淡江大學覺生紀念圖書館 (TKU Library)
進階搜尋


下載電子全文限經由淡江IP使用) 
系統識別號 U0002-1606200718230800
中文論文名稱 利用基因演算法重建埋藏多導體之影像
英文論文名稱 Image Reconstruction of Buried Multiple Conductors Using 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 呂鴻政
研究生英文姓名 Hung-Cheng Lu
學號 694350223
學位類別 碩士
語文別 中文
口試日期 2007-06-05
論文頁數 71頁
口試委員 指導教授-賴友仁
指導教授-丘建青
委員-李慶烈
委員-張道治
委員-林丁丙
中文關鍵字 逆問題  半空間  穩定型基因演算法  橫磁平面波  多重散射場 
英文關鍵字 Inverse problem  Half-space  Steady-state genetic algorithm  Transverse magnetic plane wave  Multiple scattered fields 
學科別分類 學科別應用科學電機及電子
中文摘要 本論文呈現一個在半空間中多導體形狀重建的逆散射問題之研究。在第一區分別由三個不同方向發射TM平面波照射埋藏的雙導體。經由在導體表面的邊界條件及在物體外部量測到的散射電場,我們可以推導出一組非線性的積分方程式,之後,這些散射場積分方程式透過動差法求得散射電場相關資訊,將電磁成像問題轉化為最佳化的問題。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改良型基因演算法(Steady state genetic algorithm)重建埋藏雙導體的形狀。只要適當的選取參數,並結合所求的散射公式,可以得到每一個世代所計算的散射場值。跟以往以微分為基礎求取極值的梯度法比較下,更容易找到全域最小值,而不易陷入區域最小值的陷阱。在模擬的結果中,不管初始的猜測值如何,改良型基因演算法總是能收斂至全域極值,甚至,初始猜測的形狀函數跟實際形狀函數相差甚鉅,以及兩個導體之間多重散射效應是非常嚴重的,依然可以很精準的重建其形狀,並且得到精確的數值解。另外,在本研究中即使加入高斯雜訊,我們可看到重建的結果是非常良好的,在雜訊準位為0.01以下時錯誤率在3%,由此可證明其雜訊容忍能力是相當好的。在本研究中,兩個導體埋藏的深度大約為八倍的波長,甚至物體的埋藏深度不同,其形狀還原的效果非常好,除此,埋藏較深的物體形狀的重建效果比另一個物體差。由此可知,埋藏越深的物體較不易得到散射場的資訊。
英文摘要 This paper presents an inverse scattering problem for recovering the shapes of multiple conducting cylinders with the immersed targets in a half space by genetic algorithm. Two separate perfect-conducting cylinders of unknown shapes are buried in one half space and illuminated by the transverse magnetic (TM) plane wave from the other half 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. The improved steady state genetic algorithm is used to find out the global extreme solution. Numerical results are given to demonstrate the performance of the inverse algorithm. Good reconstruction can be obtained even when the initial guesses are far different from the exact shapes, and then the multiple scattered fields between two conductors are huge. In addition, the effect of Gaussian noise on reconstruction results is investigated. We find that the effect of noise is negligible for the normalized standard deviation below 0.01.
論文目次 目錄
第一章 簡介………………………………………………………1
1.1節 研究動機與相關文…………………………………1
1.2節 本研究之貢獻………………………………………5
1.3節 各章內容簡述………………………………………6
第二章 多導體在半空間中的逆散射理論………………………7
2.1節 正散射的理論公式推導………………………………7
2.2節 數值方法………………………………………………11
2.2.1節 動差法於積分方程式的應用………………………11
2.2.2節 基因演算法…………………………………………12
2.2.3節 逆散射問題…………………………………………19
2.2.4節 任意形狀函數圖形及三次方仿樣函數的描述……21
第三章 數值模擬結果……………………………………………30
3.1節 Fourier series描述重建的形狀之數值模擬……30
3.2節 三次方仿樣函數描述重建的形狀之數值模擬……34
3.3節 結論…………………………………………………38
第四章 結論………………………………………………………59
附錄一 計算格林函數的方法……………………………………61
參考文獻………………………………………………………………64

圖目錄
圖2-1 二維雙導體在半空間的示意圖……………………………26
圖2-2 基因演算法之流程圖………………………………………27
圖2-3 基因演算法單點交配示意圖………………………………28
圖2-4 三次方仿樣函數描述任意形狀物體示意圖………………29
圖3-1(a) 例子1雙導體在半空間的形狀函數的重建情形。實線代表實際的形狀函數,星狀線代表第3世代猜測的形狀,虛線代表最後所重建之圖形…………………………………40
圖3-1(b) 例子1物體在基因演算法中每個世代重建的DR值的變化情形………………………………………………………41
圖3-1(c) 例子1在不同準位的雜訊干擾下對DR值的影響………42
圖3-2(a) 例子2雙導體在半空間的形狀函數的重建情形。實線代表實際的形狀函數,星狀線代表初始猜測的形狀,虛線代表最後所重建之圖形………………………………………43
圖3-2(b) 例子2物體在基因演算法中每個世代重建的DR值的變化情形………………………………………………………44
圖3-3(a) 例子3雙導體在半空間的形狀函數的重建情形。實線代表
實際的形狀函數,星狀線代表基因世代第4代猜測的形狀,虛線代表最後所重建之圖形………………………45
圖3-3(b) 例子3物體在基因演算法中每個世代重建的DR值的變化情形………………………………………………………46
圖3-4(a) 例子4雙導體在半空間的形狀函數的重建情形。實線代表實際的形狀函數,星狀線代表基因世代第21代猜測的形狀,虛線代表最後所重建之圖形……………………47
圖3-4(b) 例子4物體在基因演算法中每個世代重建的DR值的變化情形………………………………………………………48
圖3-5(a) 例子5雙導體在半空間的形狀函數的重建情形。實線代表實際的形狀函數,星狀線代表初始猜測的形狀函數,虛線代表最後所重建之形狀函數……………………………49
圖3-5(b) 例子5物體在基因演算法中每個世代重建的DR值的變化情形………………………………………………………50
圖3-6(a) 例子6雙導體在半空間的形狀函數的重建情形。實線代表實際的形狀函數,星狀線代表初始猜測的形狀函數,虛線代表最後所重建之形狀函數……………………………51
圖3-6(b) 例子6物體在基因演算法中每個世代重建的DR值的變化情形………………………………………………………52
圖3-6(c) 例子6物體在不同頻率的入射波照射下,DR值隨著入射頻率的變化情形…………………………………………53
圖3-6(d) 例子6兩個導體之間距離約為半波長的重建情形。實線為
實際的形狀函數,虛線代表用最後所重建之形狀函數...54
圖3-6(e) 例子6兩個導體之間距離約為1.5倍波長的重建情形。實線為實際的形狀函數,虛線代表用最後所重建之形狀函數………………………………………………55
圖3-6(f) 例子6重建的形狀函數偏差量隨兩個導體之間的距離變化的情形……………………………………………………56
圖 3-7(a) 例子7雙導體在半空間的形狀函數的重建情形。實線代表實際的形狀函數,星狀線代表初始猜測的形狀函數,虛線代表最後所重建之形狀函數……………………………57
圖3-7(b) 例子7物體在基因演算法中每個世代重建的DR值的變化情形………………………………………………………58

表目錄
表 2-1 基因演算法相關名詞解釋與中英對照表…………………25
參考文獻 [1] S. Caorsi and A. Massa “A microwave-imaging technique for electromagnetic exposure prediction: preliminary results,” Microwave and Optical Technology Letters, vol. 19, no. 5, pp. 328-332, Dec 5 1998.
[2] 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, pp. 1878-1884, Dec 2006.
[3] 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, pp. 568-576, Mar 2007.
[4] A. G. Ramm, “Uniqueness result for inverse problem of geophysics: I,” Inverse Problems., vol. 6, pp. 635-641, Aug. 1990.
[5] H. P. Baltes, Inverse scattering problems in optics., New York: Springer-verlag Berlin Heidelberg, 1980.
[6] M. M. Ney, A. M. Smith and S. S. Stuchly, “A solution of electromagnetic imaging using pseudo inverse transformation,” IEEE Trans. Med. Imaging., vol. 3, pp. 155- 162, Dec. 1984.
[7] K. P. Bube and R. Burridge, “The one-dimensional inverse problem of reflection seismology,” SIAM Rev., vol. 25 no. 4, pp. 497-559, 1983.
[8] R. M. Lewis, “Physical optics inverse diffraction,” IEEE Trans. Antennas Propagat., vol. AP-17, pp. 308-314, 1969.
[9] G. N. Balanis, “The plasma inverse problem,” J. Math. Phys., vol. 13, pp. 1001-1005, 1972.
[10] R. Burridge, “The Gel’fand- Levitan, The Marchenko, and the Gopinath-Sondhi integral equation of inverse scattering theory, regarded in the context of inverse impulse-response problems,” Waves Motion., vol. 2, pp. 305-323, 1980.
[11] N. N. Bojarski, “A survey of the physical optics inverse scattering identity,” IEEE Trans. Antennas Propagat., vol. 30, pp. 980-989, Sept. 1982.
[12] 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, pp. 860-874, Aug. 1984.
[13] 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, pp. 453-462, 1997.
[14] J. B. Keller, “Accuracy and validity of Born and Rytov approximations,” J. Opt. Soc. Amer., vol. 59, pp. 1003-1004, 1969.
[15] D. Colton and P. Monk, “A novel method for solving the inverse scattering problem for time-harmonic acoustic waves in the resonance region D,” SIAMJ. Appl. Math., vol. 46, pp. 506-523, June 1986.
[16] W. C. Chew and Y. M. Wang, “Reconstruction of two-dimensional permittivity using the distorted Born iterative method,” IEEE Trans. Med. Imag., vol. 9, pp.218-225, 1990.
[17] C. C. Chiu and Y. W. Kiang, “Microwave imaging of a Buried cylinder,” Inv. Probl., vol. 7, pp. 182-202, 1991.
[18] M. Moghaddam and W. C. Chew, “Nonlinear two-dimensional velocity profile inversion using time-domain data,” IEEE Trans. Geosci. Remote Sensing., vol. 30 pp. 147-156, Jan. 1992.
[19] W. C. Chew and G. P. Otto, “Microwave imaging of multiple conducting cylinders using local shape functions,” IEEE Microwave Guided Wave Lett., vol. 2, pp. 284-286, July 1992.
[20] C. C. Chiu and Y. W. Kiang, “Microwave imaging of multiple conducting cylinders,” IEEE Trans. Antennas Propagat., vol. 40, pp. 933-941, Aug. 1992.
[21] W. C. Chew and G. P. Otto, “Microwave inverse scattering-local shape function imaging for improved resolution of strong scatterers,” IEEE Trans. Microwave Theory Tech., vol. 42, pp. 137-141, Jan. 1994.
[22] H. T. Lin and Y. W. Kiang, “Microwave imaging for a dielectric cylinder,” IEEE Trans. Microwave Theory Tech., vol. 42, pp. 1572-1579, Aug. 1994.
[23] T. A. W. M. Lanen and D. W. Watt, “Singular value decomposition: A diagnostic tool for ill-posed inverse problems in optical computed tomography,” in Detection Technology for Mines and Minelike Targets, A. C. Dubey et al., Eds. Bellingham, WA: SPIE, pp. 174-185, 1995.
[24] P. M. van den Berg and M. van der Horst, “Nonlinear inversion in induction logging using the modified gradient method,” Radio Sci., vol. 30, pp. 1355-1369, 1995.
[25] I. T. Rekanos, T. V. Yioultsis and T. D. Tsiboukis, “Inverse scattering using the finite-element method and a nonlinear optimization technique,” IEEE Trans. Microwave Theory., vol. 47, pp. 336-344, Mar. 1999.
[26] 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, pp. 249-253, 1996.
[27] R. Tang et al., “Combined strategy of improved simulated annealing and genetic algorithm for inverse problem,” IEEE Trans. Magn., vol. 32, pp. 1326-1329. Mar. 1996.
[28] C. A. Borghi and M. Fabbri, “A combined technique for the global optimization of the inverse electromagnetic problem solution,” IEEE Trans. Magn., vol. 33 pp. 1947-1950, Feb. 1997.
[29] A. K. Hamid and M. Alsunaidi, “Inverse scattering by dielectric circular cylindrical scatterers using a neural network approach,” in 1997 IEEE Int. Symp. Antennas Propagat., Montreal, QC, Canada, pp. 2278-2281, July 1997.
[30] 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, pp. 2968-2971, May 1998.
[31] F. Xiao and H. Yabe, “Microwave imaging of perfectly conducting cylinders from real data by micro genetic algorithm couple with deterministic method,” IEICE Trans. Electron., vol. E81-C, no. 12, pp. 1784-1792, Aug. 1998.
[32] C. S. Park and B. S. Jeong, “Reconstruction of a high-contrast and large object by using the hybrid algorithm combining a Levenberg-Marquardt algorithm and a genetic algorithm,” IEEE Trans. Magn., vol. 35, pp. 1582-1585, Mar. 1999.
[33] M. Pastorino and S. Caorsi, “A microwave inverse scattering techniques for image reconstruction based on a genetic algorithm,” in Proc. 16th IEEE Instrumentation Measurement Technology Conf., Venice, Italy, pp. 118-123, May 1999.
[34] A. Qing and C. K. Lee, “Shape reconstruction of a perfectly conducting cylinder using real-coded genetic algorithm,” in 1999 IEEE Antennas and Propagation Int. Symp., Orlando, FL, pp. 2148-2151, July 1999.
[35] Hung-Yi Li, ”Solution of inverse blackbody radiation problem with conjugate gradient method,” IEEE Trans. Antennas Propagate., vol. 53, issue 5, pp.1840-1842, May. 2005.
[36] A. Roger, “Newton-Kantorovitch algorithm applied to an electromagnetic inverse problem,” IEEE Trans. Antennas Propagate., vol. AP-29, pp.232-238, Mar. 1981.
[37] C. C. Chiu and Y. M. Kiang, “Electromagnetic imaging for an imperfectly conducting cylinder,” IEEE Trans. Microwave Theory Tech., vol. 39, pp. 1631- 1639, Sept. 1991.
[38] A. Kirsch, R. Kress, P. Monk and A. Zinn, “Two methods for solving the inverse acoustic scattering problem,” Inverse Problems., vol. 4, pp.749-770, Aug. 1988.
[39] F. Hettlich, “Two methods for solving an inverse conductive scattering problem,” Inverse Problems., vol. 10, pp. 375-385, 1994.
[40] 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, pp. 961-966, Dec. 2001
[41] W. Chien and C. C. Chiu, “Electromagnetic imaging for shape and variable conductivity”, International Journal of RF and Microwave Computer-Aided Engineering., Vol. 14, issue 2, pp. 433-440, Sept. 2004.
[42] W. Chien, C. C Chiu, and C. L. Li, “Image and conductivity reconstruction of a variable conducting cylinder in half space”, International Journal of Applied Electromagnetics and Mechanics., Vol. 21, No. 2, pp. 51-62, Feb. 2005.
[43] W. Chien and C. C. Chiu, “Cubic-spline expansion with GA for half-space inverse problems”, Applied Computational Electromagnetics Society Journal., Vol. 20, No. 2, pp. 136-143, July 2005.
[44] 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, pp. 3128-3134, Oct. 2005.
[45] 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, pp. 1251-1262, June 2003.
[46] 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, pp. 1386-1397, June 2004.
[47] Ching-Lieh Li, Shao-Hon Chen, Chih-Ming Yang, and C. C. Chiu, “Image reconstruction for a partially immersed perfectly conducting cylinder using the steady state genetic algorithm,” Radio Science., vol. 39, RS2016, pp. 1-10, 26 Jun. 2002.
[48] 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, pp. 3118-3127, Oct. 2005.
[49] 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, pp. 1784-1787, May 2005.
[50] F. B. Hildebrand, Methods of applied mathematics, New Jersey: Prentice-Hall, 1965.
[51] “A practical guide to splines,” New York: Spring-Verlag, 1987.
[52] Shoichiro Nakamura, “Applied numerical methods in C,” Prentice-Hall int. 1993.
[53] W. Wang and S. Zhang , “Unrelated illumination method for electromagnetic inverse scattering of inhomogeneous lossy dielectric bodies,” IEEE Antennas Propagat., vol. 40, pp. 1292-1296, Nov. 1992.
論文使用權限
  • 同意紙本無償授權給館內讀者為學術之目的重製使用,於2008-06-26公開。
  • 同意授權瀏覽/列印電子全文服務,於2008-06-26起公開。


  • 若您有任何疑問,請與我們聯絡!
    圖書館: 請來電 (02)2621-5656 轉 2281 或 來信