Finite dimensional surrogates for extreme events

Abstract

Finite dimensional (FD) models are developed for random processes X(t) with continuous samples. The FD models Xd(t) are deterministic functions of time and finite sets of random variables which are defined on the same probability space as the target processes X(t). Conditions are established under which extremes of X(t) over bounded time intervals can be estimated from surrogate samples, i.e., samples of processes Xd(t) for sufficiently large stochastic dimensions d. Developments involve technicalities since the relationship between target and FD samples has to be quantified in the space of real-valued continuous samples. Yet, the implementation of the proposed method involves simple concepts.

FD surrogates Xd(t) are developed for the wind pressure time series X(t) recorded at the University of Florida Boundary Layer Wind Tunnel facility. The time series is highly non-Gaussian so that the random entries of Xd(t) are dependent non-Gaussian variables whose joint distribution is described by an extension of polynomial chaos representations, referred as translation polynomial chaos models. It is shown that extremes of Xd(t) provide accurate approximations for the extremes of X(t).