Efficient random field uncertainty propagation in design using multiscale analysis

Xiaolei Yin*, Sanghoon Lee, Wei Chen, Wing Kam Liu, M. F. Horstemeyer

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

71 Scopus citations


An integrated design framework that employs multiscale analysis to facilitate concurrent product, material, and manufacturing process design is presented in this work. To account for uncertainties associated with material structures and their impact on product performance across multiple scales, efficient computational techniques are developed for propagating material uncertainty with random field representation. Random field is employed to realistically model the uncertainty existing in material microstructure, which spatially varies in a product inherited from the manufacturing process. To reduce the dimensionality of random field representation, a reduced order Karhunen-Loeve expansion is used with a discretization scheme applied to finite-element meshes. The univariate dimension reduction method and the Gaussian quadrature formula are used to efficiently quantify the uncertainties in product performance in terms of its statistical moments, which are critical information for design under uncertainty. A control arm example is used to demonstrate the proposed approach. The impact of the initial microscale porosity random field produced during a casting process on the product damage is studied and a reliability-based design of the control arm is performed.

Original languageEnglish (US)
Pages (from-to)210061-2100610
Number of pages1890550
JournalJournal of Mechanical Design, Transactions of the ASME
Issue number2
StatePublished - Feb 2009


  • Control arm design
  • Design under uncertainty
  • Gaussian quadrature formula
  • Karhunen-Loeve expansion
  • Multiscale analysis
  • Random field
  • Uncertainty propagation
  • Univariate dimension-reduction method

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design


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