A dimensional reduction outcrossing rate method for time-dependent system reliability analysis

Abstract

Reliability assessment of engineering structures requires accounting for the stochastic nature of loads and material properties, as well as the interaction among multiple components. These characteristics make time-dependent system reliability (TSR) a critical yet challenging problem. The outcrossing rate method has been introduced for TSR analysis, while its extension to multi-component systems suffers from exponential growth in the number of sub-events and high-dimensional computations. To address these challenges, a dimensional reduction outcrossing rate (DRO) method is proposed for efficient TSR analysis of both series and parallel systems. To address the challenge induced by the multiple outcrossing events, a theoretical model for the outcrossing rate is proposed, expressed in terms of two sub-events. An efficient numerical method is developed to compute the probability of these two events. Specifically, the instantaneous reliability indices and the correlation matrix of all component failure events are evaluated in a reduced-dimensional random space, which further improve the efficiency. Additionally, the failure probability, defined by a multiple integral, is computed using a dimensional reduction technique. The accuracy and efficiency of the DRO method are demonstrated through four case studies.