Using response surface approximations in fuzzy set based design optimization

The paper focuses on modelling uncertainty typical of the aircraft industry. The design problem involves maximizing a safety measure of an isotropic plate for a given weight. Additionally, the dependence of the weight on the level of uncertainty, for a specified allowable possibility of failure, is also studied. It is assumed that the plate will be built from future materials, with little information available on the uncertainty. Fuzzy set theory is used to model the uncertainty. Response surface approximations that are accurate over the entire design space are used throughout the design process, mainly to reduce the computational cost associated with designing for uncertainty. All of the problem parameters are assumed to be uncertain, and both a yield stress and a buckling load constraint are considered. The fuzzy set based design is compared to a traditional deterministic design that uses a factor of safety to account for the uncertainty. It is shown that, for the example problem considered, the fuzzy set based design is superior. Additionally, the use of response surface approximations results in substantial reductions in computational cost, allowing the final results to be presented in the form of design charts.