Itô-SDE MCMC method for Bayesian characterization of errors associated with data limitations in stochastic expansion methods for uncertainty quantification

Journal Article · Wed Nov 15 04:00:00 EST 2017 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2017.08.005· OSTI ID:22701628

Abello Álvarez, B. ^[1]; Ponthot, J. -P.; Boman, R. ^[1]

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1. Université de Liège, Aérospatiale et Mécanique, Quartier Polytech 1, Allée de la Découverte 9, 4000 Liège (Belgium)

This paper is concerned with the characterization and the propagation of errors associated with data limitations in polynomial-chaos-based stochastic methods for uncertainty quantification. Such an issue can arise in uncertainty quantification when only a limited amount of data is available. When the available information does not suffice to accurately determine the probability distributions that must be assigned to the uncertain variables, the Bayesian method for assigning these probability distributions becomes attractive because it allows the stochastic model to account explicitly for insufficiency of the available information. In previous work, such applications of the Bayesian method had already been implemented by using the Metropolis–Hastings and Gibbs Markov Chain Monte Carlo (MCMC) methods. In this paper, we present an alternative implementation, which uses an alternative MCMC method built around an Itô stochastic differential equation (SDE) that is ergodic for the Bayesian posterior. We draw together from the mathematics literature a number of formal properties of this Itô SDE that lend support to its use in the implementation of the Bayesian method, and we describe its discretization, including the choice of the free parameters, by using the implicit Euler method. We demonstrate the proposed methodology on a problem of uncertainty quantification in a complex nonlinear engineering application relevant to metal forming.

• OSTI ID: 22701628
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 349; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIFFERENTIAL EQUATIONS
ERRORS
MARKOV PROCESS
MONTE CARLO METHOD
NONLINEAR PROBLEMS