Fuzzy-based robust structural optimization

Robust optimization is conventionally defined as the collection of the possible problem solutions that can ensure acceptable performances and sufficient immunity against the effects of uncertain parameter variability. Methods proposed until now use a probabilistic way to model uncertainty and to quantify the final sensitivity. In this work, a fuzzy uncertainty modellization is adopted for structural engineering. In particular, to define solution performance scattering, the fuzzy entropy is used as a global measure of variable dispersion. The final formulation of the problem deals with two antithetical objective functions, the fuzzy expected value of structural performance and its fuzzy entropy. This fuzzy-based approach in robust design is able to give a set of Pareto optimal solutions in terms of structural efficiency and sensitivities regarding uncertainty, and represents a suitable tool in supporting the decision maker. Finally, different applications have been developed to demonstrate the applicability of the proposed method.