Effective random field characterization considering statistical dependence for probability analysis and design

Zhimin Xi, Byeng D. Youn, Chao Hu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The Proper Orthogonal Decomposition (POD) method has been employed to extract the important signatures of the random field presented in an engineering product or process. Our preliminary study found that coefficients of the signatures are statistically uncorrelated but may be dependent. In general, the statistical dependence of the coefficients is ignored in the random field characterization for probability analysis and design. This paper thus proposes an effective approach to characterize the random field for probability analysis and design while accounting for the statistical dependence among the coefficients. The proposed approach is composed of two technical contributions. The first contribution is to develop a generic approximation scheme of random field as a function of the most important field signatures while preserving prescribed approximation accuracy. The coefficients of the signatures can be modeled as random field variables and their statistical properties are identified using the Chi-Square goodness-of-fit test. Second, the Rosenblatt transformation is employed to transform the statistically dependent random field variables into statistically independent random field variables. There exist so many transformation sequences when the number of random field variables becomes large. It was found that an improper selection of a transformation sequence may introduce high nonlinearity into system responses, which causes inaccuracy in probability analysis and design. Hence, a novel procedure is proposed for determining an optimal transformation sequence that introduces the least degree of nonlinearity to the system response after the Rosenblatt transformation. The proposed random field characterization can be integrated with one of the

Original languageEnglish (US)
Title of host publicationASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2010
Pages1133-1148
Number of pages16
EditionPARTS A AND B
DOIs
StatePublished - 2010
Externally publishedYes
EventASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2010 - Montreal, QC, Canada
Duration: Aug 15 2010Aug 18 2010

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
NumberPARTS A AND B
Volume1

Other

OtherASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2010
Country/TerritoryCanada
CityMontreal, QC
Period8/15/108/18/10

All Science Journal Classification (ASJC) codes

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

Keywords

  • Eigenvector dimension reduction
  • Probability analysis and design
  • Proper orthogonal decomposition
  • Random field

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