An enhanced RBF-HDMR integrated with an adaptive sampling method for approximating high dimensional problems in engineering design

Metamodels are often used in engineering design optimization problems with expensive simulations to save computational cost. But these metamodels often face "curse-of-dimensionality" when used in approximating high dimensional problems. Therefore, a new high dimensional model representation (HDMR) by combining Cut-HDMR with an enhanced RBF based on ensemble model is proposed. The developed HDMR, termed as ERBF-HDMR, sufficiently utilizes advantages of RBF and ensemble model in the modeling process. It can naturally explore and exploit the linearity/nonlinearity and correlations among variables of underlying problems, which are unknown or computationally expensive. Besides, to improve the efficiency of the ERBF-HDMR, an adaptive sampling method is proposed to add new sample points. Moreover, a mathematical function is used to illustrate the modeling principles and procedures of the adaptive ERBF-HDMR. And a comprehensive comparison between the adaptive ERBF-HDMR and other different Cut-HDMRs in literature has been made on eleven numerical examples with a wide scope of dimensionalities to show the prediction ability of different HDMRs. Finally, the proposed HDMR is used in the structural design optimization of the bearings of an all-direction propeller with the aim of reducing vibration.