First-Passage Reliability Evaluation Based on the Probability Density Evolution of Stochastic Processes

Abstract

First-passage reliability of structures has been playing a central role in engineering performance evaluation and design for decades. It is well recognized that nonlinear stochastic dynamics of high-dimensional systems is the embedded essential tool for reliability evaluation, but great challenges still exist in this field. In the past decade, a family of probability density evolution method (PDEM) was developed. In this method, the coupling between the nonlinearity and the randomness was broken, and thereby a family of generalized density evolution equation was derived. Most recently, it is also applied in the dimension reduction of FPK equation for additively excited systems. In the present paper, this method is employed to capture the first-passage reliability of additively excited systems by imposing an absorbing boundary condition on the governing probability density evolution equation. Numerical examples are illustrated. Problems to be further studied are discussed.