Probabilistic inference of reaction rate parameters from summary statistics

Abstract

This investigation tackles the probabilistic parameter estimation problem involving the Arrhenius parameters for the rate coefficient of the chain branching reaction H + O₂ → OH + O. This is achieved in a Bayesian inference framework that uses indirect data from the literature in the form of summary statistics by approximating the maximum entropy solution with the aid of approximate bayesian computation. The summary statistics include nominal values and uncertainty factors of the rate coefficient, obtained from shock-tube experiments performed at various initial temperatures. The Bayesian framework allows for the incorporation of uncertainty in the rate coefficient of a secondary reaction, namely OH + H₂ → H₂O + H, resulting in a consistent joint probability density on Arrhenius parameters for the two rate coefficients. It also allows for uncertainty quantification in numerical ignition predictions while conforming with the published summary statistics. The method relies on probabilistic reconstruction of the unreported data, OH concentration profiles from shock-tube experiments, along with the unknown Arrhenius parameters. The data inference is performed using a Markov chain Monte Carlo sampling procedure that relies on an efficient adaptive quadrature in estimating relevant integrals needed for data likelihood evaluations. For further efficiency gains, local Padé–Legendre approximants are used as surrogates for the time histories of OH concentration, alleviating the need for 0-D auto-ignition simulations. The reconstructed realisations of the missing data are used to provide a consensus joint posterior probability density on the unknown Arrhenius parameters via probabilistic pooling. Uncertainty quantification analysis is performed for stoichiometric hydrogen–air auto-ignition computations to explore the impact of uncertain parameter correlations on a range of quantities of interest.

Keywords:

• uncertainty quantification
• maximum relative entropy
• Bayesian inference
• reaction rates
• Arrhenius parameters
• shock-tube experiments

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. The germ must have a density p( ξ ) uniquely determined by its moments [58].

Additional information

Funding

This work was supported by the US Department of Energy (DOE), Office of Basic Energy Sciences (BES) Division of Chemical Sciences, Geosciences, and Biosciences. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the US Department of Energy's National Nuclear Security Administration [contract DE-NA-0003525].