A new ANN driven MCMC method for multi-parameter estimation in two-dimensional conduction with heat generation

Abstract

This paper proposes a hybrid approach, wherein Markov Chain Monte Carlo (MCMC) simulations are used in a Bayesian framework, in conjunction with artificial neural networks (ANN) for solving an inverse heat conduction problem. The proposed algorithm was tested for the problem of steady state two-dimensional heat conduction from a square slab with uniform volumetric internal heat generation. Two variants of this problem namely: (a) estimation of the convection heat transfer coefficient, h and the thermal conductivity of the material, k given the rate of heat generation q v and (b) estimation of k and q v given the heat transfer coefficient h, are considered. For both the problems, temperature data at certain fixed locations in the slab serves as the input. For the purposes of establishing the soundness and efficacy of the algorithm, temperatures obtained by a numerical solution to the governing equation for known values of the parameters to be retrieved are treated as “measured” data. However, white noise was added to these data not only to make the analysis realistic but also to ascertain the robustness of the retrieval methodology. In order to significantly reduce the computational time associated with the MCMC simulations, first, a neural network was trained with limited number of solutions to the forward model. This network was used to replace the forward model (conduction equation) during the process of retrievals with Markov Chain Monte Carlo simulations in a Bayesian framework, thereby making the retrievals hybrid. The performance of the proposed hybrid technique was evaluated for different priors and various levels of noise. Comparisons with retrievals done directly by ANN revealed that the performance of the hybrid method is demonstrably superior, particularly with noisy data.