Encoding nonlinear and unsteady aerodynamics of limit cycle oscillations using nonlinear sparse Bayesian learning

Journal Article · Mon May 29 00:00:00 EDT 2023 · Journal of Sound and Vibration

DOI:https://doi.org/10.1016/j.jsv.2023.117816· OSTI ID:1986500

Sandhu, Rimple Singh ^[1]; Robinson, Brandon ^[2]; Khalil, Mohammad ^[3]; Pettit, Chris L. ^[4]; Poirel, Dominique ^[5]; Sarkar, Abhijit ^[2]

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1. Carleton University, Ottawa, ON (Canada); National Renewable Energy Laboratory (NREL), Golden, CO (United States)
2. Carleton University, Ottawa, ON (Canada)
3. Sandia National Laboratories (SNL-CA), Livermore, CA (United States)
4. US Naval Academy, Annapolis, MD (United States)
5. Royal Military College of Canada, Kingston, ON (Canada)

This article investigates the applicability of a recently proposed, nonlinear sparse Bayesian learning (NSBL) algorithm to identify and estimate the complex aerodynamics of limit cycle oscillations. NSBL provides a semi-analytical framework for determining the data-optimal sparse model nested within a (potentially) over-parameterized model. This is particularly relevant to nonlinear dynamical systems where modelling approaches involve the use of physics-based and data-driven components. In such cases, the data-driven components, where analytical descriptions of the physical processes are not readily available, are often prone to overfitting, meaning that the empirical aspects of these models will often involve the calibration of an unnecessarily large number of parameters. While an overparameterized model may fit the observed data well, such models may be inadequate for making predictions in regimes that are different from those wherein the data were recorded. In view of this, it is desirable to not only calibrate the model parameters, but also identify the optimal compromise between data fit and model complexity. In this article, we exhibit the optimal model discovery for an aeroelastic system wherein the structural dynamics are well-known and described by a differential equation model, coupled with a semi-empirical aerodynamic model for laminar separation flutter, resulting in low-amplitude limit cycle oscillations (LCO). To illustrate the performance of the algorithm, in this article, we use synthetic data and demonstrate the ability of the algorithm to correctly rediscover the optimal model and model parameters, given a known data-generating model. The synthetic data are generated from a forward simulation of a known differential equation model with parameters selected so as to mimic the dynamics observed in wind-tunnel experiments. Subsequently, we demonstrate the performance of the algorithm for model selection using noisy LCO data from wind tunnel experiments. As there is no ground truth available for the experimental data case, we provide a comparison between NSBL and Bayesian model selection to validate the results, and demonstrate the use of NSBL as an efficient alternative to traditional methods.

• Research Organization: National Renewable Energy Laboratory (NREL), Golden, CO (United States)
• Sponsoring Organization: USDOE Office of Energy Efficiency and Renewable Energy (EERE), Renewable Power Office. Wind Energy Technologies Office
• Grant/Contract Number: AC36-08GO28308
• OSTI ID: 1986500
• Report Number(s): NREL/JA--2C00-84301; MainId:85074; UUID:dabe3add-c396-4fab-931b-c49197616da2; MainAdminID:69345
• Journal Information: Journal of Sound and Vibration, Journal Name: Journal of Sound and Vibration Vol. 569; ISSN 0022-460X
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
Bayesian inference
aeroelasticity
inverse problems
nonlinear dynamics
sparse learning
unsteady aerodynamics