# Passive Vibration Control of a Semi-Submersible Floating Offshore Wind Turbine
## 5 Conclusions  
To find the optimal tuned mass damper (TMD) for the semi-submersible OC4-DeepCwind wind turbine efficiently, we propose a simplified multi-rigid-body dynamic model, in which only the motion of platform pitch and surge, tower tilt and TMD translation are considered. The inertia and gravity forces, restoring and damping forces from hydrodynamics and mooring, and the TMD forces are included in the dynamic model derivation. After the ten unknown parameters are identified by the Levenberg-Marquardt algorithm, the accuracy of the simplified model is verified by the pitch free decay motions. In order to obtain the globally optimized parameters of TMDs, the primary variations of objective function can be predicted firstly by method of exhaustion and a set of optimal parameters are determined in this complex lower stiffness region. Furthermore, genetic algorithm is helpful in finding the optimal stiffness in the higher range efficiently. According to the performance in realistic environmental conditions, the lower stiffness TMDs mainly dissipate the energy of platform pitch vibration, whereas the higher stiffness TMDs absorb the energy of tower vibration. However, the periods of platform pitch motion are mostly determined by the incoming wave spectrum. Consequently, the high stiffness TMDs that exhibit a more stable performance are recommended for practical use. Of all the three environmental conditions, TMD is certainly helpful to reduce the fatigue loads, but may slightly harm the extreme loads (95 th percentile). Compared with spar-type floating wind turbines, the response reduction ratios show that the application of TMD device on semi-submersible floating wind turbines is equally promising. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Case** & **Evaluation Index** & **OC3-Hywind (Spar)** & **OC4-DeepCwind (Semi-Submersible)** \\ \hline \multirow{6}{*}{10 m/s} & 95 th Pitch & \(-\)2.08\% & \(-\)1.55\% \\  & 95 th Roll & \(-\)1.67\% & \(-\)0.92\% \\  & 95 th fore-aft \(T_{\text{TB}}\) & \(-\)2.00\% & \(-\)2.00\% \\  & DEL of side-side \(T_{\text{TB}}\) & 32.18\% & 39.32\% \\  & DEL of fore-aft \(T_{\text{TB}}\) & 6.35\% & 7.78\% \\ \hline \multirow{6}{*}{18 m/s} & 95 th Pitch & \(-\)1.04\% & \(-\)1.41\% \\  & 95 th Roll & 6.58\% & \(-\)0.52\% \\ \cline{1-1}  & 95 th fore-aft \(T_{\text{TB}}\) & \(-\)3.25\% & \(-\)1.71\% \\ \cline{1-1}  & DEL of side-side \(T_{\text{TB}}\) & 21.24\% & 15.32\% \\ \cline{1-1}  & DEL of fore-aft \(T_{\text{TB}}\) & 3.35\% & 0.18\% \\ \hline \multirow{6}{*}{37 m/s} & 95 th Pitch & 4.41\% & 0.63\% \\  & 95 th Roll & \(-\)0.30\% & 1.04\% \\ \cline{1-1}  & 95 th fore-aft \(T_{\text{TB}}\) & \(-\)0.77\% & \(-\)2.97\% \\ \cline{1-1}  & DEL of side-side \(T_{\text{TB}}\) & 0.18\% & 1.67\% \\ \cline{1-1}  & DEL of fore-aft \(T_{\text{TB}}\) & 1.22\% & 1.97\% \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison of TMD performances between spar and semi-submersible foundations. Figure 9: Power spectral density of tower base moments under rated operation condition with and without TMD: (**a**) Side–side; and (**b**) Fore–aft. **Acknowledgments:** This study was supported by the National Natural Science Foundation of China (51278161, 51308167), and Shenzhen Knowledge innovation program (KQJSCX20160226201838). **Author Contributions:** [PERSON] and [PERSON] conceived the idea and designed the framework; [PERSON] and [PERSON] set up the numerical model; [PERSON] analyzed the simulation data; and [PERSON] and [PERSON] wrote the paper. **Conflicts of Interest:** The authors declare no conflict of interest.