volume | PIER Journals

Abstract

This paper presents the development of a novel‘maximum entropy'-based numerical methodology for the solution of electromagnetic problems, where the inputs and system parameters vary statistically. The application of this methodology to the problem of a plane wave impinging on an array of cylindrical conducting rods with stochastic variations in its parameters is then presented. To address this problem, a statistically significant number of replicas of this array of conductors are constructed. The current profiles in these coupled conductors are estimated by using the Method of Moments (MoM). Upon estimation of the current profiles on the conductors, the monostaticradar cross-section is estimated for each replica of the array. The probability density function isthen constructed through the estimation of a finite number of moments from the available output data subject to the constraint of maximum entropy. The methodology is very general in its scope and its application to scatterers with other geometries such as spheres, spheroids and ellipsoids as well as to other application areas would form the basis of our future work.

1. Holland, R. and R. S. John, "Statistical Electromagnetics," Taylor & Francis, 1999.

2. Manfredi, P. and F. G. Canavero, "Impact of dielectric variability on modal signaling over cable bundles," Proc. ESA Workshop on Aerospace EMC, 1-4, May 2012.

3. De Menezes, L., D. Thomas, and C. Christopoulos, "Accounting for uncertainty in EMC studies," Proc. EMC09, 753-756, 2009.

4. Lallechere, S., S. Girard, P. Bonnet, and F. Paladian, "Enforcing experimentally stochastic techniques in uncertain electromagnetic environments," Proc. ESA Workshop on Aerospace EMC, 1-6, May 2012.

5. Taflove, A. and S. C. Hagness, "Computational Electromagnetics: The Finite-diFFerence Time Domain Method," Artech House, 2005.

6. Hughes, T. J. R., The Finite Element Method, Linear Static and Dynamic Finite Element Analysis, 2000.

7. Harrington, R. F., Field Computation by Moment Methods, IEEE Press Series on Electromagnetic Wave Theory , 1993.
doi:10.1109/9780470544631

8. Xiu, D. and G. E. Karniadakis, "The Wiener-Askey polynomial chaos for stochastic differential equations," SIAM J. Sci. Comput., Vol. 24, No. 2, 619-644, 2002.
doi:10.1137/S1064827501387826

9. Soize, C. and R. Ghanem, "Physical systems with random uncertainties: Chaos representations with arbitrary probability measure," SIAM J. Sci. Comput., Vol. 26, No. 2, 395-410, 2005.
doi:10.1137/S1064827503424505

10. Stievano, I. S., P. Manfredi, and F. G. Canavero, "Parameter variability effects on multiconductor interconnects via hermite polynomial chaos," IEEE Transactions on Components, Packaging and Manufacturing Technology, Vol. 1, No. 8, 1234-1239, Aug. 2011.
doi:10.1109/TCPMT.2011.2152403

11. Eldred, M., C. Webster, and P. Constantine, "Evaluation of non-intrusive approaches for Wiener-Askey generalized polynomial chaos," 49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Apr. 2008.

12. Papoulis, A. and S. U. Pillai, Probability, Random Variable and Stochastic Processes, 4th Ed., 664-673, McGraw Hill, 2002.

13. Konrad, K., "Probability distributions and maximum entropy,".
doi:www.math.uconn.edu/~kconrad/blurbs/analysis/entropypost.pdf.

14. Pathria, R. K., Statistical Mechanics, 2nd Ed., 1999.

15. Shannon, C. E., "A mathematical theory of communication," The Bell System Technical Journal, Vol. 27, 379-423, Jul. 1948.
doi:10.1002/j.1538-7305.1948.tb01338.x

16. Balanis, C. A., Advanced Engineering Electromagnetics, 718-720, John Wiley & Sons, 1989.

17. Miano, G., L. Verolino, and V. G. Vaccaro, "A new numerical treatment for Pocklington's integral equation ," IEEE Tran. on Mag., Vol. 32, No. 3, 918-921, May 1996.
doi:10.1109/20.497391

18. Anders, R., "Minimum continuity requirements for basis functions used with the Pocklington integral equation," Antennas and Propagation Society International Symposium, Vol. 15, 284-287, Jun. 1977.

19. Nazareth, J. L., "Linear and nonlinear conjugate-gradient related methods," Proc. App. Math., Vol. 85, Jan. 1996.

Dr. Kausik Chatterjee