# Passive Vibration Control of a Semi-Submersible Floating Offshore Wind Turbine
## 4 Performance Verification and Analysis of the Optimized TMDs  
Combined results of the above two optimization algorithms, three TMD masses (8000 kg, 10,000 kg and 20,000 kg) with two sets of corresponding parameters (lower and higher stiffness) are chosen for validating the control effects in a realistic offshore environment. The validation is performed in the FAST program, a fully nonlinear simulator of FOWT dynamics and with all system DOFs enabled. To make a convenient comparison with previous study ([PERSON], 2010; [PERSON] et al., 2008), the same environmental load conditions are adopted in this study and listed in Table 6. The three selected conditions approximately correspond to the rated operation, maximum-wind operation and self-survival. The Kaimal and JONSWAP spectrum are used in the generation of stochastic wind and wave field respectively. Under each load condition, the total simulation time is 630 s and only the last 600 s are recorded for analysis. The time step for all the cases is 0.05 s, which is small enough to obtain an independent solution. To eliminate the influence of random seed, the final statistical results are averaged based on three sets of stochastic environment field for each case. The wind and wave time-history samples for the three selected cases are plotted in Figure 7. Obviously, the generated environmental loads essentially captured the predefined characteristics in Table 6. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Case** & **Rated Operation** & **Maximum Wind Operation** & **Self-Survival** \\ \hline Mean wind speed at hub height (m/s) & 10 & 18 & 37 \\ Turbulence intensity & 18\% & 15\% & 11\% \\ Roughness coefficient & 0.14 & 0.14 & 0.11 \\ Significant wave height (m) & 2.3 & 3.7 & 13.8 \\ Peak-spectral period of incident waves (s) & 14 & 14 & 19 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Realistic environmental load conditions. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Mass (kg)**} & \multicolumn{4}{c}{**Optimized Values**} & \multirow{2}{*}{\(f_{n}\) **(Hz)**} & \multirow{2}{*}{\(\xi\)} & \multirow{2}{*}{\(\mathbf{er_{TTD}\) (m)}} & \multirow{2}{*}{\(\mathbf{Reduction}\)} \\  & **Spring Coefficient** & & & & & \\
**(N/m)** & & & & & & \\ \hline
6000 & 43,207 & 1580 & 0.4271 & 4.907\% & 0.08838 & 10.71\% \\
8000 & 56,970 & 2419 & 0.4247 & 5.665\% & 0.08824 & 10.85\% \\
10,000 & 70,429 & 3367 & 0.4224 & 5.344\% & 0.08825 & 10.84\% \\
12,000 & 83,596 & 4410 & 0.4201 & 6.962\% & 0.08834 & 10.75\% \\
14,000 & 96,477 & 5534 & 0.4178 & 7.529\% & 0.08850 & 10.58\% \\
16,000 & 109,078 & 6720 & 0.4156 & 8.043\% & 0.08868 & 10.40\% \\
18,000 & 121,406 & 7984 & 0.4133 & 8.540\% & 0.08890 & 10.18\% \\
20,000 & 133,467 & 9293 & 0.4111 & 8.993\% & 0.08914 & 9.94\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Optimized results by genetic algorithm. Similar to [12; 27], to evaluate the performance of TMD controllers, the 95 th percentile of response is employed to represent the extreme value, and the short-term damage equivalent load (DEL) [28] is used to measure the fatigue loads. Response reduction ratios \(\eta\) with different TMD parameters are shown in Table 7. As defined in Equation (19), a positive reduction ratio indicates that the TMD device has a mitigation effect on the response of turbine system, and vice versa. Since the TMD parameters are obtained by minimizing the standard deviation of tower top displacements in the pitch free decay motion, the low stiffness TMD devices mitigate \(\sigma_{\text{TID}}\) by dissipating the energy in the platform pitch motion, whereas the high stiffness TMD devices dissipate the energy in the tower oscillation. However, in the real environment, the frequencies of platform pitch motion are mainly controlled by the incoming wave spectrum. The peak-spectral period of incident waves listed in Table 6 is 14 s for operating conditions, which is greatly less than the pitch natural period of OC4-DeepCwind 26.8 s [29].