A response surface based optimisation algorithm for the calculation of fuzzy envelope FRFs of models with uncertain properties

This paper describes a response surface based optimisation technique for the calculation of envelope frequency response functions (FRFs) of imprecisely defined structures using the interval and fuzzy finite element method. The authors developed a hybrid – global optimisation and interval arithmetic – procedure for interval and fuzzy envelope FRF calculation. This hybrid approach reduces the computational cost of the analysis compared to a full global optimisation approach and reduces the conservatism on the envelope FRF compared to a full interval arithmetic approach. Still, the optimisation step is the computationally most expensive part of the algorithm. To handle industrially sized applications, a very efficient optimisation procedure is imperative. The response surface based procedure described in this paper decreases the computational cost of a fuzzy envelope FRF calculation with a factor 50 or more compared to the commonly used two-level full factorial design of experiments, while giving a comparable accuracy.