Multi-fidelity (MF) surrogate models have shown great potential in simulation-based design since they can make a trade-off between high prediction accuracy and low computational cost by augmenting the small number of expensive high-fidelity (HF) samples with a large number of cheap low-fidelity (LF) data. In this work, a generalized hierarchical co-Kriging (GCK) surrogate model is proposed for MF data fusion with both nested and non-nested sampling data. Specifically, a comprehensive Gaussian process (GP) Bayesian framework is developed by aggregating calibrated LF Kriging model and discrepancy stochastic Kriging model. The stochastic Kriging model enables the GCK model to consider the predictive uncertainty from the LF Kriging model at HF sampling points, making it possible to estimate the model parameter separately under both nested and non-nested sampling data. The performance of the GCK model is compared with three well-known Kriging-based MF surrogates, i.e., hybrid Kriging–scaling (HKS) model, KOH autoregressive (KOH) model, and hierarchical Kriging (HK) model, by testing them on two numerical examples and two real-life cases. The influence of correlations between LF and HF samples and the cost ratio between them are also analyzed. Comparison results on the illustrated cases demonstrate that the proposed GCK model shows great potential in MF modeling under non-nested sampling data, especially when the correlations between LF and HF samples are weak.

多保真（MF）替代模型在基于仿真的设计中显示出了巨大的潜力，因为它们可以通过增加大量昂贵的高保真（HF）样本，从而在高预测精度和低计算成本之间做出取舍。廉价低保真（LF）数据的数量。在这项工作中，提出了用于嵌套和非嵌套采样数据的MF数据融合的广义分层协同Kriging（GCK）替代模型。具体而言，通过汇总校准的LF克里格模型和差异随机克里格模型，开发了一个全面的高斯过程（GP）贝叶斯框架。随机Kriging模型可以使GCK模型考虑HF采样点处LF Kriging模型的预测不确定性，因此，可以在嵌套和非嵌套采样数据下分别估算模型参数。将GCK模型的性能与三种著名的基于Kriging的MF替代物进行了比较，分别通过混合Kriging-scaling（HKS）模型，KOH自回归（KOH）模型和分层Kriging（HK）模型对它们进行了测试数值示例和两个实际案例。还分析了低频和高频样本之间的相关性以及它们之间的成本比的影响。在所示案例上的比较结果表明，所提出的GCK模型在非嵌套采样数据下，特别是在LF和HF样本之间的相关性较弱的情况下，在MF建模中显示出巨大的潜力。通过在两个数值示例和两个实际案例中对它们进行混合测试，分别进行了混合Kriging-scaling（HKS）模型，KOH自回归（KOH）模型和分层Kriging（HK）模型。还分析了低频和高频样本之间的相关性以及它们之间的成本比的影响。在所示案例上的比较结果表明，所提出的GCK模型在非嵌套采样数据下，特别是在LF和HF样本之间的相关性较弱的情况下，在MF建模中显示出巨大的潜力。通过在两个数值示例和两个实际案例中对它们进行混合测试，分别进行了混合Kriging-scaling（HKS）模型，KOH自回归（KOH）模型和分层Kriging（HK）模型。还分析了低频和高频样本之间的相关性以及它们之间的成本比的影响。在所示案例上的比较结果表明，所提出的GCK模型在非嵌套采样数据下，特别是在LF和HF样本之间的相关性较弱的情况下，在MF建模中显示出巨大的潜力。