Risk quantification of fatigue-induced sequential failures by branch-and-bound method employing system reliability bounds

Various types of structural systems are often subjected to the risk of fatigue-induced failures. If a structure does not have an adequate level of structural redundancy, local failures may initiate sequential failures and cause exceedingly large damage. For the risk-informed design and maintenance of such structural systems, it is thus essential to quantify the risk of fatigue-induced sequential failure. However, such risk analysis is often computationally intractable because one needs to explore innumerable failure sequences, each of which demands component and system reliability analyses in conjunction with structural analyses to account for various uncertainties and the effect of load re-distributions. To overcome this computational challenge, many research efforts have been made to identify critical failure sequences with the highest likelihood and to quantify the overall risk by system reliability analysis based on the identified sequences. One of the most widely used approaches is the so-called ???branch-and-bound??? method. However, only the lower bound on the system risk is usually obtained because of challenges in system reliability analysis, while the changes of the lower bound by newly identified sequences are not diminishing monotonically. This paper aims to improve the efficiency and accuracy of risk analysis of fatigue-induced sequential failures by developing a new branch-and-bound method employing system reliability bounds (termed the B3 method). On the basis of a recursive formulation of the limit-state functions of fatigue-induced failures, a system failure event is formulated as a disjoint cut-set system event. A new search scheme identifies critical fatigue-induced failure sequences in the decreasing order of their probabilities while it systematically updates both lower and upper bounds on the system failure probability without additional system reliability analyses. As a result, the method can provide reasonable criteria for terminating the branch-and-bound search without missing critical failure sequences and reduce the number of computational simulations required to obtain reliable estimates on the system risk. The B3 method is tested and demonstrated by numerical examples of a multi-layer Daniels system and a three-dimensional offshore structure