Evaluation of the Probability Distribution of the Extreme Value of the Response of Nonlinear Structures Subjected to Fully Nonstationary Stochastic Seismic Excitations

Abstract

A two-step methodology is presented for evaluating the extreme value distribution (EVD) of the response of random nonlinear structures under fully nonstationary stochastic seismic excitations. The fully nonstationary stochastic seismic excitations are modeled by the spectral representation method (SRM) based on the evolutionary power spectral density. In this regard, the randomness in both structural properties and external excitations is considered, whereby a problem involving a high-dimensional random-variate space needs to be tackled. In the proposed methodology, the probability density evolution method (PDEM) is first employed, where Latin hypercube simulation (LHS) is incorporated, to provide an estimated solution of the EVD of the response with efficiency. Then, a highly flexible distribution model named the shifted generalized lognormal distribution (SGLD) model is fitted, where the estimated solution is served as the original data. The parameters in SGLD model are then specified, and the entire range of accurate EVD of the response can be recovered accordingly. A numerical example involving a nonlinear random structure exhibiting hysteretic behavior under stochastic seismic ground motions is used to illustrate the implementation of the proposed methodology and assess its accuracy and efficiency, especially for the tail distribution. Some features of the EVD of the dynamic response are also discussed.