Application of time-periodic stochastic subspace identification on operating wind turbine rotor data

The stochastic subspace identification (SSI) algorithm is a robust-working method to identify mode shapes, eigenfrequencies and damping ratios from response time histories of linear time-invariant systems (LTI), which are operated under random excitation. In case of rotating substructures, e.g. wind turbine rotors, the periodic responses contain participation of several higher harmonics of the rotor speed. For such timeperiodic systems the modal analysis can be described by characteristic exponents called Floquet multipliers, which postulate periodic modal deformation except for the total amplitude (determined by damping ratio) after one period of revolution. The presented periodically expanded subspace algorithm (SSI-LTP) projects the system response from one period to the next. The algorithm is applied to the evaluation of simulated and experimental rotor blade deformation data of a wind turbine operating at different wind and rotor speeds, which were measured with a commercially available optical rotor blade deformation measurement system