On the construction and analysis of stochastic models: Characterization and propagation of the errors associated with limited data

Journal Article · Fri Sep 01 04:00:00 EDT 2006 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2006.01.037· OSTI ID:20840337

Ghanem, Roger G ^[1]; Doostan, Alireza ^[2]

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1. Aerospace and Mechanical Engineering, University of Southern California, 3620 S. Vermont, 210 KAP Hall USC, Los Angeles, CA 90089 (United States)
2. Department of Civil Engineering, Johns Hopkins University, Baltimore, MD 21218 (United States)

This paper investigates the predictive accuracy of stochastic models. In particular, a formulation is presented for the impact of data limitations associated with the calibration of parameters for these models, on their overall predictive accuracy. In the course of this development, a new method for the characterization of stochastic processes from corresponding experimental observations is obtained. Specifically, polynomial chaos representations of these processes are estimated that are consistent, in some useful sense, with the data. The estimated polynomial chaos coefficients are themselves characterized as random variables with known probability density function, thus permitting the analysis of the dependence of their values on further experimental evidence. Moreover, the error in these coefficients, associated with limited data, is propagated through a physical system characterized by a stochastic partial differential equation (SPDE). This formalism permits the rational allocation of resources in view of studying the possibility of validating a particular predictive model. A Bayesian inference scheme is relied upon as the logic for parameter estimation, with its computational engine provided by a Metropolis-Hastings Markov chain Monte Carlo procedure.

• OSTI ID: 20840337
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 1 Vol. 217; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ACCURACY
CALIBRATION
CHAOS THEORY
ERRORS
FINITE ELEMENT METHOD
MARKOV PROCESS
MONTE CARLO METHOD
PARTIAL DIFFERENTIAL EQUATIONS
POLYNOMIALS
PROBABILITY
RANDOMNESS