Sparse identification of nonlinear unsteady aerodynamics of the oscillating airfoil

Abstract

Reduced-order models are widely used in aerospace engineering. A model for unsteady aerodynamics is desirable for designing the blades of wind turbines. Recently, sparse identification of nonlinear dynamics with control was introduced to identify the parameters of an input-output dynamical system. In this paper, two models for attached flows and one for separated flows are identified through this technique. For the unsteady lift of the attached flow, Model I is a linear model that presents the dynamic change of an unsteady lift to a static lift. Model II was built based on Model I in order to obtain a more general system with closed-loop control. It has a first-order inert element that delays the overall input of the static lift. The Model II results replicate the training data very well and give an accurate prediction of other oscillating cases with different oscillation amplitudes, reduced frequency or mean angle of attack. For the unsteady lift of the separated flow, Model III is identified as a nonlinear model, which also has a first-order inert element. This model captures the nonlinear aerodynamics of the separated flow and replicates the training cases well. In addition, the prediction of Model III has good agreement with the numerical results.

Modelling the unsteady lift of a pitching NACA 0018 aerofoil using state-space neural networks

“…In recent times, the abundance of numerical and experimental datasets has stimulated the use of data-driven methods. Many different data-driven modelling strategies have been investigated for the identification of unsteady aerodynamics systems, such as linear/linearised state-space models (Brunton, Rowley & Williams 2013;Dawson et al 2015), polynomial nonlinear state-space models (Decuyper et al 2018;Siddiqui et al 2022), block-oriented models (Kou, Zhang & Yin 2016) and the sparse identification of nonlinear dynamics method (Brunton, Proctor & Kutz 2016;Loiseau, Noack & Brunton 2018;Sun et al 2021). A promising data-driven technique is the state-space neural network (SS-NN) methodology (Schoukens 2021), which exploits the flexibility of artificial neural networks within a classical state-space representation.…”

“…2022), block-oriented models (Kou, Zhang & Yin 2016) and the sparse identification of nonlinear dynamics method (Brunton, Proctor & Kutz 2016; Loiseau, Noack & Brunton 2018; Sun et al. 2021). A promising data-driven technique is the state-space neural network (SS-NN) methodology (Schoukens 2021), which exploits the flexibility of artificial neural networks within a classical state-space representation.…”