volume | PIER Journals

Abstract

We consider the inverse problem of determining both the shape and the conductivity of an un-uniform conductivity scatterer buriedin a three-layer structure by the genetic algorithm. An ununiform conductivity scatterer of unknown shape and conductivity buriedin the secondla yer scatters the incident wave from the first layer or the thirdla yer. We measure the scatteredfieldin the first andthird layers. Based on the boundary condition and the measured scattered field, a set of nonlinear integral equations is derived and the imaging problem is reformulatedin to an optimization problem. The genetic algorithm is then employedto findout the global extreme solution of the object function. As a result, the shape andthe conductivity of the scatterer can be obtained. Numerical results are given to demonstrate that even in the presence of noise, good reconstruction has been obtained.

1. Roger, A., "Newton-Kantorovitch algorithm appliedto an electromagnetic inverse problem," IEEE Trans. Antennas Propagat., Vol. 29, 232-238, Mar. 1981.
doi:10.1109/TAP.1981.1142588 Google Scholar

2. Tobocman, W., "Inverse acoustic wave scattering in two dimensions from impenetrable targets," Inverse Problems, Vol. 5, 1131-1144, Dec. 1989.
doi:10.1088/0266-5611/5/6/018 Google Scholar

3. Chiu, C. C. and Y. W. Kiang, "Electromagnetic imaging for an imperfectly conducting cylinders," IEEE Trans. Microwave Theory Tech., Vol. 39, 1632-1639, Sept. 1991.
doi:10.1109/22.83840 Google Scholar

4. Colton, D. 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, 506-523, June 1986.
doi:10.1137/0146034 Google Scholar

5. Kirsch, A., R. Kress, P. Monk, and A. Zinn, "Two methods for solving the inverse acoustic scattering problem," Inverse Problems, Vol. 4, 749-770, Aug. 1988.
doi:10.1088/0266-5611/4/3/013 Google Scholar

6. Hettlich, F., "Two methods for solving an inverse conductive scattering problem," Inverse Problems, Vol. 10, 375-385, 1994.
doi:10.1088/0266-5611/10/2/012 Google Scholar

7. Kleiman, R. E. and P. M. van den Berg, "Two-dimensional location and shape reconstruction," Radio Sci., Vol. 29, 1157-1169, July/Aug. 1994.
doi:10.1029/93RS03445 Google Scholar

8. Xiao, F. and H. Yabe, "Microwave imaging of perfectly conducting cylinders from real data by micro genetic algorithm coupled with deterministic method," IEICE Trans. Electron., Vol. E81-C, No. 12, 1784-1792, Dec. 1998. Google Scholar

9. Chiu, C. C. and W. T. Chen, "Electromagnetic imaging for an imperfectly conducting cylinder by the genetic algorithm," IEEE Trans. Microwave Theory and Tec., Vol. 48, 1901-1905, Nov. 2000. Google Scholar

10. Goldgerg, D. E., Genetic Algorithm in Search, Optimization and Machine Learning, Addison-Wesley, 1989.

11. Rahmat-Samiia, Y. and E. Michielessen, Electromagnetic Optimization by Genetic Algorithms, Wiley Interscience, 1999.

12. Tu, T. C. and C. C. Chiu, "Path loss reduction in an urban area by genetic algorithms," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 3, 319-330, 2006.
doi:10.1163/156939306775701696 Google Scholar

13. Tian, Y. B. and J. Qian, "Ultraconveniently finding multiple solutions of complex transcendental equations based on genetic algorithm," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 4, 475-488, 2006.
doi:10.1163/156939306776117090 Google Scholar

14. Lu, Y. Q. and J. Y. Li, "Optimization of broad band top-load antenna using micro-genetic algorithm," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 6, 793-801, 2006.
doi:10.1163/156939306776143370 Google Scholar

15. Chen, X., D. Liang, and K. Huang, "Microwave imaging 3-D buried objects using parallel genetic algorithm combined with FDTD technique," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 13, 1761-1774, 2006.
doi:10.1163/156939306779292264 Google Scholar

16. Mitilineos, S. A., S. C. Thomopoulos, and C. Capsalis, "Genetic design of dual-band, switched-beam dipole arrays, with elements failure conrrection, retaining constant excitation coefficients," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 14, 1925-1942, 2006.
doi:10.1163/156939306779322738 Google Scholar

17. Ayestaran, R. G., J. Laviada-Martinez, and F. Las-Heras, "Synthesis of passive-dipole array with a genetic-neural hybrid method," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 15, 2123-2135, 2006.
doi:10.1163/156939306779322549 Google Scholar

18. Zhai, Y.-W., X.-W. Shi, and Y.-J. Zhao, "Optimized design of ideal and actual transformer based on improved micro-genetic algorithm," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 13, 1761-1771, 2006. Google Scholar

19. Chiu, C. C. and P. T. Liu, "Image reconstruction of a perfectly conducting cylinder by the genetic algorithm," IEE Proc. Microw. Antennas Propag., Vol. 143, 249-253, June 1996.
doi:10.1049/ip-map:19960363 Google Scholar

20. Xiao, F. 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, Dec. 1998. Google Scholar

21. Meng, Z. Q., T. Takenaka, and T. Tanaka, "Image reconstruction of two-dimensional impenetrable objects using genetic algorithm," Journal of Electromagnetic Waves and Applications, Vol. 13, 95-118, 1999.
doi:10.1163/156939399X01654 Google Scholar

22. Qian, Z. P., Z. Y. Ding, and W. Hong, "Application of genetic algorithm and boundary element method to electromagnetic imaging of two-dimensional conducting targets," 5th International Symposium on ISAPE, 211-214, 2000. Google Scholar

23. Li, C. L., S. H. Chen, C. M. Yang, and C. C. Chiu, "Image reconstruction for a patially immersedp erfectly conducting cylinder using the steady state algorithm," Radio Sci., Vol. 39, RS2016, April 2004.
doi:10.1029/2002RS002742 Google Scholar

24. Vavak, F. 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, 192-195, 1996.
doi:10.1109/ICEC.1996.542359 Google Scholar

25. Johnson, J. M. and Y. Rahmat-Samii, "Genetic algorithms in engineering electromagnetics," IEEE Trans. Antennas Propagat., Vol. 39, 7-21, Aug. 1997. Google Scholar

26. Tesche, F. M., "On the inclusion of loss in time domain solutions of electromagnetic interaction problems," IEEE Trans. Electromagn. Compat., Vol. 32, 1-4, 1990.
doi:10.1109/15.45244 Google Scholar

27. Jordan, E. C. and K. G. Balmain, Electromagnetic Waves and Radiating Systems, Prentice-Hall, 1968.

Dr. Wei Chien