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A Sparse Data-Driven Polynomial Chaos Expansion Method for Uncertainty Propagation

[+] Author Affiliations
F. Wang, F. Xiong, S. Yang

Beijing Institute of Technology, Beijing, China

Y. Xiong

Bank of America, Charlotte, NC

Paper No. DETC2016-59795, pp. V02AT03A003; 9 pages
doi:10.1115/DETC2016-59795
From:
  • ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 2A: 42nd Design Automation Conference
  • Charlotte, North Carolina, USA, August 21–24, 2016
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5010-7
  • Copyright © 2016 by ASME

abstract

The data-driven polynomial chaos expansion (DD-PCE) method is claimed to be a more general approach of uncertainty propagation (UP). However, as a common problem of all the full PCE approaches, the size of polynomial terms in the full DD-PCE model is significantly increased with the dimension of random inputs and the order of PCE model, which would greatly increase the computational cost especially for high-dimensional and highly non-linear problems. Therefore, a sparse DD-PCE is developed by employing the least angle regression technique and a stepwise regression strategy to adaptively remove some insignificant terms. Through comparative studies between sparse DD-PCE and the full DD-PCE on three mathematical examples with random input of raw data, common and nontrivial distributions, and a ten-bar structure problem for UP, it is observed that generally both methods yield comparably accurate results, while the computational cost is significantly reduced by sDD-PCE especially for high-dimensional problems, which demonstrates the effectiveness and advantage of the proposed method.

Copyright © 2016 by ASME

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