Articlegreen2015

Polynomial Chaos Expansion of a Multimodal Random Vector

54 citations0/0 files storedSIAM/ASA Journal on Uncertainty Quantification

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Probabilistic and Robust Engineering Design Mathematical functions and polynomials Gaussian Processes and Bayesian Inference

Abstract

A methodology and algorithms are proposed for constructing the polynomial chaos expansion (PCE) of multimodal random vectors. An algorithm is developed for generating independent realizations of any multimodal multivariate probability measure that is constructed from a set of independent realizations using the Gaussian kernel-density estimation method. The PCE is then performed with respect to this multimodal probability measure, for which the realizations of the polynomial chaos are computed with an adapted algorithm. Finally, a numerical application is presented for analyzing the convergence properties.

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References

1991Stochastic Finite Elements: A Spectral Approach 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations 2007Global sensitivity analysis using polynomial chaos expansions 2008Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics 2004Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure 2010Spectral methods for uncertainty quantification : with applications to computational fluid dynamics 2006Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures 2004Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes

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