380 K. Motte et al. Fig. 40.1 Spectrum of one measurement of the FA motion of the wind turbine rotating at nominal speed. The structural modes (S), the harmonics (3p, 6p, etc.) and the wave period (W) are indicated 00.511.522.533.544.55 Acceleration PSD [(m/s2)2/Hz] Frequency [Hz] 15p W 3p 6p 9p 12p S S S 40.2 Available Techniques and Common Assumptions In the literature several techniques have been proposed to resolve the issues of non-white excitation in OMA. These techniques can be divided into four different categories: • Statistics driven identification of the harmonics: determine which resonance frequencies can be attributed to structural modes and which can be attributed to harmonics. • Preprocessing techniques: remove the harmonics from the measured signals. • Modification to existing identification techniques: modify existing identification techniques such that they incorporate the harmonic. • Input spectrum independent techniques: these techniques deliver an identification of the modal parameters which is independent of the input spectrum and thus unaffected by the input coloration, for instance transmissibility based OMA (TOMA)[10] and poly-reference TOMA (pTOMA) [11]. The discussed techniques have been studied extensively in [12] on both simulations and actual measurements. An overview and an excerpt focussed on the application of a three-blade offshore wind turbine is provided here. Generally it is assumed that harmonics will result in a sharp peak in the spectrum. If an identification of these peaks would be carried out, they would have a damping ratio of zero. In the case of the wind turbine this is no longer true [4, 5, 9]. The spectrum for the front-aft (FA) motion for one measurement of the wind turbine shows none of these sharp peaks, Fig. 40.1. The harmonics are in that case identified as if they were structural modes with a damping Fig. 40.2. In the continuation of this document we will refer to this type of harmonics as damped harmonics. 40.3 Statistics Driven Identification of the Harmonics 40.3.1 Probability Density Function The use of the probability density function (PDF) [13] is based on the difference in statistic properties of a harmonic component and a narrow band stochastic response of a structural mode. The measured signal is band-pass filtered and the PDF is calculated. For a structural mode, typically the left shape in Fig. 40.3 is obtained. A harmonic results in the shape on the right. A second important property is the symmetry of the PDF around a given frequency. In Figs. 40.4 and 40.5, a simulated system is considered with superposed harmonics at multiples of 1.5 Hz. In the legend the frequencies are shown around which the band-pass filtering is carried out. The shapes associated with the structural mode and the harmonic, both in red, correspond to the theoretical results. In both cases the amplitudes of the PDF reach a distinct minimum when the exact natural or harmonic frequency is reached. At equal frequency intervals of the exact natural frequency (or harmonic frequency), the
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