Variable-fidelity (VF) surrogate models have attracted significant attention recently in simulation-based design because they can achieve a desirable accuracy at a reasonable cost by making use of the data from both low-fidelity (LF) and high-fidelity (HF) simulations. To facilitate the usage of VF surrogate models assisted efficient global optimization, there are still challenging issues on (1) how to construct the VF surrogate model for simulations with variable-fidelity levels under the non-nested sampling data, (2) how to determine the location and fidelity level of the samples simultaneously, and (3) how to handle constraints when VF surrogate models are also used for constraints. In this work, a variable-fidelity probability of improvement (VF-PI) method is proposed for computationally expensive black-box problems. First, a multi-level generalized Co-Kriging (GCK) model, which is extended from the two-level GCK model, is developed for VF surrogate modeling of simulations with three or more levels of fidelities under non-nested sampling data. Second, to determine the location and fidelity level of the sequential samples, an extended probability of improvement (EPI) function is developed. In EPI function, the model correlation and cost ratio between the LF and HF models, together with the sample density, are considered. Third, the probability of satisfying the constraints is introduced and combined with the EPI function, enabling the proposed approach to handle VF optimization problems with constraints. The comparison results illustrate that the proposed VF-PI method is more efficient and robust than the four compared methods on the illustrated cases.

可变保真度（VF）替代模型最近在基于仿真的设计中引起了广泛的关注，因为它们可以通过利用来自低保真度（LF）和高保真度（HF）的数据以合理的成本获得理想的精度。模拟。为了促进VF替代模型辅助高效全局优化的使用，仍然存在以下挑战性问题：（1）如何在非嵌套采样数据下构造具有可变保真度水平的仿真的VF替代模型；（2）如何确定同时定位样本的位置和保真度，以及（3）当VF替代模型也用于约束时如何处理约束。在这项工作中，提出了一种可变保真度改进概率（VF-PI）方法，用于计算量大的黑盒问题。第一，针对两层GCK模型的扩展，开发了一个多层次的通用Co-Kriging（GCK）模型，用于在非嵌套采样数据下使用三级或三级以上保真度的仿真的VF代理建模。第二，为了确定顺序样本的位置和保真度，开发了改进的扩展概率（EPI）函数。在EPI函数中，考虑了LF和HF模型之间的模型相关性和成本比以及样本密度。第三，引入满足约束的概率并将其与EPI函数结合，从而使所提出的方法能够处理具有约束的VF优化问题。比较结果表明，在所示情况下，所提出的VF-PI方法比四种比较方法更为有效和稳健。