期刊
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
卷 332, 期 -, 页码 382-407出版社
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2017.12.019
关键词
Polynomial chaos; Least squares approximation; Optimal sampling; Optimal design of experiments; Coherence-optimal
资金
- National Science Foundation [CMMI-1201207]
- U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research [DE-SC0006402]
- NSF [CMMI-1454601]
- Div Of Civil, Mechanical, & Manufact Inn
- Directorate For Engineering [1454601] Funding Source: National Science Foundation
As non-intrusive polynomial chaos expansion (PCE) techniques have gained growing popularity among researchers, we here provide a comprehensive review of major sampling strategies for the least squares based PCE. Traditional sampling methods, such as Monte Carlo, Latin hypercube, quasi-Monte Carlo, optimal design of experiments (ODE), Gaussian quadratures, as well as more recent techniques, such as coherence-optimal and randomized quadratures are discussed. We also propose a hybrid sampling method, dubbed alphabetic-coherence-optimal, that employs the so-called alphabetic optimality criteria used in the context of ODE in conjunction with coherence-optimal samples. A comparison between the empirical performance of the selected sampling methods applied to three numerical examples, including high-order PCE's, high-dimensional problems, and low oversampling ratios, is presented to provide a road map for practitioners seeking the most suitable sampling technique for a problem at hand. We observed that the alphabetic-coherence-optimal technique outperforms other sampling methods, specially when high-order ODE are employed and/or the oversampling ratio is low. Published by Elsevier B. V.
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