A probability of improvement-based multi-fidelity robust optimization approach for aerospace products design

Abstract

Uncertainty is inevitable in aerospace products design optimization, which may lead to the undesired performance of aerospace products and even infeasible designs. Robust design optimization (RDO) aims to obtain a solution with a desirable performance mean and is insensitive to uncertainty. However, it is computationally intensive during the RDO process, which is unaffordable for aerospace product design optimization. Multi-fidelity (MF) surrogate modeling is a widely used strategy to alleviate the heavy computational burden in RDO problems. The existing MF surrogate modeling-based RDO approaches, however, generate the samples in a one-shot way, which requires sufficient samples distributed in the entire design space. In this work, a probability of improvement-based adaptive sampling approach is proposed for multi-fidelity robust design optimization. The multi-level hierarchical Kriging (MHK) model is used for multi-fidelity modeling, which allows the proposed approach to deal with data of multiple fidelities. Both design variable uncertainty and interpolation uncertainty are considered within the approach. An extended PI (EPI) function is developed to simultaneously select the design location and fidelity level of the updated sample. To deal with RDO problems with constraints, the proposed EPI function is extended by combining with the probability of feasibility functions. The proposed approach is demonstrated using four numerical examples and an engineering example of robust design optimization for a micro-aerial vehicle fuselage.