Optimal Design and Model Validation for Combustion Experiments in a Shock Tube

Abstract

We develop a Bayesian framework for the optimal experimental design of the shock tube experiments which are being carried out at the KAUST Clean Combustion Center. The unknown parameters are the pre-exponential parameters and the activation energies in the reaction rate functions. The control parameters are the initial hydrogen concentration and the temperature. First, we build a polynomial based surrogate model for the observable related to the reactions in the shock tube. Second, we use a novel MAP based approach to estimate the expected information gain in the proposed experiments and select the best experimental set-ups corresponding to the optimal expected information gains. Third, we use the synthetic data to carry out virtual validation of our methodology.