## 2 Methodology
### Wind Turbine Model and Simulations  
The wind turbine chosen for performing this work is the NREL 5 MW turbine, developed by the NREL in Boulder, CO, USA, for its data availability and open-source documentation [24]. This turbine is designed for research purposes, providing all the details necessary for performing a complete aeroelastic analysis, including all possible flow and operating conditions and configurations. The key parameters of the wind turbine are shown in Table 1.  
The NREL 5 MW definition report completely defines the blade's structural properties. The blade is designed from fiberglass, and the structural properties are calculated along the blade span, which is divided into 49 sections along the 63 m span of the blade. The most effective parameters in the structural analysis are the blade mass density and blade stiffnesses in the flapwise and edgewise directions. The distributions of those properties along the span are shown in Figure 1. \begin{table}
\begin{tabular}{c c} \hline \hline
**Property** & **Value** \\ \hline Rated Power & 5 MW \\ Rotor Orientation & Upwind \\ Rotor Diameter & 126 m \\ Hub Diameter & 3 m \\ Hub Height & 90 m \\ Cut-in Wind Speed & 3 m/s \\ Rated Wind Speed & 11.4 m/s \\ Cut-off Wind Speed & 25 m/s \\ Rated Rotor Speed & 121 m/m \\ Rotor Overhang & 5 m \\ Shatt Tilt Angle & 5\({}^{\circ}\) \\ Precone Angle & 2.5\({}^{\circ}\) \\ Rotor Mass & 110,000 kg \\ Nacelle Mass & 240,000 kg \\ \hline \hline \end{tabular}
\end{table} 
Table 1: NREL 5 MW general properties [24]. Figure 1: Blade structural properties distributions. To generate the datasets, aeroelastic simulations are performed on the OpenFAST simulation tool on the onshore configuration of the turbine. It uses deterministic models to calculate the aerodynamic loads and structural behavior, coupling between them for an aeroelastic analysis. Three different wind fields are generated using the TurbSim open-source tool [25] developed by NREL for the turbulence classes A, B, and C according to the International Electrotechnical Committee standard IEC 61400-1 [26], denoting high, medium, and low turbulence intensities, respectively. TurbSim generates the wind fields based on stochastic models in the frequency domain to produce a binary wind field that covers the rotor area and shows velocities in the directions of downwind facing the rotor and crosswind and vertical wind components in the rotor plane. The Kaimal spectral model was chosen to generate the wind field since it gives better accuracy in modeling atmospheric turbulence [27]. The Kaimal model is shown in Equation (1) [28]  
\[\frac{nS_{u}(n)}{\sigma_{u}^{2}}=\frac{4 nL_{u}/\overline{U}}{\left(1+6 nL_{u}/ \overline{U}\right)^{5/3}} \tag{1}\]  
where \(n\) is the frequency, \(S_{u}(n)\) is the spectral density function, \(\sigma_{u}\) is the standard deviation of the longitudinal wind speed component, \(\overline{U}\) is the mean wind speed, and \(L_{u}\) is a length scale that varies based on the surface roughness and the altitude. The mean wind speed chosen is 12 m/s, which is slightly above the turbine's rated wind speed to activate the pitch control of the blade. The difference in turbulence classes does not change the mean value; it does, however, change the standard deviation and variation of wind speeds around the mean value. This is shown in Figure 2, where the quartiles of the generated wind speeds in the three directions are shown for the three turbulence classes. The main control systems defined in the NREL 5 MW definition report are a variable speed controller for the generator-torque control system and a blade pitch-to-feather controller for the blade's collective pitch control. Both controllers take the generator wind speed as an input to the system to produce a control action. The generator speeds are filtered using a low-pass filter with a single pole to eliminate high excitations in the generator speed.