Dynamic reliability analysis of structures under nonstationary stochastic excitations using tail-modified extreme value distribution

Abstract

In practical engineering, it is usually necessary to compute the small first-passage probability of dynamic systems exposed to nonstationary stochastic excitations. However, it is still a challenging problem to efficiently estimate the super-small failure probability using an approximate extreme value distribution (EVD) based on a small number of simulated samples. In this study, a novel EVD model is proposed to describe the probability distribution of the structural extreme response induced by nonstationary stochastic excitations. This EVD model consists of two parts: the main body is modeled by a truncated-shifted generalized lognormal distribution, and a monotonic exponential model is proposed to fit the tail region. Besides that, a criterion for determining the breakpoint between the main body and tail region is proposed, which ensures the non-negativity and normativity of the proposed EVD model and allows the EVD to be reconstructed accurately and efficiently, particularly in its tail region. In this regard, the corresponding first passage probabilities under different thresholds can be straightly evaluated. The precision and completeness of the proposed EVD model are investigated using two numerical examples that consider linear and nonlinear frame structures subjected to nonstationary ground motion accelerations. The results show that the proposed model is in excellent agreement with the results of Monte Carlo simulation, even when the failure probability is very small.