Coupled POD-Bayesian estimation of the parameters of mathematical model of the packed-bed drying of cherry stones

Abstract

This paper deals with the Bayesian estimation of flow parameters in a porous material based on the measurements of local temperature at selected points inside the packed-bed. The unknown probability distribution function of estimated parameters was sampled using a Markov Chain Monte Carlo (MCMC) method. The MCMC method is efficient in sampling unknown distributions, but it is extremely time-consuming. The Proper Orthogonal Decomposition was used to construct off-line, low order approximation of the porous media flow problem. This model was further incorporated into the Metropolis-Hastings algorithm to retrieve the posterior distribution of the unknown parameters. This approach allowed us to decrease the computational time necessary to generate an ergodic Markov Chain. The efficiency of the proposed approach was tested on the simulated data generated with commercial CFD tools, and finally, it was applied to the real data acquired on the dedicated experimental stand.