A two-level surrogate framework for demand-objective time-variant reliability-based design optimization

Complex engineering problems in the real world often involve uncertainties and require time-consuming simulations and experiments, hindering the efficiency of constraints processing. Additionally, practical engineering problems may have varying demands that pose new challenges for dealing with dynamic environments. However, most existing methods focus on immediate demands, making it inevitable to undergo tedious procedures to find feasible solutions. To address these issues, this paper proposes a demand-objective time-variant reliability-based design optimization framework to meet different demands in varying environments. Meanwhile, a corresponding two-level surrogate-based solving strategy is developed to reduce the computational resources required. The framework consists of two stages: time-variant reliability-based constraint handling and demand-objective optimization. An adaptive two-level surrogate method is proposed for time-variant reliability-based constraint handling by combining Kriging to reduce computational costs associated with evaluating constraints. This paper introduces moderate, conservative, and radical models for demand-objective optimization, combining the two-level surrogate method to deal with dynamic cost functions with different demands. Also, a new constrained minimax optimization method is developed for the radical model, which is the trickiest but very useful in practical engineering problems so that the algorithm can converge quickly. Finally, some examples are demonstrated to specify the proposed framework in applications.