Comparison of strategies for the optimal sampling of random functions

Abstract

In engineering problems and applications are usually characterized by uncertainty. The accurate quantification of possible effects of those uncertainties is of vital importance. The most common approach to do so is probabilistic simulation, but this strategy may become impractical if the associated deterministic problem is very complex and only a small number of its evaluations is possible. The selection of a small-to-moderate number of samples able to capture the probabilistic characteristics of the whole set of samples is an important open problem. One approach to perform this selection is a technique called ﾓFunctional Quantization Infinite Dimensional Centroidal Voronoi Tessellation (FQ-IDCVT)ﾔ. However, this method of selection focuses on mean-square optimality, and usually leads to reduction in the variability of the set of random sample functions. Hence, to capture the extremity as well as the other probabilistic characteristics of the whole set of random samples, different methods for the selection of the set of samples are presented and new approaches are proposed in this study. To show differences among different methods, a numerical application is presented, consisting in the selection of ground motion time histories, and the results are compared using several performance measures.