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

Ziheng Feng,Xinmin Li,Xiao Wang,Min Li,Jianxin Zhao,Suzanne M Shontz

doi:10.1155/2022/4486311

Abstract

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.

Highlights

When building a surrogate model, it is important to identify a proper mean function for the kriging model. e commonly used variable selection method is the penalized blind kriging (PBK) method
In the Test function, compared with the traditional PBK method, the prediction accuracy of Method 2 (M2) is improved by 69.08% and 26.13%, respectively, under the penalty of Lasso and Elastic Net, and the time efficiency of Method 1 (M1) is improved by 85.15% and 90.33%, respectively, under the penalty of Lasso and Elastic Net
Ree new approaches are proposed for variable selection. e first method is to select the variables using a linear model at the first and estimate the parameters in the kriging model. e second method is first to estimate the parameters with the ordinary kriging (OK) model and select the variables via the penalized kriging model and refit the kriging model. e third method is an improvement of PBK, which is a refitting based on the variable selection of PBK. ese methods are proved to improve the prediction accuracy and time efficiency by several analytic functions and two examples

Summary

Step-by-Step Variable Selection Methods

We first review some of the details; three methods are proposed for variable selection based on PBK methods. Two penalty functions are used for variable selection in the PBK model by Hung [11], i.e., Lasso [14] and adaptive Lasso [15] It estimates the regression coefficients β by minimizing the negative penalized log-likelihood function. Us, we propose three step-by-step variable selection methods to improve the prediction accuracy and time efficiency. Eoretically, M1 and M2 do not need the iterative step of parameter estimation of β such as PBK in variable selection; they can improve time efficiency greatly. En, we can select active variables by minimizing the negative penalized log-likelihood function Q(β, θ􏽢OK, σ􏽢2OK) and update correlation parameters. The PBK method is used to select active variables β based on the kriging model via where N is the number of testing samples.

Method

Empirical Application

Conclusion and Discussion

Findings

Disclosure