Design Analysis for Optimal Calibration of Diffusivity in Reactive Multilayers

TL;DR

This paper develops a Bayesian framework to optimize experimental conditions for better calibration of diffusion parameters in reactive multilayers, enhancing inference accuracy in different temperature regimes.

Contribution

It introduces a rigorous method combining Monte Carlo, sparse quadrature, and polynomial chaos to identify optimal experimental designs for diffusion parameter inference.

Findings

Optimal foil heating rate and pulse duration identified for low temperature regime.

Increasing sample size and reducing measurement uncertainty improves information gain at high temperature.

Optimal designs lead to sharper posterior distributions of diffusion parameters.

Abstract

Calibration of the uncertain Arrhenius diffusion parameters for quantifying mixing rates in Zr-Al nanolaminate foils was performed in a Bayesian setting [Vohra et al., 2014]. The parameters were inferred in a low temperature regime characterized by homogeneous ignition and a high temperature regime characterized by self-propagating reactions in the multilayers. In this work, we extend the analysis to find optimal experimental designs that would provide the best data for inference. We employ a rigorous framework that quantifies the expected in- formation gain in an experiment, and find the optimal design conditions using numerical techniques of Monte Carlo, 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 sharper posterior distributions of the diffusion parameters. For the high temperature regime, we demonstrate potential for increase in the expected information gain of the posteriors by increasing sample size and reducing uncertainty in measurements. Moreover, posterior marginals are also produced to verify favorable experimental scenarios for this regime.