Advanced two

In this paper, an attempt is made to examine a new method for designing and applying the active vibration control system to improve building performance under mainshock–aftershock sequences. In this regard, three different structures are considered; 5-, 10-, and 15-story buildings. Seven mainshock–aftershock sequences are selected from the Iranian accelerogram database for analyzing the structures. By implementing an advanced two-step optimization method, buildings equipped with the active vibration control system (linear–quadratic regulator (LQR) algorithm) are designed to withstand all events of mainshock–aftershock sequences. In the first optimization step, a multi-objective optimization with the genetic algorithm is performed and a set of optimal Pareto front results is obtained. In the next step, the life-cycle cost of each optimal design sample of the Pareto front is calculated by considering the cumulative damage and the design sample with the minimum cost is selected as a final optimal property. The results prove that the active vibration control system is capable of reducing structural responses, including acceleration, drift, and residual drift under mainshock–aftershock sequences, and consequently the life-cycle cost of buildings, especially the taller ones. In addition, obtaining the building design variables (story stiffness and yielding force) and active LQR algorithm properties simultaneously leads to a slightly softer final building model than the conventional structure designed by the common building design code. Moreover, it is revealed that, by considering the aftershocks, the building life-cycle cost increases significantly