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Random Field Characterization With Insufficient Data Sets for Probability Analysis and Design

[+] Author Affiliations
Zhimin Xi

University of Michigan, Dearborn, MI

Byung C. Jung

University of Maryland at College Park, College Park, MD

Byeng D. Youn

Seoul National University, Seoul, South Korea

Paper No. DETC2011-48319, pp. 133-144; 12 pages
doi:10.1115/DETC2011-48319
From:
  • ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5: 37th Design Automation Conference, Parts A and B
  • Washington, DC, USA, August 28–31, 2011
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5482-2
  • Copyright © 2011 by ASME

abstract

Random field is a generalization of a stochastic field, of which randomness can be characterized as a function of spatial variables. Examples of the random field can often be found as a geometry, material, and process variation in engineering products and processes. It has been widely acknowledged that consideration of the random field is quite significant to accurately predict variability in system performances. However, current approaches for characterizing the random field can only be applied to the situation with sufficient random field data sets and are not suitable to most engineering problems where the data sets are insufficient. The contribution of this paper is to model the random field based on the insufficient data sets such that sufficient data sets can be simulated or generated according to the random field modeling. Therefore, available random field characterization approaches and probability analysis methods can be used for probability analysis and design of many engineering problems with the lack of random field data sets. The proposed random field modeling is composed of two technical components including: 1) a Bayesian updating approach using the Markov Chain Monte Carlo (MCMC) method for modeling the random field based on available random field data sets; and 2) a Bayesian Copula dependence modeling approach for modeling statistical dependence of random field realizations at different measurement locations. Three examples including a mathematical problem, a heat generation problem of the Lithium-ion battery, and a refrigerator assembly problem are used to demonstrate the effectiveness of the proposed approach.

Copyright © 2011 by ASME
Topics: Design , Probability

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