A new solution framework for time-dependent reliability-based design optimization

•A new solution framework for time-dependent RBDO (TRBDO) is proposed.•Three different time-independent equivalent models are developed in this framework.•This solution framework avoids time-consuming time-dependent reliability analysis.•The proposed decoupled model is superior in efficiency to existing TRBDO methods.•Numerical examples and engineering problems validate this solution framework. Time-dependent reliability-based design optimization (TRBDO) has attracted intensive research attentions in recent years by virtue of its unique ability to allow consideration of dynamic uncertainties caused by stochastic processes and material property degradation. However, existing TRBDO methods are generally too intricate to be practically applicable for practical engineering application. On top of that, extremely high computational cost for complex TRBDO problems further hinders its practicability. To facilitate smooth implementation via enhancing computational efficiency in solving TRBDO problems, this study proposes an innovative and efficient solution framework. The strategy is that time-dependent performance function in each probabilistic constraint is discretized into a series of instantaneous performance functions to transform the original TRBDO problem into a RBDO problem. The reliability of each probabilistic constraint in the transformed RBDO problem is then considered under extreme value condition. With engagement of the first-order reliability method, the RBDO problem is transformed into two different triple-loop timeindependent RBDO problem. However, the issue of expensive computational cost still persists due to the triple-loop structure and identification of temporal variables under extreme value condition. To this gap, a decoupled strategy is adopted to resolve the triple-loop structure into a series of cycles of double-loop reliability analyses and deterministic optimization. Two numerical examples and three engineering applications are employed to demonstrate the supreme computational performance of the currently proposed solution framework. Results show that the proposed framework is capable of achieving a reliable optimal design at a fast convergence speed.