Probability of failure of nonlinear oscillators with fractional derivative elements subject to imprecise Gaussian loads

In this paper, an approach for bounding the first-passage probability of a class of nonlinear oscillators with fractional derivative elements and subjected to imprecise stationary Gaussian loads is presented. Specifically, the statistical linearization and stochastic averaging methodologies are used in conjunction with an operator norm-based solution framework to estimate the bounds of the failure probability in a fully decoupled manner. The proposed technique can treat a wide range of nonlinear and hysteretic behaviors with relatively low computational cost. A numerical example is considered to demonstrate the applicability of the proposed approach. Specifically, the bounds of the first-passage probability of a bilinear hysteretic oscillator with fractional derivative elements are estimated.