Journal article
A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics
Probabilistic engineering mechanics, Vol.19(4), pp.393-408
2004
DOI: 10.1016/j.probengmech.2004.04.003
Abstract
This paper presents a new, univariate dimension-reduction method for calculating statistical moments of response of mechanical systems subject to uncertainties in loads, material properties, and geometry. The method involves an additive decomposition of a multi-dimensional response function into multiple one-dimensional functions, an approximation of response moments by moments of single random variables, and a moment-based quadrature rule for numerical integration. The resultant moment equations entail evaluating
N number of one-dimensional integrals, which is substantially simpler and more efficient than performing one
N-dimensional integration. The proposed method neither requires the calculation of partial derivatives of response, nor the inversion of random matrices, as compared with commonly used Taylor expansion/perturbation methods and Neumann expansion methods, respectively. Nine numerical examples involving elementary mathematical functions and solid-mechanics problems illustrate the proposed method. Results indicate that the univariate dimension-reduction method provides more accurate estimates of statistical moments or multidimensional integration than first- and second-order Taylor expansion methods, the second-order polynomial chaos expansion method, the second-order Neumann expansion method, statistically equivalent solutions, the quasi-Monte Carlo simulation, and the point estimate method. While the accuracy of the univariate dimension-reduction method is comparable to that of the fourth-order Neumann expansion, a comparison of CPU time suggests that the former is computationally far more efficient than the latter.
Details
- Title: Subtitle
- A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics
- Creators
- S RahmanH Xu
- Resource Type
- Journal article
- Publication Details
- Probabilistic engineering mechanics, Vol.19(4), pp.393-408
- Publisher
- Elsevier Ltd
- DOI
- 10.1016/j.probengmech.2004.04.003
- ISSN
- 0266-8920
- eISSN
- 1878-4275
- Language
- English
- Date published
- 2004
- Academic Unit
- Mechanical Engineering
- Record Identifier
- 9984064211202771
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