A new time-frequency analysis method based on single mode function decomposition for offshore wind turbines

The Hilbert-Huang transform (HHT) has been widely applied and recognised as a
powerful time-frequency analysis method for nonlinear and non-stationary signals in numerous engineering fields. One of its major challenges is that the HHT is frequently subject to mode mixing in the processing of practical signals such as those of offshore wind turbines, as the frequencies of offshore wind turbines are typically close and contaminated by noise. To address this issue, this paper proposes a new timefrequency analysis method based on single mode function (SMF) decomposition to overcome the mode mixing problem in the structural health monitoring (SHM) of offshore wind turbines. In this approach, the structural vibration signal is first decomposed into a set of window components using complex exponential decomposition. A state-space model is introduced in the signal decomposition to improve the numerical stability of the decomposition, and then a novel windowalignment strategy, named energy gridding, is proposed and the signals are constructed in the corresponding gridding. Furthermore, energy recollection is implemented in each gridding, and the reassembling of these components yields an SMF that is comparable to the intrinsic mode function (IMF) of the HHT, but with a significant improvement in terms of mode mixing. Four case studies are conducted to evaluate the performance of the proposed method. The first case attempts to detect three different frequencies in a simulated time-invariant signal. The second case attempts to test a synthesised signal with segmental time-varying frequencies (each segment contains three different frequencies components). The analysis results in these two cases indicate that mode mixing can be reduced by the proposed method. Furthermore, a synthesised signal with slowly varying frequencies is used. These analysis results demonstrate the effective suppression of non-relevant frequency components using SMF decomposition. In the third case, the experimental data from vortex-induced vibration (VIV) experiments sponsored by the Norwegian Deepwater Programme (NDP) are used to evaluate the proposed SMF decomposition for vibration mode identification. In the final case, field data acquired from an offshore wind turbine foundation and offshore wind turbine are analysed. The mode identification results obtained using SMF decomposition are compared with those produced by the HHT. The comparison demonstrates superior performance of the proposed method in identifying the vibration modes of the VIV experimental and field data.