Identification of equivalent modal damping for a wind turbine at standstill using Fourier and wavelet analysis

The current paper presents approaches to evaluate the equivalent modal viscous damping ratios for a wind turbine tower, using Fourier and wavelet analysis based linear regression. In the Fourier analysis, the estimated damping ratios are constant, but in the wavelet analysis, temporally varying damping ratios using a time-segmented least squares approach can be identified. The estimation of time varying damping is important in assessing the risk of negative aeroelastic damping in wind turbines. In absence of experimental data, the proposed approaches have been illustrated on numerically simulated response obtained from a simple wind turbine model. The model used for generating the response time history data for the wind turbine tower is composed of a flexible tower and rotor blade system, inter-connected using a substructuring technique, which facilitates the blade/tower coupling. A model order reduction technique is first used to model each of the two substructures (tower/nacelle and rotor system) as single-degree-of-freedom systems (DOF), allowing both systems to be later coupled together to form an equivalent two-DOF coupled tower/blade wind turbine tower model with equivalent viscous damping. A wind-induced forced vibration analysis of the coupled system is then carried out using artificially generated wind drag time histories. Two identification procedures based on (a) Fourier and (b) wavelet analysis, and linear regression, are used to solve the inverse problem for evaluating the first- and second-equivalent modal damping ratios of the coupled system. For the numerical example presented in order to demonstrate the applicability of the proposed approaches, good agreement was observed between the originally specified modal damping ratios and the subsequently estimated values. The estimation of damping using wavelet analysis techniques can be applied to situations where damping may vary with time. The proposed approaches can be used without any limitation on response data obtained for more complex models of turbines and loadings or on experimentally measured data from wind turbines.