Estimating material properties under extreme conditions by using Bayesian model calibration with functional outputs

J. L. Brown and L. B. Hund

Journal of the Royal Statistical Society Series C, 2018, vol. 67, issue 4, 1023-1045

Abstract: Dynamic material properties experiments provide access to the most extreme temperatures and pressures attainable in a laboratory setting; the data from these experiments are often used to improve our understanding of material models at these extreme conditions. We apply Bayesian model calibration to dynamic material property applications where the experimental output is a function: velocity over time. This framework can accommodate more uncertainties and facilitate analysis of new types of experiments relative to techniques traditionally used to analyse dynamic material experiments. However, implementation of Bayesian model calibration requires more sophisticated statistical techniques, because of the functional nature of the output as well as parameter and model discrepancy identifiability. We propose a novel Bayesian model calibration process to simplify and improve the estimation of the material property calibration parameters. Specifically, we propose scaling the likelihood function by an effective sample size rather than modelling the auto‐correlation function to accommodate the functional output. Additionally, we propose sensitivity analyses by using the notion of 'modularization' to assess the effect of experiment‐specific nuisance input parameters on estimates of the physical parameters. The Bayesian model calibration framework proposed is applied to dynamic compression of tantalum to extreme pressures, and we conclude that the procedure results in simple, fast and valid inferences on the material properties for tantalum.

Date: 2018
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