Transforming reliability limit-state constraints into deterministic limit-state constraints

This research proposes an efficient methodology that can transform a reliability limit-state constraint into a deterministic limit-state constraint. This new method may have broad applications in reliability-based design and optimization. The method is based on subset simulation and is applicable to general systems, e.g. linear or nonlinear systems and static and dynamical systems with high-dimensional uncertainties. Once the reliability constraint is transformed into a deterministic one, it is no longer necessary to conduct reliability analyses to verify the former. This can potentially save lots of computational time during the process of reliability-based design and optimization. The main idea of the new method is the introduction of the limit-state factor and nominal limit-state function, from which a deterministic nominal limit-state constraint is established. We propose two methods of establishing this nominal constraint, and they are verified with several simulated examples, showing that the established nominal constraint is indeed a satisfactory approximation of the target reliability constraint. Finally, we propose a simplified procedure requiring only two reliability analyses that can effectively transform reliability constraints into deterministic nominal constraints.