Extended Polynomial Dimensional Decomposition for Arbitrary Probability Distributions
Publication: Journal of Engineering Mechanics
Volume 135, Issue 12
Abstract
This paper presents an extended polynomial dimensional decomposition method for solving stochastic problems subject to independent random input following an arbitrary probability distribution. The method involves Fourier-polynomial expansions of component functions by orthogonal polynomial bases, the Stieltjes procedure for generating the recursion coefficients of orthogonal polynomials and the Gauss quadrature rule for a specified probability measure, and dimension-reduction integration for calculating the expansion coefficients. The extension, which subsumes nonclassical orthogonal polynomials bases, generates a convergent sequence of lower-variate estimates of the probabilistic characteristics of a stochastic response. Numerical results indicate that the extended decomposition method provides accurate, convergent, and computationally efficient estimates of the tail probability of random mathematical functions or reliability of mechanical systems. The convergence of the extended method accelerates significantly when employing measure-consistent orthogonal polynomials.
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Acknowledgments
The writer acknowledges financial support from the U.S. National Science Foundation under Grant Nos. UNSPECIFIEDDMI-0355487 and UNSPECIFIEDCMMI-0653279.
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 135 • Issue 12 • December 2009
Pages: 1439 - 1451
Copyright
© 2009 ASCE.
History
Received: Oct 31, 2008
Accepted: Mar 31, 2009
Published online: May 2, 2009
Published in print: Dec 2009
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