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Research Papers

Propagation of Parametric Uncertainties in a Nonlinear Aeroelastic System Using an Improved Adaptive Sparse Grid Quadrature Routine

[+] Author and Article Information
Harshini Devathi

Department of Aerospace Engineering,
IIT Madras,
Chennai 600036, India
e-mail: harshinidevathi90@gmail.com

Sunetra Sarkar

Department of Aerospace Engineering,
IIT Madras,
Chennai 600036, India
e-mail: sunetra.sarkar@gmail.com

1Corresponding author.

Manuscript received October 19, 2017; final manuscript received February 21, 2018; published online April 30, 2018. Assoc. Editor: Athanasios Pantelous.

ASME J. Risk Uncertainty Part B 4(4), 041009 (Apr 30, 2018) (9 pages) Paper No: RISK-17-1095; doi: 10.1115/1.4039471 History: Received October 19, 2017; Revised February 21, 2018

A novel uncertainty quantification routine in the genre of adaptive sparse grid stochastic collocation (SC) has been proposed in this study to investigate the propagation of parametric uncertainties in a stall flutter aeroelastic system. In a hypercube stochastic domain, presence of strong nonlinearities can give way to steep solution gradients that can adversely affect the convergence of nonadaptive sparse grid collocation schemes. A new adaptive scheme is proposed here that allows for accelerated convergence by clustering more discretization points in regimes characterized by steep fronts, using hat-like basis functions with nonequidistant nodes. The proposed technique has been applied on a nonlinear stall flutter aeroelastic system to quantify the propagation of multiparametric uncertainty from both structural and aerodynamic parameters. Their relative importance on the stochastic response is presented through a sensitivity analysis.

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References

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Figures

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Fig. 1

Schematic diagram of an airfoil in dynamic stall-induced oscillations

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Fig. 2

Nested quadrature: (a) trapezoidal rule and (b) Gauss-Patterson rule

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Fig. 3

Adaptive mesh refinement: (a) father–son concept and (b) creating the sons based on the value of hierarchical surplus associated with the father

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Fig. 4

Deterministic bifurcation analysis: (a) variation of response amplitude R as a function of U; (b) variation of αmax and αmin with U; (c) time history for α(τ) when U = 7; and (d) time history for α(τ) when U = 10

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Fig. 5

Uncertainty in β and ζ; U = 8.8: (a) comparison of the pdf pR(R) obtained using the MCS method and the adaptive PCE method; (b) the collocation point grid generated by the adaptive PCE method; (c) response surface obtained using the MCS method; and (d) response surface obtained using the adaptive PCE method

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Fig. 6

Uncertainty in β and ζ: (a) variation of the pdf pR(R) with U; (b) variation of the mean and standard deviation of the response with U; and (c) variation of the Sobol sensitivity indices for β and ζ with U

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Fig. 7

Uncertainty in β and μ; U = 8.8: (a) comparison of the pdf pR(R) obtained using the MCS and the adaptive PCE method; (b) the collocation point grid generated by the adaptive PCE method; (c) response surface obtained using the MCS method; and (d) response surface obtained using the adaptive PCE method

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Fig. 8

Uncertainty in β and μ: (a) variation of pdf pR(R) with U; (b) variation of mean and standard deviation of the response with U; and (c) variation of Sobol sensitivity indices for β and μ with U

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Fig. 9

Uncertainty in β, ζ, and μ: (a) variations in the pdf pR(R) with U as the bifurcation parameter; (b) mean and standard deviation of the response with U; (c) sobol sensitivity indices for β, ζ and μ; and (d) sobol sensitivity indices for β and ζ

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