CUBIC-SPLINE EXPANSION FOR A PARTIALLY IMMERSED CONDUCTING CYLINDER ILLUMINATED BY TE WAVES
Keywords:cubic-spline, inverse problem, partially immersed, conductor, steady-state genetic algorithm, transverse electric wav
This paper presents a computational approach to the imaging of a partially immersed perfectly conducting cylinder. Both cubic-spline method and trigonometric series for shape description are used and compared. A conducting cylinder of unknown shape scatters the incident transverse electric (TE) wave in free space while the scattered field is recorded outside. 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. An improved steady-state genetic algorithm is employed to find out the global extreme solution of the object function. It is found that the shape described by Fourier series can be reconstructed by cubic-spline expansion. On the contrary, the shape described by cubic-spline and reconstructed by Fourier series expansion will fail. Numerical results are given to show that the shape description by using cubic-spline method is much better than that by the Fourier series.
R. Kress, "A Newton method in inverse obstacle scattering Inverse Problem in Engineering Mechanics,`` ed H D Bui et al (Rotterdam: Balkema), pp. 425-432, 1994
D. Colton and P. Monk, "A novel method for solving the inverse scattering problem for time-harmonic acoustic waves in the resonance region II,`` SIAM J. Appl. Math., vol. 46, pp. 506-523, June 1986.
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. 1998.
R. E. Kleiman and P. M. van den Berg, "Two-dimensional location and shape reconstruction,`` Radio Sci., vol. 29, pp. 1157-1169, Aug. 1994.
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, May 1996.
J. M. Johnson and R. S. Yahya, "Genetic algorithms in engineering electromagnetics,`` IEEE Transactions on Antennas Propagation., vol. 39, pp. 7-21, Aug. 1997.
W. Zhong, J. Liu, M. Xue and L. Jiao, "A Multiagent Genetic Algorithm for Global Numerical Optimization,`` IEEE Transactions on Systems, Man and Cybernetics., vol. 34, pp. 1128 -1141, April. 2004.
A. Massa, D. Franceschini, G. Franceschini, M. Pastorino, M. Raffetto, and M. Donelli, "Parallel GA-Based Approach for Microwave Imaging Applications,`` IEEE Transactions on Antennas and Propagation., vol. 53, no. 10, October 2005.
M. Benedetti, M. Donelli, and A. Massa, "Multicrack Detection in Two-Dimensional Structures by Means of GA-Based Strategies,`` IEEE Transaction on Antennas and Propagation., vol. 55, no. 1, January 2007.
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, Aug. 1998.
C. C. Chiu and W. T. Chen, "Electromagnetic imaging for an imperfectly conducting cylinder by the genetic algorithm,`` IEEE Transactions on Microwave Theory and Tec., vol. 48, pp. 1901-1905, Nov. 2000.
K. Barkeshli, M. Mokhtari and N. M. Amiri, "Image reconstruction of impenetrable cylinders using cubic B-splines and genetic algorithms,`` Proceedings of IEEE International Symposium Antennas Propagat., vol. 2 , pp. 686 -689, 2001
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
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
I. T. Rekanos, T. V. Yioultsis, and C. S. Hilas, "An Inverse Scattering Approach Based on the Differential E-Formulation,`` IEEE Transactions on Geoscience and Remote Sensing., vol. 42, no. 7, July 2004.
C. C. Chiu and P. T. Liu, "Image reconstruction of a perfectly conducting cylinder by the genetic algorithm,`` IEE Proc.-Micro. Antennas Propagat., vol. 143, pp.249-253, June 1996.
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.
Z. Q. Meng, T. Takenaka and T. Tanaka, "Image reconstruction of two-dimensional impenetrable objects using genetic algorithm``, Journal of Electromagnetic Waves and Applications., vol. 13, pp. 95-118, 1999.
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
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.
Y. C. Chen, Y. F. Chen, C. C. Chiu and C. Y Chang, "Image Reconstruction of Buried Perfectly Cylinder Illuminated by Transverse Electric Waves, `` International Journal of Imaging Systems and Technology Vol. 15 , pp. 261-265, April 2006
C. H. Huang, C. L. Liu, C. C. Chiu, Y. D. Wu, T. Wysocki and B. J Wysock, "Electromagnetic Transverse Electric-Wave Inverse Scattering of a Two-dimensional Dielectric Object by Genetic Algorithm,`` Electromagnetics Vol. 27, No. 5, pp. 241-251, June 2007.
C. H. Huang, H. C. Lu and C. C. Chiu, T. Wysocki and B. J Wysock,,, "Image Reconstruction of Buried Multiple Conductors by Genetic Algorithms,`` International Journal of Imaging Systems and Technology Vol. 18 , pp. 276-281, Oct. 2008
C. H. Sun, C.-L. Liu, K. C. Chen, C. C. Chiu, C. L. Li, and C. C. Tasi, "Electromagnetic Transverse Electric Wave Inverse Scattering of a Partially Immersed Conductor by Steady-State Genetic Algorithm,`` Electromagnetics.. Vol. 28, No. 6, pp. 389-400, Aug. 2008.
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.
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.
W. Chien and C. C. Chiu, "Cubic-Spline expansion with GA for a Partially Immersed Conducting Cylinder,`` IEICE Trans. Electron Vol. E88-C, No.12, pp. 2223-2228, Dec. 2005.
W. Chien, C. C. Chiu and C. L. Li, "Cubic-Spline Expansion with GA for a Conducting Cylinder Buried in a Slab Medium,`` Electromagnetics Vol. 26, No. 5, pp. 329-343, July 2006.
W. Chien, C. H. Huang and C. C Chiu, "Cubic-Spline expansion for a Two-Dimensional Periodic Conductor in Free Space,`` International Journal of Applied Electromagnetics and Mechanics. Vol. 24, No. 1-2, Nov. 2006
C. C. Chiu and Y. W. Kiang, "Inverse scattering of a buried conducting cylinder,`` Inverse Problems., vol. 7, April 1990, pp. 187-202.
Shoichiro Nakamura, "Applied Numerical Method in C,`` New Jersey: Prentice-Hall.1992.
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