The inclusive and simplified forms of Bayesian interpolation for general and monotonic models using Gaussian and Generalized Beta distributions with application to Monte Carlo simulations |
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Authors: | Mohammadreza Rajabalinejad Tew-Fik Mahdi |
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Institution: | (1) Department of Civil, Geological and Mining Engineering, Ecole Polytechnique de Montreal, Montreal, QC, Canada |
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Abstract: | A recently developed Bayesian interpolation method (BI) and its application to safety assessment of a flood defense structure
are described in this paper. We use a one-dimensional Bayesian Monte Carlo method (BMC) that has been proposed in (Rajabalinejad
2009) to develop a weighted logical dependence between neighboring points. The concept of global uncertainty is adequately explained
and different uncertainty association models (UAMs) are presented for linking the local and global uncertainty. Based on the
global uncertainty, a simplified approach is introduced. By applying the global uncertainty, we apply the Guassian error estimation
to general models and the Generalized Beta (GB) distribution to monotonic models. Our main objective in this research is to
simplify the newly developed BMC method and demonstrate that it can dramatically improve the simulation efficiency by using
prior information from outcomes of the preceding simulations. We provide theory and numerical algorithms for the BI method
geared to multi-dimensional problems, integrate it with a probabilistic finite element model, and apply the coupled models
to the reliability assessment of a flood defense for the 17th Street Flood Wall system in New Orleans. |
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