## 6 Conclusions  
As the size of offshore wind turbines continues rising, the low-frequency vibration related to hydrodynamic frequency caused by waves is becoming nonnegligible. The load and torque pulsation of wind turbines caused by wind shear and tower shadow becomes more serious, which greatly increases the fatigue damage of wind turbines and shortens the service life of wind turbines. For this reason, in this paper, the mechanism of how wind and waves jointly affect the vibration characteristics of offshore wind turbines is analyzed, and an improved individual pitch control strategy is proposed to suppress fluctuations caused by wind and waves. The related main conclusions are summarized as follows:  
1. A mathematical model of how waves affect load and aerodynamic torque of wind turbines is derived, and we show the existence of fluctuating components of the hydrodynamic frequency in both blade root load and the aerodynamic torque. Simulation results further support the theoretical analysis. It is found that the greater the wave height of the wave, the greater the impact of the wave on the vibration of the wind turbine and the tower, and the greater the fluctuation of the fore-aft load on the tower at the MWL and aerodynamic torque.
2. The parameters of the proposed controller can be determined by simulations considering the trade-off between the vibration reduction and the impact on the system of the control strategy, as well as the coupling relationship between the vibration of the wind turbines.
3. By fine-tuning the pitch angle, the individual pitch control strategy proposed in this paper can not only effectively alleviate the wind turbine load fluctuation caused by wind and waves, but also restrain the wind turbine torque pulsation, thus further smoothing its output power, which is more economical than the individual pitch control method based on combined azimuth and load feedback.  
Figure 15: Simulation results of different data of wind turbine under turbulent wind and random wave: (**a**) Frequency spectrum density of the pitch angle; (**b**) Frequency spectrum density of the blade root flap-wise load; (**c**) Frequency spectrum density of the aerodynamic torque; (**d**) Frequency spectrum density of the output power.  
In addition to waves, the complexity of the operation environment of offshore wind turbines is further enhanced by ocean currents, tides and other factors. Vibration control strategies of offshore wind turbines under the influence of multiple environmental factors will be studied in the future.  
Conceptualization, H.L. and M.Z.; methodology, H.L., S.Y. and M.Z.; software, S.Y., W.T. and M.Z.; validation, S.Y., W.T. and M.Z.; formal analysis, H.L., M.Z. and X.Y.; investigation, S.Y. and W.T.; writing--original draft preparation, H.L., S.Y. and W.T.; writing--review and editing, H.L., M.Z. and B.X. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the \"111\" project of \"Renewable Energy and Smart Grid\" of China, grant number B14022; the Fundamental Research Funds for the Central Universities of China, grant number 2016B07014; the National Natural Science Foundation of China, grant number 51607058; and Six Talent Peaks Project of Jiangsu Province of China, grant number 2015-XNY-005.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.