A new sparse grid based method for uncertainty propagation

Fenfen Xiong, Ying Xiong, Steven Greene, Wei Chen*, Shuxing Yang

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

Although a variety of uncertainty propagation methods exist for estimating the statistical moments and the probability of failure in design under uncertainty, current methods suffer from their limitations in providing accurate and efficient solutions to high-dimension problems with interactions of random variables. A new sparse grid based uncertainty propagation method is proposed in this work to overcome this difficulty. The existing sparse grid technique, originally invented for numerical integration and interpolation, is extended to uncertainty propagation in the probabilistic domain. In particular, the concept of Sparse Grid Numerical Integration (SGNI) is extended for estimating the first two moments of performance in robust design, while the Sparse Grid Interpolation (SGI) is employed to determine failure probability by interpolating the limit-state function at the Most Probable Point (MPP) in reliability analysis. The proposed methods are demonstrated by several high-dimension mathematical examples with notable variate interactions and one complex multidisciplinary rocket design problem. Results show that the use of sparse grid methods works better than popular counterparts. Furthermore, the automatic sampling, special interpolation process, and dimension-adaptivity feature make SGI more flexible and efficient than using the uniform sample based metamodeling techniques.

Original languageEnglish (US)
Title of host publicationASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2009
Pages1205-1215
Number of pages11
Volume5
EditionPARTS A AND B
DOIs
StatePublished - Dec 1 2009
EventASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2009 - San Diego, CA, United States
Duration: Aug 30 2009Sep 2 2009

Other

OtherASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2009
CountryUnited States
CitySan Diego, CA
Period8/30/099/2/09

ASJC Scopus subject areas

  • Modeling and Simulation
  • Mechanical Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design

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    Xiong, F., Xiong, Y., Greene, S., Chen, W., & Yang, S. (2009). A new sparse grid based method for uncertainty propagation. In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2009 (PARTS A AND B ed., Vol. 5, pp. 1205-1215) https://doi.org/10.1115/DETC2009-87430