skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Bayesian analysis of the flutter margin method in aeroelasticity

Abstract

A Bayesian statistical framework is presented for Zimmerman and Weissenburger flutter margin method which considers the uncertainties in aeroelastic modal parameters. The proposed methodology overcomes the limitations of the previously developed least-square based estimation technique which relies on the Gaussian approximation of the flutter margin probability density function (pdf). Using the measured free-decay responses at subcritical (preflutter) airspeeds, the joint non-Gaussain posterior pdf of the modal parameters is sampled using the Metropolis–Hastings (MH) Markov chain Monte Carlo (MCMC) algorithm. The posterior MCMC samples of the modal parameters are then used to obtain the flutter margin pdfs and finally the flutter speed pdf. The usefulness of the Bayesian flutter margin method is demonstrated using synthetic data generated from a two-degree-of-freedom pitch-plunge aeroelastic model. The robustness of the statistical framework is demonstrated using different sets of measurement data. In conclusion, it will be shown that the probabilistic (Bayesian) approach reduces the number of test points required in providing a flutter speed estimate for a given accuracy and precision.

Authors:
 [1];  [2];  [3]
  1. Carleton Univ., Ottawa, ON (Canada); Sandia National Lab. (SNL-CA), Livermore, CA (United States)
  2. Royal Military College of Canada, Kingston, ON (Canada)
  3. Carleton Univ., Ottawa, ON (Canada)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1325157
Report Number(s):
SAND-2016-4788J
Journal ID: ISSN 0022-460X; 640508; TRN: US1700147
Grant/Contract Number:
AC04-94AL85000
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Sound and Vibration
Additional Journal Information:
Journal Name: Journal of Sound and Vibration; Journal ID: ISSN 0022-460X
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; aeroelasticity; coalescence flutter; Bayesian estimation; Metropolis-Hastings algorithm; non-Gaussian; parameter estimation

Citation Formats

Khalil, Mohammad, Poirel, Dominique, and Sarkar, Abhijit. Bayesian analysis of the flutter margin method in aeroelasticity. United States: N. p., 2016. Web. doi:10.1016/j.jsv.2016.07.016.
Khalil, Mohammad, Poirel, Dominique, & Sarkar, Abhijit. Bayesian analysis of the flutter margin method in aeroelasticity. United States. doi:10.1016/j.jsv.2016.07.016.
Khalil, Mohammad, Poirel, Dominique, and Sarkar, Abhijit. 2016. "Bayesian analysis of the flutter margin method in aeroelasticity". United States. doi:10.1016/j.jsv.2016.07.016. https://www.osti.gov/servlets/purl/1325157.
@article{osti_1325157,
title = {Bayesian analysis of the flutter margin method in aeroelasticity},
author = {Khalil, Mohammad and Poirel, Dominique and Sarkar, Abhijit},
abstractNote = {A Bayesian statistical framework is presented for Zimmerman and Weissenburger flutter margin method which considers the uncertainties in aeroelastic modal parameters. The proposed methodology overcomes the limitations of the previously developed least-square based estimation technique which relies on the Gaussian approximation of the flutter margin probability density function (pdf). Using the measured free-decay responses at subcritical (preflutter) airspeeds, the joint non-Gaussain posterior pdf of the modal parameters is sampled using the Metropolis–Hastings (MH) Markov chain Monte Carlo (MCMC) algorithm. The posterior MCMC samples of the modal parameters are then used to obtain the flutter margin pdfs and finally the flutter speed pdf. The usefulness of the Bayesian flutter margin method is demonstrated using synthetic data generated from a two-degree-of-freedom pitch-plunge aeroelastic model. The robustness of the statistical framework is demonstrated using different sets of measurement data. In conclusion, it will be shown that the probabilistic (Bayesian) approach reduces the number of test points required in providing a flutter speed estimate for a given accuracy and precision.},
doi = {10.1016/j.jsv.2016.07.016},
journal = {Journal of Sound and Vibration},
number = ,
volume = ,
place = {United States},
year = 2016,
month = 8
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 1work
Citation information provided by
Web of Science

Save / Share:
  • A review of the finite element method applied to the problem of supersonic aeroelastic stability of plates and shells is presented. The review is limited to linear models. Some new contributions in the field are presented and future trends are discussed. 105 refs., 18 figs., 6 tabs.
  • First-harmonic Fourier analysis of a gated blood-pool study is based on the assumption that the cardiac chambers contract once per cardiac cycle. In atrial arrhythmias this condition may not exist for the atria. We recently studied a patient with atrial flutter and 2:1 artioventricular conduction. There were predictable alterations in the first-harmonic Fourier phase and amplitude images. The observed changes from first-harmonic Fourier analysis were: (a) very low atrial amplitude values, and (b) absence of identifiable atrial regions on the phase image.
  • In this paper, the authors consider the local structure of energy functions for electric power networks near points (parameter values) of incipient flutter instability. Previous work by several investigators clearly indicate the subtle nature of energy functions and energy- like Lyapunov functions when the system exhibits such an instability mechanism. In fact the question of existence of an energy function under these circumstances has been raised. The issue is important because it is now well known that power systems with loads contain such bifurcation points. It is shown, herein, that a local energy function does exist in a sense consistentmore » with the inverse problem of analytical mechanics. However, sufficiently near points of flutter instability the energy function for both stable and unstable systems is not sign definite. Such an energy function can not be used as a Lyapunov function. Nevertheless, it is possible to obtain natural Lyapunov functions by combining the energy function with one or more additional first integrals. The analysis is based on the association of the linearized undamped power system with loads with a quadratic Hamiltonian system. General (universal) perturbations of the normal forms of the degenerate quadratic Hamiltonians at such bifurcation points are derived and lead to the stated conclusions. An example is included.« less
  • Previous attempts to harvest energy from aeroelastic vibrations have been based on attaching a beam to a moving wing or structure. Here, we exploit self-excited oscillations of a fluttering composite beam to harvest energy using piezoelectric transduction. Details of the beam properties and experimental setup are presented. The effects of preset angle of attack, wind speed, and load resistance on the levels of harvested power are determined. The results point to a complex relation between the aerodynamic loading and its impact on the static deflection and amplitudes of the limit cycle oscillations on one hand and the load resistance andmore » level of power harvested on the other hand.« less