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research-article

Generalized polynomial chaos with optimized quadrature applied to a turbulent boundary layer forced plate

[+] Author and Article Information
Andrew S. Wixom

Applied Research Laboratory, Pennsylvania State University
axw274@arl.psu.edu

Gage S. Walters

Applied Research Laboratory, Pennsylvania State University
gvw5074@arl.psu.edu

Sheri L. Martinelli

Applied Research Laboratory, Pennsylvania State University
slm77@arl.psu.edu

David M. Williams

Department of Mechanical Engineering, Pennsylvania State University
dmw72@psu.edu

1Corresponding author.

ASME doi:10.1115/1.4041772 History: Received May 31, 2018; Revised October 10, 2018

Abstract

We explore the use of generalized polynomial chaos expansion with stochastic collocation for modeling the uncertainty in the noise radiated by a plate subject to turbulent boundary layer forcing. The stochastic collocation form of polynomial chaos permits re-use of existing computational models, while drastically reducing the number of evaluations of the deterministic code compared to Monte Carlo sampling, for instance. Further efficiency is attained through the application of new, efficient, quadrature rules to compute the generalized polynomial chaos expansion coefficients. We demonstrate that our approach accurately reconstructs the statistics of the radiated sound power by propagating the input uncertainty through the computational physics model. The use of optimized quadrature rules permits these results to be obtained using far fewer quadrature nodes than with traditional methods, such as tensor product quadrature and Smolyak sparse grid methods. As each quadrature node corresponds to an expensive deterministic model evaluation the computational cost of the analysis is seen to be greatly reduced.

Copyright (c) 2018 by ASME
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