A weighted three-point-based strategy for variance estimation

Thaweepat Buranathiti, Jlan Cao*, Wei Chen

*Corresponding author for this work

Research output: Contribution to conferencePaperpeer-review

7 Scopus citations


In manufacturing processes, it is widely accepted that uncertainty plays an important role and should be taken into account during analysis and design processes. However, uncertainty quantification of its effects on an end-product is a very challenging task, especially when an expensive computational effort is already needed in deterministic models such as sheet metal forming simulations. In this paper, we focus our work on the variance estimation of the system response. A weighted three-point-based strategy is proposed to efficiently and effectively estimate the variance of the system response. Three first-order derivatives for each variable are used to estimate the nonlinear behavior and variance of the system. The details of the derivation of the approach are presented in the paper. The optimal locations of the three points along each axis in the standard normal space and weights for input variables following normal distributions are proposed as (-1.8257,0.0,+1.8257) and (0.075,0.850,0.075), respectively. For input variables following uniform distributions U(-1,1), the optimal locations and weights are proposed as (-0.84517, 0.0,+0.84517) and (0.04667,0.90666,0.04667), respectively. The proposed approach is applicable to nonlinear and multivariable systems as well as problems having no explicit function such as those design simulations based on finite element methods. The significant accuracy improvement over the traditional first-order approximation is demonstrated with a number of test problems. The proposed method requires significantly less computational effort compared with the Monte Carlo simulations. Discussions and conclusions of this work are given at the end of the paper.

Original languageEnglish (US)
Number of pages9
StatePublished - 2004
Event2004 ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference - Salt Lake City, UT, United States
Duration: Sep 28 2004Oct 2 2004


Other2004 ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference
Country/TerritoryUnited States
CitySalt Lake City, UT


  • Design under uncertainty
  • First order approximation
  • Uncertainty propagation
  • Variance estimation
  • Weighted three-point-based strategy

ASJC Scopus subject areas

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


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