Computer simulations (a.k.a. white-box models) are more indispensable than ever to model intricate engineering systems. However, computational models alone often fail to fully capture the complexities of reality. When physical experiments are accessible though, it is of interest to enhance the incomplete information offered by computational models. Gray-box modeling is concerned with the problem of merging information from data-driven (a.k.a. black-box) models and white-box (i.e., physics-based) models. In this paper, we propose to perform this task by using multi-fidelity surrogate models (MFSMs). A MFSM integrates information from models with varying computational fidelity into a new surrogate model. The multi-fidelity surrogate modeling framework we propose handles noise-contaminated data and is able to estimate the underlying noise-free high-fidelity function. Our methodology emphasizes on delivering precise estimates of the uncertainty in its predictions in the form of confidence and prediction intervals, by quantitatively incorporating the different types of uncertainty that affect the problem, arising from measurement noise and from lack of knowledge due to the limited experimental design budget on both the high- and low-fidelity models. Applied to gray-box modeling, our MFSM framework treats noisy experimental data as the high-fidelity and the white-box computational models as their low-fidelity counterparts. The effectiveness of our methodology is showcased through synthetic examples and a wind turbine application.

翻译：计算机模拟（即白盒模型）在建模复杂工程系统方面变得前所未有的不可或缺。然而，纯计算模型往往无法完全捕捉现实的复杂性。当物理实验可获取时，增强计算模型提供的非完备信息便具有重要价值。灰盒建模关注如何融合数据驱动（即黑盒）模型与白盒（即基于物理）模型的信息。本文提出采用多保真代理模型（MFSMs）实现该目标。多保真代理模型将不同计算保真度的模型信息整合为新型代理模型。我们提出的多保真代理建模框架能够处理含噪数据，并估计底层无噪高保真函数。该方法通过定量整合受测量噪声及高、低保真模型有限实验设计预算所致知识缺失影响的不同类型不确定性，强调以置信区间和预测区间形式精确估算预测不确定性。应用于灰盒建模时，我们的MFSM框架将含噪实验数据视为高保真数据，将白盒计算模型视为低保真对应物。通过合成示例与风力涡轮机应用案例验证了该方法的有效性。