A decoupled method for time-dependent reliability-based design optimization

Time-dependent reliability-based design optimization (TRBDO) has received extensive attention because of its ability to achieve optimal solutions that help meet the requirement for whole lifecycle reliability by quantitatively considering dynamic uncertainties. However, directly solving TRBDO problems is computationally expensive, if not prohibitive, owing to the need to repeatedly evaluate time-dependent probabilistic constraints. To address this challenge, an efficient decoupled method called sequential optimization and time-dependent reliability assessment (SOTRA) is proposed in this study. This method transforms the original TRBDO problem, initially formulated probabilistically, into a problem using percentile formulation after discretizing time-dependent performance functions. By adopting the equivalent minimum performance target point (EMPTP) concept, the TRBDO problem is further converted into an equivalent deterministic optimization problem, which is subsequently solved through a sequential iteration process involving deterministic optimization and time-dependent reliability analysis. To efficiently and robustly search an EMPTP for reliability analysis, a time-dependent self-adaptive finite-step length method is developed. To verify the proposed SOTRA method against existing TRBDO methods, a numerical example, a benchmark structural design case of a simply supported beam, and an engineering application for flexible wheel design are exemplified in this study. The results demonstrate that the proposed SOTRA method exhibits high efficiency and robustness in solving TRBDO problems.