Single-step reliability-based optimization of Visco-frictional multiple tuned mass dampers (VFMTMDs) for minimizing the seismic failure probability of buildings using CIOA

This paper proposes a single-step reliability-based optimization framework for the design of Visco-Frictional Multiple Tuned Mass Dampers (VFMTMDs), which integrate both viscous and frictional damping mechanisms within a single device, unlike traditional approaches that consider only one type of damping. The proposed methodology simultaneously optimizes the number, placement, and mechanical parameters of VFMTMDs to minimize the probability of structural failure under seismic loading, explicitly accounting for the inherent uncertainties of ground motion. The optimization process employs the Circle-Inspired Optimization Algorithm (CIOA), a state-of-the-art metaheuristic developed by the authors. A ten-story benchmark building under seven actual seismic accelerograms served as a case study. The results of three independent optimization runs produced identical solutions, confirming the robustness and repeatability of the proposed approach. The optimal configuration consisted of two VFMTMDs installed on the top two floors, each with a mass ratio of only 1.5%. The optimized design achieved a 96.85% reduction in the probability of structural failure and a more than 35% increase in the seismic acceleration associated with the average fragility, demonstrating a substantial improvement in seismic reliability. Overall, the findings validate the proposed methodology as a robust and efficient framework for the optimal design of VFMTMDs, significantly enhancing the seismic performance of buildings in earthquake-prone regions.