988, pp.749-770.
[18]F. Hettlich, “Two methods for solving an inverse conductive scattering problem,” Inverse Problems., vol. 10, 1994, pp. 375-385.
[19]W. C. Chew and Y. M. Wang, “Reconstruction of two-dimensional permittivity using the distorted Born iterative method,” IEEE Trans. Med. Imag., vol. 9, 1990, pp.218-225.
[20]C. C. Chiu and Y. W. Kiang, “Microwave imaging of a Buried cylinder,” Inverse Problems., vol. 7, 1991, pp. 182-202.
[21]C. C. Chiu and P. T. Liu, “Image reconstruction of a perfectly conducting cylinder by the genetic algorithm,” Proc. Inst. Elect. Eng., Microw., Antennas Propagat., vol. 143, no. 3, 1996, pp. 249-253.
[22]C. C. Chiu, C. L. Li and W. Chien, “Image reconstruction of a buried conductor by the genetic algorithm”, IEICE Trans. Electron., Vol. E84-C, No. 7, Dec. 2001, pp. 961-966.
[23]W. Chien and C. C. Chiu, “Using NU-SSGA to reduce the searching time in inverse problem of a buried metallic object,” IEEE Transactions on Antennas and Propagation., Vol. 53, No. 10, Oct. 2005, pp. 3128-3134.
[24]Anyong Qing, “Electromagnetic inverse scattering of multiple two-dimensional perfectly conducting objects by the differential evolution strategy,” IEEE Transactions on Antennas and Propagation., Vol. 51, No. 6, June 2003, pp. 1251-1262.
[25]S. Caorsi, Massa A., Pastorino M. and Donelli, M., “Improved microwave imaging procedure for nondestructive evaluations of two-dimensional structures,” IEEE Transactions on Antennas and Propagation., Vol. 52, No. 6, June 2004, pp. 1386-1397.
[26]Andrea Massa, Davide Franceschini, Gabriele Franceschini, Matteo Pastorino, Micro Raffetto, and Massimo Doneli, “Parallel GA-based approach for microwave imaging applications,” IEEE Trans. Antennas Propag., vol. 53, no.10, Oct. 2005, pp. 3118-3127.
[27]D. Cherubini, Fanni A., Montisci A. and Testoni P., “Inversion of MLP neural networks for direct solution of inverse problems,” IEEE Transactions on Magnetics., Vol. 41, issue 5, May 2005, pp. 1784-1787.
[28]F. C. Morabito, A. Formisano and R. Martone, “Wavelet tools for improving the accuracy of neural network solution of electromagnetic inverse problems,” IEEE Trans. Magn., vol. 34, May 1998, pp. 2968-2971.
[29]M. Donelli and A. Massa, “Computational approach base on a particle swarm optimizer for microwave imaging of two-dimensional dielectric scatterers,” IEEE Transactions on Microwave Theory and Techniques, vol. 53, issue 5, May, 2005, pp. 1761-1776.
[30]T. Huang and A. S. Mohan, “Application of particle swarm optimization for microwave image of lossy dielectric objects,” IEEE Transaction on Antennas and Propagation, vol. 1B, Dec., 2005, pp. 852-855.
[31]M, Donelli and G. Franceschini, A. Martini, A. Massa, “An integrated multiscaling strategy based on a particle swarm algorithm for inverse scattering problems,” IEEE Transactions on Geoscience and Remote Sensing, vol. 44, issue 2, Feb. 2006, pp. 298-312.
[32]M. Clerc, J. Kenneydy, “The particle swarm-explosion, stability, and convergence in a multidimensional complex space,” IEEE Transactions on Evolutionary Computation, vol. 6, issue 1, 2002, pp. 58-79.
[33]A. Carlisle and G. Dozier, “An off-the-shelf PSO,” in Proc. Of the Workshop on Particle Swarm Optimization, Indianapolis, April, 2001.
[34]Chen Dong, Gaofeng Wang, Zhenyi Chen, Zuqiang Yu, “A Method of Self-Adaptive Inertia Weight for PSO,” Computer Science and Software Engineering, vol. 1, Dec. 2008, pp. 1195-1198.
[35]M. Senthil Arumugam, Aarthi Chandramohan, M.V.C. Rao, “Competitive Approaches to PSO Algorithms via New Acceleration Co-efficient Variant with Mutation Operators,” Computational Intelligence and Multimedia Applications, Aug. 2005, pp. 225-230.
[36]Chen Dong, Gaofeng Wang, Zhenyi Chen, “The inertia weight self-adapting in PSO,” Intelliqent Control and Automation, June. 2008, pp. 5313-5316.
[37]M. Aliyari Shoorehdeli, M. Teshnehlab, A. K. Sedigh,“Novel Hybrid Learning Algorithms for Tuning ANFIS Parameters Using Adaptive Weighted PSO, ” IEEE International Fuzzy Systems, July. 2007, pp. 1-6.
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