Extreme Value of Response to Nonstationary Excitation

An efficient method is presented for approximate computation of extreme value characteristics of the response of a linear structure subjected to nonstationary Gaussian excitation. The characteristics considered are the mean and standard deviation of the extreme value and fractile levels having specific probabilities of not being exceeded by the random process within a specified 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 extreme value theory. The method is based on the approximation of the cumulative distribution function (CDF) of the extreme value of a nonstationary process by the CDF of a corresponding "equivalent" stationary process. Approximate procedures are developed for both the Poisson and Vanmarcke approaches to the extreme value problem, and numerical results are obtained for an example problem. These results demonstrate that the simple approximate method agrees quite well with the direct application of extreme value theory, while avoiding the difficulties associated with solution of nonlinear equations containing complicated time integrals.