Robust Optimization of Multiple Tuned Mass Dampers for the Offshore Monopile-Supported Wind Turbine

Abstract

Offshore wind turbine (OWT) towers are continuously subjected to highly variable wind-wave excitations, where structural parameter uncertainties arising from manufacturing tolerances and material heterogeneity may significantly degrade vibration control performance. Conventional tuned mass dampers (TMDs), particularly single-TMD configurations, are highly sensitive to detuning effects and thus lack robustness under uncertain operating conditions. This study proposes a robust optimization framework for vibration mitigation of offshore wind turbine towers using multiple tuned mass dampers (MTMDs). Structural parameter uncertainties in total mass and stiffness are explicitly considered through Latin hypercube sampling (LHS), enabling a sample-based evaluation of control performance. Inverse Element Exchange Method with Multi-level Programming (MulIEEM) is applied to determine the optimal distribution of damping coefficient, mass, and for the TMDs. Three objective functions are investigated, including minimization of the sample mean, sample standard deviation, and single-sample response, allowing a systematic assessment of vibration reduction effectiveness and robustness. Stochastic wind and wave loads are synthesized using the Kaimal wind spectrum and JONSWAP wave spectrum, while structural uncertainties are represented through Latin Hypercube Sampling (LHS). The statistical characteristics of the displacement responses across all samples are used to evaluate robustness and provide an indirect measure of sensitivity to uncertainty-induced detuning effects. Three objective functions are investigated, including minimization of the sample mean, sample standard deviation, and single-sample response, allowing a systematic assessment of vibration reduction effectiveness and robustness, defined herein as reduced sensitivity to structural uncertainties. Numerical results demonstrate that the proposed MulIEEM-based MTMD designs significantly reduce both the mean and variability of tower displacement responses across a wide range of wind speeds. Furthermore, single-sample-based optimization is shown to achieve a favorable balance between control effectiveness and computational efficiency. The proposed framework provides a practical and robust design strategy for vibration control of offshore wind turbine towers under structural uncertainty.