Robust Optimum Design of Tuned Mass Damper in Seismic Vibration Control of Structures Under Uncertain Bounded System Parameters

Abstract

The optimum design of tuned mass damper (TMD) system considering model parameter uncertainty is usually performed by minimising the performance measure obtained by the total probability theory concept without any consideration to the variation of the performance of TMD due to uncertainty. However, such a design method does not necessarily correspond to an optimum design in terms of maximum response reduction as well as its minimum dispersion. The present study is focused on robust optimum design of TMD system of protection to mitigate the seismic vibration effect of structures considering uncertain but bounded (UBB)-type system parameters. The root mean square displacement (rmsd) of the primary structures is considered as the performance index. The robust optimisation is obtained by using a two-criterion equivalent deterministic optimisation problem where the weighted sum of the nominal value of the performance function and its dispersion is minimised. The conventional interval analysis-based bounded optimum solution is also obtained to demonstrate the effectiveness of the robust optimum solution. A numerical study is performed to elucidate the effect of parameter uncertainty on the robust optimum design of TMD parameters by comparing the robust optimisation results with the optimisation results obtained by solving usually adopted interval optimisation procedure.