Advanced Operational Modal Analysis Methods for Linear Time Periodic System Identification

Often structural dynamic systems cannot be modeled with constant stiffness, mass and damping. For example, wind turbines, helicopters, turbomachinery, and a variety of nonlinear structures linearized about a periodic limit cycle all may contain time-periodic terms in their equations of motion even if the equations are still linear. Linear time periodic systems such as these may exhibit parametric resonance, where the damping in the system is negative at certain rotational frequencies, leading to catastrophic failure. The authors previously presented an extension of operational modal analysis to linear time periodic systems. The previous work introduced a new type of spectrum, dubbed the harmonic autospectrum, discussed how to interpret the spectra, and showed how the simple peak picking method could be used to extract an estimate for the linear time-periodic model of a system from measurements. This paper builds on that work, revealing how more advanced operational modal analysis methods can be extended to linear time-periodic systems. Curve fitting approaches for both the harmonic autospectra and the positive harmonic spectra are applied to simulated measurements from two time-periodic systems, and the OMA based Enhanced Mode Indicator Function (EMIF) method is used to extract the modal parameters from the enhanced positive power spectrum. These extensions are found to provide more accurate estimates of the damping of the modes of the time-periodic systems, and to provide good estimates of the mode shapes of the systems so long as the measurements stand out clearly above the noise. Application of the complex mode indicator function an the EMIF algorithm makes it possible to separate the forward and backward whirling modes of a wind turbine, which is difficult since each of these modes is manifest at several harmonics due to the anisotropy in the tower supporting the turbine.