Probability of Failure of High-Rise Buildings Equipped with Magnetorheological Dampers by Considering Uncertainty in Stationary and Nonstationary Earthquakes

Abstract

In this study, the reliability analysis of magnetorheological (MR) dampers in semiactive control of structural responses under uncertainty in seismic excitation is investigated. Uncertainties in the input earthquake exerted to the base of the structure are evaluated in two cases by considering the stationary and nonstationary natures of the earthquake amplitude and frequency content. A clipped optimal control algorithm with a linear quadratic regulator control strategy is used for the semiactive control system. In this regard, an unconstrained optimization problem is proposed to minimize the maximum structural responses in order to optimize the control system’s performance of the damper. In reliability analysis, two limit state functions (LSFs) are defined based on structural safety and human comfort criteria. By using the standard Monte Carlo simulation method, the structure’s probability of failure for each LSF is calculated, and the system’s reliability in controlling the structure’s seismic responses is determined. The results show that the proposed optimization method results in better performance of dampers in reducing the structural seismic responses. Furthermore, by deriving the reliability graphs, the system’s reliability for any desired values of controlled responses can be obtained, which helps to design a reliable and safe smart structure.