Imprecise global sensitivity analysis using bayesian multimodel inference and importance sampling

Zhang, Jiaxin; TerMaath, Stephanie; Shields, Michael D.

doi:10.1016/j.ymssp.2020.107162

Title: Imprecise global sensitivity analysis using bayesian multimodel inference and importance sampling

Journal Article · Sun Aug 09 00:00:00 EDT 2020 · Mechanical Systems and Signal Processing

DOI:https://doi.org/10.1016/j.ymssp.2020.107162· OSTI ID:1651313

Zhang, Jiaxin ^[1]; TerMaath, Stephanie ^[2]; Shields, Michael D. ^[3]

Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Univ. of Tennessee, Knoxville, TN (United States)
Johns Hopkins Univ., Baltimore, MD (United States)

Global Sensitivity Analysis (GSA) aims to understand the relative importance of uncertain input variables to model response. Conventional GSA involves calculating sensitivity (Sobol’) indices for a model with known model parameter distributions. However, model parameters are affected by aleatory and epistemic uncertainty, with the latter often caused by lack of data. In this paper, we propose a new framework to quantify uncertainty in probability model-form and model parameters resulting from small datasets and integrate these uncertainties into Sobol’ index estimates. First, the process establishes, through Bayesian multimodel inference, a set of candidate probability models and their associated probabilities. Imprecise Sobol’ indices are calculated from these probability models using an importance sampling reweighting approach. This results in probabilistic Sobol’ indices, whose distribution characterizes uncertainty in the sensitivity resulting from small dataset size. The imprecise Sobol’ indices thus provide a measure of confidence in the sensitivity estimate and, moreover, can be used to inform data collection efforts targeted to minimize the impact of uncertainties. Through an example studying the parameters of a Timoshenko beam, we show that these probabilistic Sobol’ indices converge to the true/deterministic Sobol’ indices as the dataset size increases and hence, distribution-form uncertainty reduces. The approach is then applied to assess the sensitivity of the out-of-plane properties of an E-glass fiber composite material to its constituent properties. This second example illustrates the approach for an important class of materials with wide-ranging applications when data may be lacking for some input parameters.

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Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); US Department of the Navy, Office of Naval Research (ONR)

Grant/Contract Number:: AC05-00OR22725; N00014-16-1-2582; N00014-16-1-2370; ERKJ352

OSTI ID:: 1651313

Alternate ID(s):: OSTI ID: 2325479

Journal Information:: Mechanical Systems and Signal Processing, Vol. 148, Issue na; ISSN 0888-3270

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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