A comparative study of uncertainty propagation methods for black-box-type problems

S. H. Lee, Wei Chen*

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review

199 Scopus citations


A wide variety of uncertainty propagation methods exist in literature; however, there is a lack of good understanding of their relative merits. In this paper, a comparative study on the performances of several representative uncertainty propagation methods, including a few newly developed methods that have received growing attention, is performed. The full factorial numerical integration, the univariate dimension reduction method, and the polynomial chaos expansion method are implemented and applied to several test problems. They are tested under different settings of the performance nonlinearity, distribution types of input random variables, and the magnitude of input uncertainty. The performances of those methods are compared in moment estimation, tail probability calculation, and the probability density function construction, corresponding to a wide variety of scenarios of design under uncertainty, such as robust design, and reliability-based design optimization. The insights gained are expected to direct designers for choosing the most applicable uncertainty propagation technique in design under uncertainty.

Original languageEnglish (US)
Pages (from-to)239-253
Number of pages15
JournalStructural and Multidisciplinary Optimization
Issue number3
StatePublished - Jan 1 2009


  • Comparative study
  • Design under uncertainty
  • Dimension reduction method
  • Full factorial numerical integration
  • Polynomial chaos expansion
  • Uncertainty propagation

ASJC Scopus subject areas

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

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