Extreme value distribution and small failure probabilities estimation of structures subjected to non-stationary stochastic seismic excitations

A new method is proposed for efficient estimating the extreme value distribution (EVD) and small failure probabilities of structures subjected to non-stationary stochastic seismic excitations. This method first involves a preliminary estimation by kernel density estimation (KDE), which oscillates across the true probability density function (PDF), as the original data for fitting. The selection of bandwidth in KDE is suggested. Then, two least-square fitting procedures are performed to reconstruct the EVD, where a two-section form parametric model for the EVD is proposed. The shifted generalized lognormal distribution (SGLD), which has a rich flexibility in shape, is fitted based on the preliminary estimation to obtain the main body of EVD. On the other hand, the tail distribution of EVD can be obtained by fitting the probability of exceedance (POE) curve in logarithmic coordinate via a quadratic equation. Two numerical examples, involving both linear and highly nonlinear structures subjected to non-stationary stochastic seismic excitations are investigated. The EVDs and POE curves obtained by direct KDE and the proposed method are all compared with those by Monte Carlo simulation (MCS). The investigations indicate the accuracy and efficiency of the proposed method.