Accelerating MCMC Using Model Reduction for the Estimation of Boundary Properties Within Bayesian Framework

Abstract

In this work, Artificial Neural Network (ANN) and Approximation Error Model (AEM) are proposed as model reduction methods for the simultaneous estimation of the convective heat transfer coefficient and the heat flux from a mild steel fin subject to natural convection heat transfer. The complete model comprises of a three-dimensional conjugate heat transfer from fin whereas the reduced model is simplified to a pure conduction model. On the other hand, the complete model is then replaced with ANN model that acts as a fast forward model. The modeling error that arises due to reduced model is statistically compensated using Approximation Error Model. The estimation of the unknown parameters is then accomplished using the Bayesian framework with Gaussian prior. The sampling space for both the parameters is successfully explored based on Markov chain Monte Carlo method. In addition, the convergence of the Markov chain is ensured using Metropolis–Hastings algorithm. Simulated measurements are used to demonstrate the proposed concept for proving the robustness; finally, the measured temperatures based on in-house experimental setup are then used in the inverse estimation of the heat flux and the heat transfer coefficient for the purpose of validation.