Journal article
Adaptive-sparse polynomial dimensional decomposition methods for high-dimensional stochastic computing
Computer methods in applied mechanics and engineering, Vol.274, pp.56-83
06/01/2014
DOI: 10.1016/j.cma.2014.01.027
Abstract
This article presents two novel adaptive-sparse polynomial dimensional decomposition (PDD) methods for solving high-dimensional uncertainty quantification problems in computational science and engineering. The methods entail global sensitivity analysis for retaining important PDD component functions, and a full- or sparse-grid dimension-reduction integration or quasi Monte Carlo simulation for estimating the PDD expansion coefficients. A unified algorithm, endowed with two distinct ranking schemes for grading component functions, was created for their numerical implementation. The fully adaptive-sparse PDD method is comprehensive and rigorous, leading to the second-moment statistics of a stochastic response that converges to the exact solution when the tolerances vanish. A partially adaptive-sparse PDD method, obtained through regulated adaptivity and sparsity, is economical and is, therefore, expected to solve practical problems with numerous variables. Compared with past developments, the adaptive-sparse PDD methods do not require their truncation parameter(s) to be assigned a priori or arbitrarily. The numerical results reveal that an adaptive-sparse PDD method achieves a desired level of accuracy with considerably fewer coefficients compared with existing PDD approximations. For a required accuracy in calculating the probabilistic response characteristics, the new bivariate adaptive-sparse PDD method is more efficient than the existing bivariately truncated PDD method by almost an order of magnitude. Finally, stochastic dynamic analysis of a disk brake system was performed, demonstrating the ability of the new methods to tackle practical engineering problems.
Details
- Title: Subtitle
- Adaptive-sparse polynomial dimensional decomposition methods for high-dimensional stochastic computing
- Creators
- Vaibhav Yadav - University of IowaSharif Rahman - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Computer methods in applied mechanics and engineering, Vol.274, pp.56-83
- DOI
- 10.1016/j.cma.2014.01.027
- ISSN
- 0045-7825
- eISSN
- 1879-2138
- Publisher
- Elsevier B.V
- Grant note
- CMMI-0653279; CMMI-1130147 / U.S. National Science Foundation
- Language
- English
- Date published
- 06/01/2014
- Academic Unit
- Mechanical Engineering
- Record Identifier
- 9984196530902771
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