Vol. 41

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Higher-Order Statistics for Stochastic Electromagnetic Interactions: Applications to a Thin-Wire Frame

By Ousmane Oumar Sy, Martijn Constant van Beurden, Bastiaan L. Michielsen, Jean-Pierre A. H. M. Vaessen, and Antonius G. Tijhuis
Progress In Electromagnetics Research B, Vol. 41, 307-332, 2012


Uncertainties in an electromagnetic observable, that arise from uncertainties in geometric and electromagnetic parameters of an interaction configuration, are here characterized by combining computable higher-order moments of the observable with higher-order Chebychev inequalities. This allows for the estimation of the range of the observable by rigorous confidence intervals. The estimated range is then combined with the maximum-entropy principle to arrive at an efficient and reliable estimation of the probability density function of the observable. The procedure is demonstrated for the case of the induced voltage of a thin-wire frame that has a random geometry, is connected to a random load, and is illuminated by a random incident field.


Ousmane Oumar Sy, Martijn Constant van Beurden, Bastiaan L. Michielsen, Jean-Pierre A. H. M. Vaessen, and Antonius G. Tijhuis, "Higher-Order Statistics for Stochastic Electromagnetic Interactions: Applications to a Thin-Wire Frame," Progress In Electromagnetics Research B, Vol. 41, 307-332, 2012.


    1. Balanis, C., "Antenna theory: A review," Proc. of the IEEE, Vol. 80, No. 1, 7-23, 1992.

    2. Bruns, H. D., C. Schuster, and H. Singer, "Numerical electromagnetic field analysis for EMC problems," IEEE Trans. EMC., Vol. 49, No. 2, 253-262, 2007.

    3. Bai, L., Z.-S. Wu, H.-Y. Li, and T. Li, "Scalar radiative transfer in discrete media with random oriented prolate spheroids particles," Progress In Electromagnetics Research B, Vol. 33, 21-44, 2011.

    4. Moglie, F., V. M. Primiani, and A. P. Pastore, "Modeling of the human exposure inside a random plane wave field," Progress In Electromagnetics Research B, Vol. 29, 251-267, 2011.

    5. Lang, R., M. Bahie-El Din, and R. Pickholtz, "Stochastic effects in adaptive null-steering antenna array performance," IEEE Journal on Selected Areas in Communications, Vol. 3, No. 5, 767-778, 1985.

    6. Bellan, D. and S. Pignari, "Complex random excitation of electrically-short transmission lines," Proc. IEEE International Symposium on EMC, Vol. 3, 663-668, 2006.

    7. Hill, D., "Plane wave integral representation for fields in reverberation chambers," IEEE Trans. EMC., Vol. 40, No. 3, 209-217, 1998.

    8. Primiani, V. M. and F. Moglie, "Numerical simulation of LOS and NLOS conditions for an antenna inside a reverberation chamber," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 17-18, 2319-2331, 2010.

    9. Li, Z., L. L. Liu, and C. Q. Gu, "Generalized equivalent cable bundle method for modeling EMC issues of complex cable bundle terminated in arbitrary loads," Progress In Electromagnetics Research, Vol. 123, 13-30, 2012.

    10. Xie, H., J. Wang, S. Li, H. Qiao, and Y. Li, "Analysis and efficient estimation of random wire bundles excited by plane-wave fields," Progress In Electromagnetics Research B, Vol. 35, 167-185, 2011.

    11. Sy, O. O., M. C. van Beurden, B. L. Michielsen, J. A. H. M. Vaessen, and A. G. Tijhiuis, "Second-order statistics of complex observables in fully stochastic electromagnetic interactions: Applications to EMC," Radio Science, Vol. 45, RS4004.1{RS4004.16, 2010.

    12. Sy, O. O., M. C. Van Beurden, B. L. Michielsen, J. A. H. M. Vaessen, and A. G. Tijhuis, "A statistical characterization of resonant electromagnetic interactions with thin wires: Variance and kurtosis analysis," Scientific Computing in Electrical Engineering (SCEE), 117-124, Springer-Verlag, Berlin, Heidelberg, 2010.

    13. Papoulis, A. and S. U. Pillai, Probability, Random Variables and Stochastic Processes, Series in Electrical and Computer Engineering, McGraw-Hill, 2002.

    14. Jaynes, E. T., "Information theory and statistical mechanics," Phys. Rev., Vol. 106, No. 4, 620-630, 1957.

    15. Mrozynski, G., V. Schulz, and H. Garbe, "A benchmark catalog for numerical field calculations with respect to EMC problems," Proc. IEEE International Symposium on EMC, Vol. 1, 497-502, 1999.

    16. Parmantier, J.-P., "Numerical coupling models for complex systems and results," IEEE Trans. EMC., Vol. 46, No. 3, 359-367, 2004.

    17. Rumsey, V. H., "Reaction concept in electromagnetic theory," Phys. Rev., Vol. 94, No. 6, 1483-1491, 1954.

    18. Michielsen, B. L. and C. Fiachetti, "Covariance operators, green functions, and canonical stochastic electromagnetic fields," Radio Science, Vol. 40, No. 5, RS5001.1{RS5001.12, 2005.

    19. King, R., Transmission-Line Theory, Dover Publications, 1965.

    20. Larrabee, D. A., "Reduced coupling of electromagnetic waves to transmission lines due to radiation effects," PIERS Proceedings, Pisa, Italy, March 28-31, 2004.

    21. Larrabee, D. A., "Electromagnetic effects on transmission lines," International Conf. Software in Telecom. and Computer Networks (SoftCOM), 37-42, 2006.

    22. Mei, K. K., "On the integral equation of thin wire antennas," IEEE Trans. Ant. Prop., Vol. 13, No. 3, 374-378, 1965.

    23. Harrington, R., Field Computation by Moment Methods, Macmillan, New York, 1968.

    24. Bharucha-Reid, A., Random Integral Equations, Vol. 96, R. Bellman, Ed., Mathematics in Science and Engineering, 1972.

    25. Krommer, A. R. and C. W. Ueberhuber, Computational Integration, SIAM, Philadelphia, 1998.

    26. Gerstner, T. and M. Griebel, "Numerical integration using sparse grids," Numerical Algorithms, Vol. 18, No. 3, 209-232, 1998.

    27. Fletcher, R., Practical Methods of Optimization, Wiley, 1987.

    28. Einbu, J., "On the existence of a class of maximum-entropy probability density function," IEEE Trans. Info. Theory, Vol. 23, 772-775, 1977.

    29. Graybill, F. and H. Iyer, Regression Analysis, Concepts and Applications, Duxbury Press, 1994.

    30. Nitsch, J. B. and S. V. Tkachenko, "Propagation of high-frequency current waves along periodical thin-wire structures," Third International Conference on Ultrawideband and Ultrashort Impulse Signals, 279-281, 2006.

    31. Champagne II, N. J., J. T. Williams, and D. R. Wilton, "The use of curved segments for numerically modeling thin wire antennas and scatterers," IEEE Trans. Ant. Prop., Vol. 40, No. 6, 682-689, 1992.

    32. Sy, O. O., M. van Beurden, B. Michielsen, and A. Tijhuis, "Variance and kurtosis-based characterization of resonances in stochastic transmission lines: Local versus global random geometries," Turk. J. Elec. Eng. & Comp. Sci., Vol. 17, No. 3, 2009.