Stochastic modeling and statistical calibration with model error and scarce data

Wang, Zhiheng; Ghanem, Roger

doi:10.1016/j.cma.2023.116339

Stochastic modeling and statistical calibration with model error and scarce data

Journal Article · Wed Aug 23 00:00:00 EDT 2023 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2023.116339· OSTI ID:3024505

^[1]; Ghanem, Roger ^[1]

University of Southern California, Los Angeles, CA (United States)

This paper introduces a procedure to assess the predictive accuracy of stochastic models subject to model error and sparse data. Model error is introduced as uncertainty on the coefficients of appropriate polynomial chaos expansions (PCE). The error associated with finite sample size allows us to conceive of these coefficients as statistics of the data that we describe as random variables whose influence on output quantities of interest is evaluated through the extended polynomial chaos expansion (EPCE). A Bayesian data assimilation scheme is introduced to update these expansions by considering the resulting nested chaos expansion as a hierarchical probabilistic model. Stochastic models of quantities of interest (QoI) are thus constructed and efficiently evaluated. Here, the Metropolis–Hastings Markov chain Monte Carlo procedure is used to sample the posterior. Two illustrative analytical and numerical problems are used to demonstrate the proposed approach.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). FASTMath SciDAC-5 Institute; University of Southern California, Los Angeles, CA (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC02-05CH11231; SC0021307

Other Award/Contract Number:: 1661052

OSTI ID:: 3024505

Alternate ID(s):: OSTI ID: 1997312
OSTI ID: 2580914

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Vol. 416; ISSN 0045-7825

Publisher:: Elsevier BVCopyright Statement

Country of Publication:: United States

Language:: English

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