Oo Ousmane Sy

Probabilistic Study of the Coupling between Deterministic Electromagnetic Fields and a Stochastic Thin-Wire over a PEC Plane

A stochastic approach is presented to statistically characterize uncertainties in electromagnetic interactions. A stochastically undulating thin wire over a perfectly conducting ground plane is studied. The aim of this paper is to present methods to compute the statistical moments of the voltage induced by a deterministic incident field. Three methods have been developed to compute these moments: a quadrature method, a perturbation approach and a Monte-Carlo method.

Analysis of stochastic resonances in electromagnetic couplings to transmission lines

Resonances present in coupling phenomena between a randomly varying thin-wire transmission-line, and an electro-magnetic field are stochastically characterized. This is achieved by using the first 4 statistical moments in order to appreciate the intensity of the resonance phenomena. The stochastic method proposed is applied to a thin-wire transmission line connected to a variable impedance, and, undergoing random geometrically localized perturbations.

A statistical characterization of resonant electromagnetic interactions with thin wires : variance and kurtosis analysis

A statistical characterization of random electromagnetic interactions affected by resonances is presented. It hinges on the analysis of the variance and the kurtosis to assess the intensity of the resonances. The method is illustrated by the study of a randomly varying thin wire modeled by a Pocklington integral equation.

Experimental validation of the stochastic model of a randomly fluctuating transmission-line

A modeling method is proposed to quantify uncertainties affecting electromagnetic interactions. This method considers the uncertainties as random and measures them thanks to probability theory. A practical application is considered through the case of a transmission-line of varying geometry, illuminated by a fixed electromagnetic field. The results of the stochastic numerical model are compared to the measurements performed on the transmission-line setup.

Higher-order statistics for stochastic electromagnetic interactions: applications to a thin-wire frame

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.

Modelling the interaction of stochastic systems with electromagnetic fields

The analysis presented in this paper, shows how the basic statistics in the interaction of stochastic systems with electromagnetic fields, i.e., the average and the variance of linear observables, can be computed from the probability distributions defining the stochastic geometry. The most difficult part in this computation is the construction of the covariance operator which requires the solution of a series of integral equations over the average geometry. The RHSs of these integral equations are determined by an expansion of the covariance operator of a regular field trace on the stochastic geometry. This determines the computational complexity of the probabilistic approach. In the presentation of this paper, some numerical experiments on concrete examples are shown, and the computational complexity of the probabilistic approach are investigated whether it also determines the minimal computational effort of the statistical approach

Characterization of linear electromagnetic observables in stochastic field-to-wire couplings

This article presents a method to characterize stochastic observables defined by induced surface currents and fields in electromagnetic interactions with uncertain configurations. As the covariance operators of the stochastic distributions and fields are not compact, a strict Karhunen-Loeve (KL) approach is not possible. Instead, we apply a point-spectrum regularization by expanding the stochastic quantities on a finite-element-like basis. The coefficients of the KL expansion are approximated analytically in a polynomial-chaos (PC) expansion. The novelty of our approach resides in its ability to handle multiple PC expansions simultaneously and determine the orders of the KL and PC expansions adaptively. Thismethod is illustrated through the example of the voltage induced at the port of a random thin-wire frame illuminated by random plane waves. The results show the accuracy and computational efficiency of the proposed method, which provides a complete characterization of the randomness of the observable.

Semi-intrusive quantification of uncertainties in stochastic electromagnetic interactions: Analysis of a spectral formulation

A stochastic approach is presented to statistically characterise uncertainties in electromagnetic interactions. A spectral definition of the observables allows for the assessment of the effect of a randomly deformed device independent of the incident field.