First passage probability of structures under non-Gaussian stochastic behavior

Abstract

An analytical moment-based method was proposed for calculating first passage probability of structures under non-Gaussian stochastic behaviour. In the method, the third-moment standardization that constants can be obtained from first three-order response moments was used to map a non-Gaussian structural response into a standard Gaussian process; then the mean up-crossing rates, the mean clump size and the initial passage probability of some critical barrier level by the original structural response were estimated. Finally, the formula for calculating first passage probability was established on the assumption that the corrected up-crossing rates are independent. By a nonlinear single-degree-of-freedom system excited by a stationary Gaussian load, it is demonstrated how the procedure can be used for the type of structures considered. Further, comparisons between the results from the present procedure and those from Monte-Carlo simulation are performed.