Structural and Multidisciplinary Optimization

, Volume 41, Issue 3, pp 335–349 | Cite as

A new sparse grid based method for uncertainty propagation

  • Fenfen Xiong
  • Steven Greene
  • Wei ChenEmail author
  • Ying Xiong
  • Shuxing Yang
Research Paper


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.


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


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Fenfen Xiong
    • 1
    • 2
  • Steven Greene
    • 3
  • Wei Chen
    • 2
    Email author
  • Ying Xiong
    • 4
  • Shuxing Yang
    • 1
  1. 1.School of Aerospace Science and EngineeringBeijing Institute of TechnologyBeijingChina
  2. 2.Department of Mechanical EngineeringNorthwestern UniversityEvanstonUSA
  3. 3.Theoretical & Applied MechanicsNorthwestern UniversityEvanstonUSA
  4. 4.Bank of AmericaPhoenixUSA

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