Proceedings of the Thirty-second (2022) International Ocean and Polar Engineering Conference
Shanghai, China, June 5–10, 2022
Copyright © 2022 by the International Society of Offshore and Polar Engineers (ISOPE)
ISBN 978-1-880653-81-4; ISSN 1098-6189

www.isope.org

A Wind Load Estimation Method for Offshore Wind Turbines
Considering Multivariate Coherence Effects
Kai Xu, Fushun Liu*
Department of Ocean Engineering, Ocean University of China.
Qingdao, Shandong, China

the problem, it is assumed that the isotropic homogeneous turbulence at
the hub height represents the turbulence in the rotor field, so themultivariate rotation frequency effect of blade rotation is not considered.
Zhang and Fitzgerald (2020) proposed the use of the tuned mass-damperinerter (TMDI) to mitigate edgewise vibration of wind turbine blades. A
blade edgewise model was developed using Euler-Lagrangian approach,which can effectively represent centrifugal stiffening and centrifugal
softening effect of the blade. These studies show that the developmentof a real model for offshore wind turbine blades requires two elements:
one is to establish the mechanical model which can accurately describe
the dynamic characteristics of the blades, and the other is to consider therotating effect of the blades on the wind.

ABSTRACT
A novel multivariate coherent effect-based estimation method of windloads is proposed to consider the coherent effect of wind loads in rotating
and nonrotating regions during blade rotation. Firstly, a wind spectrum
model with rotation effect is derived. Then multivariate coherence
effects in the rotational and non-rotational regions are incorporated into
the rotational effect wind spectrum. The results show that the proposed
multivariate coherence effect model can effectively characterize themultiplicative frequency such as 0.201Hz, 0.403Hz and 0.605Hz for theNREL-5MW wind turbine blade. Also, the multivariate coherent effectbased wind loads can be evaluated simultaneously in both rotating andnon-rotating regions.

Initially, the study of wind was mainly focused on fixed tower structures
assumed to be stationary. The wind loads on the structures were solved
based on fluctuating wind spectrum theory combined with spatial
correlation models (Davenport, 1962; Simiu, 1974). Later, static anddynamic winds were established along with high-quality offshore wind
turbulence data from the west coast of Norway. More critically theinverse Fourier transform technique was used to improve the efficiencyof wind speed calculations (Andersen and Lovseth, 2006). To consider
the rotation effect of blades, Connell (1982) used the Von Karman
spectrum as the source spectrum and then obtained the corresponding
correlation function by inverse Fourier transform. The Cross-correlation
function of two points was used to represent the autocorrelation functionof the same point at different times. However, not all the wind spectra
can be analytically expressed, so this method is limited. Anotherimportant model is the Sandia National Laboratory model (Moriarty,Hansen, 2005; Jonkman, Buhl, 2007). The model was used to simulate
the wind speed at a sampling point on the rotating surface by defining
the turbulent wind spectrum. With the movement of the blade, therotating surface is sampled in turn to obtain the rotating sampling windspeed. But the discrete sampling mode leads to the discontinuity of themodel. In addition, both types of models are time-domain approaches
and do not describe the blade rotation effect from the perspective ofphysical mechanisms. Therefore, some researchers have proposed arotation sampling spectrum with physical meaning from the frequency
domain perspective (Tian, He and Wang, 2013). In this method, the effectof blade rotation is derived from the angle of frequency domain, and thedecay parameter of blade rotation is considered. The improvement in thefrequency domain effectively simulates the interference effect of theKEY WORDS: Rotation effect; multivariate coherence effect; blade.

INTRODUCTION
As an important strategic resource, offshore wind energy has attracted
extensive attention and become an indispensable energy component. In
recent years, large wind turbines have been widely used in offshore windenergy development around the world (Jonkman, Butterfield, Musial andScott, 2009). With the development of large-scale and high-power
structure of wind turbine, the blade of wind turbine presents thecharacteristics of large slenderness ratio and flexibility. It is worth notingthat the wind loads applied on the blade are easily affected by the blade
rotation to produce undesirable cross wind loads. Various fatigue
problems can easily be caused by the vibrations arising from the actionof cross wind loads, which in turn affects the blade life (Colwell and Basu,2009). Therefore, it is significant for the safe operation and maintenanceof the offshore wind turbine blades to analyze the wind-induced
vibration response (Liu, Yang, Tian, Zhao and Xu, 2020; Damgaard, Ibsen,Andersen, and Andersen, 2013).
In recent years, Zheng, Yang and Yang (2017) simplified the offshore
wind blades as a lumped total mass at the top of the tower. Thissimplification results in the geometric properties of the blade static state
and the stiffening and softening effects during dynamic rotation not
being considered. To accurately develop blade models, Zuo, Bi and Hao(2019) developed a finite element blade model to mitigate tower and outof-plane blade vibrations of offshore wind turbines. In order to simplify302