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Article
Probabilistic Uncertainty Analysis by Mean-Value First Order Saddlepoint Approximation
Reliability Engineering & System Safety
  • Beiqing Huang
  • Xiaoping Du, Missouri University of Science and Technology
Abstract
Probabilistic uncertainty analysis quantifies the effect of input random variables on model outputs. It is an integral part of reliability-based design, robust design, and design for Six Sigma. The efficiency and accuracy of probabilistic uncertainty analysis is a trade-off issue in engineering applications. In this paper, an efficient and accurate mean-value first order Saddlepoint Approximation (MVFOSA) method is proposed. Similar to the mean-value first order Second Moment (MVFOSM) approach, a performance function is approximated with the first order Taylor expansion at the mean values of random input variables. Instead of simply using the first two moments of the random variables as in MVFOSM, MVFOSA estimates the probability density function and cumulative distribution function of the response by the accurate Saddlepoint Approximation. Because of the use of complete distribution information, MVFOSA is generally more accurate than MVFOSM with the same computational effort. Without the nonlinear transformation from non-normal variables to normal variables as required by the first order reliability method (FORM), MVFOSA is also more accurate than FORM in certain circumstances, especially when the transformation significantly increases the nonlinearity of a performance function. It is also more efficient than FORM because an iterative search process for the so-called Most Probable Point is not required. The features of the proposed method are demonstrated with four numerical examples.
Department(s)
Mechanical and Aerospace Engineering
Sponsor(s)
National Science Foundation (U.S.)
University of Missouri--Rolla. Intelligent Systems Center
University of Missouri Research Board
Keywords and Phrases
  • Cumulant Generating Function,
  • Saddlepoint Approximation,
  • Uncertainty Analysis
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2005 Elsevier, All rights reserved.
Publication Date
1-1-2005
Citation Information
Beiqing Huang and Xiaoping Du. "Probabilistic Uncertainty Analysis by Mean-Value First Order Saddlepoint Approximation" Reliability Engineering & System Safety (2005)
Available at: http://works.bepress.com/xiaoping-du/50/