Identification of Critical Sequences of Fatigue-Induced Failures by Branch-and-Bound Method Employing System Reliability Bounds

Aircraft structures are often subjected to risk of failures caused by repeated loadings during their service. If such structural systems do not have adequate level of redundancy, local failures may initiate sequential failures or exceedingly large damage. It is thus essential to evaluate the risk of fatigue-induced failures and identify critical failure sequences for riskinformed decision making regarding design, inspection, and maintenance of aircraft. This requires complex system-level risk analysis dealing with sequential local failures towards a system failure. A challenge in such risk quantification is that the definition of system failure is not determined a priori, but identified through computational simulations as investigating the likelihoods and consequences of local failure sequences. For a sophisticated structural system with structural redundancy, there exist innumerable sequences of local failures that may lead to the system failure. Therefore, such a system-level risk analysis may require overwhelming costs of computational simulation and structural/system reliability analysis. Branch-and-Bound based methods have been widely used for efficient identification of critical sequences. However, these methods are either still time-consuming or prone to miss critical failure sequences with significant likelihood due to heuristic rules introduced to improve efficiency. This paper proposes a new Branch-and-Bound method employing system reliability Bounds (termed as B 3 method) to identify critical fatigue-induced failure sequences efficiently and accurately. The B 3 method identifies critical sequences of fatigueinduced failures in the decreasing order of their likelihoods as it systematically updates the bounds on the system failure probability. The updated bounds provide reasonable criteria for terminating the Branch-and-Bound search without missing critical sequences. The method is demonstrated by numerical example of a three-dimensional truss structure, and it will be applied to an aircraft longeron system.