A generalized hierarchical co-Kriging model for multi-fidelity data fusion

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.