Proposal for a function generator and extrapolation analysis

We propose a polynomial-based function generator to support decision-making in the context of experimental modeling (identification). The function generator tries to imitate regression problems in engineering applications. Stochastic elements ensure high variability between generated functions, while the user is able to choose a general complexity level defined by the strength of the nonlinearity and the order of interactions. An extension to overcome unfavorable properties of the polynomial-based structure is made. The ability to generate an arbitrary amount of test functions offers the possibility to statistically secure decisions in the development of algorithms or for the modeling task at hand. To demonstrate the abilities of our proposed function generator, it is utilized to pick a strategy for the design of experiments that should be used for the metamodeling of a centrifugal fan. We show, that for the application at hand the inclusion of all corners in the experimental design is destructive for the meta model's generalization performance.