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Reducing parametric uncertainty in limit-cycle oscillation computational models

Published online by Cambridge University Press:  23 May 2017

R. Hayes ,
R. Dwight  and
S. Marques
R. Hayes
Affiliation:
Queen’s University Belfast, School of Mechanical & Aerospace Engineering, Belfast, Northern Ireland
R. Dwight
Affiliation:
Delft University of Technology, Aerospace Faculty, Delft, Netherlands
S. Marques*
Affiliation:
Queen’s University Belfast, School of Mechanical & Aerospace Engineering, Belfast, Northern Ireland
*
s.marques@qub.ac.uk
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Abstract

The assimilation of discrete data points with model predictions can be used to achieve a reduction in the uncertainty of the model input parameters, which generate accurate predictions. The problem investigated here involves the prediction of limit-cycle oscillations using a High-Dimensional Harmonic Balance (HDHB) method. The efficiency of the HDHB method is exploited to enable calibration of structural input parameters using a Bayesian inference technique. Markov-chain Monte Carlo is employed to sample the posterior distributions. Parameter estimation is carried out on a pitch/plunge aerofoil and two Goland wing configurations. In all cases, significant refinement was achieved in the distribution of possible structural parameters allowing better predictions of their true deterministic values. Additionally, a comparison of two approaches to extract the true values from the posterior distributions is presented.

Type
Research Article
Information
The Aeronautical Journal , Volume 121 , Issue 1241 , July 2017 , pp. 940 - 969
Copyright
Copyright © Royal Aeronautical Society 2017 

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References

REFERENCES

1. Pettit, C.L. Uncertainty quantification in aeroelasticity: Recent results and research challenges, J Aircr, 2004, 41, (5), pp 1217-1229.Google Scholar
2. Marques, S., Badcock, K.J., Khodaparast, H.H. and Mottershead, J.E. Transonic aeroelastic stability predictions under the influence of structural variability, J Aircr, 2010, 47, (4), pp 1229-1239.CrossRefGoogle Scholar
3. Marques, S., Badcock, K.J., Khodaparast, H.H. and Mottershead, J.E. How structural model variability influences transonic aeroelastic stability, J Aircr, 2012, 49, (5), pp 1189-1199.Google Scholar
4. Bunton, R.W. and Denegri, C.M. Limit cycle oscillation characteristics of fighter aircraft, J Aircr, 2000, 37, (5), pp 916-918.CrossRefGoogle Scholar
5. Thomas, J., Dowell, E., Hall, K. and Denegri, C. Modeling limit cycle oscillation behavior of the F-16 Fighter using a harmonic balance approach, 2004, AIAA-2004-1696, Presented at the 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Palm Springs, California, US.Google Scholar
6. Beran, P.S., Pettit, C.L. and Millman, D.R. Uncertainty quantification of limit-cycle oscillations, J Computational Physics, 2006, 217, (1), pp 217-247.Google Scholar
7. Witteveen, J.A.S., Loeven, A., Sarkar, S. and Bijl, H. Probabilistic collocation for period-1 limit cycle oscillations, J Sound and Vibration, 2008, 311, (1–2), pp 421-439.CrossRefGoogle Scholar
8. Le Meitour, J., Lucor, D. and Chassaing, C. Prediction of stochastic limit cycle oscillations using an adaptive polynomial chaos method, J Aeroelasticity and Structural Dynamics, 2010, 2, (1), pp 3-22.Google Scholar
9. Hayes, R. and Marques, S. Prediction of limit cycle oscillations under uncertainty using a harmonic balance method, Computers and Structures, 2015, 148, pp 1-13.CrossRefGoogle Scholar
10. Kennedy, M.C. and O’Hagan, A. Bayesian calibration of computer models, J Royal Statistical Soc B, 2001, 63, (3), pp 425-464.CrossRefGoogle Scholar
11. Tanner, M.A. Tools for Statistical Inference: Methods for the Exploration of Posterior Distributions and Likelihood Functions, 1996, Springer-Verlag, New York, US.CrossRefGoogle Scholar
12. Leonard, T. and Hsu, J.S.J. Bayesian Methods: An Analysis for Statisticians and Interdisciplinary Researchers, Cambridge Series in Statistical and Probabilistic Mathematics, volume 5, 1999, Cambridge University Press.Google Scholar
13. Congdon, P. Bayesian Statistical Modelling, Wiley Series in Probability and Statistics, John Wiley & Sons, 2006.CrossRefGoogle Scholar
14. Smith, R. Uncertainty Quantification Theory, Implementation, and Applications, Computational Science & Engineering, 2014, Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania, US.Google Scholar
15. Fellin, W. H., Lessmann, W., Oberguggenberger, M. and Vieider, R. Analyzing Uncertainty in Civil Engineering, 2005, Springer-Verlag, Berlin, Germany.CrossRefGoogle Scholar
16. Dwight, R.P., Haddad-Khodaparast, H. and Mottershead, J.E. Identifying structural variability using Bayesian inference, Proceedings of International Conference on Uncertainty in Structural Dynamics (ISMA/USD), Leuven, Belgium, 2012.Google Scholar
17. Oliver, T. and Moser, R. Bayesian uncertainty quantification applied to RANS turbulence models, J Physics: Conference Series, 2011, 318, 042032.Google Scholar
18. Edeling, W.N., Cinnella, P., Dwight, R.P. and Bijl, H. Bayesian estimates of parameter variability in the k-ε turbulence model, J Computational Physics, 2014, 258, pp 73-94 Google Scholar
19. Dwight, R.P., Bijl, H., Marques, S. and Badcock, K. Reducing uncertainty in aeroelastic flutter boundaries using experimental data, (IFASD-2011-71), 2011, Presented at the International Forum for Aeroelasticity and Structural Dynamics, Paris, France.Google Scholar
20. Hastings, W.K. Monte Carlo sampling methods using Markov chains and their applications, Biometrika, 1970, 57, (1), pp 97-109.Google Scholar
21. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H. and Teller, E. Equations of state calculations by fast computing machines, J Chemical Physics, 1953, 21, pp 1087-1092.Google Scholar
22. Hall, K.C., Thomas, J.P. and Clark, W.S. Computation of unsteady nonlinear flows in cascades using a harmonic balance technique, AIAA J, 2002, 40, (5), pp 879-886.Google Scholar
23. Liu, L., Thomas, J.P., Dowell, E.H., Attar, P. and Hall, K.C. A comparison of classical and high dimensional harmonic balance approaches for a duffing oscillator, J Computational Physics, 2006, 215, (1), pp 298-320.CrossRefGoogle Scholar
24. Thomas, J.P., Dowell, E.H. and Hall, K.C. Nonlinear inviscid aerodynamic effects on transonic divergence, flutter, and limit-cycle oscillations, AIAA J, 2002, 40, (4), pp 638-646.Google Scholar
25. Lee, B.H.K., Liu, L. and Chung, K.W. Airfoil motion in subsonic flow with strong cubic nonlinear restoring forces, J Sound and Vibration, 2005, 218, (3–5), pp 699-717.Google Scholar
26. Lee, B.H.K., Gong, L. and Wong, Y.S. Analysis and computation of nonlinear dynamic response of a two-degree-of-freedom system and its applications in aeroelasticity, J Fluids and Structures, 1997, 11, (FL960075), pp 225-246.Google Scholar
27. Bol’shev, L.N. Statistical Estimator:Encyclopedia of Mathematics, Springer, 2001.Google Scholar
28. Beran, P.S., Knot, N.S., Eastep, F.E., Synder, R.D. and Zweber, J.V. Numerical analysis of store-induced limit cycle oscillation, J Aircr, 2004, 41, (6), pp 1315-1326.CrossRefGoogle Scholar
29. Badcock, K.J., Khodaparast, H.H., Timme, S. and Mottershead, J.E. Calculating the influence of structural uncertainty on aeroelastic limit cycle response, AIAA-2011-1741, 2011, Presented at the 52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Denver, Colorado, US.Google Scholar
30. Platten, M.F., Wright, J.R., Worden, K., Dimitriadis, G. and Cooper, J.E. Non-linear identification in modal space using a genetic algorithm approach for model selection, Int J Applied Mathematics and Mech, 2007, 3, (1), pp 72-89.Google Scholar
31. Platten, M.F., Wright, J.R., Dimitriadis, G. and Cooper, J.E. Identification of multi-degree of freedom non-linear systems using an extended modal space approach, J Mech Systems and Signal Processing, 2009, 23, pp 8-29.Google Scholar
32. Eversman, W. and Tewari, A. Consistent rational-function approximation for unsteady aerodynamics, J Aircr, 1991, 28, (9), pp 545-552.Google Scholar
33. Dimitriadis, G., Vio, G.A. and Cooper, J.E. Application of higher-order harmonic balance to non-linear aeroelastic systems, AIAA-2006-2023, 2006, Presented at the 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Newport, Rhode Island, US.CrossRefGoogle Scholar
34. Segaran, T. Programming collective intelligence: Building smart Web 2.0 applications, 2007, O’Reilly Media, Inc.Google Scholar
35. Hayes, R., Marques, S. and Yao, W. The influence of structural modeshape variability on limit cycle oscillation behaviour, 2014, Paper presented at 15th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Atlanta, Georgia, US.Google Scholar