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Higher-order Spectra For Identification Of Nonlinear Modal Coupling

机译：用于识别非线性模态耦合的高阶谱

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Over the past four decades considerable work has been done in the area of power spectrum estimation. The information contained within the power spectrum relates to a signal's autocorrelation or 'second-order statistics'. The power spectrum provides a complete statistical description of a Gaussian process; however, a problem with this information is that it is phase blind. This problem is addressed if one turns to a system's frequency response function (FRF). The FRF graphs the magnitude and phase of the frequency response of a system; in order to do this it requires information regarding the frequency content of the input and output signals.rnSituations arise in science and engineering whereby signal analysts are required to look beyond second-order statistics and analyse a signal's higher-order statistics (HOS). HOS or spectra give information on a signal's deviation from Gaussianity and consequently are a good indicator function for the presence of nonlinearity within a system.rnOne of the main problems in nonlinear system identification is that of high modal density. Many modelling schemes involve making some expansion of the nonlinear restoring force in terms of polynomial or other basis terms. If more than one degree-of-freedom is involved this becomes a multivariate problem and the number of candidate terms in the expansion grows explosively with the order of nonlinearity and the number of degrees-of-freedom.rnThis paper attempts to use HOS to detect and qualify nonlinear behaviour for a number of symmetrical and asymmetrical systems over a range of degrees-of-freedom. In doing so the paper also attempts to show that HOS are a more sensitive tool than the FRF in detecting nonlinearity. Furthermore, the object of this paper is to try and identify which modes couple in a nonlinear manner in order to reduce the number of candidate coupling terms, for a model, as much as possible. The bispectrum method has previously been applied to simple low-DOF systems with high symmetry and has been shown to work well in this limited case. The current paper will consider a model of a continuous wing-pylon model with reduced symmetry in order to assess the utility of the method in a more general situation, the analysis is also extended to assess the utility of the trispectrum.
机译：在过去的四十年中，在功率谱估计领域已经做了大量工作。功率谱中包含的信息与信号的自相关或“二阶统计”有关。功率谱提供了高斯过程的完整统计描述；但是，此信息的问题在于它是相位盲的。如果人们转向系统的频率响应功能（FRF），则会解决此问题。 FRF绘制了系统频率响应的幅度和相位图。为了做到这一点，它需要有关输入和输出信号的频率内容的信息。在科学和工程学中出现了这样的情况，即信号分析人员需要超越二阶统计量，并分析信号的高阶统计量（HOS）。 HOS或频谱可提供有关信号偏离高斯性的信息，因此是系统内部存在非线性的良好指示函数。非线性系统识别的主要问题之一是高模式密度。许多建模方案都涉及根据多项式或其他基本项对非线性恢复力进行某种扩展。如果涉及多个自由度，则这将成为一个多变量问题，并且扩展中的候选项的数量会随着非线性和自由度的数量爆炸性地增长。本文试图使用HOS进行检测并在一定的自由度范围内对许多对称和非对称系统的非线性行为进行鉴定。在此过程中，本文还尝试表明，在检测非线性方面，HOS比FRF更灵敏。此外，本文的目的是尝试并确定哪些模式以非线性方式进行耦合，以尽可能减少模型的候选耦合项的数量。双谱方法先前已应用于具有高对称性的简单低DOF系统，并已证明在这种有限的情况下效果很好。本文将考虑具有减小的对称性的连续翼塔模型的模型，以便在更一般的情况下评估该方法的实用性，分析也将扩展至评估三光谱的实用性。

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