Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 229, Issue 23, Pages 8966-8980Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2010.08.022
Keywords
Failure probability; Sampling; Polynomial chaos; Stochastic computation
Funding
- AFOSR, DOE/NNSA, NSF
- Div Of Information & Intelligent Systems
- Direct For Computer & Info Scie & Enginr [0914564] Funding Source: National Science Foundation
- Div Of Information & Intelligent Systems
- Direct For Computer & Info Scie & Enginr [0914447] Funding Source: National Science Foundation
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Evaluation of failure probability of a given system requires sampling of the system response and can be computationally expensive. Therefore it is desirable to construct an accurate surrogate model for the system response and subsequently to sample the surrogate model. In this paper we discuss the properties of this approach. We demonstrate that the straightforward sampling of a surrogate model can lead to erroneous results, no matter how accurate the surrogate model is. We then propose a hybrid approach by sampling both the surrogate model in a large portion of the probability space and the original system in a small portion. The resulting algorithm is significantly more efficient than the traditional sampling method, and is more accurate and robust than the straightforward surrogate model approach. Rigorous convergence proof is established for the hybrid approach, and practical implementation is discussed. Numerical examples are provided to verify the theoretical findings and demonstrate the efficiency gain of the approach. (C) 2010 Elsevier Inc. All rights reserved.
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