Reliability-based optimal control design for seismic-excited structures: A hybrid IS-MTLBO pseudo-double loop method

Abstract

This study addressed a reliability-based optimal control design (RBOCD) approach for seismic-excited structures. For this aim, a hybrid importance sampling-modified teaching-learning based optimization (IS-MTLBO) pseudo-double loop method is developed. Uncertainty sources such as structural model, stochastic model of the ground acceleration, structural response measurements in sensors, and designed/applied forces in actuators are considered in this study. Numerical studies are carried out on a 10-story building subjected to earthquake excited. A deterministic optimal control design (DOCD) approach based on the MTLBO algorithm is firstly conducted for the structure. Then, a sensitivity analysis using the Borgonovo sensitivity method is carried out to identify and measure the effectiveness of the mentioned uncertainty sources on the seismic responses. Finally, the IS-MTLBO pseudo-double loop approach as an RBOCD approach is implemented for the studied structure. The average reductions of the seismic responses in terms of maximum displacement, acceleration, and drift of floors are obtained as 18.95%, 27.7%, and 24.65% for the RBOCD approach, while, the corresponding reduction are 7.30%, 19.45%, and 14.05% for the DOCD approach. It is shown that although the designed controller based on the DOCD approach satisfies the limitation considered for the maximum floor drift in the nominal model, it is not able to satisfy it in the presence of uncertainties. In other words, the RBOCD approach represents a robust control design against uncertainties, while the DOCD approach gives an uncertainty-sensitive control scheme. Considering four well-known earthquakes, the failure probabilities of the structure controlled by both DOCD and RBOCD approaches are compared. The results indicate the failure probability of the structure controlled by the RBOCD approach is much less than those given using the DOCD approach.