A Kriging-based adaptive parallel sampling approach with threshold value

Most of Kriging-based adaptive sampling approaches were focused only on the sequence architectures for producing limited (i.e., one or two) updating points, but few attention was given to the parallel sampling strategy to obtain multiple updating points in one iteration. In this study, a novel Kriging-based adaptive parallel sampling approach (KAPS-MEIGF) is proposed. This parallel sampling approach selects the first most informative update point by maximizing the expected improvement of global fit (EIGF) criterion that considers both the bias and variance information. Then the parallel sampling criterion with a threshold value is used to generate multiple potential sample points. Particularly, the cross-validation strategy is used to dynamically balance the global exploitation and local exploitation. The results of 18 test cases show that the proposed KAPS-MEIGF outperforms the EIGF sampling approach but it is worse than the maximum mean square error (MMSE) sampling approach and the combined expectation (CE) sampling approach for most of the 2-dimension test cases. However, for high-dimensional complex problems, KAPS-MEIGF exhibits significantly competing performance compared with the MMSE sampling approach and the CE sampling approach, which indicates the robustness of stability of KAPS-MEIGF. In addition, the running speed of KAPS-MEIGF is 2.8-30.9 times that of the MMSE sampling approach. Therefore, it is a very promising sampling approach to build Kriging models for the problems with diverse characteristics, especially for simulation-based high-dimensional problems. Finally, a multi-objective optimization of rotating impeller module with static cascade (RIM-SC) for rotary separated range hood illustrates the engineering application value of KAPS-MEIGF method. The result shows that the searching efficiency of KAPS-MEIGF method is about 4.4 times higher when compared to other sequence sampling strategy. For the optimized RIM-SC, both separation efficiency and exhaust airflow rate at design condition are improved by 20.3% and 63.6%, respectively, and the impeller input power is decreases by 2.8%.