Estimating the joint distribution of rate parameters across multiple reactions in the absence of experimental data

Journal Article · Tue Jul 31 00:00:00 EDT 2018 · Proceedings of the Combustion Institute

DOI:https://doi.org/10.1016/j.proci.2018.06.190· OSTI ID:1465187

Casey, Tiernan A. ^[1]; Najm, Habib N. ^[1]

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1. Sandia National Lab. (SNL-CA), Livermore, CA (United States)

Here, a procedure for determining the joint uncertainty of Arrhenius parameters across multiple combustion reactions of interest is demonstrated. This approach is capable of constructing the joint distribution of the Arrhenius parameters arising from the uncertain measurements performed in specific target experiments without having direct access to the underlying experimental data. The method involves constructing an ensemble of hypothetical data sets with summary statistics consistent with the available information reported by the experimentalists, followed by a fitting procedure that learns the structure of the joint parameter density across reactions using this consistent hypothetical data as evidence. The procedure is formalized in a Bayesian statistical framework, employing maximum-entropy and approximate Bayesian computation methods and utilizing efficient Markov chain Monte Carlo techniques to explore data and parameter spaces in a nested algorithm. We demonstrate the application of the method in the context of experiments designed to measure the rates of selected chain reactions in the H₂-O₂ system and highlight the utility of this approach for revealing the critical correlations between the parameters within a single reaction and across reactions, as well as for maximizing consistency when utilizing rate parameter information in predictive combustion modeling of systems of interest.

• Research Organization: Sandia National Lab. (SNL-CA), Livermore, CA (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: AC04-94AL85000
• OSTI ID: 1465187
• Report Number(s): SAND-2018-7013J; 665270
• Journal Information: Proceedings of the Combustion Institute, Vol. 37, Issue 1; ISSN 1540-7489
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
Uncertainty quantification
Arrhenius parameters
Bayesian statistics
Missing data