Local Reduced-Order Modeling and Iterative Sampling for Parametric Analyses of Aero-Icing Problems

Zhao, Zhan; Habashi, Wagdi G.; Fossati, Marco

doi:10.2514/1.j053654

Cited by 32 publications

(38 citation statements)

References 28 publications

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“…Instead of a unique global POD basis, several local bases are computed using machine learning tools yielding to more flexible behaviors bringing out a precise delimitation of the physical regimes. One can note that a comparable approach has been used for aero-icing certification [28]. The specificity of the presented method includes the introduction of a feature extraction with a shock sensor, a novel resampling strategy and the application to a aerodynamics case.…”

Section: Local Decomposition Methodsmentioning

confidence: 99%

“…The choice of the quantity characterizing the physical regimes, on which the clustering is performed, is a question of central importance impacting the quality of the classification. Usually, the unsupervised learning clusters directly the quantity of interest into groups with patterns of small differences [23,24,28]. However, the aim of the clustering in this paper is the physical regime separation and the previous approach can lead to classification error.…”

Section: Physical-based Shock Sensor To Detect Flow Regimesmentioning

confidence: 99%

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Surrogate Modeling of Aerodynamic Simulations for Multiple Operating Conditions Using Machine Learning

2018

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This article presents an original methodology for the prediction of steady turbulent aerodynamic fields. Due to the important computational cost of high-fidelity aerodynamic simulations, a surrogate model is employed to cope with the significant variations of several inflow conditions. Specifically, the Local Decomposition Method presented in this paper has been derived to capture nonlinear behaviors resulting from the presence of continuous and discontinuous signals. A combination of unsupervised and supervised learning algorithms is coupled with a physical criterion. It decomposes automatically the input parameter space, from a limited number of high-fidelity simulations, into subspaces. These latter correspond to different flow regimes. A measure of entropy identifies the subspace with the expected strongest non-linear behavior allowing to perform an active resampling on this low-dimensional structure. Local reduced-order models are built on each subspace using Proper Orthogonal Decomposition coupled with a multivariate interpolation tool. The methodology is assessed on the turbulent two-dimensional flow around the RAE2822 transonic airfoil. It exhibits a significant improvement in term of prediction accuracy for the Local Decomposition Method compared with the classical method of surrogate modeling for cases with different flow regimes. Nomenclature A= matrix of the reduced coordinates a k = k-th reduced coordinate B = matrix of the reduced coordinates of the sensor b k = k-th reduced coordinate of the sensorthe quantity of interest E = averaged normalized error f = high fidelity model g = acceleration due to the gravity or normal distribution H = global entropy h = altitude L = temperature lapse rate l = latent function matrix l = latent function M = Mach number m = number of predictions N = Gaussian probability distribution * PhD. Student, Embedded Systems Department, 118 route de Narbonne, Toulouse. n = number of training samples p = dimension of an input parameter or static pressure Q 2 = predictivity coefficient q = number of clusters r = specific gaz constant or correlation function S = matrix of the snapshots s i = quantity of interet at node i T = temperature U = velocity w = weight of the Gaussian Mixture Model X = horizontal coordinate along the chord Y = vertical coordinate y = target value α = angle of attack Γ = spatial domain δ = Kronecker symbol = energy ratio θ = hyperparameters λ = eigenvalues matrix λ = eigenvalues µ = mean of the Gaussian Process ρ = density Σ = covariance matrix σ 2 0 = prior covariance σ = sigmoid function τ w = wall shear stress Φ = mixture coefficient φ = proper orthogonal decomposition matrix χ = input parameter 1 C = hard splitting function = Subscripts = t = training p = prediction 0 = sea level ∞ = freestream = Superscripts = (k) = k-th component or element = fluctuating part = Operators= · = surrogate model · = mean | · | = absolute value · 2 = Euclidian norm (· , · ) = canonical inner product

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Section: Local Decomposition Methodsmentioning

confidence: 99%

Section: Physical-based Shock Sensor To Detect Flow Regimesmentioning

confidence: 99%

Surrogate Modeling of Aerodynamic Simulations for Multiple Operating Conditions Using Machine Learning

2018

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“…The most interesting features of POD is that it is linear and that, among all linear representations, it is also optimal, since it minimizes the average squared distance between the actual state of the system and its reduced counterpart. POD represents the system as a linear combination of primitives using the linear manifold in the configuration space represented by the data; therefore, it might show limitations when the nonlinearity of the original system is severe [24]. The mathematical treatment of POD is well covered in the literature and will be briefly outlined here following the method of snapshots proposed by Sirovich [29].…”

Section: B Proper Orthogonal Decomposition Via the Methods Of Snapshotsmentioning

confidence: 99%

“…In the area of fixed-wing aerodynamics, early works can be found that address only inviscid flows or two-dimensional problems, whereas more recent publications target more realistic three-dimensional geometries and viscous turbulent flows. Nonintrusive approaches are more popular when it comes to optimization, parametric analyses, and flow control [21,22]; whereas intrusive methods appear more frequently in the context of aeroelastic studies [23,24]. In the area of helicopter aerodynamics, the use of modal ROMs is not very well documented in the literature.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of Aerodynamic Loads via Reduced-Order Methodology

Fossati

2015

AIAA Journal

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Centroidal Voronoi tessellation, leave-one-out cross validation, proper orthogonal decomposition, and multidimensional interpolation are integrated to define a reduced-order modeling approach for the parametric evaluation of steady aerodynamic loads. The proper orthogonal decomposition-based methodology allows reducing the number of degrees of freedom of the problem while maintaining good accuracy for the solution of complex threedimensional viscous turbulent flows. As a result, it yields fairly accurate solutions at a fraction of the time required by standard computational fluid dynamics approaches. Three-dimensional examples for fixed-and rotary-wing cases of industrial relevance are used to assess the method in the cases of subsonic and transonic flow conditions.

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“…This might happen when relying for example on Proper Orthogonal Decomposition (POD) (Weller, Lombardi and Iollo 2009;Cazemier 1998) to identify the RBM modes. POD was introduced for the analysis of turbulent flows by Lumley (Lumley 1967) and it has been widely used in literature for both steady and unsteady problems (Stabile and Rozza 2018;Ripepi et al 2018;Stabile et al 2017;Ripepi and Goertz 2015;Zhan, Habashi and Fossati 2015;Iuliano and Quagliarella 2013;Carlberg and Farhat 2008;Lieu, Farhat and Lesoinne 2005;Bui-Thanh 2003;Legresley and Alonso 2000), since it allows to describe most of the information of the initial data set with the lowest number of modes possible (Holmes et al 2012). It identifies a basis, which is the closest to the set of snapshots in terms of an average projection error based on an energy norm.…”

Section: Introductionmentioning

confidence: 99%

Impact of POD modes energy redistribution on flow reconstruction for unsteady flows of impulsively started airfoils and wings

Pascarella

Fossati

Barrenechea

2019

International Journal of Computational Fluid Dynamics

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Obtaining accurate CFD solutions of unsteady flows during the design process of an aircraft can be a highly-demanding task in terms of computational and time resources. A common practice is the recourse to Reduced Basis Methods (RBM), which manage to reduce the number of degrees of freedom to be solved yet allow preserving high accuracy, as opposed for example to low-fidelity methods like vortexlattice or panel methods. RBM based on Proper Orthogonal Decomposition have been extensively studied and adopted but limitations are observed when trying to solve unsteady problems, where the temporal sequence of snapshots and the evolving nonlinear dynamics of the flow field need to be addressed carefully while building the reduced model. The present work investigates the problem of the accuracy in reconstructing nonlinear unsteady fluid flows by means of RBM methods for a specific class of impulsively started lifting bodies. The classical snapshot POD approach and a recent variant named Spectral POD will be comparatively studied to assess their capacity to reconstruct unsteady flow fields typical of aerospace applications. The periodic motion past a cylinder will be considered first as a benchmark test while the impulsive start of a 2D three element airfoil and a 3D wing in high-lift configurations will be considered as use cases.

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Local Reduced-Order Modeling and Iterative Sampling for Parametric Analyses of Aero-Icing Problems

Cited by 32 publications

References 28 publications

Surrogate Modeling of Aerodynamic Simulations for Multiple Operating Conditions Using Machine Learning

Surrogate Modeling of Aerodynamic Simulations for Multiple Operating Conditions Using Machine Learning

Evaluation of Aerodynamic Loads via Reduced-Order Methodology

Impact of POD modes energy redistribution on flow reconstruction for unsteady flows of impulsively started airfoils and wings

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