Fuzzy-entropy based robust optimization criteria for tuned mass dampers

Tuned mass dampers (TMD) are well known as one of the most widely adopted devices in vibration control passive strategies. In the past few decades, many methods have been developed to find the optimal parameters of a TMD installed on a structure and subjected to a random base excitation process, but most of them are usually based on an implicit assumption that all of the structural parameters are deterministic. However, in many real cases this simplification is unacceptable, so robust optimal design criteria becomes a viable alternative to better support engineers in the design process. In Robust Design Optimization (RDO) approaches, indeed the solution must be able to not only minimize the performance but also to limit its variation induced by uncertainty. Most of the currently available RDO methods are based on a probabilistic description of the model uncertainty, even if in many cases they are not able to explicitly include the influence of all the possible sources of uncertainties. Therefore, in this study, a fuzzy version of the robust TMD design optimization problem is proposed. The consistency of the fuzzy approach is studied with respect to the available non-probabilistic formulations reported in the literature and an application to an example of a robust design of a linear TMD subjected to base random vibrations in the presence of fuzzy uncertainties. The results show that the proposed fuzzy-based approach is able to give a set of optimal solutions both in terms of structural efficiency and sensitivity to mechanical and environmental uncertainties.