A Computational Statistics Approach to Stochastic Inverse Problems and Uncertainty Quantification in Heat Transfer

As most engineering systems and processes operate in an uncertain environment, it becomes increasingly important to address their analysis and inverse design in a stochastic manner using statistical data-driven methods. Recent advances in computational Bayesian and spatial statistics enable complete and efficient solution procedures to such problems. Herein, a novel framework based on Bayesian inference is presented for the solution of stochastic inverse problems in heat transfer. The posterior probability density function (PPDF) of unknowns (modeled as random variables or stochastic processes), such as material thermal properties and boundary heat flux, is computed given finite set of thermocouple temperature measurements. Markov Chain Monte Carlo (MCMC) algorithms are exploited to obtain estimates of statistics of random unknowns. A parameter estimation problem is first solved using simple, hierarchical and augmented Bayesian models. Boundary heat flux reconstruction in heat conduction is then studied. Simulation results demonstrate the great potential of applying a Bayesian approach to stochastic estimation and design problems. Although discussed in the context of thermal systems, the methodology presented is general and applicable to design and estimation problems in diverse areas of engineering.