Aspects of adaptive hierarchical RBF metamodels for optimization

  • Authors:

  • Georg van Bühren;Nils Homung;Tanja Clees;Lialia Nikitina

  • Affiliations:

  • Fraunhofer SeAl, Sankt Augustin, Gennany;Fraunhofer SeAl, Sankt Augustin, Gennany;Fraunhofer SeAl, Sankt Augustin, Gennany;Fraunhofer SeAl, Sankt Augustin, Gennany

  • Venue:
  • Journal of Computational Methods in Sciences and Engineering - Special issue on Advances in Simulation-Driven Optimization and Modeling
  • Year:
  • 2012

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Abstract

Radial basis functions (RBFs), among other techniques, are used to construct metamodels that approximate multiobjective 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 ofa 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 RBF-based models. We also briefly discuss implementation details and first industrial test cases.