# Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations

## Abstract

A Bayesian model selection and parameter estimation algorithm is applied to investigate the influence of nonlinear and unsteady aerodynamic loads on the limit cycle oscillation (LCO) of a pitching airfoil in the transitional Reynolds number regime. At small angles of attack, laminar boundary layer trailing edge separation causes negative aerodynamic damping leading to the LCO. The fluid–structure interaction of the rigid, but elastically mounted, airfoil and nonlinear unsteady aerodynamics is represented by two coupled nonlinear stochastic ordinary differential equations containing uncertain parameters and model approximation errors. Several plausible aerodynamic models with increasing complexity are proposed to describe the aeroelastic system leading to LCO. The likelihood in the posterior parameter probability density function (pdf) is available semi-analytically using the extended Kalman filter for the state estimation of the coupled nonlinear structural and unsteady aerodynamic model. The posterior parameter pdf is sampled using a parallel and adaptive Markov Chain Monte Carlo (MCMC) algorithm. The posterior probability of each model is estimated using the Chib–Jeliazkov method that directly uses the posterior MCMC samples for evidence (marginal likelihood) computation. The Bayesian algorithm is validated through a numerical study and then applied to model the nonlinear unsteady aerodynamic loads using wind-tunnel test data at variousmore »

- Authors:

- Department of Civil and Environmental Engineering, Carleton University, Ottawa, Ontario (Canada)
- Department of Mechanical and Aerospace Engineering, Royal Military College of Canada, Kingston, Ontario (Canada)
- Department of Aerospace Engineering, United States Naval Academy, Annapolis, MD (United States)

- Publication Date:

- OSTI Identifier:
- 22572328

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Computational Physics

- Additional Journal Information:
- Journal Volume: 316; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9991

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AERODYNAMICS; ALGORITHMS; APPROXIMATIONS; BOUNDARY LAYERS; COMPUTERIZED SIMULATION; DIFFERENTIAL EQUATIONS; FLUID-STRUCTURE INTERACTIONS; LIMIT CYCLE; MARKOV PROCESS; MONTE CARLO METHOD; NONLINEAR PROBLEMS; NUMERICAL ANALYSIS; OSCILLATIONS; PROBABILITY DENSITY FUNCTIONS; REYNOLDS NUMBER; WIND TUNNELS

### Citation Formats

```
Sandhu, Rimple, Poirel, Dominique, Pettit, Chris, Khalil, Mohammad, and Sarkar, Abhijit, E-mail: abhijit.sarkar@carleton.ca.
```*Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations*. United States: N. p., 2016.
Web. doi:10.1016/J.JCP.2016.03.006.

```
Sandhu, Rimple, Poirel, Dominique, Pettit, Chris, Khalil, Mohammad, & Sarkar, Abhijit, E-mail: abhijit.sarkar@carleton.ca.
```*Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations*. United States. doi:10.1016/J.JCP.2016.03.006.

```
Sandhu, Rimple, Poirel, Dominique, Pettit, Chris, Khalil, Mohammad, and Sarkar, Abhijit, E-mail: abhijit.sarkar@carleton.ca. Fri .
"Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations". United States. doi:10.1016/J.JCP.2016.03.006.
```

```
@article{osti_22572328,
```

title = {Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations},

author = {Sandhu, Rimple and Poirel, Dominique and Pettit, Chris and Khalil, Mohammad and Sarkar, Abhijit, E-mail: abhijit.sarkar@carleton.ca},

abstractNote = {A Bayesian model selection and parameter estimation algorithm is applied to investigate the influence of nonlinear and unsteady aerodynamic loads on the limit cycle oscillation (LCO) of a pitching airfoil in the transitional Reynolds number regime. At small angles of attack, laminar boundary layer trailing edge separation causes negative aerodynamic damping leading to the LCO. The fluid–structure interaction of the rigid, but elastically mounted, airfoil and nonlinear unsteady aerodynamics is represented by two coupled nonlinear stochastic ordinary differential equations containing uncertain parameters and model approximation errors. Several plausible aerodynamic models with increasing complexity are proposed to describe the aeroelastic system leading to LCO. The likelihood in the posterior parameter probability density function (pdf) is available semi-analytically using the extended Kalman filter for the state estimation of the coupled nonlinear structural and unsteady aerodynamic model. The posterior parameter pdf is sampled using a parallel and adaptive Markov Chain Monte Carlo (MCMC) algorithm. The posterior probability of each model is estimated using the Chib–Jeliazkov method that directly uses the posterior MCMC samples for evidence (marginal likelihood) computation. The Bayesian algorithm is validated through a numerical study and then applied to model the nonlinear unsteady aerodynamic loads using wind-tunnel test data at various Reynolds numbers.},

doi = {10.1016/J.JCP.2016.03.006},

journal = {Journal of Computational Physics},

issn = {0021-9991},

number = ,

volume = 316,

place = {United States},

year = {2016},

month = {7}

}