## 1 Introduction  
Offshore wind power is inevitably becoming an important clean energy source in coastal areas of China due to its advantages of high wind speed, low turbulence intensity and no occupation of land area [1]. However, compared with onshore wind turbines, offshore wind turbines face a more complex environment. Sustainable wind and wave forces on the structure of wind turbines are prone to vibration problems, which not only affect the normal operation characteristics of offshore wind turbines and reduce the output power quality, but also increase the fatigue load of the components of the wind turbines and shorten the life of the units. Therefore, when analyzing the vibration characteristics of offshore wind turbines, the effects of wind and wave on them should be fully considered. The research on the influence of wind on the vibration characteristics of wind turbines shows that with the continuous expansion of wind turbine blades, wind shear and tower shadow cause a great imbalance of the wind speed distribution in the rotating plane of wind turbines, which causes the aerodynamic load of wind turbines to pulsate mainly at the 1P frequency [2], and the aerodynamic torque to pulsate mainly at the 3P frequency [3]. The term 'P' refers to per revolution and indicates multiples of the rotational frequency of the turbine. In addition, due to wind shear and tower shadow,the periodic aerodynamic load acts on the tower, which makes the tower fore-aft moment fluctuate, and then the fore-aft vibrations of the tower occur. There have been many achievements in the research on vibration reduction of onshore wind turbines and the pitch control methods, especially the individual pitch control methods, which have been proved to be common and effective methods for wind turbine vibration reduction. In general, such researches can be summarized into three groups. First, some literature concentrates on the tower vibration reduction by pitch control methods. Based on analyzing the causes of tower vibration, the optimization control strategy is proposed by increasing the tiny pitch angle in the pitch control system, which can increase the aerodynamic damping of the tower. The proposed strategy can effectively reduce the fore-aft vibration and torque of tower, and has little influence on the power [4]. [PERSON] et al. [5] presented a method to estimate the tower fore-aft velocity using the measured data of blade load sensors and a control strategy of increasing tower damping based upon an individual pitch control architecture. Second, a number of pitch control strategies for structural load control in blades or rotor have been proposed. It was found that the individual pitch control method is very effective for smoothing the fluctuation of the blade root load of wind turbines in [6; 7]. [PERSON] et al. [8] provided two individual pitch control schemes to attenuate the main periodic load components of blade flap-wise and hub yaw/tilt-wise bending moments in wind turbines under varying-frequency conditions. [PERSON] et al. [9] pointed out the limitations of conventional individual pitch control based on blade root load feedback, and then presented an additional cascaded feedback controller based upon a local blade inflow measurement on each blade to better reduce blade root flap-wise load. [PERSON] et al. [10] designed an individual blade pitch control law using multivariable linear parameter-varying control techniques to reduce the structural loads both on the rotating and non-rotating parts of the turbine. [PERSON] et al. [11] provided a novel individual pitch control strategy using a wavelet linear quadratic regulator control algorithm to reduce blade vibration. [PERSON] et al. [12] proposed a new fuzzy logic proportional control approach applied to individual pitch angles, which can mitigate the moment load on the blades and tower to a minimum possible value while keeping the output power of wind turbines at a constant value. [PERSON] et al.