Bayesian uncertainty analysis with applications to turbulence modeling

Cheung, Sai Hung; Oliver, Todd; Prudencio, Ernesto E.; Prudhomme, Serge; Moser, Robert D.

doi:10.1016/j.ress.2010.09.013

Cited by 222 publications

(191 citation statements)

References 24 publications

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“…It may include information both about the observational error on the data and the model error, including the effect of surrogate modeling if needed. In the following, we use a likelihood function resulting from a multiplicative/additive error model, similar to that used in [22] for calibrating the closure coefficients of turbulence model from measured velocity profiles in a turbulent boundary layer. We refer to [42], [22] and the references cited therein for more details about possible choices for the construction of likelihood functions.…”

Section: Bayesian Calibration Methodologymentioning

confidence: 99%

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Bayesian quantification of thermodynamic uncertainties in dense gas flows

Merle

Cinnella

2015

Reliability Engineering & System Safety

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. for a dense gas flow over a wing section. Flow thermodynamic conditions are such that the gas thermodynamic behavior strongly deviates from that of a perfect gas. In the aim of assessing the proposed methodology, synthetic calibration data -specifically, wall pressure data-are generated by running the numerical solver with a more complex and accurate thermodynamic model. The statistical model used to build the likelihood function includes a model-form inadequacy term, accounting for the gap between the model output associated to the best-fit parameters, and the true phenomenon. Results show that, for all of the relatively simple models under investigation, calibrations lead to informative posterior probability density distributions of the input parameters and improve the predictive distribution significantly. Nevertheless, calibrated parameters strongly differ from their expected physical values. The relationship between this behavior and model-form inadequacy is discussed.

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Section: Bayesian Calibration Methodologymentioning

confidence: 99%

“…The statistical model adopted is similar to that used in [22] and [23] to calibrate closure parameters of turbulence models for a boundary layer flow. The procedure includes a statistical "model-inadequacy" term accounting for the gap between the model response obtained with the best-fit parameters, and the (unobserved) true phenomenon.…”

Section: Introductionmentioning

confidence: 99%

Bayesian quantification of thermodynamic uncertainties in dense gas flows

Merle

Cinnella

2015

Reliability Engineering & System Safety

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“…In [11,12,15,19,20,24,29,32,39,[42][43][44]. In most applications to civil structures, authors have assumed that modelling uncertainties can be represented by independent Gaussian noise centered on zero.…”

Section: Bayesian Inferencementioning

confidence: 99%

“…When known, correlations can be included in the covariance matrix Σ. Outside of the scope of structural identification, authors such as Cheung et al [12] included spatially correlated uncertainties during the Bayesian identification of turbulent flow models. In the field of geophysics, Arroyo and Ordaz [3] include spatial decencies in multivariate Bayesian regression analyzes.…”

Section: Bayesian Inferencementioning

confidence: 99%

Structural identification with systematic errors and unknown uncertainty dependencies

Goulet

Smith

2013

Computers & Structures

121

124

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“…This process is known as estimating the "structural" or "model-form" error in RANS models and has been performed for simple flows e.g., channel flow, flow over flat plate etc. [27,28,29]. However, the method is very data-intensive i.e., in order to estimate the structural error, the "good" DNS/LES results have to be made available at each point of the RANS mesh.…”

Section: Introductionmentioning

confidence: 99%

Tuning a RANS k-e model for jet-in-crossflow simulations.

Lefantzi¹,

Ray²,

Arunajatesan³

et al. 2013

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We develop a novel calibration approach to address the problem of predictive k − ε RANS simulations of jet-incrossflow. Our approach is based on the hypothesis that predictive k − ε parameters can be obtained by estimating them from a strongly vortical flow, specifically, flow over a square cylinder. In this study, we estimate three k − ε parameters, C µ , C ε2 and C ε1 by fitting 2D RANS simulations to experimental data. We use polynomial surrogates of 2D RANS for this purpose. We conduct an ensemble of 2D RANS runs using samples of (C µ ,C ε2 ,C ε1 ) and regress Reynolds stresses to the samples using a simple polynomial. We then use this surrogate of the 2D RANS model to infer a joint distribution for the k − ε parameters by solving a Bayesian inverse problem, conditioned on the experimental data. The calibrated (C µ ,C ε2 ,C ε1 ) distribution is used to seed an ensemble of 3D jet-in-crossflow simulations. We compare the ensemble's predictions of the flowfield, at two planes, to PIV measurements and estimate the predictive skill of the calibrated 3D RANS model. We also compare it against 3D RANS predictions using the nominal (uncalibrated) values of (C µ ,C ε2 ,C ε1 ), and find that calibration delivers a significant improvement to the predictive skill of the 3D RANS model. We repeat the calibration using surrogate models based on kriging and find that the calibration, based on these more accurate models, is not much better that those obtained with simple polynomial surrogates. We discuss the reasons for this rather surprising outcome.

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Bayesian uncertainty analysis with applications to turbulence modeling

Cited by 222 publications

References 24 publications

Bayesian quantification of thermodynamic uncertainties in dense gas flows

Bayesian quantification of thermodynamic uncertainties in dense gas flows

Structural identification with systematic errors and unknown uncertainty dependencies

Tuning a RANS k-e model for jet-in-crossflow simulations.

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