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Least action criteria for blind separation of structural modes

机译：结构模式盲分离的最小动作准则

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It was recently shown that blind source separation (BSS), as originally developed in the signal processing community, can be used in operational modal analysis to separate the responses of a structure into its individual modal contributions. This, in turn, allows the application of simple single-of-degree-freedom techniques to identify the modal parameters of interest. Several publications have recently attempted to give a posteriori physical interpretations to BSS - as initially developed in telecommunication signal processing - when applied to the field of structural dynamics. This paper proposes to follow the route the other way round. It shows that several separation criteria purposely dedicated to operational modal analysis can be deduced from general physical considerations. Three such examples are introduced, based on very different properties that uniquely characterise a structural mode. The first criterion, coined the "principle of shortest envelope", conjectures that the envelope of a modal response has, among all possible envelopes, the shortest length. That such a principle leads to the governing differential equation of a single-degree-of-freedom oscillator is proved from calculus of variation. The second criterion, coined the "principle of minimum spectral variance", conjectures that the frequency spectrum of a structural mode is maximally concentrated around its central frequency. Finally, the third criterion, coined the "principle of least spectral complexity", states that a structural mode has the lowest possible entropy in the frequency domain. All three criteria can be expressed in terms of a mixing matrix whose columns contain the unknown mode shapes. The recovery of the latter is then trivially achieved by minimising the criteria. Extensive simulations show that the proposed criteria lead to figures of merit very similar to those of the state-of-the-art, while at the same time providing physical insight that other algorithms issued form the signal processing community may dramatically lack.
机译：最近显示，信号处理社区中最初开发的盲源分离（BSS）可用于操作模态分析，以将结构的响应分为其单独的模态贡献。反过来，这允许应用简单的单自由度技术来识别感兴趣的模态参数。当应用于结构动力学领域时，一些出版物最近试图对BSS进行后验的物理解释-如最初在电信信号处理中开发的。本文建议沿另一条路线走。它表明，可以从一般的物理考虑中得出一些专门用于运行模式分析的分离标准。基于三个非常不同的特性（独特地描述了结构模式），介绍了三个这样的示例。第一个标准是“最短包络原理”，它推测模态响应的包络在所有可能的包络中具有最短的长度。从变化的演算可以证明这种原理导致了单自由度振荡器的控制微分方程。第二个标准是“最小频谱方差原理”，它推测结构模式的频谱最大程度地集中在其中心频率附近。最后，第三个标准是“最小频谱复杂性原理”，它指出结构模式在频域中具有最低的熵。这三个标准可以用混合矩阵表示，混合矩阵的列包含未知的模式形状。然后通过最小化标准来轻松实现后者的恢复。大量的仿真表明，所提出的标准得出的品质因数与最新技术非常相似，同时提供了从信号处理社区发布的其他算法可能会严重缺乏的物理洞察力。

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