Polynomial metamodeling with dimensional analysis and the effect heredity principle

Polynomial metamodels (PMs) are widely used in simulation experiments for product design. However, construction of these metamodels is difficult if the number of inputs is large or the degree of the polynomial used to approximate the true function is high because the number of basis functions would be very large. This paper describes the use of dimensional information and the effect of heredity principle to reduce the number of models that need to be considered. A version of the Buckingham π Theorem is employed to reduce the inputs, some of which may be fixed physical quantities, to a smaller number of dimensionless variables. The effect heredity principle is generalized for arbitrary polynomial basis functions and a justification for the generalization is provided. A simple Bayesian approach that incorporates the principle is employed for model selection. Realistic examples show that PMs obtained by utilizing dimensional analysis and the effect heredity principle have better prediction accuracy.