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A method for the correlation dimension estimation for on-line condition monitoring of large rotating machinery

机译：大型旋转机械在线状态监测的相关维数估计方法

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In this paper, we introduce a robust method for the correlation dimension estimation in an automatic way for its implementation in on-line condition monitoring of large rotating machinery. The method is called Automatic-Attractor Dimension-Quantitative Estimation (A-AD-QE). It is based on a systemic analysis of the second derivative of the correlation integral obtained by the Grassberger and Procaccia algorithm. The A-AD-QE method concentrates its attention on the scaling region definition and it also has the possibility to analyse the geometrical structure of the obtained multidimensional second derivative of the correlation integral and its relation with the pseudo-phase portrait. The effectiveness of the introduced method was verified by means of the calculation of well-known analytic models as Lorenz attractor, van der Pol oscillator and Henon Map. Furthermore, the A-AD-QE method was applied to process real vibration signals of large rotating machines. As a typical example we analysed four measurements, recorded at different points. The obtained results demonstrate the applicability of the method in real vibration signal processing for this kind of machines.
机译：在本文中，我们介绍了一种鲁棒的自动进行相关维数估计的方法，以便将其用于大型旋转机械的在线状态监测。该方法称为“自动吸引器维定量估计”（A-AD-QE）。它基于对通过Grassberger and Procaccia算法获得的相关积分的二阶导数的系统分析。 A-AD-QE方法将注意力集中在缩放区域定义上，并且还可能分析获得的相关积分多维二阶导数的几何结构及其与伪相位肖像的关系。通过计算著名的解析模型，如劳伦兹吸引子，范德波尔振子和亨农图，验证了该方法的有效性。此外，A-AD-QE方法被用于处理大型旋转机械的真实振动信号。作为一个典型示例，我们分析了在不同点记录的四个测量值。获得的结果证明了该方法在这种机器的真实振动信号处理中的适用性。

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