Comparison of Metamodel Performances on an Electronic Circuit Problem

Aims: Investigation of building and validation of metamodels which of linear regression, simple kriging, ordinary kriging and radial basis function for an electronic circuit problem are the main aim of this study.

Study Design: An electronic circuit problem was considered to compare the performances of the metamodels. Latin hypercube design was used for experimental design of five input variables of the considered problem.

Methodology: A training data set consisting of 45 experiments and a validation data set consisting of 500 experiments were obtained using Latin hypercube design. Input variables were used by coded to calculate the spatial distances between observation points more consistently. Then using training data set linear regression, simple kriging, ordinary kriging and radial basis function metamodels were built. And, performance measures were calculated for the validation data set.

Results: It has been shown that simple kriging which are applied to outputs the differences from the mean, and ordinary kriging metamodels, produce superior solutions compared to the linear regression and radial basis function metamodels for the electronic circuit problem considered in this study. Prediction superiority of SK and OK than RBF on five-dimensional problem is another important result of the study.

Conclusion: Kriging metamodels are considered to be strong alternatives to the other metamodels for the problems that are considered in this study and have a similar nature. Since the superiority of metamodel methods to each other may vary from problem to problem, it is another important issue to compare their performance by considering more than one method in problem solving stage.