Evaluation of Aerodynamic Loads via Reduced-Order Methodology

Fossati, Marco

doi:10.2514/1.j053755

Cited by 51 publications

(27 citation statements)

References 31 publications

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“…Local methods look for particular points which could improve the accuracy of the model. One can cite for example leave-one-out cross-validation [44] testing the sensibility of the surrogate model to each training sample. The more critical sample for the surrogate defines a neighborhood in which an extra snapshot is added.…”

Section: B An Entropy-based Active Resamplingmentioning

confidence: 99%

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: B An Entropy-based Active Resamplingmentioning

confidence: 99%

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

2018

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“…As anticipated above, this is consistent for n = 2 in equation (22), since it leads back to equation (20). However it is not rigorously correct to calculate all the moments of the Maxwellian needed to compute the high-resolution numerical fluxes [38,39]. A more rigorous methodology is here proposed to calculate the moments for thermally perfect gases where the hypothesis of calorically perfect gas is lost.…”

Section: Vibrational and Electronic Energy Modesmentioning

confidence: 99%

A kinetic BGK edge-based scheme including vibrational and electronic energy modes for high-Mach flows

et al. 2019

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“…These POD methods may be categorized as either intrusive or non-intrusive [19]. Galerkin projection is an example of an intrusive method.…”

Section: Pod-based Rommentioning

confidence: 99%

Reduced-order models for aerodynamic applications, loads and MDO

et al. 2018

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This article gives an overview of reduced order modeling work performed in the DLR project Digital-X. Parametric aerodynamic reduced order models (ROMs) are used to predict surface pressure distributions based on high-fidelity computational fluid dynamics (CFD), but at lower evaluation time and storage than the original CFD model. ROMs for steady aerodynamic applications are built using proper orthogonal decomposition (POD) and Isomap, a manifold learning method. Approximate solutions in the so obtained low-dimensional representations of the data are found with interpolation techniques, or by minimizing the corresponding steady flow-solver residual. The latter approach produces physics-based ROMs driven by the governing equations. The steady ROMs are used to predict the static aeroelastic loads in a multidisciplinary design and optimization (MDO) context, where the structural model is to be sized for the (aerodynamic) loads. They are also used in a process where an a priori identification of the critical load cases is of interest and the sheer number of load cases to be considered does not lend itself to high-fidelity CFD. An approach to correct a linear loads analysis model using steady CFD solutions at various Mach numbers and angles of attack and a ROM of the corrected Aerodynamic Influence Coefficients (AICs) is also shown. This results in a complete loads analysis model preserving aerodynamic nonlinearities while allowing fast evaluation across all model parameters. The different ROM methods are applied to a 3D test case of a transonic wing-body transport aircraft configuration. Keywords reduced order model • proper orthogonal decomposition • isomap • manifold learning • multidisciplinary design and optimization • aerodynamic influence coefficients • loads analysis • CFD

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Evaluation of Aerodynamic Loads via Reduced-Order Methodology

Cited by 51 publications

References 31 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

A kinetic BGK edge-based scheme including vibrational and electronic energy modes for high-Mach flows

Reduced-order models for aerodynamic applications, loads and MDO

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