Structural Expected Lifetime Estimation for Systems With Multiple Failure Modes Based on Adaptive Learning Kriging Models

Structural safety is a critical concern when dealing with uncertainty, and the expected lifetime is an essential metric for its quantification. Physics-driven methods offer adequate simulation data in the initial design stage, eliminating the requirement for time-consuming lifetime testing experiments. However, performance functions of failure modes often involve implicit functions and/or partial differential equations, requiring numerous simulations that consume significant time. An adaptive learning Kriging method was developed to estimate the expected lifetime of a structure based on the first failure time. However, it is limited to a single-failure mode and cannot adequately address systems with multiple failure modes. This study proposes two effective methods for estimating the expected lifetime of systems with multiple failure modes using the adaptive Kriging model. These methods involve developing two novel learning functions to determine the failure mode and the new training sample that contribute the most to the expected lifetime. The Kriging models are adaptively refined until the proposed two stopping criteria are fulfilled. To prevent high-concentration training samples, this study proposes a system correlation function strategy that uses the correlation function of the failure mode contributing most to the system expected lifetime. Three examples demonstrate the efficiency and accuracy of the proposed methods.