A novel quantum-theory-based optimization of tuned mass dampers for structural vibration control

Tuned Mass Dampers (TMDs) are widely used to suppress excessive vibrations in dynamically excited structures. However, traditional optimization techniques such as Genetic Algorithms (GA) and Particle Swarm Optimization (PSO) often struggle with slow convergence and suboptimal tuning. This study introduces a Quantum-Theory-Based Optimization (QPSO) approach for optimizing TMD parameters in Single-Degree-of-Freedom (SDOF) systems. By leveraging quantum mechanics-inspired principles, QPSO enhances global search efficiency, leading to improved damping performance while reducing computational costs (50 and 200 population size). The optimization objective is to minimize peak structural response, ensuring optimal energy dissipation and vibration suppression. The study systematically evaluates the effectiveness of QPSO by comparing its performance with GA in both deterministic and uncertain environments. Deterministic analysis demonstrates that QPSO significantly reduces peak displacement and acceleration, particularly for high-rise structures where longer tuning periods enhance damping efficiency. The uncertainty analysis, conducted using Monte Carlo Simulations (MCS), discloses that QPSO-optimized TMDs remain robust even when structural parameters (stiffness and damping) vary within a ± 15 % range. Additionally, statistical evaluations using Probability Density Functions (PDFs) and Cumulative Distribution Functions (CDFs) confirm that QPSO minimizes the likelihood of extreme vibration events more effectively than GA. The findings establish QPSO as a superior alternative to conventional metaheuristic methods for optimizing TMD parameters. By integrating closed-form solutions (Den Hartog, Sadek) as initial estimates, QPSO achieves faster convergence and ensures globally optimized damping configurations. The proposed method is particularly beneficial for high-rise buildings, bridges, and dynamically sensitive structures, where vibration mitigation under uncertainty is critical. Furthermore, the application of the proposed QPSO approach to Multi-Degree-of-Freedom (MDOF) systems is also presented, demonstrating its effectiveness for more complex structural models.