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Aspects of adaptive hierarchical RBF metamodels for optimization

: Bühren, Georg van; Hornung, Nils; Clees, Tanja; Nikitina, Lialia


Journal of computational methods in sciences and engineering : JCMSE 12 (2012), Nr.1-2, S.5-23
ISSN: 1472-7978
ISSN: 1875-8983
Fraunhofer SCAI ()
surrogate-based optimization; RBF interpolation; metamodel refinement; hierarchical metamodelling

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.