Output-Only Modal Analysis of Linear Time Periodic Systems with Application to Wind Turbine Simulation Data

Many important systems, such as turbomachinery, helicopters and wind turbines, must be modeled with linear time-periodic equations of motion to correctly predict resonance phenomena. Time periodic effects in wind turbines might arise due to stratification in the velocity of the wind with height, changes in the aerodynamics of the blades as they pass the tower and/or blade-to-blade manufacturing variations. These effects may cause parametric resonance or other unexpected resonances, so it is important to properly characterize them so that these machines can be designed that achieve the high reliability, safety, and long lifetimes demanded to provide economical power. This work presents an output-only system identification methodology that can be used to identify models for linear, periodically time-varying systems. The methodology is demonstrated for the simple Mathieu oscillator and then used to interrogate simulated measurements from a rotating wind turbine, revealing that at least one of the turbine’s modes seems to be time-periodic. The measurements were simulated using a state-of-the-art wind turbine model called HAWC2 that includes both structural dynamic and aerodynamic effects. Simulated experiments such as this may be useful both to validate dynamic models for a turbine or to obtain a set of time-periodic equations of motion from a numerical model; these are not readily available by other means due to the way that the aeroelastic effects are treated in the simulation code