Application of a sampling-based method for estimation of cumulative failure probability functions of mechanisms

Abstract

This contribution addresses the estimation of cumulative failure probability functions of mechanisms subject to random inputs and with random process outputs, which is still a challenging topic for mechanism design. The cumulative failure probability function over a whole time interval is time-dependent and estimated by combining the concept of composite limit state function with Generalized Subset Simulation. The failure domain associated with a composite limit state function at a certain time instant is viewed as a response from the time-dependent mechanism system. Then, a multiple-response system is formed by considering all discrete time instants along the motion locus of a mechanism. The failure domains at all time instants are explored taking advantage of the dependency among multiple responses. Such a method allows estimating small failure probabilities with high accuracy and precision while requiring a reduced number of samples with only one simulation run. A mathematical example is used for parametric study, followed by the time-dependent reliability analysis of a slider-crank mechanism and a four-bar function generator mechanism. The results show that the presented method possesses high accuracy and efficiency for time-dependent mechanism reliability analysis.