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首页> 外文会议>ASME International Conference on Ocean, Offshore and Arctic Engineering >IDENTIFYING HIGHER-ORDER INTERACTIONS IN WAVE TIME-SERIES
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IDENTIFYING HIGHER-ORDER INTERACTIONS IN WAVE TIME-SERIES

机译：识别波时间序列中的高阶相互作用

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Reliable design and reanalysis of coastal and offshore structures requires, amongst other things, characterisation of extreme crest elevation corresponding to long return periods, and of the evolution of a wave in space and time conditional on an extreme crest. Extreme crests typically correspond to focussed wave events enhanced by wave-wave interactions of different orders. Higher-order spectral analysis can be used to identify wave-wave interactions in time-series of water surface elevation. The bispectrum and its normalised form (the bicoherence) have been reported by numerous authors as a means to characterise three-wave interactions in laboratory, field and simulation experiments. The bispectrum corresponds to a frequency-domain representation of the third order cumulant of the time-series, and can be thought of as an extension of the power spectrum (itself the frequency-domain representation of the second order cumulant). The power spectrum and bispectrum can both be expressed in terms of the Fourier transforms of the original time-series. The Fast Fourier transform (FFT) therefore provides an efficient means of estimation. However, there are a number of important practical considerations to ensuring reasonable estimation. To detect four-wave interactions, we need to consider the trispectrum and its normalised form (the tricoherence). The trispectrum corresponds to a frequency-domain (Fourier) representation of the fourth-order cumulant of the time-series. Four-wave interactions between Fourier components can involve interactions of the type where f_1 + f_2 + f_3 = f_4 and where f_1 + f_2 = f_3 + f_4, resulting in two definitions of the trispectrum, depending on which of the two interactions is of interest. We consider both definitions in this paper. Both definitions can be estimated using the FFT, but it's estimation is considerably more challenging than estimation of the bispectrum. Again, there are important practicalities to bear in mind. In this work, we consider the key practical steps required to correctly estimate the trispectrum and tricoherence. We demonstrate the usefulness of the trispectrum and tricoherence for identifying wave-wave interactions in synthetic (based on combinations of sinusoids and on the HOS model) and measured wave time-series.
机译：沿海和近海结构的可靠设计和再分析尤其需要表征与长回波周期相对应的极端波峰高程，并要求以极端波峰为条件的时空波演化。极端波峰通常对应于通过不同阶次的波波相互作用增强的聚焦波事件。高阶谱分析可用于识别水面高程时间序列中的波波相互作用。许多作者已经报道了双谱及其规范化形式（双相干性），作为表征实验室，野外和模拟实验中三波相互作用的一种手段。双谱对应于时间序列的三阶累积量的频域表示，并且可以认为是功率谱的扩展（本身就是二阶累积量的频域表示）。功率谱和双谱都可以用原始时间序列的傅立叶变换表示。因此，快速傅立叶变换（FFT）提供了一种有效的估计方法。但是，要确保合理的估算，有许多重要的实际考虑因素。为了检测四波相互作用，我们需要考虑三光谱及其归一化形式（三相干性）。三光谱对应于时间序列的四阶累积量的频域（傅里叶）表示。傅立叶分量之间的四波相互作用可能涉及类型为f_1 + f_2 + f_3 = f_4且其中f_1 + f_2 = f_3 + f_4的相互作用，从而产生了三光谱的两个定义，具体取决于两个相互作用中的哪个。我们在本文中考虑了这两种定义。可以使用FFT来估计这两个定义，但与双谱估计相比，它的估计要困难得多。同样，要记住一些重要的实用性。在这项工作中，我们考虑了正确估计三光谱和三相干性所需的关键实际步骤。我们证明了三光谱和三相干性在识别合成波（基于正弦波组合和HOS模型）和测量波时间序列中的波-波相互作用的有用性。

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