Journal article
Global sensitivity analysis by polynomial dimensional decomposition
Reliability engineering & system safety, Vol.96(7), pp.825-837
2011
DOI: 10.1016/j.ress.2011.03.002
Abstract
This paper presents a polynomial dimensional decomposition (PDD) method for global sensitivity analysis of stochastic systems subject to independent random input following arbitrary probability distributions. The method involves Fourier-polynomial expansions of lower-variate component functions of a stochastic response by measure-consistent orthonormal polynomial bases, analytical formulae for calculating the global sensitivity indices in terms of the expansion coefficients, and dimension-reduction integration for estimating the expansion coefficients. Due to identical dimensional structures of PDD and analysis-of-variance decomposition, the proposed method facilitates simple and direct calculation of the global sensitivity indices. Numerical results of the global sensitivity indices computed for smooth systems reveal significantly higher convergence rates of the PDD approximation than those from existing methods, including polynomial chaos expansion, random balance design, state-dependent parameter, improved Sobol's method, and sampling-based methods. However, for non-smooth functions, the convergence properties of the PDD solution deteriorate to a great extent, warranting further improvements. The computational complexity of the PDD method is polynomial, as opposed to exponential, thereby alleviating the curse of dimensionality to some extent.
Details
- Title: Subtitle
- Global sensitivity analysis by polynomial dimensional decomposition
- Creators
- Sharif Rahman - College of Engineering, The University of Iowa, Iowa City, IA 52242, USA
- Resource Type
- Journal article
- Publication Details
- Reliability engineering & system safety, Vol.96(7), pp.825-837
- Publisher
- Elsevier Ltd
- DOI
- 10.1016/j.ress.2011.03.002
- ISSN
- 0951-8320
- eISSN
- 1879-0836
- Language
- English
- Date published
- 2011
- Academic Unit
- Mechanical Engineering
- Record Identifier
- 9984064226202771
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