Comparative Study on Optimal Distribution of Viscous Dampers Using Genetic Algorithm and Intelligent Water Drops Under Energy-Compatible Endurance Time Excitations

Nonlinear time-history analysis (NLTHA) remains one of the most rigorous tools for evaluating the seismic performance of structures; however, its high computational cost limits practical application within optimization frameworks. The endurance time (ET) method, which applies intensifying accelerograms to structures, enables continuous assessment of seismic demands across multiple hazard levels with a significantly reduced number of analyses. This study investigates the optimal distribution of fluid viscous dampers (FVDs) in a three-story deficient steel moment-resisting frame using the ET method, subject to performance-level constraints prescribed by ASCE/SEI ۴۱-۰۶ at the life safety (LS) and collapse prevention (CP) levels. Two metaheuristic algorithms – a standard genetic algorithm (GA) and the intelligent water drops (IWD) algorithm – are employed in a controlled comparative setting with identical modeling assumptions, objective functions, and constraint formulations. The optimization problem is formulated to minimize the total damping demand while satisfying interstory drift ratio (IDR) limits at basic safety earthquake (BSE) hazard levels BSE-۱ and BSE-۲. The study further extends the formulation to a multi-objective framework that simultaneously addresses peak drift, peak floor acceleration, and total damper cost. Results demonstrate that both algorithms concentrate the dominant damping contribution at the second story, consistent with the fundamental mode deformation profile. The IWD algorithm exhibits faster convergence and achieves a marginally lower total damping coefficient (approximately ۶-۹% reduction in mean IDR) compared with GA, while both algorithms satisfy the prescribed performance limits. Validation against conventional NLTHA confirms that ET-based predictions remain within an acceptable engineering error margin of less than ۱۲%. Energy balance analyses indicate that FVDs dissipate approximately ۳۵-۴۵% of seismic input energy, confirming the efficacy of the supplemental damping system.

کلیدواژه ها:

Endurance time method ، Fluid viscous damper ، Structural optimization hysteretic energy ، Genetic Algorithm ، Intelligent water drops