Polynomial Chaos Expansion with Random and Fuzzy Variables

E Jacquelin (Universite de Lyon, France), MI Friswell, S Adhikari (Swansea University), O Dessombz & J-J Sinou (Ecole Centrale de Lyon, France)

Mechanical Systems and Signal Processing, Vol. 75, June 2016, pp. 41-56

Abstract

A dynamical uncertain system is studied in this paper. Two kinds of uncertainties are addressed, where the uncertain parameters are described through random variables and/or fuzzy variables. A general framework is proposed to deal with both kinds of uncertainty using a polynomial chaos expansion (PCE). It is shown that fuzzy variables may be expanded in terms of polynomial chaos when Legendre polynomials are used. The components of the PCE are a solution of an equation that does not depend on the nature of uncertainty. Once this equation is solved, the post-processing of the data gives the moments of the random response when the uncertainties are random or gives the response interval when the variables are fuzzy. With the PCE approach, it is also possible to deal with mixed uncertainty, when some parameters are random and others are fuzzy. The results provide a fuzzy description of the response statistical moments.

Paper Availability

This material has been published in the Mechanical Systems and Signal Processing, Vol. 75, June 2016, pp. 41-56, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by Elsevier.


Link to paper using doi: 10.1016/j.ymssp.2015.12.001

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