Monte–Carlo Based Method for Predicting Extreme Value Statistics of Uncertain Structures

Abstract

In the present paper, a simple method is proposed for predicting the extreme response of uncertain structures subjected to stochastic excitation. Many of the currently used approaches to extreme response predictions are based on the asymptotic generalized extreme value distribution, whose parameters are estimated from the observed data. However, in most practical situations, it is not easy to ascertain whether the given response time series contain data above a high level that are truly asymptotic, and hence the obtained parameter values by the adopted estimation methods, which points to the appropriate extreme value distribution, may become inconsequential. In this paper, the extreme value statistics are predicted taking advantage of the regularity of the tail region of the mean upcrossing rate function. This method is instrumental in handling combined uncertainties associated with nonergodic processes (system uncertainties) as well as ergodic ones (stochastic loading). For the specific applications considered, it can be assumed that the considered time series has an extreme value distribution that has the Gumbel distribution as its asymptotic limit. The present method is numerically illustrated through applications to a beam with spatially varying random properties and wind turbines subjected to stochastic loading.