Virtual fatigue diagnostics of wake-affected wind turbine via Gaussian Process Regression

We propose a data-driven model to predict the short-term fatigue Damage Equivalent Loads (DEL) on a wake-affected wind turbine based on wind field inflow sensors and/or loads sensors deployed on an adjacent up-wind wind turbine. Gaussian Process Regression (GPR) with Bayesian hyperparameters calibration is proposed to obtain a surrogate from input random variables to output DELs in the blades and towers of the up-wind and wake-affected wind turbines. A sensitivity analysis based on the hyperparameters of the GPR and Kullback-Leibler divergence is conducted to assess the effect of different input on the obtained DELs. We provide qualitative recommendations for a minimal set of necessary and sufficient input random variables to minimize the error in the DEL predictions on the wake-affected wind turbine. Extensive simulations are performed comprising different random variables, including wind speed, turbulence intensity, shear exponent and inflow horizontal skewness. Furthermore, we include random variables related to the blades lift and drag coefficients with direct impact on the rotor aerodynamic induction, which governs the evolution and transport of the meandering wake. In addition, different spacing between the wind turbines and Wöhler exponents for calculation of DELs are considered. The maximum prediction normalized mean squared error, obtained in the tower base DELs in the fore-aft direction of the wake affected wind turbine, is less than 4%. In the case of the blade root DELs, the overall prediction error is less than 1%. The proposed scheme promotes utilization of sparse structural monitoring (loads) measurements for improving diagnostics on wake-affected turbines.