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International Journal for Uncertainty Quantification

Impact factor: 1.000

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2014006990
pages 387-421

AN OVERVIEW OF NONINTRUSIVE CHARACTERIZATION, PROPAGATION, AND SENSITIVITY ANALYSIS OF UNCERTAINTIES IN COMPUTATIONAL MECHANICS

Maarten Arnst
University de Liege, Departement d'Aerospatiale et Mecanique, B-4000 Liege, Belgium
Jean-Philippe Ponthot
University de Liege, Departement d'Aerospatiale et Mecanique, B-4000 Liege, Belgium

ABSTRACT

In this paper, we offer a short overview of a number of methods that have been reported in the computational-mechanics literature for quantifying uncertainties in engineering applications. Within a probabilistic framework, we describe the characterization of uncertainties using mathematical statistics methods, the propagation of uncertainties through computational models using either Monte Carlo sampling or stochastic expansion methods, and the sensitivity analysis of uncertainties using variance- and differentiation-based methods. We restrict our attention to nonintrusive methods that can be implemented as wrappers around existing computer programs, thus requiring no modification of the source code. We include some recent advances in the propagation and sensitivity analysis of uncertainties that are characterized by arbitrary probability distributions that may exhibit statistical dependence. Finally, we demonstrate the methods integrated in the proposed overview through a nonlinear engineering application relevant to metal forming.