A Sequential Sampling Approach for Multi-Fidelity Surrogate Modeling-Based Robust Design Optimization

Multi-fidelity surrogate modeling has been extensively used in engineering design to achieve a balance between computational efficiency and prediction accuracy. Sequential sampling strategies have been investigated to improve the computational efficiency of surrogate-assisted design optimization. The existing sequential sampling approaches, however, are dedicated to either deterministic multi-fidelity design optimization or robust design under uncertainty using single-fidelity models. This paper proposes a sequential sampling method for robust design optimization based on multi-fidelity modeling. The proposed method considers both design variable uncertainty and interpolation uncertainty during the sequential sampling. An extended upper confidence boundary (EUCB) function is developed to determine both the sampling locations and the fidelity levels of the sequential samples. In the EUCB function, the cost ratio between high- and low-fidelity models and the sampling density are considered. Moreover, the EUCB function is extended to handle constrained robust design optimization problems by combining the probability of feasibility. The performance of the proposed approach is verified using two analytical examples and an engineering case. Results show that the proposed sequential approach is more efficient than the one-shot sampling method for robust design optimization problems.