Robust optimum design of tuned liquid column damper in seismic vibration control of structures under uncertain bounded system parameters

The optimum design of a tuned liquid column damper (TLCD) considering system parameter uncertainty is usually performed by minimising the performance measure obtained by the total probability theory without any consideration to the variation of its performance due to parameter 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. Furthermore, such approach cannot be applied in many real situations when the required detailed information about the uncertain parameters is limited. The robust design optimisation (RDO) of a TLCD system to mitigate seismic vibration effect in which the bounds on the magnitude of the uncertain properties of the structural and ground motion model parameters are only required is attempted in this study. The RDO is formulated as a two-criterion optimisation problem where the weighted sum of the maximum root mean square displacement of the structure and its dispersion is minimised. The conventional interval analysis-based bounded optimum solution is also obtained to demonstrate the effectiveness of the proposed RDO approach. A numerical study elucidates the effect of parameter uncertainty on the RDO of TLCD parameters by comparing the RDO results with the bounded optimum results.