Adaptive multi-fidelity sparse polynomial chaos-Kriging metamodeling for global approximation of aerodynamic data

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.