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Estimation of Model Error Using Bayesian ModelScenario Averaging with Maximum a PosteroriEstimates
http://hdl.handle.net/10985/15499
Estimation of Model Error Using Bayesian ModelScenario Averaging with Maximum a PosteroriEstimates
SCHMELZER, Martin; DWIGHT, Richard P.; EDELING, Wouter Nico; CINNELLA, Paola
http://hdl.handle.net/10985/15499
SCHMELZER, Martin
DWIGHT, Richard P.
EDELING, Wouter Nico
CINNELLA, Paola

DataDriven Deterministic Symbolic Regression of Nonlinear StressStrain Relation for RANS Turbulence Modelling
http://hdl.handle.net/10985/15556
DataDriven Deterministic Symbolic Regression of Nonlinear StressStrain Relation for RANS Turbulence Modelling
SCHMELZER, Martin; DWIGHT, Richard P.; CINNELLA, Paola
This work presents developments towards a deterministic symbolic regression method to derive algebraic Reynoldsstress models for the ReynoldsAveraged NavierStokes (RANS) equations. The models are written as tensor polynomials, for which optimal coe cients are found using Bayesian inversion. These coe cient fields are the targets for the symbolic regression. A method is presented based on a regularisation strategy in order to promote sparsity of the inferred models and is applied to highfidelity data. By being datadriven the method reduces the assumptions commonly made in the process of model development in order to increase the predictive fidelity of algebraic models.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10985/15556
20180101T00:00:00Z
SCHMELZER, Martin
DWIGHT, Richard P.
CINNELLA, Paola
This work presents developments towards a deterministic symbolic regression method to derive algebraic Reynoldsstress models for the ReynoldsAveraged NavierStokes (RANS) equations. The models are written as tensor polynomials, for which optimal coe cients are found using Bayesian inversion. These coe cient fields are the targets for the symbolic regression. A method is presented based on a regularisation strategy in order to promote sparsity of the inferred models and is applied to highfidelity data. By being datadriven the method reduces the assumptions commonly made in the process of model development in order to increase the predictive fidelity of algebraic models.

Bayesian Predictions of ReynoldsAveraged Navier–Stokes Uncertainties Using Maximum a Posteriori Estimates
http://hdl.handle.net/10985/15497
Bayesian Predictions of ReynoldsAveraged Navier–Stokes Uncertainties Using Maximum a Posteriori Estimates
CINNELLA, Paola; SCHMELZER, Martin; EDELING, Wouter Nico
Computational fluid dynamics analyses of highReynoldsnumber flows mostly rely on the Reynoldsaveraged Navier–Stokes equations. The associated closure models are based on multiple simplifying assumptions and involve numerous empirical closure coefficients, which are calibrated on a set of simple reference flows. Predicting new flows using a single closure model with nominal values for the closure coefficients may lead to biased predictions. Bayesian modelscenario averaging is a statistical technique providing an optimal way to combine the predictions of several competing models calibrated on various sets of data (scenarios). The method allows a stochastic estimate of a quantity of interest in an unmeasured prediction scenario to be obtain by 1) propagating posterior probability distributions of the parameters obtained for multiple calibration scenarios, and 2) computing a weighted posterior predictive distribution. Although step 2 has a negligible computational cost, step 1 requires a large number of samples of the solver. To enable the application of the proposed approach to computationally expensive flow configurations, a modified formulation is used where a maximum posterior probability approximation is used to drastically reduce the computational burden. The predictive capability of the proposed simplified approach is assessed for twodimensional separated and threedimensional compressible flows.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10985/15497
20180101T00:00:00Z
CINNELLA, Paola
SCHMELZER, Martin
EDELING, Wouter Nico
Computational fluid dynamics analyses of highReynoldsnumber flows mostly rely on the Reynoldsaveraged Navier–Stokes equations. The associated closure models are based on multiple simplifying assumptions and involve numerous empirical closure coefficients, which are calibrated on a set of simple reference flows. Predicting new flows using a single closure model with nominal values for the closure coefficients may lead to biased predictions. Bayesian modelscenario averaging is a statistical technique providing an optimal way to combine the predictions of several competing models calibrated on various sets of data (scenarios). The method allows a stochastic estimate of a quantity of interest in an unmeasured prediction scenario to be obtain by 1) propagating posterior probability distributions of the parameters obtained for multiple calibration scenarios, and 2) computing a weighted posterior predictive distribution. Although step 2 has a negligible computational cost, step 1 requires a large number of samples of the solver. To enable the application of the proposed approach to computationally expensive flow configurations, a modified formulation is used where a maximum posterior probability approximation is used to drastically reduce the computational burden. The predictive capability of the proposed simplified approach is assessed for twodimensional separated and threedimensional compressible flows.

CFDdriven symbolic identification of algebraic Reynoldsstress models
http://hdl.handle.net/10985/23745
CFDdriven symbolic identification of algebraic Reynoldsstress models
BEN HASSAN SAIDI, Ismaïl; SCHMELZER, Martin; CINNELLA, Paola; GRASSO, Francesco
Reynoldsstress models (EARSM) from highfidelity data is developed building on the frozentraining SpaRTA algorithm of [1]. Corrections for the Reynolds stress tensor and the production of transported turbulent quantities of a baseline linear eddy viscosity model (LEVM) are expressed as functions of tensor polynomials selected from a library of candidate functions. The CFDdriven training consists in solving a blackbox optimization problem in which the fitness of candidate EARSM models is evaluated by running RANS simulations. The procedure enables training models against any target quantity of interest, computable as an output of the CFD model. Unlike the frozentraining approach, the proposed methodology is not restricted to data sets for which full fields of highfidelity data, including second flow order statistics, are available. However, the solution of a highdimensional expensive blackbox function optimization problem is required. Several steps are then undertaken to reduce the associated computational burden. First, a sensitivity analysis is used to identify the most influential terms and to reduce the dimensionality of the search space. Afterwards, the Constrained Optimization using Response Surface (CORS) algorithm, which approximates the blackbox cost function using a response surface constructed from a limited number of CFD solves, is used to find the optimal model parameters. Model discovery and crossvalidation is performed for three configurations of 2D turbulent separated flows in channels of variable section using different sets of training data to show the flexibility of the method. The discovered models are then applied to the prediction of an unseen 2D separated flow with higher Reynolds number and different geometry. The predictions of the discovered models for the new case are shown to be not only more accurate than the baseline LEVM, but also of a multipurpose EARSM model derived from purely physical arguments. The proposed deterministic symbolic identification approach constitutes a promising candidate for building accurate and robust RANS models customized for a given class of flows at moderate computational cost.
©2022 Elsevier Inc. All rights reserved.
Tue, 01 Feb 2022 00:00:00 GMT
http://hdl.handle.net/10985/23745
20220201T00:00:00Z
BEN HASSAN SAIDI, Ismaïl
SCHMELZER, Martin
CINNELLA, Paola
GRASSO, Francesco
Reynoldsstress models (EARSM) from highfidelity data is developed building on the frozentraining SpaRTA algorithm of [1]. Corrections for the Reynolds stress tensor and the production of transported turbulent quantities of a baseline linear eddy viscosity model (LEVM) are expressed as functions of tensor polynomials selected from a library of candidate functions. The CFDdriven training consists in solving a blackbox optimization problem in which the fitness of candidate EARSM models is evaluated by running RANS simulations. The procedure enables training models against any target quantity of interest, computable as an output of the CFD model. Unlike the frozentraining approach, the proposed methodology is not restricted to data sets for which full fields of highfidelity data, including second flow order statistics, are available. However, the solution of a highdimensional expensive blackbox function optimization problem is required. Several steps are then undertaken to reduce the associated computational burden. First, a sensitivity analysis is used to identify the most influential terms and to reduce the dimensionality of the search space. Afterwards, the Constrained Optimization using Response Surface (CORS) algorithm, which approximates the blackbox cost function using a response surface constructed from a limited number of CFD solves, is used to find the optimal model parameters. Model discovery and crossvalidation is performed for three configurations of 2D turbulent separated flows in channels of variable section using different sets of training data to show the flexibility of the method. The discovered models are then applied to the prediction of an unseen 2D separated flow with higher Reynolds number and different geometry. The predictions of the discovered models for the new case are shown to be not only more accurate than the baseline LEVM, but also of a multipurpose EARSM model derived from purely physical arguments. The proposed deterministic symbolic identification approach constitutes a promising candidate for building accurate and robust RANS models customized for a given class of flows at moderate computational cost.
©2022 Elsevier Inc. All rights reserved.