Sampling strategy for fuzzy numbers in the context of surrogate models

Abstract

Abstract The paper presents an investigation of the accuracy of surrogate models for systems with uncertainties, where the uncertain parameters are represented by fuzzy numbers. Since the underlying fuzzy arithmetic using $$\alpha$$ α -level optimisation requires a large number of system evaluations, the use of numerically expensive systems becomes prohibitive with a higher number of fuzzy parameters. However, this problem can be overcome by employing less expensive surrogate models, where the accuracy of the surrogate depends strongly on the choice of the sampling points. In order to find a sufficiently accurate surrogate model with as few as possible sampling points, the influence of various sampling strategies on the accuracy of the fuzzy evaluation is investigated. As well suited for fuzzy systems, the newly developed Fuzzy Oriented Sampling Shift method is presented and compared with established sampling strategies. For the surrogate models radial basis functions and a Kriging model are employed. As test cases, the Branin and the Camelback function with fuzzy parameters are used, which demonstrate the varying accuracy for different sampling strategies. A more application oriented example of a finite element simulation of a deep drawing process is given in the end.

Keywords

• Surrogate modelling
• Fuzzy numbers
• Kriging
• DACE
• Radial basis function
• Uncertainty