Combustion kinetic model uncertainty quantification, propagation and minimization

Abstract

The current interest in the combustion chemistry of hydrocarbon fuels, including the various alcohol and biodiesel compounds, motivates this review of the methods and application of kinetic uncertainty quantification (UQ). Our intent is to provide a self-contained review about the mathematical principles and methods of uncertainty quantification and their application in highly complex, multi-parameter combustion chemistry problems. We begin by outlining the reasons why the kinetic uncertainty must be considered and treated as a part of the combustion chemistry development in order to make progress. This is followed by a brief discussion about the sources and classification of kinetic uncertainties and the meanings and definitions of model verification and validation. We discuss the histories of UQ studies with an emphasis on how the combustion community has a long tradition of UQ consideration through standard sensitivity analysis. Such efforts have motivated the advancements of UQ methods specifically tailored to combustion chemistry. They also led to the recent growing interests in applying UQ methods as a part of our recommended long-term solution to the chemical kinetic problem of combustion. We then review and classify the various UQ methods and illustrate their applications for problems involving forward uncertainty quantification and propagation, and as an inverse problem leading to model uncertainty constraining. For the inverse problem, the focus of discussion is in the use of methods originating from Bayes' Theorem. We show that, for combustion chemistry problems, while UQ alone cannot produce precise, individual rate parameters, it can be instrumental in measuring the progress of our understanding of combustion chemistry and in utilizing fundamental combustion property data beyond a simple "agreedisagree" statement. When treated as a Bayesian inference problem, UQ also aids the development of predictive kinetic models in two ways: the use of fundamental combustion property data, global or local, to provide a better constrained kinetic model, and along with forward kinetic uncertainty propagation, to yield estimates for the confidence of a model to make predictions outside of the thermodynamic regimes where the model has been tested. We provide several examples to illustrate the utility of the UQ methods discussed and to demonstrate that, in the field of combustion chemistry, further progress will be better achieved through a combination of fundamental studies of reaction rates through well-defined and designed experiments and ab initio theoretical calculations, and of analyses of global experimental measurements. These studies together must be supplemented by UQ analyses, in such a way that a measurable progress can be made over time.

mumpce_py: A Python Implementation of the Method of Uncertainty Minimization Using Polynomial Chaos Expansions

“…The Method of Uncertainty Minimization using Polynomial Chaos Expansions (MUM-PCE) [1][2][3][4][5][6] was developed as a software tool to constrain physical models against experimental measurements. These models contain parameters that cannot be easily determined from first principles and so must be measured, and some which cannot even be easily measured.…”

The combustion mitigation of methane as a non-CO 2 greenhouse gas

“…To analyse the uncertainties in these schemes, uncertainty quantification (UQ) which tries to determine how likely certain outcomes are if some aspects of the system are not exactly known, is becoming increasingly important. The uncertainty quantification, propagation and minimization for the combustion kinetic models were recently systematically reviewed by Wang and Sheen [118], which detailed the sources of uncertainties and provided a classification for them. The application of UQ in highly complex, multi-parameter combustion chemistry problems has to be considered and treated as an integral part of the combustion chemistry development.…”

“…When UQ is applied to combustion chemical kinetics, the main methods related to model and parameter evaluation employ probability-based approaches [112]. The standard sensitivity analysis for chemical kinetic schemes can be regarded as a consideration of UQ, which can aid the development of predictive kinetic models in different ways when treated as a Bayesian inference problem [118]. UQ is playing an increasingly important role in the development of chemical kinetic schemes, which is also essential for the development of the much needed chemical kinetic schemes for ultra-lean CH 4 oxidation/combustion.…”

Investigation of the effect of correlated uncertain rate parameters on a model of hydrogen combustion using a generalized HDMR method

“…Sheen and Wang calculated the covariance matrix of the fitted parameters for ethylene and n-heptane combustion mechanisms [14][15][16], which carries information on the joint uncertainty of the parameters. The optimized rate parameters were Arrhenius A parameters and 3 rd body collision efficiency factors.…”