Surrogate-accelerated Bayesian framework for high-temperature thermal diffusivity characterization

Abstract

Precise determination of thermal diffusivity at high temperatures is crucial for aerospace and energy industries. Periodic heating techniques such as Å ngström’s method are data-rich and commonly used for measuring thermal diffusivity of a solid material. In previous Å ngström’s method studies, regression techniques have been used to solve the associated inverse problem and to estimate thermal diffusivity by minimizing the residual between measurements and model predictions. This approach lacks rigorous uncertainty quantification and does not allow incorporation of prior knowledge for parameters. Adopting a Bayesian framework addresses these issues; however, probing the Bayesian posterior distribution is prohibitively expensive using Markov chain Monte Carlo (MCMC) methods, especially when the physical model is computationally expensive, as in the present study for which an analytical solution does not exist. This study employs a parametric surrogate model in the form of polynomial chaos to accelerate the physical model by several orders of magnitude to support Bayesian analysis. Moreover, high-temperature testing environments are difficult to control precisely, and many unknown parameters exist beyond the quantity of interest. Previous studies have employed random walks to set new parameters in the MCMC sampling process. However, random walks are inefficient in exploring high-dimensional parameter spaces and thus suffer high auto-correlation and poor convergence. To improve the efficiency of the MCMC sampler, this study employs a No-U-Turn sampler that explores the parameter space thoroughly and efficiently. We demonstrate the effectiveness of this Bayesian framework by analyzing experimental results on a graphite sample at approximately 1000 K.