Uncertainty Analysis by Dimension Reduction Integration and Saddlepoint Approximations
Uncertainty analysis, which assesses the impact of the uncertainty of input variables on responses, is an indispensable component in engineering design under uncertainty, such as reliability-based design and robust design. However, uncertainty analysis is an unaffordable computational burden in many engineering problems. In this paper, an uncertainty analysis method is proposed with the purpose of accurately and efficiently estimating the cumulative distribution function (CDF), probability density function (PDF), and statistical moments of a response given the distributions of input variables. The bivariate dimension reduction method and numerical integration are used to calculate the moments of the response; then saddlepoint approximations are employed to estimate the CDF and PDF of the response. The proposed method requires neither the derivatives of the response nor the search of the most probable point, which is needed in the commonly used first and second order reliability methods (FORM and SORM) and the recently developed first order saddlepoint approximation. The efficiency and accuracy of the proposed method is illustrated with three example problems. with the same computational cost, this method is more accurate for reliability assessment and much more efficient for estimating the full range of the distribution of a response than FORM and SORM. This method provides results as accurate as Monte Carlo simulation, with significantly reduced computational effort.
B. Huang and X. Du, "Uncertainty Analysis by Dimension Reduction Integration and Saddlepoint Approximations," Journal of Mechanical Design, American Society of Mechanical Engineers (ASME), Jan 2006.
The definitive version is available at http://dx.doi.org/10.1115/1.2118667
Mechanical and Aerospace Engineering
University of Missouri Research Board
University of Missouri--Rolla. Intelligent Systems Center
National Science Foundation (U.S.)
Keywords and Phrases
Design Engineering; Monte Carlo Methods; Probability; Reliability
Article - Journal
© 2006 American Society of Mechanical Engineers (ASME), All rights reserved.