Short-term damping identification of wind turbine blade modes under environmental and operational variability using Gaussian process time series models

The dynamic response and stability of wind turbines are governed by the aeroelastic modal characteristics, which tend to fluctuate under influence of varying Environmental and Operational Conditions (EOCs), due to complex aero-servo-elastic interactions. In case of blade dominated modes, such interactions cause the modal properties to be dependent on, e.g., wind speed, rotor speed, azimuth angle and pitch angle, which can
result in substantial variations in the effective modal damping ratios over just a few minutes. Conventional methods for estimating modal parameters of wind turbines in operational conditions, such as Stochastic Subspace Identification (SSI), require long time series (>30 min) to converge and assumes the system properties are time-invariant and the conditions stationary. This limits the efficacy of such methods in tracking short-term modal properties. For wind turbine design, representative and accurate modal parameter estimates are important for validating and improving the numerical models. Thus, alternative identification methods are needed. In this work, a GP-TARMA model is used to model edgewise blade response leveraging measured Environmental and Operational Variables (EOVs), to capture the short-term variability due to varying EOCs.
The GP-TARMA model have a structure similar to that of a Functional Series (FS) TARMA model, but with the estimated model parameters considered Gaussian variables rather than scalars. Additionally, dependence of the functional series on EOVs is assumed to improve tracking of EOV dependent variability. Once the model is estimated, the corresponding natural frequencies and damping ratios can be extracted from the AR-coefficients and the uncertainties of the modal parameter estimates can be assessed, due to the GP structure of the model. The GP-TARMA approach is tested on a simulated edgewise bending moment response resembling normal operation of an SG 11.0-200 DD turbine, generated with Siemens Gamesa’s in-house aeroelastic code BHawC. Natural frequency and damping ratio estimates (and corresponding uncertainties) extracted from the estimated GP-TARMA model, show good agreement with reference values obtained by linearizing the model around representative operating points. The performance of the GP-TARMA model and the SSI approach are compared in terms of the capability to produce representative damping ratio estimates of modes under influence of varying EOCs. The results show, that the GP-TARMA model approach is a promising method for estimating short-term operational damping for wind turbines.