System reliability updating of fatigue-induced sequential failures

Abstract

Many structural systems are subjected to the risk of fatigue-induced failures caused by repeated loading during their service. For effective management of such risk, it is essential to estimate the reliability of a structure against fatigue-induced sequential failures and update the estimated reliability based on actual observations made during structural inspections. Despite much research effort dedicated to inspection-based reliability updating of structures, many previous studies aimed at updating the reliability estimates of individual structural members instead of system-level reliability. Moreover, such studies tend to focus on structures which show uniform stress distribution in discrete members such as truss. This paper proposes a new method to update the system-level reliability of a wide variety of structures under the risk of fatigue-induced sequential failures based on inspection results. The proposed system reliability updating method employs the Branch-and-Bound method employing system reliability Bounds (termed the B3 method). For both discrete and continuum structures, the B3 method can identify critical sequences of fatigue-induced failure in the decreasing order of their likelihood through integration with structural analysis and crack growth analysis. Next, the proposed method updates the probabilities of the most critical failure and nonfailure cases identified by the B3 method, so the upper and lower bounds on the system failure probability are efficiently updated with a reasonable size of gap without additional search of failure sequences. The proposed method is first demonstrated by a relatively simple numerical example, whose results can be verified by Monte Carlo simulation. Next, the method is applied to an aircraft longeron example to demonstrate that the method enables efficient and accurate system reliability updating of fatigue-induced sequential failures for a continuum structure under various inspection scenarios.