Reliability Updating with a System Reliability Method Based on Adaptive Kriging

Abstract

Reliability updating can improve the failure probability estimates of structural systems when new observations are obtained. At present, an efficient reliability updating method is one that transforms the equality observation information into the inequality type by introducing an auxiliary variable and then employs structural reliability methods to perform reliability updating. For this method, the computation of posterior failure probability Pr(F|Z), where Z is an observation event, requires two reliability analysis processes to estimate Pr(Z) and Pr(F∩Z), respectively. To improve the efficiency, this paper develops a reliability updating method with output observations, where the computation of Pr(Z) and Pr(F∩Z) is integrated into one system reliability problem, which is then solved by adaptive kriging with truncated candidate region (AKTCR). A composite adaptive learning process is developed to construct the kriging model, which can provide accurate estimates for both Pr(Z) and Pr(F∩Z). In this way, the proposed method can also deal with the problem of multiple failure modes and multiple observation events. In addition, a combined global and local sampling method is embedded into the proposed algorithm to reduce the size of candidate sample pool and improve the modeling efficiency. Finally, three examples can prove the efficiency and accuracy of the proposed reliability updating method. In this work, we present a reliability updating framework for structural systems with output observations based on kriging. Although mathematical models often replace physical systems for reliability analysis, deviation between the real physical system and its model is inevitable. Thus, it is very necessary to reevaluate the failure probability of a structural system with the available observations when its model is used. In general, these observations can be collected from various sensors, such as force sensors, accelerometers, and so on. Once observations are obtained, the likelihood function and therefore the transformed inequality limit state function can be constructed, and reliability updating can be performed. Given that many models of physical systems are still expensive, such as the finite-element model, a kriging model is adopted to replace the expensive forward model and fit the inequality limit state function for simulation. Our reliability updating framework is also applicable to cases where there are multiple failure modes and multiple observation events. We expect our reliability updating framework can significantly save computational costs in engineering practice.