Design analysis for optimal calibration of diffusivity in reactive multilayers


Journal Article

© 2017 Informa UK Limited, trading as Taylor & Francis Group. Calibration of the uncertain Arrhenius diffusion parameters for quantifying mixing rates in Zr–Al nanolaminate foils have been previously performed in a Bayesian setting [M. Vohra, J. Winokur, K.R. Overdeep, P. Marcello, T.P. Weihs, and O.M. Knio, Development of a reduced model of formation reactions in Zr–Al nanolaminates, J. Appl. Phys. 116(23) (2014): Article No. 233501]. The parameters were inferred in a low-temperature, homogeneous ignition regime, and a high-temperature self-propagating reaction regime. In this work, we extend the analysis to determine optimal experimental designs that would provide the best data for inference. We employ a rigorous framework that quantifies the expected information gain in an experiment, and find the optimal design conditions using Monte Carlo techniques, sparse quadrature, and polynomial chaos surrogates. For the low-temperature regime, we find the optimal foil heating rate and pulse duration, and confirm through simulation that the optimal design indeed leads to sharp posterior distributions of the diffusion parameters. For the high-temperature regime, we demonstrate the potential for increasing the expected information gain concerning the posteriors by increasing the sample size and reducing the uncertainty in measurements. Moreover, posterior marginals are also obtained to verify favourable experimental scenarios.

Full Text

Cited Authors

  • Vohra, M; Huan, X; Weihs, TP; Knio, OM

Published Date

  • November 2, 2017

Published In

Volume / Issue

  • 21 / 6

Start / End Page

  • 1023 - 1049

Electronic International Standard Serial Number (EISSN)

  • 1741-3559

International Standard Serial Number (ISSN)

  • 1364-7830

Digital Object Identifier (DOI)

  • 10.1080/13647830.2017.1329938

Citation Source

  • Scopus