Active learning Kriging-based multi-objective modeling and optimization for system reliability-based robust design

Reliability-based robust design optimization (RBRDO) has been widely studied to ensure the necessary robustness and reliability throughout the product life cycle. However, most of the existing researches on RBRDO could obtain robust solutions that meet the minimal reliability requirements but make reliability improvement difficult. The critical contribution of this work is to propose a novel multi-objective RBRDO framework based on active learning Kriging modeling. Specifically, the framework incorporates quality loss and system reliability in the objective, enabling it to enhance reliability while maintaining robustness. According to the merits of the active learning Kriging model, an improved U learning function is introduced to the system failure boundary modeling. Additionally, the modified expected improvement criterion is adopted for the target response modeling in the system safe domain. Moreover, the Kriging model of the system reliability index is established with a two-stage active learning strategy. Finally, using the NSGA-II algorithm to obtain a uniformly distributed Pareto front. Example results show that the proposed framework can serve as a new approach to solving the RBRDO problem and the Pareto front provides the opportunity to enhance reliability while maintaining robustness.