Two-step translation method for time-dependent reliability of structures subject to both continuous deterioration and sudden events

Civil infrastructure can be subjected to different deterioration scenarios (e.g., continuous deterioration and sudden events) during its service life. Time-dependent reliability analysis of a deteriorating system is of vital importance in the structural design, assessment, and management process. In this paper, a general and novel probability density function-informed framework for time-dependent reliability analysis is developed, considering different deterioration processes and system-level performance. Both continuous deterioration and sudden events are considered within the proposed framework. For the scenario with random sudden drops and/or significant differences in deterioration rates, a novel two-step translation method is proposed to assess the probability density of the performance function within the service life of a structure. In this method, translation operation is conducted twice; the first time to build a virtual and differentiable performance function, and the second, to solve the actual probability density function based on the results from the first step. Then, three illustrative examples are assessed: a simple deteriorating case, a component-level case, and a system-level case. The relevant results demonstrate the feasibility and efficiency of the proposed method.