Reduced-Order Modeling for Limit-Cycle Oscillation Using Recurrent Artificial Neural Network

Yao, Weigang; Liou, Meng-Sing

doi:10.2514/6.2012-5446

Cited by 19 publications

(21 citation statements)

References 19 publications

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“…(1) must be determined through an optimization procedure. Because of the dynamic behavior of the model, and since the problem is formulated in the continuous time domain, simple linear least-square approaches cannot be used here [10,19].…”

Section: A Reduced-order Model Trainingmentioning

confidence: 99%

Reduced-Order Models for Computational-Fluid-Dynamics-Based Nonlinear Aeroelastic Problems

Mannarino

Dowell

2015

AIAA Journal

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In this work, a nonlinear state-space-based identification method is proposed to describe compactly unsteady aerodynamic responses. Such a reduced-order model is trained on a series of signals that implicitly represent the relationship between the structural motion and the aerodynamic loads. The determination of the model parameters is obtained through a two-level training procedure where, in the first stage, the matrices associated to the linear part of the model are computed by a robust subspace projection technique, whereas the remaining nonlinear terms are determined by an output error-minimization procedure in the second stage. The present approach is tested on two different problems, proving the convergence toward the reference results obtained by a computational fluid dynamics solver in linear and nonlinear, aerodynamic, and aeroelastic applications, whereas the aerodynamic reduced-order models are coupled with the related structural mechanical systems, demonstrating the ability of capturing the main nonlinear features of the response. The robustness of the reduced-order model is then tested considering a series of inputs with varying amplitudes and frequencies outside the range of interest and computing aeroelastic responses with nonnull pretwist angles. NomenclatureA a , B a , C a , D a = linear subparts of the reduced-order model b = half-chord, c∕2 E a , F a = nonlinear subparts of the reduced-order model f a = aerodynamic loads h, θ = plunge and pitch degrees of freedom k = ωc∕U ∞ ; reduced frequency N a = number of aerodynamic states, size of x a N out = number of aerodynamic output, size of f a q ∞ = 1 2 ρ ∞ U 2 ∞ ; dynamic pressure t = continuous time V = U ∞ ∕ω θ b μ p ; reduced velocity V bif = bifurcation speed x a = aerodynamic state x s = structural dynamics state β LE , β TE = leading-and trailing-edge control surface deflections μ = m∕πρ ∞ b; mass-to-fluid ratio τ = ω θ t; nondimensional time ϕx a = nonlinear functions of the aerodynamic reduced-order model ω i = natural frequency of the ith degree of freedom

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Section: A Reduced-order Model Trainingmentioning

confidence: 99%

Reduced-Order Models for Computational-Fluid-Dynamics-Based Nonlinear Aeroelastic Problems

Mannarino

Dowell

2015

AIAA Journal

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“…To further exercise the proposed method, a cropped-delta wing test case derived from reference [13], is explored. The wing plan form is shown in Fig.…”

Section: Delta Wingmentioning

confidence: 99%

“…For several years, the research community has developed Reduced Order Models (ROM) to avoid the penalty of full order time domain analysis. Several methods have been proposed and used, for example: Proper Orthogonal Decomposition (POD) [8,9], Volterra Series [10][11][12], Neural Networks [13]. Typically, ROMs lack generality as their application is dependent on the original parameters used in building the ROM.…”

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confidence: 99%

Prediction of Transonic Limit-Cycle Oscillations Using an Aeroelastic Harmonic Balance Method

Yao

Marques²

2015

AIAA Journal

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“…For several years, the research community has developed Reduced Order Models (ROM) to avoid the penalty of full order time domain analysis. Several methods have been proposed and used: Proper Orthogonal Decomposition (POD), 4, 5 Volterra Series, [6][7][8] Neural Networks, 9 etc. Typically, ROMs lack generality and their application is restricted to a limited vicinity of the original parameters used in building the ROM.…”

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confidence: 99%

Prediction of Transonic LCO using an Harmonic Balance Method

Yao

Marques

2014

44th AIAA Fluid Dynamics Conference

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This work proposes a novel approach to compute transonic Limit Cycle Oscillations using high fidelity analysis. CFD based Harmonic Balance methods have proven to be efficient tools to predict periodic phenomena. This paper's contribution is to present a new methodology to determine the unknown frequency of oscillations, enabling HB methods to accurately capture Limit Cycle Oscillations (LCOs); this is achieved by defining a frequency updating procedure based on a coupled CFD/CSD Harmonic Balance formulation to find the LCO condition. A pitch/plunge aerofoil and delta wing aerodynamic and respective linear structural models are used to validate the new method against conventional timedomain simulations. Results show consistent agreement between the proposed and timemarching methods for both LCO amplitude and frequency, while producing at least one order of magnitude reduction in computational time. * Research Fellow, MAIAA † Lecturer, MAIAA 1 of 20 Downloaded by UNIVERSITY OF TENNESSEE on August 8, 2015 | http://arc.aiaa.org | Nomenclature A = Harmonic Balance frequency domain matrix b, c = aerofoil semi-chord and chord, respectively D = Harmonic Balance operator matrix E = energy E = Tranformation matrix between frequency and time domains f = fluid force acting on structure F, G, H = convective fluxes for fluid equations h = plunge coordinate I = HB residual K = structure stiffness matrix L = frequency updating figure of merit M = structure mass matrix p = pressure R = vector of fluid and/or structural equation residual t = time step U ∞ = free-stream velocity u, v, w = fluid cartesian velocity components V, V s = reduced velocity and velocity index W = vector of fluid unknowns x, y = vector of structural unknowns α = angle of attack ω, κ = frequency and reduced frequency, κ = 2ω U∞c ρ = density τ = pseudo-time step

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Reduced-Order Modeling for Limit-Cycle Oscillation Using Recurrent Artificial Neural Network

Cited by 19 publications

References 19 publications

Reduced-Order Models for Computational-Fluid-Dynamics-Based Nonlinear Aeroelastic Problems

Reduced-Order Models for Computational-Fluid-Dynamics-Based Nonlinear Aeroelastic Problems

Prediction of Transonic Limit-Cycle Oscillations Using an Aeroelastic Harmonic Balance Method

Prediction of Transonic LCO using an Harmonic Balance Method

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