New Type of Sensitivity Analysis Using Bayesian Approach with Artificially Designed Data

Abstract

A new type of sensitivity analysis is proposed with the help of a Bayesian approach. The main idea is the use of two calibration data sets: one is experimental, and the other is artificially designed in such a way that features observed in the experimental data set are magnified. An advantage of this approach is to capture nonlinear dependence among the physics involved (e.g., model parameters), simultaneously taking into account both modeling and experimental uncertainties. To demonstrate how the proposed method works, a combustion kinetic problem that is a highly nonlinear system of several ordinary differential equations is considered. More specifically, uncertainties in the reduced chemistry (six reactions) model of the mixture kinetics proposed by Thielen and Roth (“Resonance Absorption Measurements of N, O, and H Atoms in Shock Heated Mixtures,” Combustion and Flame, Vol. 69, No. 2, 1987, pp. 141–154) are quantified, and then one critical reaction is attempted to be identified out of the pool of 27 extra reactions, which could improve its predictions of species concentration profiles at a high-temperature condition. With the help of the proposed sensitivity analysis, the identification process is shown to be more effective. Because of its simplicity, the approach has the potential to be applied to a wide variety of engineering applications.