希尔伯特—黄变换及其模态混淆问题的研究

发布时间：2018-05-15 23:44

本文选题：希尔伯特-黄变换 + 模态混淆　；参考：《合肥工业大学》2012年硕士论文

【摘要】：希尔伯特-黄变换(HHT)是一种新型的信号处理方法，它创造性的提出了固有模态函数(IMF)和经验模态分解(EMD)，使瞬时频率有了明确的物理意义。本文对HHT理论体系以及其中的模态混淆问题开展了一系列研究。首先，以瞬时频率为主线，介绍了HHT的基本理论，对EMD和Hilbert变换进行了详细的阐述。通过数值仿真算例，说明了HHT在处理非线性、非稳态信号中的优越性，并指出了HHT方法中存在的一些问题。其次，介绍了应用HHT识别结构振动模态参数的方法。由于HHT理论没有建立严格的数学基础，其自身的缺陷会影响模态参数的识别精度。针对模态混淆和端点效应对识别精度的影响，阐述了利用带通滤波抑制模态混淆的方法，提出了选择滤波器截止频率的经验公式和选择拟合数据段的判别条件，仿真算例证明了其有效性。最后，，针对EMD中的模态混淆问题开展了深入的研究。在总结了模态混淆产生的原因和现有解决办法的基础上，结合HHT理论体系和实际工程信号的特点，扩展了信号的数学模型。提出了瞬时模态混淆的概念，将对模态混淆的讨论从全局细化到了局部。仿真算例反映了基于瞬时模态混淆概念的模态参数识别具有的特点。
[Abstract]:Hilbert-Huang transform (HHT) is a new signal processing method, which creatively proposes the inherent mode function IMF) and empirical mode decomposition (EMD), which makes the instantaneous frequency have a clear physical meaning. In this paper, a series of studies on HHT theory system and modal confusion are carried out. Firstly, taking instantaneous frequency as the main line, the basic theory of HHT is introduced, and the EMD and Hilbert transformations are described in detail. Through numerical simulation examples, the superiority of HHT in dealing with nonlinear and unsteady signals is illustrated, and some problems in HHT method are pointed out. Secondly, the method of identifying vibration modal parameters by HHT is introduced. Because the HHT theory does not establish a strict mathematical foundation, its own defects will affect the identification accuracy of modal parameters. Aiming at the influence of modal confusion and endpoint effect on the recognition accuracy, the method of suppressing modal confusion using bandpass filter is expounded, and the empirical formula for selecting the cut-off frequency of filter and the discriminant condition for selecting fitting data segment are presented. A simulation example shows its effectiveness. Finally, the modal confusion in EMD is studied deeply. On the basis of summing up the causes of modal confusion and the existing solutions, the mathematical model of the signal is extended by combining the characteristics of the HHT theory system and the practical engineering signal. The concept of instantaneous modal confusion is proposed and the discussion of modal confusion is refined from global to local. The simulation example shows the characteristics of modal parameter identification based on instantaneous modal confusion concept.
【学位授予单位】：合肥工业大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TH113

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