Efficient Hierarchical Kriging Modeling Method for High-dimension Multi-fidelity Problems

The multi-fidelity Kriging model is a promising technique in surrogate-based design, balancing model accuracy and the cost of sample generation by combining low- and high-fidelity data. However, the cost of building a multi-fidelity Kriging model increases significantly as problem complexity grows. To address this issue, we propose an efficient Hierarchical Kriging modeling method. In building the low-fidelity model, distance correlation is used to determine the relative value of the hyperparameter. This transforms the maximum likelihood estimation problem into a one-dimensional optimization task, which can be solved efficiently, significantly improving modeling efficiency. The high-fidelity model is built similarly, with the low-fidelity model's hyperparameter used as the relative value for the high-fidelity model's hyperparameter. The proposed method's effectiveness is evaluated through analytical problems and a real-world engineering problem involving modeling the isentropic efficiency of a compressor rotor. Experimental results show that the proposed method reduces modeling time significantly without compromising accuracy. For the compressor rotor isentropic efficiency model, the proposed method yields over 99% cost savings compared to conventional approaches, while also achieving higher accuracy.