A new sparse grid based method for uncertainty propagation

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

114 Scopus citations


Current methods for uncertainty propagation suffer from their limitations in providing accurate and efficient solutions to high-dimension problems with interactions of random variables. The sparse grid technique, originally invented for numerical integration and interpolation, is extended to uncertainty propagation in this work to overcome the difficulty. 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 high-dimension mathematical examples with notable variate interactions and one 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)
Pages (from-to)335-349
Number of pages15
JournalStructural and Multidisciplinary Optimization
Issue number3
StatePublished - Apr 2010


  • High dimension
  • Most probable point
  • Reliability analysis
  • Robust design
  • Sparse grid
  • Uncertainty propagation
  • Variate interaction

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Software
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Control and Optimization


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