Inference of reaction rate parameters based on summary statistics from experiments
Abstract
Here, we present the results of an application of Bayesian inference and maximum entropy methods for the estimation of the joint probability density for the Arrhenius rate para meters of the rate coefficient of the H _{2}/O _{2}mechanism chain branching reaction H + O _{2} → OH + O. Available published data is in the form of summary statistics in terms of nominal values and error bars of the rate coefficient of this reaction at a number of temperature values obtained from shocktube experiments. Our approach relies on generating data, in this case OH concentration profiles, consistent with the given summary statistics, using Approximate Bayesian Computation methods and a Markov Chain Monte Carlo procedure. The approach permits the forward propagation of parametric uncertainty through the computational model in a manner that is consistent with the published statistics. A consensus joint posterior on the parameters is obtained by pooling the posterior parameter densities given each consistent data set. To expedite this process, we construct efficient surrogates for the OH concentration using a combination of Pad'e and polynomial approximants. These surrogate models adequately represent forward model observables and their dependence on input parameters and are computationally efficient to allow their use inmore »
 Authors:

 Sandia National Lab. (SNLCA), Livermore, CA (United States)
 Publication Date:
 Research Org.:
 Sandia National Lab. (SNLCA), Livermore, CA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22)
 OSTI Identifier:
 1325156
 Alternate Identifier(s):
 OSTI ID: 1397963
 Report Number(s):
 SAND20164787J
Journal ID: ISSN 15407489; 640507
 Grant/Contract Number:
 AC0494AL85000; AC0494AL85000
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Proceedings of the Combustion Institute
 Additional Journal Information:
 Journal Name: Proceedings of the Combustion Institute; Journal ID: ISSN 15407489
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; uncertainty quantification; Bayesian inference; reaction rates; Arrhenius parameters; shock tube experiments
Citation Formats
Khalil, Mohammad, Chowdhary, Kamaljit Singh, Safta, Cosmin, Sargsyan, Khachik, and Najm, Habib N. Inference of reaction rate parameters based on summary statistics from experiments. United States: N. p., 2016.
Web. doi:10.1016/j.proci.2016.08.058.
Khalil, Mohammad, Chowdhary, Kamaljit Singh, Safta, Cosmin, Sargsyan, Khachik, & Najm, Habib N. Inference of reaction rate parameters based on summary statistics from experiments. United States. doi:10.1016/j.proci.2016.08.058.
Khalil, Mohammad, Chowdhary, Kamaljit Singh, Safta, Cosmin, Sargsyan, Khachik, and Najm, Habib N. Sat .
"Inference of reaction rate parameters based on summary statistics from experiments". United States. doi:10.1016/j.proci.2016.08.058. https://www.osti.gov/servlets/purl/1325156.
@article{osti_1325156,
title = {Inference of reaction rate parameters based on summary statistics from experiments},
author = {Khalil, Mohammad and Chowdhary, Kamaljit Singh and Safta, Cosmin and Sargsyan, Khachik and Najm, Habib N.},
abstractNote = {Here, we present the results of an application of Bayesian inference and maximum entropy methods for the estimation of the joint probability density for the Arrhenius rate para meters of the rate coefficient of the H2/O2mechanism chain branching reaction H + O2 → OH + O. Available published data is in the form of summary statistics in terms of nominal values and error bars of the rate coefficient of this reaction at a number of temperature values obtained from shocktube experiments. Our approach relies on generating data, in this case OH concentration profiles, consistent with the given summary statistics, using Approximate Bayesian Computation methods and a Markov Chain Monte Carlo procedure. The approach permits the forward propagation of parametric uncertainty through the computational model in a manner that is consistent with the published statistics. A consensus joint posterior on the parameters is obtained by pooling the posterior parameter densities given each consistent data set. To expedite this process, we construct efficient surrogates for the OH concentration using a combination of Pad'e and polynomial approximants. These surrogate models adequately represent forward model observables and their dependence on input parameters and are computationally efficient to allow their use in the Bayesian inference procedure. We also utilize GaussHermite quadrature with Gaussian proposal probability density functions for moment computation resulting in orders of magnitude speedup in data likelihood evaluation. Despite the strong nonlinearity in the model, the consistent data sets all res ult in nearly Gaussian conditional parameter probability density functions. The technique also accounts for nuisance parameters in the form of Arrhenius parameters of other rate coefficients with prescribed uncertainty. The resulting pooled parameter probability density function is propagated through stoichiometric hydrogenair autoignition computations to illustrate the need to account for correlation among the Arrhenius rate parameters of one reaction and across rate parameters of different reactions.},
doi = {10.1016/j.proci.2016.08.058},
journal = {Proceedings of the Combustion Institute},
issn = {15407489},
number = ,
volume = ,
place = {United States},
year = {2016},
month = {10}
}
Web of Science