Model-form and predictive uncertainty quantification in linear aeroelasticity

Nitschke, Christian Thomas; Cinnella, Paola; Lucor, Didier; Chassaing, Jean-Camille

doi:10.1016/j.jfluidstructs.2017.05.007

“…In all cases, the random variable η may involve additional parameters proper to the statistical model introduced for describing the error behavior, referred to as hyperparameters. Sometimes these are known before hand or are estimated independently based on likelihood maximization criteria [109] but most often they need to be calibrated from the data along with the physical model parameters θ. Another important point is that η is expected to correlate modeling errors for a QoI evaluated at different locations in the flow field or for even various QoI for various datasets.…”

Section: Accounting For Structural Uncertainties In Rans Modelsmentioning

confidence: 99%

Quantification of model uncertainty in RANS simulations: A review

Xiao

¹

,

Cinnella

²

2019

Progress in Aerospace Sciences

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In computational fluid dynamics simulations of industrial flows, models based on the Reynoldsaveraged Navier-Stokes (RANS) equations are expected to play an important role in decades to come. However, model uncertainties are still a major obstacle for the predictive capability of RANS simulations. This review examines both the parametric and structural uncertainties in turbulence models. We review recent literature on data-free (uncertainty propagation) and data-driven (statistical inference) approaches for quantifying and reducing model uncertainties in RANS simulations. Moreover, the fundamentals of uncertainty propagation and Bayesian inference are introduced in the context of RANS model uncertainty quantification. Finally, the literature on uncertainties in scale-resolving simulations is briefly reviewed with particular emphasis on large eddy simulations.

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“…A coherent framework for making predictions in situations where multiple competing models are available is represented by multi-model approaches, used in a plethora of applications including oil price predictions, meteorology, ground-water modeling, aerodynamics, and aeroelasticity [19][20][21][22][23][24][25][26]. Bayesian model averaging (BMA) [19,27] is among the most widely used multi-model approaches, where posterior average predictions are inferred by weighing individual forecasts from competing models based on their relative skill, with predictions from better performing models receiving higher weights than those of worse performing models.…”

Section: E-mail Addressesmentioning

confidence: 99%

“…beginning end beginning end (25) This z-score is theoretically distributed as standard normal variate.…”

Section: Bayesian Calibrationmentioning

confidence: 99%

Robust prediction of dense gas flows under uncertain thermodynamic models

Merle

¹

,

Cinnella

²

2019

Reliability Engineering & System Safety

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A Bayesian approach is developed to quantify uncertainties associated with the thermodynamic models used for the simulation of dense gas flows, i.e. flows of gases characterized by complex molecules of moderate to high molecular weight, in thermodynamic conditions of the general order of magnitude of the liquid/vapor critical point. The thermodynamic behaviour of dense gases can be modelled through equations of state with various mathematical structures, all involving a set of material-dependent coefficients. For several organic fluids of industrial interest abundant and high-quality thermodynamic data required to specify such coefficients are hardly available, leading to undetermined levels of uncertainty of the equation output. Additionally, the best choice for the kind of equation of state (mathematical form) to be used is not always easy to determine and it is often based on expert opinion. In other terms, equations of state introduce both parametric and model-form uncertainties, which need to be quantified to make reliable predictions of the flow field. In this paper we propose a statistical inference methodology for estimating both kinds of uncertainties simultaneously. Our approach consists of a calibration step and a prediction step. The former allows to infer on the parameters to be input to the equation of state, based on the observation of aerodynamic quantities like pressure measurements at some locations in the dense gas flow. The subsequent prediction step allows to predict unobserved flow configurations based on the inferred posterior distributions of the coefficients. Model-form uncertainties are incorporated in the prediction step by using a Bayesian model averaging (BMA) approach. This consists in constructing an average of the predictions of various competing models weighted by the posterior model probabilities. Bayesian averaging also provides a useful tool for making robust predictions from a set of alternative calibration scenarios (Bayesian model-scenario averaging or BMSA). The proposed methodology is assessed for a class of dense gas flows, namely transonic flows around an isolated airfoil, at various free-stream thermodynamic conditions in the dense-gas region.

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“…Xiao et al [14] emphasized the Bayesian inference technique (BIT) over the Kalman filter because BIT is more accurate and less time-consuming. BIT has been proven to be an efficient method for ill-posed heat transfer problems and other problems [25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Bayesian interface technique-based inverse estimation of closure coefficients of standard k − ϵ turbulence model by limiting the number of DNS data points for flow over a periodic hill

Kumar Chaurasia,

Chakraborty

2024

Inverse Problems

2

0

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Among different numerical methods for modeling turbulent flow, Reynolds-averaged Navier–Stokes (RANS) is the most commonly used and computationally reasonable. However, the accuracy of RANS is lower than that of other high-fidelity numerical methods. In this work, the uncertainties associated with the coefficients of the standard k − ϵ RANS turbulence model are estimated and calibrated to improve the accuracy. The calibration is performed by considering the coefficients individually as well as collectively. The first three coefficients of the standard k − ϵ turbulence model are calibrated among the five coefficients ( C μ , C ϵ 1 , C ϵ 2 , σ ϵ and σ k ). The Bayesian inference technique using the Metropolis–Hastings algorithm is applied to quantify uncertainties and calibration. Flow over a periodic hill is selected as a test case. The separation height of the bubble at x / h = 2 and x / h = 4 , along with the streamwise velocity at various locations, has been chosen as the quantities of interest for comparing the results with DNS. The calibration is performed using known high-fidelity data (direct numerical simulation) from the available data set. The velocity field is re-calculated from the calibrated closure coefficients and compared with the same calculated with the standard coefficients of k − ϵ turbulence model (baseline). The deviation of calibrated C µ is almost 50%–60% from baseline and for C ϵ 1 and C ϵ 2 it is 3%–12% and 6%–9% respectively. The algorithm is tested for different Reynold numbers and data points. A sensitivity analysis is also performed.

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Model-form and predictive uncertainty quantification in linear aeroelasticity

Cited by 7 publications

References 46 publications

Quantification of model uncertainty in RANS simulations: A review

Quantification of model uncertainty in RANS simulations: A review

Robust prediction of dense gas flows under uncertain thermodynamic models

Bayesian interface technique-based inverse estimation of closure coefficients of standard k − ϵ turbulence model by limiting the number of DNS data points for flow over a periodic hill

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