The multi-fidelity metamodeling method can dramatically improve the efficiency of metamodeling for computationally expensive engineering problems when multiple levels of fidelity data are available. In this paper, an efficient and novel adaptive multi-fidelity sparse polynomial chaos-Kriging (AMF-PCK) metamodeling method is proposed for accurate global approximation. This approach, by first using low-fidelity computations, builds the PCK model as a model trend for the high-fidelity function and captures the relative importance of the significant sparse polynomial bases selected by least angle regression (LAR). Then, by using high-fidelity model evaluations, the developed method utilizes the trend information to adaptively refine a scaling PCK model using an adaptive correction polynomial expansion-Gaussian process modeling. Here, the most relevant sparse polynomial basis set and the optimal correction expansion are adaptively identified and constructed based on a devised nested leave-one-out cross-validation-based LAR procedure. As a result, the optimal AMF-PCK metamodel is adaptively established, which combines advantages of high flexibility and strong nonlinear modeling ability. Moreover, an adaptive sequential sampling approach is specially developed to further improve the multi-fidelity metamodeling efficiency. The developed method is evaluated by several benchmark functions and two practically challenging transonic aerodynamic modeling applications. A comprehensive comparison with the popular hierarchical Kriging, universal Kriging, and LAR-PCK approaches demonstrates that the proposed method is the most efficient and provides the best global approximation accuracy, with particular superiority for quantities of interest in the multimodal and highly nonlinear landscape. This novel method is very promising for efficient uncertainty analysis and surrogate-based optimization of expensive engineering problems.

当可获得多个级别的保真度数据时，多保真度元建模方法可以显着提高针对计算量大的工程问题的元建模效率。本文提出了一种高效，新颖的自适应多保真稀疏多项式混沌-Kriging（AMF-PCK）元建模方法，用于精确的全局逼近。该方法首先使用低保真度计算，将PCK模型构建为高保真度函数的模型趋势，并捕获通过最小角度回归（LAR）选择的重要稀疏多项式基的相对重要性。然后，通过使用高保真模型评估，所开发的方法利用趋势信息通过自适应校正多项式展开-高斯过程建模来自适应地优化缩放PCK模型。这里，基于设计的基于嵌套式留一法式交叉验证的LAR程序，自适应地识别和构造最相关的稀疏多项式基集和最佳校正扩展。结果，自适应地建立了最佳的AMF-PCK元模型，该模型结合了高灵活性和强大的非线性建模能力的优点。此外，专门开发了一种自适应顺序采样方法，以进一步提高多保真度元建模效率。通过几个基准功能和两个实际具有挑战性的跨音速空气动力学建模应用程序对开发的方法进行了评估。与流行的分层Kriging，Universal Kriging和LAR-PCK方法进行的全面比较表明，所提出的方法是最有效的，并且提供了最佳的全局逼近精度，在多峰和高度非线性景观中，对于感兴趣的数量具有特别的优势。这种新颖的方法对于有效的不确定性分析和基于代理的昂贵工程问题的优化非常有前途。