Abstract 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 time-frequency 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 window-alignment 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.

中文翻译：

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一种基于单模函数分解的海上风电机组时频分析新方法

摘要 Hilbert-Huang变换(HHT)作为一种强大的非线性非平稳信号时频分析方法在众多工程领域得到了广泛的应用和认可。其主要挑战之一是 HHT 在处理实际信号（例如海上风力涡轮机的信号）时经常受到模式混合的影响，因为海上风力涡轮机的频率通常很近并被噪声污染。针对这一问题，本文提出了一种基于单模函数（SMF）分解的新时频分析方法，以克服海上风力发电机结构健康监测（SHM）中的模态混合问题。在这种方法中，首先使用复指数分解将结构振动信号分解为一组窗口分量。在信号分解中引入状态空间模型以提高分解的数值稳定性，然后提出一种新的窗口对齐策略，称为能量网格，并在相应的网格中构建信号。此外，在每个网格中都实现了能量回收，这些组件的重新组装产生了与 HHT 的固有模式函数 (IMF) 相当的 SMF，但在模式混合方面有显着改善。进行了四个案例研究来评估所提出方法的性能。第一种情况试图在模拟的时不变信号中检测三个不同的频率。第二种情况尝试测试具有分段时变频率的合成信号（每个分段包含三个不同的频率分量）。这两种情况的分析结果表明，所提出的方法可以减少模式混合。此外，使用频率缓慢变化的合成信号。这些分析结果表明使用 SMF 分解可以有效抑制不相关的频率分量。在第三种情况下，来自挪威深水计划 (NDP) 赞助的涡激振动 (VIV) 实验的实验数据用于评估建议的用于振动模式识别的 SMF 分解。在最后一种情况下，分析从海上风力涡轮机基础和海上风力涡轮机获取的现场数据。使用 SMF 分解获得的模式识别结果与 HHT 产生的结果进行比较。