Jaideep Ray

Bayesian calibration of a k-ε turbulence model for predictive jet-in-crossflow simulations

‡§ We propose a Bayesian method to calibrate parameters of a RANS model to improve its predictive skill in jet-in-crossflow simulations. The method is based on the hypotheses that (1) informative parameters can be estimated from experiments of flow configurations that display the same, strongly vortical features of jet-in-crossflow interactions and (2) one can construct surrogates of RANS models for certain judiciously chosen RANS outputs which serve as calibration variables (alternatively, experimental observables). We estimate three ke parameters (C∝, C 2 , C 1 ) from Reynolds stress measurements from an incompressible flowover-a-square-cylinder experiment. The k-e parameters are estimated as a joint probability density function. Jet-in-crossflow simulations performed with (C∝, C 2 , C 1 ) samples drawn from this distribution are seen to provide far better predictions than those obtained with nominal parameter values. We also find a (C∝, C 2 , C 1 ) combination which provides < 15% error in a number of performance metrics; in contrast, the errors obtained with nominal parameter values may exceed 60%.

Bayesian Calibration of a RANS Model with a Complex Response Surface - A Case Study with Jet-in-Crossflow Configuration

We demonstrate a Bayesian method that can be used to calibrate computationally expensive 3D RANS models with complex response surfaces. Such calibrations, conditioned on experimental data, can yield turbulence model parameters as probability density functions (PDF), concisely capturing the uncertainty in the estimation. Methods such as Markov chain Monte Carlo construct the PDF by sampling, and consequently a quickrunning surrogate is used instead of the RANS simulator. The surrogate can be very difficult to design if the model’s response i.e., the dependence of the calibration variable (the observable) on the parameters being estimated is complex. We show how the training data used to construct the surrogate models can also be employed to isolate a promising and physically realistic part of the parameter space, within which the response is wellbehaved and easily modeled. We design a classifier, based on treed linear models, to model the “well-behaved region”. This classifier serves as a prior in a Bayesian calibration study aimed at estimating 3 k − parameters C = (Cμ, C 2, C 1) from experimental data of a transonic jet-in-crossflow interaction. The robustness of the calibration is investigated by checking its predictions of variables not included in the calibration data. We also check the limit of applicability of the calibration by testing at an off-calibration point.

Robust Bayesian Calibration of a RANS Model for Jet-in-Crossflow Simulations

Compressible jet-in-crossflow interactions are poorly simulated using Reynolds-Averaged Navier Stokes (RANS) equations. This is due to model-form errors (physical approximations) in RANS as well as the use of parameter values simply picked from literature (henceforth, the nominal values of the parameters). Previous work on the Bayesian calibration of RANS models has yielded joint probability densities of C = (Cμ, C 2, C 1), the most influential parameters of the RANS equations. The calibrated values were far more predictive than the nominal parameter values and the advantage held across a range of freestream Mach numbers and jet strengths. In this work we perform Bayesian calibration across a range of Mach numbers and jet strengths and compare the joint densities, with a view of determining whether compressible jet-in-crossflow could be simulated with either a single joint probability density or a point estimate for C. We find that probability densities for C 2 agree and also indicate that the range typically used in aerodynamic simulations should be extended. The densities for C 1 agree, approximately, with the nominal value. The densities for Cμ do not show any clear trend, indicating that they are not strongly constrained by the calibration observables, and in turn, do not affect them much. We also compare the calibrated results to a recently developed analytical model of a jet-in-crossflow interaction. We find that the values of C estimated by the analytical model delivers prediction accuracies comparable to the calibrated joint densities of the parameters across a range of Mach numbers and jet strengths.

Efficient uncertainty quantification methodologies for high-dimensional climate land models.

In this report, we proposed, examined and implemented approaches for performing efficient uncertainty quantification (UQ) in climate land models. Specifically, we applied Bayesian compressive sensing framework to a polynomial chaos spectral expansions, enhanced it with an iterative algorithm of basis reduction, and investigated the results on test models as well as on the community land model (CLM). Furthermore, we discussed construction of efficient quadrature rules for forward propagation of uncertainties from high-dimensional, constrained input space to output quantities of interest. The work lays grounds for efficient forward UQ for high-dimensional, strongly non-linear and computationally costly climate models. Moreover, to investigate parameter inference approaches, we have applied two variants of the Markov chain Monte Carlo (MCMC) method to a soil moisture dynamics submodel of the CLM. The evaluation of these algorithms gave us a good foundation for further building out the Bayesian calibration framework towards the goal of robust component-wise calibration.

Estimation of k-ε parameters using surrogate models and jet-in-crossflow data

We demonstrate a Bayesian method that can be used to calibrate computationally expensive 3D RANS (Reynolds Av- eraged Navier Stokes) models with complex response surfaces. Such calibrations, conditioned on experimental data, can yield turbulence model parameters as probability density functions (PDF), concisely capturing the uncertainty in the parameter estimates. Methods such as Markov chain Monte Carlo (MCMC) estimate the PDF by sampling, with each sample requiring a run of the RANS model. Consequently a quick-running surrogate is used instead to the RANS simulator. The surrogate can be very difficult to design if the models response i.e., the dependence of the calibration variable (the observable) on the parameter being estimated is complex. We show how the training data used to construct the surrogate can be employed to isolate a promising and physically realistic part of the parameter space, within which the response is well-behaved and easily modeled. We design a classifier, based on treed linear models, to model the well-behaved region. This classifier serves as a prior in a Bayesian calibration study aimed at estimating 3 k [?] e parameters ( C u , C e 2 , C e 1 ) from experimental data of a transonic jet-in-crossflow interaction. Themorexa0» robustness of the calibration is investigated by checking its predictions of variables not included in the cal- ibration data. We also check the limit of applicability of the calibration by testing at off-calibration flow regimes. We find that calibration yield turbulence model parameters which predict the flowfield far better than when the nomi- nal values of the parameters are used. Substantial improvements are still obtained when we use the calibrated RANS model to predict jet-in-crossflow at Mach numbers and jet strengths quite different from those used to generate the ex- perimental (calibration) data. Thus the primary reason for poor predictive skill of RANS, when using nominal values of the turbulence model parameters, was parametric uncertainty, which was rectified by calibration. Post-calibration, the dominant contribution to model inaccuraries are due to the structural errors in RANS.«xa0less

Kalman-filtered compressive sensing for high resolution estimation of anthropogenic greenhouse gas emissions from sparse measurements.

The estimation of fossil-fuel CO2 emissions (ffCO2) from limited ground-based and satellite measurements of CO2 concentrations will form a key component of the monitoring of treaties aimed at the abatement of greenhouse gas emissions. The limited nature of the measured data leads to a severely-underdetermined estimation problem. If the estimation is performed at fine spatial resolutions, it can also be computationally expensive. In order to enable such estimations, advances are needed in the spatial representation of ffCO2 emissions, scalable inversion algorithms and the identification of observables to measure. To that end, we investigate parsimonious spatial parameterizations of ffCO2 emissions which can be used in atmospheric inversions. We devise and test three random field models, based on wavelets, Gaussian kernels and covariance structures derived from easily-observed proxies of human activity. In doing so, we constructed a novel inversion algorithm, based on compressive sensing and sparse reconstruction, to perform the estimation. We also address scalable ensemble Kalman filters as an inversion mechanism and quantify the impact of Gaussian assumptions inherent in them. We find that the assumption does not impact the estimates of mean ffCO2 source strengths appreciably, but a comparison with Markov chain Monte Carlo estimates show significant differences in themorexa0» variance of the source strengths. Finally, we study if the very different spatial natures of biogenic and ffCO2 emissions can be used to estimate them, in a disaggregated fashion, solely from CO2 concentration measurements, without extra information from products of incomplete combustion e.g., CO. We find that this is possible during the winter months, though the errors can be as large as 50%.«xa0less

An approach for estimating the uncertainty in ParaDiS predictions.

This report outlines an approach for computing the uncertainties in the predictions of computationally expensive models. While general, we use ParaDiS , a dislocation dynamics simulator originating in Lawrence Livermore National Laboratory, as the target application. ParaDiS is a mesoscale model, and uses submodels constructed/upscaled from microscale (molecular statics and dynamics) simulations. ParaDiS outputs, in turn, are upscaled and used in continuum (macroscale) simulations, e.g., those performed by ALE3D. This report addresses how one may quantify the uncertainties introduced by upscaling (both from microscale to mesoscale, and mesoscale to continuum), and the dependence of uncertainties in ParaDiS predictions on those of the inputs. This dependence is established via sensitivity analysis, and we address how this may be performed with a minimum of ParaDiS runs, given its immense computational cost. This includes constructing a smaller version of the model, sparse sampling of the parameter space, and exploiting the asymptotic nature of the time-evolution of the model outputs. The report concludes with a discussion of the computational resources required to perform this uncertainty quantification study.