Efficient Simulation Method for First Passage Problem of Linear Systems Subjected to Non-Gaussian Excitations

Abstract

This paper addresses the first passage problem of linear systems subjected to non-Gaussian excitations by means of simulation. A non-Gaussian simulation technique based on the unified Hermite polynomial model (UHPM) is adopted to model input excitations, and then the output responses are further obtained through time-domain analysis. The novel contribution of this paper is to construct an efficient importance sampling (IS) density function based on UHPM and the first-order reliability method (FORM) to release the computational burden. A simple and efficient sampling procedure is also provided for convenient implementation. Such an approach allows the failure probabilities in the order of 10−3 or lower to be estimated reliably with a reduced computational cost. The accuracy and efficiency of the proposed method are demonstrated by three examples, including a single-degree-of-freedom oscillator, a 3-story linear shear frame, and a relatively large-scale finite-element model.