Robust design of tuned mass damper with hybrid uncertainty

The robust design of a tuned mass damper (TMD) with hybrid aleatory and epistemic uncertainties is proposed in this study. In this method, the aleatory uncertainty involved in the external excitation is represented with the white noise in stochastic theory. The epistemic uncertainties derived from fragmentary statistical data and incomplete preknowledge of structural model and site condition are fully captured with the discrete multi-intervals in evidence theory. In order to overcome the computational bottleneck related to the uncertainty propagation of epistemic uncertainties, a parallel-efficient global optimization (parallel-EGO) method is proposed to approximate the bounds of structural response for joint focal elements. Then, a robustness objective function, with the aim to minimize the worst system response of the primary structure, is presented to search the optimal parameters of TMD. Finally, case studies for a single-degree-of-freedom (SDOF) system and a multi-degree-freedom (MDOF) system validate that the designed TMD not only significantly reduces the worst seismic responses but also improves the robustness of the primary structure.