Constructing Meta-Models for Computer Experiments

Abstract

We used three test functions to compare all combinations of five experimental design classes with either second-order response surface (RS) or kriging modeling methods. The findings included the following: 1) conclusions about which method performed best, even for a single case study, greatly depended on the specific experimental designs used to represent each class of designs; 2) unavoidable bias errors constituted the largest source of prediction errors when regression modeling was used with designs generated to address bias errors; and 3) estimation errors, which could be attributed to the use of the likelihood estimation objective, dominated prediction errors in kriging modeling. We tentatively conclude that, for cases in which the number of runs is comparable to the number of terms in a quadratic polynomial model, similar prediction errors can be expected from both kriging and regression modeling procedures as long as regression is used in combination with experimental designs generated to address bias errors.

• Expected Integrated Mean Squared Error
• Kriging Models
• Optimal Experimental Design
• Response Surface Methods

Additional information

Notes on contributors

Theodore T. Allen

Dr. Theodore T. Allen is an Assistant Professor in the Department of Industrial, Welding & Systems Engineering. He is a Senior Member of ASQ. His e-mail address is [email protected].

Mikhail A. Bernshteyn

Dr. Mikhail Bernshteyn is a co-founder of Sagata Ltd. and the manager of Sagata Limitée in Canada. His e-mail address is [email protected].

Khalil Kabiri-Bamoradian

Dr. Khalil Kabiri-Bamoradian is a Senior Research Associate Engineer in the Department of Industrial, Welding & Systems Engineering. His e-mail address is [email protected].