Frequency-Domain Optimization of Multi-TMD Systems Using Hierarchical PSO for Offshore Wind Turbine Vibration Suppression

With the rapid advancement of offshore wind power, structural vibration induced by multi-source excitations in complex marine environments is a critical concern. This study developed a multi-degree-of-freedom (MDOF) dynamic model of an offshore wind turbine using a lumped mass approach, which was then reduced to a first-order linear system to improve frequency-domain analysis and optimization efficiency. Given the non-stationary, broadband nature of wind and wave loads, a band-pass filtering technique was applied to extract dominant frequency components, enabling linear modeling of excitations within primary modal ranges. The displacement response spectrum, derived via system transfer functions, served as the objective function for optimizing tuned mass damper (TMD) parameters. Both single TMD and multiple TMD (MTMD) strategies were designed and compared. A hierarchical particle swarm optimization (H-PSO) algorithm was proposed for MTMD tuning, using the optimized single TMD as an initial guess to enhance convergence and stability in high-dimensional spaces. The results showed that the frequency-domain optimization framework achieved a balance between accuracy and computational efficiency, significantly reducing structural responses in dominant modes and demonstrating strong potential for practical engineering applications.