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Bayesian Error Propagation for a Kinetic Model of n ‐Propylbenzene Oxidation in a Shock Tube
Author(s) -
Mosbach Sebastian,
Hong Je Hyeong,
Brownbridge George P. E.,
Kraft Markus,
Gudiyella Soumya,
Brezinsky Kenneth
Publication year - 2014
Publication title -
international journal of chemical kinetics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.341
H-Index - 68
eISSN - 1097-4601
pISSN - 0538-8066
DOI - 10.1002/kin.20855
Subject(s) - sobol sequence , shock tube , bayesian probability , mathematics , chemistry , kinetic energy , statistical physics , arrhenius equation , markov chain monte carlo , bayesian inference , monte carlo method , biological system , algorithm , thermodynamics , statistics , physics , shock wave , quantum mechanics , biology , activation energy , organic chemistry
We apply a Bayesian parameter estimation technique to a chemical kinetic mechanism for n ‐propylbenzene oxidation in a shock tube to propagate errors in experimental data to errors in Arrhenius parameters and predicted species concentrations. We find that, to apply the methodology successfully, conventional optimization is required as a preliminary step. This is carried out in two stages: First, a quasi‐random global search using a Sobol low‐discrepancy sequence is conducted, followed by a local optimization by means of a hybrid gradient‐descent/Newton iteration method. The concentrations of 37 species at a variety of temperatures, pressures, and equivalence ratios are optimized against a total of 2378 experimental observations. We then apply the Bayesian methodology to study the influence of uncertainties in the experimental measurements on some of the Arrhenius parameters in the model as well as some of the predicted species concentrations. Markov chain Monte Carlo algorithms are employed to sample from the posterior probability densities, making use of polynomial surrogates of higher order fitted to the model responses. We conclude that the methodology provides a useful tool for the analysis of distributions of model parameters and responses, in particular their uncertainties and correlations. Limitations of the method are discussed. For example, we find that using second‐order response surfaces and assuming normal distributions for propagated errors is largely adequate, but not always.