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Khalil, Mohammad

Publications and source records attributed to Khalil, Mohammad.

At least 127 records · Page 7
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DOE OSTI2016

Inference of reaction rate parameters based on summary statistics from experiments

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 shock-tube 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 Gauss-Hermite quadrature with Gaussian proposal probability density functions for moment computation resulting in orders of magnitude speedup in data likelihood evaluation. Despite the strong non-linearity 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 hydrogen-air auto-ignition computations to illustrate the need to account for correlation among the Arrhenius rate parameters of one reaction and across rate parameters of different reactions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Online mapping and forecasting of epidemics using open-source indicators

Open-source indicators have been proposed as a way of tracking and forecasting disease outbreaks. Some, such are meteorological data, are readily available as reanalysis products. Others, such as those derived from our online behavior (web searches, media article etc.) are gathered easily and are more timely than public health reporting. In this study we investigate how these datastreams may be combined to provide useful epidemiological information. The investigation is performed by building data assimilation systems to track influenza in California and dengue in India. The first does not suffer from incomplete data and was chosen to explore disease modeling needs. The second explores the case when observational data is sparse and disease modeling complexities are beside the point. The two test cases are for opposite ends of the disease tracking spectrum. We find that data assimilation systems that produce disease activity maps can be constructed. Further, being able to combine multiple open-source datastreams is a necessity as any one individually is not very informative. The data assimilation systems have very little in common except that they contain disease models, calibration algorithms and some ability to impute missing data. Thus while the data assimilation systems share the goal for accurate forecasting, they are practically designed to compensate for the shortcomings of the datastreams. Thus we expect them to be disease and location-specific.

42 ENGINEERING↗
DOE OSTI2016

Bayesian analysis of the flutter margin method in aeroelasticity

A Bayesian statistical framework is presented for Zimmerman and Weissenburger flutter margin method which considers the uncertainties in aeroelastic modal parameters. The proposed methodology overcomes the limitations of the previously developed least-square based estimation technique which relies on the Gaussian approximation of the flutter margin probability density function (pdf). Using the measured free-decay responses at subcritical (preflutter) airspeeds, the joint non-Gaussain posterior pdf of the modal parameters is sampled using the Metropolis–Hastings (MH) Markov chain Monte Carlo (MCMC) algorithm. The posterior MCMC samples of the modal parameters are then used to obtain the flutter margin pdfs and finally the flutter speed pdf. The usefulness of the Bayesian flutter margin method is demonstrated using synthetic data generated from a two-degree-of-freedom pitch-plunge aeroelastic model. The robustness of the statistical framework is demonstrated using different sets of measurement data. In conclusion, it will be shown that the probabilistic (Bayesian) approach reduces the number of test points required in providing a flutter speed estimate for a given accuracy and precision.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Convergence Study in Global Sensitivity Analysis

Monte Carlo (MC) sampling is a common method used to randomly sample a range of scenarios. The associated error follows a predictable rate of convergence of $1/\sqrt{N}$, such that quadrupling the sample size halves the error. This method is often employed in performing global sensitivity analysis which computes sensitivity indices, measuring fractional contributions of uncertain model inputs to the total output variance. In this study, several models are used to observe the rate of decay in the MC error in the estimation of the conditional variance, the total variance in the output, and the global sensitivity indices. The purpose is to examine the rate of convergence of the error in existing specialized, albeit MC-based, sampling methods for estimation of the sensitivity indices. It was found that the conditional variances and sensitivity indices all follow the $1/\sqrt{N}$ convergence rate. Future work will test the convergence of observables from more complex models such as ignition time in combustion.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations

A Bayesian model selection and parameter estimation algorithm is applied to investigate the influence of nonlinear and unsteady aerodynamic loads on the limit cycle oscillation (LCO) of a pitching airfoil in the transitional Reynolds number regime. At small angles of attack, laminar boundary layer trailing edge separation causes negative aerodynamic damping leading to the LCO. The fluid–structure interaction of the rigid, but elastically mounted, airfoil and nonlinear unsteady aerodynamics is represented by two coupled nonlinear stochastic ordinary differential equations containing uncertain parameters and model approximation errors. Several plausible aerodynamic models with increasing complexity are proposed to describe the aeroelastic system leading to LCO. The likelihood in the posterior parameter probability density function (pdf) is available semi-analytically using the extended Kalman filter for the state estimation of the coupled nonlinear structural and unsteady aerodynamic model. The posterior parameter pdf is sampled using a parallel and adaptive Markov Chain Monte Carlo (MCMC) algorithm. The posterior probability of each model is estimated using the Chib–Jeliazkov method that directly uses the posterior MCMC samples for evidence (marginal likelihood) computation. The Bayesian algorithm is validated through a numerical study and then applied to model the nonlinear unsteady aerodynamic loads using wind-tunnel test data at various Reynolds numbers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗