Sampling efficiency is important for simulation-based design optimization. While Bayesian optimization (BO) has been successfully applied in engineering problems, the cost associated with large-scale simulations has not been fully addressed. Extending the standard BO approaches to multi-fidelity optimization can utilize the information of low-fidelity models to further reduce the optimization cost. In this work, a multi-fidelity Bayesian optimization approach is proposed, in which hierarchical Kriging is used for constructing the multi-fidelity metamodel. The proposed approach quantifies the effect of HF and LF samples in multi-fidelity optimization based on a new concept of expected further improvement. A novel acquisition function is proposed to determine both the location and fidelity level of the next sample simultaneously, with the consideration of balance between the value of information provided by the new sample and the associated sampling cost. The proposed approach is compared with some state-of-the-art methods for multi-fidelity global optimization with numerical examples and an engineering case. The results show that the proposed approach can obtain global optimal solutions with reduced computational costs.

采样效率对于基于仿真的设计优化很重要。尽管贝叶斯优化（BO）已成功应用于工程问题，但与大规模仿真相关的成本尚未完全解决。将标准BO方法扩展到多保真度优化可以利用低保真度模型的信息来进一步降低优化成本。在这项工作中，提出了一种多保真贝叶斯优化方法，其中使用层次克里格法来构造多保真元模型。所提出的方法基于预期进一步改进的新概念，量化了HF和LF样本在多保真度优化中的效果。提出了一种新颖的采集功能，可以同时确定下一个样本的位置和保真度，考虑到新样本提供的信息价值与相关样本成本之间的平衡。通过数值示例和工程案例，将所提出的方法与用于多保真全局优化的一些最新方法进行了比较。结果表明，该方法可以降低计算成本，获得全局最优解。