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Finite dimensional surrogates for extreme events

Hui Xu, Mircea D. ( July 2023 , 14th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP14 Dublin, Ireland, July 9-13, 2023)

Numerical solutions of stochastic problems require the representation of random functions in their definitions by finite dimensional (FD) models, i.e., deterministic functions of time and finite sets of random variables. It is common to represent the coefficients of these FD surrogates by polynomial chaos (PC) models. We propose a novel model, referred to as the polynomial chaos translation (PCT) model, which matches exactly the marginal distributions of the FD coefficients and approximately their dependence. PC- and PCT- based FD models are constructed for a set of test cases and a wind pressure time series recorded at the boundary layer wind tunnel facility at the University of Florida. The PCT-based models capture the joint distributions of the FD coefficients and the extremes of target times series accurately while PC-based FD models do not have this capability.

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