Technical Report 133, c4e-Preprint Series, Cambridge

Authors: Sebastian Mosbach, Je Hyeong Hong, George Brownbridge, Markus Kraft*, S. Gudiyella, and K. Brezinsky

Reference: Technical Report 133, c4e-Preprint Series, Cambridge, 2013

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We apply a Bayesian parameter estimation technique to a chemical kinetic mechanism for n-propylbenzene oxidation in a shock tube in order to propagate errors in experimental data to errors in model parameters and responses. We find that, in order to apply the methodology successfully, conventional optimisation is required as a preliminary step. This is carried out in two stages: firstly, a quasi-random global search using a Sobol low-discrepancy sequence is conducted, followed by a local optimisation 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 optimised 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.

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