Mohammad Khalil

Probabilistic parameter estimation in a 2-step chemical kinetics model for n-dodecane jet autoignition

This paper demonstrates the development of a simple chemical kinetics model designed for autoignition of n-dodecane in air using Bayesian inference with a model-error representation. The model error, i.e. intrinsic discrepancy from a high-fidelity benchmark model, is represented by allowing additional variability in selected parameters. Subsequently, we quantify predictive uncertainties in the results of autoignition simulations of homogeneous reactors at realistic diesel engine conditions. We demonstrate that these predictive error bars capture model error as well. The uncertainty propagation is performed using non-intrusive spectral projection that can also be used in principle with larger scale computations, such as large eddy simulation. While the present calibration is performed to match a skeletal mechanism, it can be done with equal success using experimental data only (e.g. shock-tube measurements). Since our method captures the error associated with structural model simplifications, we believe that the optimised model could then lead to better qualified predictions of autoignition delay time in high-fidelity large eddy simulations than the existing detailed mechanisms. This methodology provides a way to reduce the cost of reaction kinetics in simulations systematically, while quantifying the accuracy of predictions of important target quantities.

Probabilistic inference of reaction rate parameters from summary statistics

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. The method relies on probabilistic reconstruction of the unreported data, OH concentration profiles from shock-tube experiments, along with the unknown Arrhenius parameters. The data inference is performed using a Markov chain Monte Carlo sampling procedure that relies on an efficient adaptive quadrature in estimating relevant integrals needed for data likelihood evaluations. For further efficiency gains, local Padé–Legendre approximants are used as surrogates for the time histories of OH concentration, alleviating the need for 0-D auto-ignition simulations. The reconstructed realisations of the missing data are used to provide a consensus joint posterior probability density on the unknown Arrhenius parameters via probabilistic pooling. Uncertainty quantification analysis is performed for stoichiometric hydrogen–air auto-ignition computations to explore the impact of uncertain parameter correlations on a range of quantities of interest.

Modeling Auto-Ignition Transients in Reacting Diesel Jets

The objective of the present work is to establish a framework to design simple Arrhenius mechanisms for simulation of Diesel engine combustion. The goal is to predict auto-ignition and flame propagation over a selected range of temperature and equivalence ratio, at a significantly reduced computational cost, and to quantify the accuracy of the optimized mechanisms for a selected set of characteristics. The methodology is demonstrated for n-dodecane oxidation by fitting the auto-ignition delay time predicted by a detailed reference mechanism to a two-step model mechanism. The pre-exponential factor and activation energy of the first reaction are modeled as functions of equivalence ratio and temperature and calibrated using Bayesian inference. This provides both the optimal parameter values and the related uncertainties over a defined envelope of temperatures, pressures, and equivalence ratios. Non-intrusive spectral projection is then used to propagate the uncertainty through homogeneous auto-ignitions. A benefit of the method is that parametric uncertainties can be propagated in the same way through coupled reacting flow calculations using techniques such as Large Eddy Simulation to quantify the impact of the chemical parameter uncertainty on simulation results.© 2015 ASME

Null-hypothesis testing using distance metrics for verification of arms-control treaties

We investigate the feasibility of constructing a data-driven distance metric for use in null-hypothesis testing in the context of arms-control treaty verification. The distance metric is used in testing the hypothesis that the available data are representative of a certain object or otherwise, as opposed to binary-classification tasks studied previously. The metric, being of strictly quadratic form, is essentially computed using projections of the data onto a set of optimal vectors. These projections can be accumulated in list mode. The relatively low number of projections hampers the possible reconstruction of the object and subsequently the access to sensitive information. The projection vectors that channelize the data are optimal in capturing the Mahalanobis squared distance of the data associated with a given object under varying nuisance parameters. The vectors are also chosen such that the resulting metric is insensitive to the difference between the trusted object and another object that is deemed to contain sensitive information. Data used in this study were generated using the GEANT4 toolkit to model gamma transport using a Monte Carlo method. For numerical illustration, the methodology is applied to synthetic data obtained using custom models for plutonium inspection objects. The resulting metric based on a relatively low number of channels shows moderate agreement with the Mahalanobis distance metric for the trusted object but enabling a capability to obscure sensitive information.