臺灣博碩士論文加值系統

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

參考文獻
[1] A. G. Ramm, "Uniqueness result for inverse problem of geophysics: I,"
Inverse Problems, vol. 6, pp. 635-641, Aug. 1990.
[2] H. P. Baltes, Inverse scattering problems in optics. New York: Springer
-verlag Berlin Heidelberg, 1980.
[3] 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.
[4] R. M. Lewis, "Physical optics inverse diffraction," IEEE Trans.
Antennas Propagat., vol. 17, pp. 308-314, May 1969.
[5] N. N. Bojarski, "A survey of the physical optics inverse scattering identity," IEEE Trans. Antennas Propagat., vol. 30, pp. 980-989,Sept. 1982.
[6] T. H. Chu and N. H. Farhat, "Polarization effects in microwave diversity imaging of perfectly conducting cylinders," IEEE Trans. Antennas Propagar., vol.37, pp. 235-244, Feb. 1989.
[7] D. B. Ge, "A study of Lewis method for target-shape reconstruction," Inverse Problems, vol. 6, pp. 363-370, June 1990.
[8] D. Colton, H. Haddar and Piana," The linear sampling method in inverse electromagnetic scattering theory," Inverse Problems, vol. 19, pp. 105-137, December 2003.
[9] Massimo Brignone and Michele Piana, " The use of constraints for solving inverse scattering problems: physical optics and the linear sampling method," Inverse Problems, vol. 21, pp. 207-222, February 2005.
[10] T. H. Chu and D. B. Lin, "Microwave diversity imaging of perfectly conducting objects in the near-field region," IEEE Trans. Microwave Theory Tech., vol. 39, pp. 480-487, Mar. 1991.
[11] G. W. Hohmann, "Electromagnetic scattering by conductors in the earth near a line source of current," Geophysics, vol. 36, pp. 101-131,Feb. 1971.
[12] N. Osumi and K. Ueno, "Microwave holographic imaging of underground objects," IEEE Trans. Antennas Propagat., vol. AP-33,pp. 152-159, Feb. 1985.
[13] L. Chommeloux, C. Pichot, and J. C. Bolomey, "Electromagnetic modeling for microwave imaging of cylindrical buries inhomogeneities," IEEE Trans. Microwave Theory Tech., vol. MTT-34, pp. 1064-1076, Oct. 1986.
[14] B. Duchene, D. Lesselier, and W. Tabbara, "Acoustical imaging of 2D fluid targets buried in a half-space: a diffraction tomography approach," IEEE Trans. Ultrason. Ferroelec. Freq. Contr., vol. UFFC-34, pp. 540-549, Sept. 1987.
[15] W. Tabbara, B. Duchene, C. Pichot, D. Lesselier, L. Chommelous,and N. Joachimowicz, "Diffraction tomography: contribution to the analysis of some applications in microwaves and ultrasonics, "Inverse Problems, vol. 4, pp. 305- 331, May 1988.
[16] R. F. Harrmgton, Field Computation by Moment Method, New York: Macmillan, 1968.
[17] A. Roger, "Newton-Kantorovitch algorithm applied to an electromagnetic inverse problem," IEEE Trans. Antennas Propagate., vol. AP-29,pp.232-238, Mar. 1981.
[18] W. Tobocman, "Inverse acoustic wave scattering in two dimensions from impenetrable targets," Inverse Problems, vol. 5,pp. 1131-1144,Dec. 1989.
[19] 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.
[20] G. P. Otto and W. C. Chew, "Microwave Inverse Scattering-Local Shape Function Imaging for Improved Resolution of Strong Scatters," IEEE Trans. Microwave Theory Tech., vol. 42, pp. I, Jan.1994.
[21] D. Colton and P. Monk, "Anovel 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.
[22] 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.
[23] F. Hettlich, "Two methods for solving an inverse conductive scattering problem," Inverse Problems, vol. 10, pp. 375-385, 1994.
[24] R. E. Kleinman and P. M. van den Berg, "Two-dimensional locationand shape reconstruction," Radio Science, vol. 29, pp. 1157-1169, July-Aug. 1994.
[25] M. Johnson, and Y. Rahmat-samii, "Genetic algorithms in engineering electromagnetics," IEEE Antennas and Propagation Magazine, vol. 39, pp.7-25, 1997.
[26] C. C. Chiu and W. T. Chen, "Electromagnetic Imaging for an Imperfectly Conducting Cylinder by the Genetic Algorithm," IEEE Trans. Microwave Theory and Tec., vol.48, pp.1901-1905, Nov.2000.
[27] T. Takenaka and Z. Q. Meng, T. Tanaka, W. C. Chew, "Local shape function combined with genetic algorithm applied to inverse scattering for strips," Microwave and Optical Technology Letters, vol. 16, pp. 337-341, December 1997.
[28] Z. Q. Meng, T. Takenaka and T. Tanaka, "Microwave imaging of conducting cylinders using genetic algorithms," Proceedings of International Conference on Microwave and Millimeter Wave Technology, pp. 933-936, 1998.
[29] Y. Zhou and H. Ling, "Electromagnetic inversion of ipswich objects with the use of the genetic algorithm," Microwave and Optical Technology Letters, vol. 33, pp. 457-459, June 2002
[30] Y. Zhou, J. Li and H. Ling, "Shape inversion of metallic cavities using hybrid genetic algorithm combined with tabu list," Electronics Letters, vol. 39, pp. 280-281, Feb. 2003.
[31] A. Qing, "An experimental study on electromagnetic inverse scattering of a perfectly conducting cylinder by using the real-coded genetic algorithm," Microwave and Optical Technology Letters, vol.30, pp.315-320, Sept. 2001.
[32] K. Barkeshli, M. Mokhtari and N.M. Amiri, "Image reconstruction of impenetrable cylinders using cubic B-splines and genetic algorithms," Proceedings of IEEE International Sym on Antennas and Propagation, 2001, vol. 2,pp. 686-689, 2001.
[33] C. C. Chiu and W. T. Chen, "Inverse scattering of a buried imperfect conductor by the genetic algorithm," International Journal of Imaging Systems and Technology, vol. 11, pp. 355-360, 2000.
[34] R. T. Ling and P. Y. Ufimtsev, "Scattering of electromagnetic by a metallic object partially immersed in a semi-infinite dielectric medium," IEEE Trans. Antennas and Propagation, vol. 49, pp. 223-233, Feb. 2001.
[35] J.Michael Johnson and Yahya Rahmat-Samii,”Genetic Algorithm in Engineering Electromagnetics”, IEEE Antennas and Propagation Magazine, Vol. 39, No.4, August 1997
[36] F. Vavak and T. C. Fogarty, “Comparison of steady state and generational genetic algorithms for use in nonstationary environments,” Proceedings of IEEE International Conference on Evolutionary Computation, pp. 192-195, 1996.
[37] Cui Jianlin, Shi Zhen and Zhang Huiping, “Parameter design of integrated altitude control system using steady state genetic algorithm,” Intelligent Control and Automation of IEEE, Vol.3, pp. 2091 – 2094, June 2004.