40 Operational Modal Analysis in the Presence of Harmonic Excitations: A Review 381 Fig. 40.2 Identification of the modal parameters of the wind turbine using PolyMAX (FA motion) for one measurement. The structural modes (S), the harmonics (3p, 6p, etc.) and the wave period (W) are indicated 00.511.522.533.544.55 0 1 2 3 4 5 6 Natural frequency [Hz] Damping ratio [%] 3p 6p 9p 12p S S S Fig. 40.3 Normalized PDF of pure structural mode (left) and pure harmonic component (right) 0 0 Amplitude Amplitude Probability Probability Fig. 40.4 PDF calculated for measurement filtered around the frequencies given in the legend. Structural mode at 1.2 Hz 0 1.16 Hz 1.18 Hz 1.20 Hz 1.22 Hz 1.24 Hz Amplitude Probability shape of the PDF is also almost identical. For example, for the structural mode (Fig. 40.4) the shape when band-pass filtered around 1.18 Hz and 1.22 Hz is almost identical. This will be referred to as the symmetry of the PDF. The PDF is an effective technique to distinguish between a structural mode and a harmonic. It can also distinguish between a structural mode and a mathematical mode, a mode identified by the estimators, e.g. LSCE, SSI-COV, LSCF, but without a physical meaning. The shape of a mathematical mode resembles the shape of a structural mode, but lacks this symmetry. Take for instance the previous example, around 1.34 Hz neither a structural mode nor a harmonic is located.The shape of the PDF around 1.32 Hz does not correspond to the shape around 1.36 Hz (Fig. 40.6). As long as the harmonic is not damped too
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