To reduce the computational cost of uncertainty propagation, multi-fidelity polynomial chaos approaches have been developed by fusing a few expensive high-fidelity data points and many less expensive lower-fidelity data points to build a stochastic metamodel. However, previous studies mainly focused on multi-model fusion. Systematically allocating sample points from multi-fidelity models to ensure both the accuracy and efficiency of the metamodel still remain challenging. To address this issue, a new maximum cost performance (MCP) sequential sampling strategy considering both the sample cost and accuracy improvement is proposed based on the recently developed multi-fidelity PC-Kriging (MF-PCK) approach. With the proposed sampling strategy, the input location with the largest prediction error is identified as the new input sample point, and then, the multi-fidelity model with the largest CP index is selected for evaluation to reduce the computational cost as much as possible. Furthermore, a sample density function is introduced to avoid the clustering of samples, which can prevent wastage of sample points and the singularity problem. The effectiveness and relative advantage of the proposed multi-fidelity sampling strategy in terms of efficiency is demonstrated by comparative studies using several numerical examples for uncertainty propagation and an airfoil robust optimization problem.

为了降低不确定性传播的计算成本，通过融合一些昂贵的高保真数据点和许多较便宜的低保真数据点来构建随机元模型，已经开发了多保真多项式混沌方法。然而，以前的研究主要集中在多模型融合上。从多保真模型中系统地分配样本点以确保元模型的准确性和效率仍然具有挑战性。为了解决这个问题，基于最近开发的多保真 PC-Kriging (MF-PCK) 方法，提出了一种新的最大成本性能 (MCP) 顺序采样策略，同时考虑了样本成本和准确性的提高。使用所提出的采样策略，将预测误差最大的输入位置识别为新的输入采样点，然后，选择CP指数最大的多保真模型进行评估，尽可能降低计算成本。此外，引入样本密度函数来避免样本的聚类，可以防止样本点的浪费和奇异性问题。所提出的多保真采样策略在效率方面的有效性和相对优势通过比较研究证明，使用几个数值例子进行不确定性传播和翼型鲁棒优化问题。