A Non-Intrusive Polynomial Chaos Method to Efficiently Quantify Uncertainty in an Aircraft T-Tail

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The problem of developing robust methods for uncertainty quantification (UQ) is of major interest in the engineering and scientific community. To quantify uncertainty, probabilistic models have been developed where traditionally Monte Carlo (MC) methods were used to capture uncertainty bounds. In the engineering context, UQ methods can be practically implemented to limit the amount of prototype redesigns. However MC methods are computationally inefficient due to the large number of samples required to obtain an accurate solution. Polynomial Chaos (PC) methods have recently emerged as an efficient method of probabilistic quantification in lower dimensions compared to MC. This paper will show the ability of a non-intrusive PC method to efficiently quantify uncertainty through first and second order statistics. This approach will lend itself to the treatment of a finite element T-Tail model, using Nastran as a black box around which PC curves can be fit based on its outputs.

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512-517

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July 2016

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© 2016 Trans Tech Publications Ltd. All Rights Reserved

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[1] V. Cirillo, A. Izzo, F. Marulo and B. Palumbo, Managing Uncertainties in Aero-Engine Combustor Design, in Proceedings of ISMA2010 including USD2010, (2010).

Google Scholar

[2] M. M. R. Williams, Polynomial Chaos Functions and Neutron Diffusion, Nuclear Science and Engineering, vol. 155, (2006).

Google Scholar

[3] C. L. Pettit, Uncertainty Quantification in Aeroelasticity: Recent Results and Research Challenges, Journal of Aircraft, vol. 41, no. 5, pp.1217-1229, (2004).

DOI: 10.2514/1.3961

Google Scholar

[4] J. G. Amar, The Monte Carlo method in Science and Engineering, Journal of Computing in Science & Engineering, vol. 8, no. 2, pp.9-19, (2006).

Google Scholar

[5] S. Kenny and L. Crespo, The Role of Uncertainty in Aerospace Vehicle Analysis and Design, NASA, Hampton, (2011).

Google Scholar

[6] N. Wiener, The Homogeneous Chaos, American Journal of Mathematics, vol. 60, no. 4, pp.897-936, (1938).

Google Scholar

[7] S. -K. Choi, R. V. Grandhi, R. A. Canfield and C. L. Pettit, Polynomial Chaos Expansion with Latin Hypercube Sampling for Estimating Response Variability, AIAA Journal, vol. 42, no. 6, pp.1191-1198, (2004).

DOI: 10.2514/1.2220

Google Scholar

[8] G. Blatman and B. Sudret, An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis, Journal of Probabilistic Engineering Mechanics, vol. 25, no. 2, pp.183-197, (2010).

DOI: 10.1016/j.probengmech.2009.10.003

Google Scholar

[9] D. Xiu, Numerical Methods for Stochastic Computations - A Spectral Method Approach, New York: Princeton University Press, (2010).

Google Scholar

[10] M. Gerritsma, J. Steen, P. Vos and G. Karniadakis, Time-dependent generalised polynomial chaos, Journal of Computational Physics, no. 229, pp.8333-8363, (2010).

DOI: 10.1016/j.jcp.2010.07.020

Google Scholar

[11] K. Sepahvand, S. Marburg and H. J. Hardtke, Numerical Solution Of One Dimensional Wave Equation With Stochastic Parameters Using Generalised Polynomial Chaos Expansion, Journal of Computational Acoustics, vol. 15, no. 4, pp.579-593, (2011).

DOI: 10.1142/s0218396x07003524

Google Scholar

[12] B. M. Ayyub, Uncertainty Modeling and Analysis in Civil Engineering, Boca Raton, Florida: CRC Press LLC, (1999).

Google Scholar

[13] M. Eldred and J. Burkardt, Comparison of Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Quantification, in AIAA Aeorospace Sciences Meeting, Orlando, Florida, (2009).

DOI: 10.2514/6.2009-976

Google Scholar

[14] E. Livne, The Effects of Damage on the Aeroelastic/ Aeroservoelastic Behaviour and Safety of Composite Aircraft, in JAMS Meeting, Washington, (2008).

Google Scholar

[15] B. P. Danowsky, J. R. Chrstos, D. H. Klyde, C. Farhat and M. Brenner, Evaluation of Aeroelastic Uncertainty Analysis Methods, Journal of Aircraft, vol. 47, no. 4, pp.1266-1273, (2010).

DOI: 10.2514/1.47118

Google Scholar

[16] A. Manan, Uncertainty and Robust Design in Aeroelastic Tailoring, University of Liverpool, (2009).

Google Scholar