Review Article

Structural and Multidisciplinary Optimization

, 37:239

First online:

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

  • S. H. LeeAffiliated withDepartment of Mechanical Engineering, Northwestern University
  • , W. ChenAffiliated withDepartment of Mechanical Engineering, Northwestern University Email author 

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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.


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