Extreme value of response to nonstationary excitation

An efficient method is presented for approximate computation of extreme val ue characteristics of the response of a linear structure subjected to nonst ationary Gaussian excitation. The characteristics considered are the mean a nd standard deviation of the extreme value and fractile levels having speci fic probabilities of not being exceeded by the random process within a spec ified time interval. The approximate procedure can significantly facilitate the utilization of nonstationary models in engineering practice. since it avoids computational difficulties associated with direct application of ext reme value theory. The method is based on the approximation of the cumulati ve distribution function (CDF) of the extreme value of a nonstationary proc ess by the CDF of a corresponding "equivalent" stationary process. Approxim ate procedures are developed for both the Poisson and Vanmarcke approaches to the extreme value problem, and numerical results are obtained for an exa mple problem. These results demonstrate that the simple approximate method agrees quite well with the direct application of extreme value theory, whil e avoiding the difficulties associated with solution of nonlinear equations containing complicated time integrals.