Metamodeling for high dimensional design problems by multi-fidelity simulations

Multi-fidelity metamodeling provides an efficient way to approximate expensive black-box problems by utilizing the samples of multiple fidelities. While it still faces the challenge of “curse-of-dimensionality” when used in approximating high dimensional problems. On the other hand, the high dimensional model representation (HDMR) method, as an efficient tool to tackle high dimensional problems, can only handle single-fidelity samples in approximation. Therefore, a hybrid metamodel which combines Cut-HDMR with Co-kriging and kriging is proposed to improve the metamodeling efficiency for high dimensional problems. The developed HDMR, termed as MF-HDMR, can efficiently use multi-fidelity samples to approximate black-box problems by using a two stage metamodeling strategy. It can naturally explore and exploit the linearity/nonlinearity and correlations among variables of underlying problems, which are unknown or computationally expensive. Besides, to further improve the efficiency of MF-HDMR, an extended maximin distance sequential sampling method is proposed to add new sample points of different fidelities in the metamodeling process. Moreover, a mathematical function is used to illustrate the modeling theory and procedures of MF-HDMR. In order to validate the proposed method, it is tested by several numerical benchmark problems and successfully applied in the optimal design of a long cylinder pressure vessel. Moreover, an overall comparison between the proposed method and several other metamodeling methods has been made. Results show that the proposed method is very efficient in approximating high dimensional problems by using multi-fidelity samples, thus making it particularly suitable for high dimensional engineering design problems involving computationally expensive simulations.