Identification of random shapes from images through polynomial chaos expansion of random level set functions

George Stefanou · Anthony Nouy · Alexandre Clément

49 citations0/0 files storedInternational Journal for Numerical Methods in Engineering

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Probabilistic and Robust Engineering Design Advanced Numerical Analysis Techniques Numerical methods in engineering

Abstract

Abstract In this paper, an efficient method is proposed for the identification of random shapes in a form suitable for numerical simulation within the extended stochastic finite element method (X‐SFEM). The method starts from a collection of images representing different outcomes of the random shape to identify. The key point of the method is to represent the random geometry in an implicit manner using the level set technique. In this context, the problem of random geometry identification is equivalent to the identification of a random level set function, which is a random field. This random field is represented on a polynomial chaos (PC) basis and various efficient numerical strategies are proposed in order to identify the coefficients of its PC decomposition. The performance of these strategies is evaluated through some ‘manufactured’ problems and useful conclusions are provided. The propagation of geometrical uncertainties in structural analysis using the X‐SFEM is finally examined. Copyright © 2009 John Wiley & Sons, Ltd.

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References

1991Stochastic Finite Elements: A Spectral Approach 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations 2004Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure 2004Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation 2006On the construction and analysis of stochastic models: Characterization and propagation of the errors associated with limited data 2006Numerical Methods for Differential Equations in Random Domains 2005Maximum likelihood estimation of stochastic chaos representations from experimental data 2008An extended stochastic finite element method for solving stochastic partial differential equations on random domains

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