Step-by-Step Penalized Blind Kriging Methods for Surrogate Modeling

When building a surrogate model, it is important to identify a proper mean function for the kriging model. The commonly used variable selection method is the penalized blind kriging (PBK) method. But this method could lead to a low time efficiency, which is not suitable for experiments with time-sensitive data. In this paper, we propose three step-by-step approaches for constructing an appropriate mean function to improve the prediction accuracy and time efficiency of the PBK method. Several functions and two engineering examples are used to prove the effectiveness of the proposed methods. From simulation results, we can see that Method 1 (M1) and Method 2 (M2) have been significantly improved in both the prediction accuracy and the time efficiency compared with PBK. Especially, in the Test function, compared with the traditional PBK method, the prediction accuracy of M2 is improved by 69.08% and 26.13%, respectively, under the penalty of Lasso and Elastic Net, and the time efficiency of M1 is improved by 85.15% and 90.33%, respectively, under the penalty of Lasso and Elastic Net. In addition, Method 3 (M3) has been significantly improved in prediction accuracy compared with PBK.