Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-22T14:42:18.875Z Has data issue: false hasContentIssue false
  • English
  • Français

A semi-intrusive stochastic perturbation method for lift prediction and global sensitivity analysis

Published online by Cambridge University Press:  03 August 2017

Anup Suryawanshi  and
Debraj Ghosh
Anup Suryawanshi
Affiliation:
Subduction Zone Consultants, Pune, Maharashtra, India
Debraj Ghosh*
Affiliation:
Department of Civil Engineering, Indian Institute of Science, Bangalore, India
*
Reprint requests to: Debraj Ghosh, Department of Civil Engineering, Indian Institute of Science, Bangalore, India 560012. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Sensitivity analysis plays an important role in finding an optimal design of a structure under uncertainty. Quantifying relative importance of random parameters, which leads to a rank ordering, helps in developing a systematic and efficient way to reach the optimal design. In this work, lift prediction and sensitivity analysis of a potential flow around a submerged body is considered. Such flow is often used in the initial design stage of structures. The flow computation is carried out using a vortex-panel method. A few parameters of the submerged body and flow are considered as random variables. To improve the accuracy in lift prediction in a computationally efficient way, a new semi-intrusive stochastic perturbation method is proposed. Accordingly, a perturbation is applied at the linear system solving level involving the inuence coefficient matrix, as opposed to using perturbation in the lift quantity itself. This proposed method, which is partially analogous to the intrusive or Galerkin projection methods in spectral stochastic finite element methods, is found to be more accurate than using perturbation directly on the lift and faster than a direct simulation. The proposed semi-intrusive stochastic perturbation method is found to yield faster estimates of the Sobol’ indices, which are used for global sensitivity analysis. From global sensitivity analysis, the flow parameters are found to be more important than the parameters of the submerged body.

Keywords

Monte Carlo SimulationsPerturbationPolynomial Chaos ExpansionSensitivityUncertainty AnalysisVortex-Panel Method
Type
Special Issue Articles
Information
AI EDAM , Volume 31 , Special Issue 3: Uncertainty Quantification for Engineering Design , August 2017 , pp. 277 - 285
Copyright
Copyright © Cambridge University Press 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Arwade, S., Moradi, M., & Louhghalam, A. (2010). Variance decomposition and global sensitivity for structural systems. Engineering Structures 32(1), 1–10.CrossRefGoogle Scholar
Blatman, G., & Sudret, B. (2010). Efficient computation of global sensitivity indices using sparse polynomial chaos expansions. Reliability Engineering and System Safety 95(11), 1216–1229.CrossRefGoogle Scholar
Bryson, D., & Rumpfkeil, M. (2016). Aerodynamic uncertainty quantification of supersonic biplane airfoil via polynomial chaos approach. Proc. 54th AIAA Aerospace Sciences Meeting, AIAA SciTech, San Diego, CA, January 4–8.Google Scholar
Crestaux, T., Le Maître, O.P., & Martinez, J.-M. (2009). Polynomial chaos expansion for sensitivity analysis. Reliability Engineering and System Safety 94(7), 1161–1172.CrossRefGoogle Scholar
Dowell, E.H., Peters, D.A., Clark, R., Scanlan, R., Cox, D., Simiu, E., Curtiss, H.C. Jr., Sisto, F., Edwards, J.W., Strganac, T.W., & Hall, K.C. (2004). A Modern Course in Aeroelasticity. Dordrecht: Kluwer Academic.Google Scholar
Ghanem, R., & Ghosh, D. (2007). Efficient characterization of the random eigenvalue problem in a polynomial chaos decomposition. International Journal for Numerical Methods in Engineering 72(4), 486–504.CrossRefGoogle Scholar
Ghanem, R., & Spanos, P.D. (2003). Stochastic Finite Elements: A Spectral Approach, rev. ed. New York: Dover.Google Scholar
Ghosh, D., Avery, P., & Farhat, C. (2009). A FETI-preconditioned conjugate gradient method for large-scale stochastic finite element problems. International Journal for Numerical Methods in Engineering 80(6–7), 914–931.CrossRefGoogle Scholar
Gilli, L., Lathouwers, D., Kloosterman, J.L., van der Hagen, T.H.J., Koning, A.J., & Rochman, D. (2013). Uncertainty quantification for criticality problems using non-intrusive and adaptive polynomial chaos techniques. Annals of Nuclear Energy 56, 71–80.CrossRefGoogle Scholar
Hess, J.L. (1990). Panel methods in computational fluid dynamics. Annual Review of Fluid Mechanics 22(1), 255–274.CrossRefGoogle Scholar
Katz, J., & Plotkin, A. (2002). Low Speed Aerodynamics: From Wing Theory to Panel Methods. Boston: McGraw-Hill.Google Scholar
Kuethe, A., & Chow, C. (1986). Foundations of Aerodynamics: Bases of Aerodynamic Design. New York: Wiley.Google Scholar
Le Maître, O.P., & Knio, O.M. (2010). Spectral Methods for Uncertainty Quantification. New York: Springer.CrossRefGoogle Scholar
Lockwood, B., & Mavriplis, D. (2013). Gradient-based methods for uncertainty quantification in hypersonic flows. Computers and Fluids 85, 27–38.CrossRefGoogle Scholar
Najm, H.N. (2011). Uncertainty quantification in fluid flow. Turbulent Combustion Modeling: Advances, New Trends and Perspectives 95, 381–407.CrossRefGoogle Scholar
Ng, L.W.T., & Eldred, M.S. (2012). Multifidelity uncertainty quantification using non-intrusive polynomial chaos and stochastic collocation. Proc. 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conf., Paper No. AIAA-1852, Honolulu, HI, April 23–26.CrossRefGoogle Scholar
Nikbay, M., & Kuru, M. (2013). Reliability based multidisciplinary optimization of aeroelastic systems with structural and aerodynamic uncertainties. Journal of Aircraft 50(3), 708–715.CrossRefGoogle Scholar
Pettit, C.L. (2004). Uncertainty quantification in aeroelasticity: recent results and research challenges. Journal of Aircraft 41(5), 1217–1229.CrossRefGoogle Scholar
Pettit, C.L., Hajj, M.R., & Beran, P.S. (2010). A stochastic approach for modeling incident gust effects on flow quantities. Probabilistic Engineering Mechanics 25(1), 153–162.CrossRefGoogle Scholar
Saltelli, A., & Sobol’, I.M. (1995). About the use of rank transformation in sensitivity analysis of model output. Reliability Engineering and System Safety 50(3), 225–239.CrossRefGoogle Scholar
Schenk, C.A., & Schuëller, G.I. (2005). Uncertainty Assessment of Large Finite Element Systems. Berlin: Springer.Google Scholar
Sobol’, I.M. (2001). Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation 55(1–3), 271–280.CrossRefGoogle Scholar
Suryawanshi, A., & Ghosh, D. (2014). Reliability based optimization in aeroelastic stability problems using polynomial chaos based metamodels. Structural and Multidisciplinary Optimization. Advance online publication.Google Scholar
Todor, R.A., & Schwab, C. (2007). Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients. IMA Journal of Numerical Analysis 27, 232–261.CrossRefGoogle Scholar
Wang, Q., Duraisamy, K., Alonso, J.J., & Iaccarino, J. (2012). Risk assessment of scramjet unstart using adjoint-based sampling methods. AIAA Journal 50(3), 581–592.CrossRefGoogle Scholar
Xiu, D., & Karniadakis, G.E. (2003). Modeling uncertainty in flow simulations via generalized polynomial chaos. Journal of Computational Physics 187(1), 137–167.CrossRefGoogle Scholar