Direct computation of statistical variations in electromagnetic problems

Ajayi, Ajibola (2008) Direct computation of statistical variations in electromagnetic problems. PhD thesis, University of Nottingham.

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Abstract

This work described in this thesis develops a computationally efficient approach to performing electromagnetic simulations in the presence of statistically defined uncertainties caused by either material inhomogeneities, or fabrication and placement tolerances. Comparisons are made with results from Monte Carlo simulations and a sequence of higher order approximation extensions is considered.

There are two main techniques used to achieve the overall objective of this thesis namely: the Direct Solution Technique (DST) and the Unscented Transform (UT) method.

The DST based on Taylor series approximations is intended to explicitly provide rapid approximate solutions that obviate the need for extremely slowly converging and time consuming Monte Carlo analysis of multiple simulations. The DST approach is useful in problems where sensitivity of system responses with respect to stochastic variables can be mathematically defined.

The UT method is similar to the Monte Carlo method but makes use of a significantly smaller number of simulations. As the number of random variables considered increases, the UT procedure requires more simulations. The advantage of the UT method is that it is applicable to black-box models and can therefore be extended to different electromagnetic solvers.

The case studies used in this thesis are developed using the Transmission Line Modelling (TLM) method. Both the DST and UT method were found to enhance the modelling of uncertainty in electromagnetic problems. The scopes of both methods are explored and observations made upon both the degree of problem complexity and the extent of stochastic variation permitted.

Item Type:Thesis (PhD)
Supervisors:Christopoulos, C.
Sewell, Phillip
Uncontrolled Keywords:computational electromagnetics, Direct Solution Technique (DST), Unscented Transform (UT), Taylor series approximation, statistical moments, Electromagnetic Compatibility (EMC), Transmission Line Modelling (TLM), skew, kurtosis, standard deviation, mean, orthogonal polynomials, statistical electromagnetics, statistics, probability distribution function (PDF), Monte Carlo (MC) simulations.
Faculties/Schools:UK Campuses > Faculty of Engineering > Department of Electrical and Electronic Engineering
ID Code:539
Deposited By:Ajibola Ajayi
Deposited On:26 Jun 2008
Last Modified:22 Sep 2010 09:17

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