Journal
STRUCTURAL SAFETY
Volume 59, Issue -, Pages 20-31Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.strusafe.2015.11.001
Keywords
Multi-dimensional integral; Generalized F-discrepancy; Non-uniform distribution; Extended Koksma-Hlawka inequality; Stochastic response; Probability density evolution method
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Funding
- National Natural Science Foundation of China (NSFC) [11172210, 51261120374]
- National R D Program [2011BAJ09B03-02]
- State Key Laboratory of Disaster Reduction in Civil Engineering [SLDRCE14-B-17]
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In the stochastic dynamic analysis of nonlinear structures, the strategy of point selection plays a critical role in achieving the tradeoffs between the accuracy and efficiency. To this end, cooperated with the concept of the extended F-discrepancy (EF-discrepancy), the Koksma-Hlawka inequality, which bounds the worst error of cubature formulae, is extended to the cases involving non-uniform distributions in the present paper. Further, in order to avoid the computational complexity of EF-discrepancy, the Generalized F-discrepancy (GF-discrepancy) is introduced. In light of the quantitative equivalence between the EF-discrepancy and GF-discrepancy, the extended Koksma-Hlawka inequality could be modified by replacing the EF-discrepancy with the GF-discrepancy. Thereby the rationality of adopting GF-discrepancy as the objective function of point selection is theoretically supported. Thus, by reducing the GF-discrepancy, a new strategy of representative point set determination via rearrangement is proposed. The proposed approach is then applied to stochastic dynamical response analysis of strong nonlinear structures by incorporated into the probability density evolution method, showing its effectiveness for practical applications. Problems to be further studied are outlined. (C) 2015 Elsevier Ltd. All rights reserved.
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