Aspects of adaptive hierarchical RBF metamodels for optimization

Radial basis functions (RBFs), among other techniques, are used to construct metamodels that approximate multi-objective expensive high-fidelity functions from a finite number of function evaluations (design of experiments, DoE). Radial basis functions can be applied if the DoE covers the parameter space in an arbitrary though uniform manner. Leave-one-out strategies allow for computing tolerance limits. The approximated value and a certain tolerance can be interpreted as expectation and variance of a random experiment. Thus, model improvement as described for Kriging models in the literature can in principal be applied to RBF-based metamodels, too. We describe our adaptive and hierarchical metamodelling approach that deals with the specific problems that such metamodel adaptions pose to R BF-based models. We also briefly discuss implementation details and first industrial test cases.