Probabilistic inference of reaction rate parameters from summary statistics

Khalil, Mohammad; Najm, Habib N.

doi:10.1080/13647830.2017.1370557

Title: Probabilistic inference of reaction rate parameters from summary statistics

Journal Article · 29 May 2018 · Combustion Theory and Modelling

DOI: https://doi.org/10.1080/13647830.2017.1370557 · OSTI ID:1465801

Khalil, Mohammad ^[1]; Najm, Habib N. ^[1]

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

Here, 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.

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Research Organization:: Sandia National Laboratories (SNL-CA), Livermore, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1465801

Report Number(s):: SAND-2017-2451J; 666595

Journal Information:: Combustion Theory and Modelling, Journal Name: Combustion Theory and Modelling Journal Issue: 4 Vol. 22; ISSN 1364-7830

Publisher:: Taylor & FrancisCopyright Statement

Country of Publication:: United States

Language:: English

References (55)

Collaborative data processing in developing predictive models of complex reaction systems Frenklach, Michael; Packard, Andrew; Seiler, Pete International Journal of Chemical Kinetics, Vol. 36, Issue 1 https://doi.org/10.1002/kin.10172	journal	January 2003
Quantifying uncertainty in chemical systems modeling Reagan, M. T.; Najm, H. N.; Pébay, P. P. International Journal of Chemical Kinetics, Vol. 37, Issue 6 https://doi.org/10.1002/kin.20081	journal	January 2005
Determination of rate parameters based on both direct and indirect measurements Turányi, T.; Nagy, T.; Zsély, I. Gy. International Journal of Chemical Kinetics, Vol. 44, Issue 5 https://doi.org/10.1002/kin.20717	journal	February 2012
Evaluation of Combustion Mechanisms Using Global Uncertainty and Sensitivity Analyses: A Case Study for Low-Temperature Dimethyl Ether Oxidation: COMBUSTION MECHANISMS USING GLOBAL UNCERTAINTY AND SENSITIVITY ANALYSES Tomlin, Alison S.; Agbro, Edirin; Nevrlý, Václav International Journal of Chemical Kinetics, Vol. 46, Issue 11 https://doi.org/10.1002/kin.20877	journal	September 2014
Sensitivity analysis and parameter estimation in dynamic modeling of chemical kinetics Miller, David; Frenklach, Michael International Journal of Chemical Kinetics, Vol. 15, Issue 7 https://doi.org/10.1002/kin.550150709	journal	July 1983
Monte Carlo Strategies in Scientific Computing Liu, Jun S. Springer Series in Statistics https://doi.org/10.1007/978-0-387-76371-2	book	January 2004
Stochastic Finite Elements: A Spectral Approach Ghanem, Roger G.; Spanos, Pol D. Springer New York, NY https://doi.org/10.1007/978-1-4612-3094-6	book	January 1991
Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics Le Maître, O. P.; Knio, Omar M. Scientific Computation https://doi.org/10.1007/978-90-481-3520-2	book	January 2010
From Laplace to Supernova SN 1987A: Bayesian Inference in Astrophysics Loredo, T. J. Maximum Entropy and Bayesian Methods https://doi.org/10.1007/978-94-009-0683-9_6	book	January 1990
Padé-Legendre Interpolants for Gibbs Reconstruction Hesthaven, J. S.; Kaber, S. M.; Lurati, L. Journal of Scientific Computing, Vol. 28, Issue 2-3 https://doi.org/10.1007/s10915-006-9085-9	journal	May 2006
Data free inference with processed data products Chowdhary, K.; Najm, H. N. Statistics and Computing, Vol. 26, Issue 1-2 https://doi.org/10.1007/s11222-014-9484-y	journal	July 2014
Optimization and analysis of large chemical kinetic mechanisms using the solution mapping method—combustion of methane Frenklach, Michael; Wang, Hai; Rabinowitz, Martin J. Progress in Energy and Combustion Science, Vol. 18, Issue 1 https://doi.org/10.1016/0360-1285(92)90032-V	journal	January 1992
Uncertainty quantification in reacting-flow simulations through non-intrusive spectral projection Reagan, Matthew T.; Najm, Habib N.; Ghanem, Roger G. Combustion and Flame, Vol. 132, Issue 3 https://doi.org/10.1016/S0010-2180(02)00503-5	journal	February 2003
Incorporation of parametric uncertainty into complex kinetic mechanisms: Application to hydrogen oxidation in supercritical water Phenix, Brian D.; Dinaro, Joanna L.; Tatang, Menner A. Combustion and Flame, Vol. 112, Issue 1-2 https://doi.org/10.1016/S0010-2180(97)81762-2	journal	January 1998
Resolution of gas phase and surface combustion chemistry into elementary reactions Warnatz, Jürgen Symposium (International) on Combustion, Vol. 24, Issue 1 https://doi.org/10.1016/S0082-0784(06)80070-6	journal	January 1992
Combustion kinetic modeling using multispecies time histories in shock-tube oxidation of heptane Sheen, David A.; Wang, Hai Combustion and Flame, Vol. 158, Issue 4 https://doi.org/10.1016/j.combustflame.2010.12.016	journal	April 2011
Uncertainty quantification of reaction mechanisms accounting for correlations introduced by rate rules and fitted Arrhenius parameters Prager, Jens; Najm, Habib N.; Sargsyan, Khachik Combustion and Flame, Vol. 160, Issue 9 https://doi.org/10.1016/j.combustflame.2013.01.008	journal	September 2013
Uncertainty propagation using Wiener–Haar expansions Le Maı̂tre, O. P.; Knio, O. M.; Najm, H. N. Journal of Computational Physics, Vol. 197, Issue 1 https://doi.org/10.1016/j.jcp.2003.11.033	journal	June 2004
Multi-resolution analysis of Wiener-type uncertainty propagation schemes Le Maı̂tre, O. P.; Najm, H. N.; Ghanem, R. G. Journal of Computational Physics, Vol. 197, Issue 2 https://doi.org/10.1016/j.jcp.2003.12.020	journal	July 2004
Stochastic spectral methods for efficient Bayesian solution of inverse problems Marzouk, Youssef M.; Najm, Habib N.; Rahn, Larry A. Journal of Computational Physics, Vol. 224, Issue 2 https://doi.org/10.1016/j.jcp.2006.10.010	journal	June 2007
Padé–Legendre approximants for uncertainty analysis with discontinuous response surfaces Chantrasmi, T.; Doostan, A.; Iaccarino, G. Journal of Computational Physics, Vol. 228, Issue 19 https://doi.org/10.1016/j.jcp.2009.06.024	journal	October 2009
Data-free inference of the joint distribution of uncertain model parameters Berry, Robert D.; Najm, Habib N.; Debusschere, Bert J. Journal of Computational Physics, Vol. 231, Issue 5 https://doi.org/10.1016/j.jcp.2011.10.031	journal	March 2012
Combustion kinetic model uncertainty quantification, propagation and minimization Wang, Hai; Sheen, David A. Progress in Energy and Combustion Science, Vol. 47 https://doi.org/10.1016/j.pecs.2014.10.002	journal	April 2015
Transforming data into knowledge—Process Informatics for combustion chemistry Frenklach, Michael Proceedings of the Combustion Institute, Vol. 31, Issue 1 https://doi.org/10.1016/j.proci.2006.08.121	journal	January 2007
Optimization of combustion kinetic models on a feasible set You, Xiaoqing; Russi, Trent; Packard, Andrew Proceedings of the Combustion Institute, Vol. 33, Issue 1 https://doi.org/10.1016/j.proci.2010.05.016	journal	January 2011
Kinetics of H atom attack on unsaturated hydrocarbons using spectral uncertainty propagation and minimization techniques Sheen, David A.; Rosado-Reyes, Claudette M.; Tsang, Wing Proceedings of the Combustion Institute, Vol. 34, Issue 1 https://doi.org/10.1016/j.proci.2012.06.062	journal	January 2013
The role of sensitivity and uncertainty analysis in combustion modelling Tomlin, Alison S. Proceedings of the Combustion Institute, Vol. 34, Issue 1 https://doi.org/10.1016/j.proci.2012.07.043	journal	January 2013
Determining predictive uncertainties and global sensitivities for large parameter systems: A case study for n -butane oxidation Hébrard, Éric; Tomlin, Alison S.; Bounaceur, Roda Proceedings of the Combustion Institute, Vol. 35, Issue 1 https://doi.org/10.1016/j.proci.2014.06.027	journal	January 2015
Inference of reaction rate parameters based on summary statistics from experiments Khalil, M.; Chowdhary, K.; Safta, C. Proceedings of the Combustion Institute, Vol. 36, Issue 1 https://doi.org/10.1016/j.proci.2016.08.058	journal	January 2017
Determination of the uncertainty domain of the Arrhenius parameters needed for the investigation of combustion kinetic models Nagy, Tibor; Turányi, Tamás Reliability Engineering & System Safety, Vol. 107 https://doi.org/10.1016/j.ress.2011.06.009	journal	November 2012
Padé Approximants Second Edition Baker, George A.; Graves-Morris, Peter Cambridge University Press https://doi.org/10.1017/CBO9780511530074	book	January 1996
Probability Theory Jaynes, E. T. https://doi.org/10.1017/CBO9780511790423	book	January 2003
Shock tube study of the reaction hydrogen atom + oxygen .fwdarw. hydroxyl + oxygen atom using hydroxyl laser absorption Masten, David A.; Hanson, Ronald K.; Bowman, Craig T. The Journal of Physical Chemistry, Vol. 94, Issue 18 https://doi.org/10.1021/j100381a033	journal	September 1990
On the convergence of generalized polynomial chaos expansions Ernst, Oliver G.; Mugler, Antje; Starkloff, Hans-Jörg ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 46, Issue 2 https://doi.org/10.1051/m2an/2011045	journal	October 2011
Updating Probabilities Caticha, Ariel; Giffin, Adom Bayesian Inference and Maximum Entropy Methods In Science and Engineering, AIP Conference Proceedings https://doi.org/10.1063/1.2423258	conference	January 2006
CVODE, A Stiff/Nonstiff ODE Solver in C Cohen, Scott D.; Hindmarsh, Alan C.; Dubois, Paul F. Computers in Physics, Vol. 10, Issue 2 https://doi.org/10.1063/1.4822377	journal	January 1996
Accurate Approximations for Posterior Moments and Marginal Densities Tierney, Luke; Kadane, Joseph B. Journal of the American Statistical Association, Vol. 81, Issue 393 https://doi.org/10.1080/01621459.1986.10478240	journal	March 1986
The Intrinsic Bayes Factor for Model Selection and Prediction Berger, James O.; Pericchi, Luis R. Journal of the American Statistical Association, Vol. 91, Issue 433 https://doi.org/10.1080/01621459.1996.10476668	journal	March 1996
Bayesian analysis of syngas chemistry models Braman, Kalen; Oliver, Todd A.; Raman, Venkat Combustion Theory and Modelling, Vol. 17, Issue 5 https://doi.org/10.1080/13647830.2013.811541	journal	October 2013
Spectral stochastic uncertainty quantification in chemical systems Reagan, M. T.; Najm 4, H. N.; Debusschere, B. J. Combustion Theory and Modelling, Vol. 8, Issue 3 https://doi.org/10.1088/1364-7830/8/3/010	journal	September 2004
Approximate Bayesian Computation in Population Genetics Beaumont, Mark A.; Zhang, Wenyang; Balding, David J. Genetics, Vol. 162, Issue 4 https://doi.org/10.1093/genetics/162.4.2025	journal	December 2002
Maximum entropy and Bayesian data analysis: Entropic prior distributions Caticha, Ariel; Preuss, Roland Physical Review E, Vol. 70, Issue 4 https://doi.org/10.1103/PhysRevE.70.046127	journal	October 2004
Modeling Auto-Ignition Transients in Reacting Diesel Jets Hakim, Layal; Lacaze, Guilhem; Khalil, Mohammad Journal of Engineering for Gas Turbines and Power, Vol. 138, Issue 11 https://doi.org/10.1115/1.4033502	journal	May 2016
Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures Wan, Xiaoliang; Karniadakis, George Em SIAM Journal on Scientific Computing, Vol. 28, Issue 3 https://doi.org/10.1137/050627630	journal	January 2006
Multi‐Resolution‐Analysis Scheme for Uncertainty Quantification in Chemical Systems Le Maître, O. P.; Najm, H. N.; Pébay, P. P. SIAM Journal on Scientific Computing, Vol. 29, Issue 2 https://doi.org/10.1137/050643118	journal	January 2007
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations Xiu, Dongbin; Karniadakis, George Em SIAM Journal on Scientific Computing, Vol. 24, Issue 2 https://doi.org/10.1137/S1064827501387826	journal	January 2002
Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes Debusschere, Bert J.; Najm, Habib N.; Pébay, Philippe P. SIAM Journal on Scientific Computing, Vol. 26, Issue 2 https://doi.org/10.1137/S1064827503427741	journal	January 2004
SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers Hindmarsh, Alan C.; Brown, Peter N.; Grant, Keith E. ACM Transactions on Mathematical Software, Vol. 31, Issue 3 https://doi.org/10.1145/1089014.1089020	journal	September 2005
Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics Najm, Habib N. Annual Review of Fluid Mechanics, Vol. 41, Issue 1 https://doi.org/10.1146/annurev.fluid.010908.165248	journal	January 2009
A Characterization Theorem for Externally Bayesian Groups Genest, Christian The Annals of Statistics, Vol. 12, Issue 3 https://doi.org/10.1214/aos/1176346726	journal	September 1984
Combining Probability Distributions: A Critique and an Annotated Bibliography Genest, Christian; Zidek, James V. Statistical Science, Vol. 1, Issue 1 https://doi.org/10.1214/ss/1177013825	journal	February 1986
Data-Free Inference of Uncertain Parameters in Chemical Models Najm, Habib N.; Berry, Robert D.; Safta, Cosmin International Journal for Uncertainty Quantification, Vol. 4, Issue 2 https://doi.org/10.1615/Int.J.UncertaintyQuantification.2013005679	journal	January 2014
TChem - A Software Toolkit for the Analysis of Complex Kinetic Models Safta, Cosmin; Najm, Habib; Knio, Omar https://doi.org/10.2172/1113874	report	May 2011
Applications of a Method for the Efficient Computation of Posterior Distributions Naylor, J. C.; Smith, A. F. M. Applied Statistics, Vol. 31, Issue 3 https://doi.org/10.2307/2347995	journal	January 1982
The Homogeneous Chaos Wiener, Norbert American Journal of Mathematics, Vol. 60, Issue 4 https://doi.org/10.2307/2371268	journal	October 1938

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Arrhenius parameters
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maximum relative entropy
reaction rates
shock-tube experiments
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Title: Probabilistic inference of reaction rate parameters from summary statistics

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