经验模态分解的改进方法及应用研究

发布时间：2019-06-24 13:01

【摘要】：经验模态分解（empirical mode decomposition，EMD）算法是一种崭新的能够自适应地处理非平稳信号的时频分析方法，目前逐渐展露出了在非平稳信号处理中的独特优势，具有重要的理论研究价值和广阔的应用前景。本文从系统的角度深入分析了EMD算法，并着重研究了该算法包络生成中三次样条插值与极值点个数的关系。在此基础上提出了一个抑制端点效应的新方法，并针对直升机声信号和爆破地震动信号进行了应用研究。从系统角度，，把EMD算法看做一个多级串联的灰箱系统，指出三次样条插值是EMD算法中至关重要的一步。通过对三次样条插值算法的分析，给出了第二类边界条件和非扭结点边界条件下不同极值点个数的插值结果的均方差表达式，并在此基础上讨论了极值点个数与插值结果的关系。通过信号仿真并与实测信号对比验证了增加的极值点数大于一定数目后，插值结果不受增加极值点个数影响的结论。通过对镜像对称法、资料扩充法和资料重建法进行对比研究，总结了三种端点效应抑制方法的特点和效率性，并在此基础上提出了一种抑制端点的效应的EMD改进算法。本方法能够在保留资料扩充法适应性的同时，提高了运算效率。通过对仿真信号和实测信号的EMD分解结果分析，证明该方法高速有效。将EMD算法应用于了直升机声信号的分析中。通过对直升机声信号的分析，不仅发现其主要特性是频谱为基频和谐波成分，而且证明对短时信号EMD算法比Fourier变换的分析结果更优。由于直接应用Fourier变换不易提取直升机声信号的谐波集，而本文经过EMD分解可以将不同的谐波成分分解到不同的IMF子带。据此并结合直升机声信号的频谱特点，提出了一种新的峰值判别准则——距离衰减准则。对EMD的分解结果做Fourier变换，再通过峰值判别准则提取谐波集，更易于目标识别与分类。爆破地震动信号也是一类典型的非线性信号，本文在对爆破地震动信号进行特性分析基础上，应用EMD算法对实测的爆破地震动信号进行了分析，研究了其速度特征和微差时间，为地震动信号研究提供了新途径。本文的研究为EMD算法的改进研究提供了有益的理论依据，并拓展了EMD算法的应用领域。
[Abstract]:Empirical Mode decomposition (empirical mode decomposition,EMD) algorithm is a new time-frequency analysis method which can deal with non-stationary signals adaptively. At present, it gradually shows its unique advantages in non-stationary signal processing, and has important theoretical research value and broad application prospects. In this paper, the EMD algorithm is analyzed systematically from a systematic point of view, and the relationship between cubic Spline interpolation and the number of extremum points in envelope generation of the algorithm is studied. On this basis, a new method to suppress the end-point effect is proposed, and the application of helicopter acoustic signal and blasting ground motion signal is studied. From the system point of view, the EMD algorithm is regarded as a multi-stage series gray box system, and it is pointed out that cubic Spline interpolation is an important step in EMD algorithm. Based on the analysis of cubic spline interpolation algorithm, the mean square error expressions of interpolation results with different number of extreme points under the boundary conditions of the second kind of boundary conditions and non-kink points are given, and the relationship between the number of extreme points and the interpolation results is discussed. Through signal simulation and comparison with the measured signal, it is verified that the interpolation results are not affected by the increase of the number of extreme points when the number of extreme points is more than a certain number. By comparing the mirror symmetry method, the data expansion method and the data reconstruction method, the characteristics and efficiency of the three end effect suppression methods are summarized, and an improved EMD algorithm for suppressing the end point effect is proposed. This method can not only preserve the adaptability of the data expansion method, but also improve the operation efficiency. Through the analysis of the EMD decomposition results of the simulation signal and the measured signal, it is proved that the method is high speed and effective. The EMD algorithm is applied to the analysis of helicopter acoustic signal. Through the analysis of helicopter acoustic signal, it is found that the main characteristic of helicopter acoustic signal is that the spectrum is fundamental frequency and harmonic component, and it is proved that the EMD algorithm of short-time signal is better than the analysis result of Fourier transform. Because it is not easy to extract the harmonic set of helicopter acoustic signal by direct application of Fourier transform, different harmonic components can be decomposed into different IMF subbands by EMD decomposition in this paper. Based on the spectrum characteristics of helicopter acoustic signal, a new peak criterion, distance attenuation criterion, is proposed. The decomposition results of EMD are transformed by Fourier, and the harmonic sets are extracted by peak discriminant criterion, which is easier to recognize and classify targets. Blasting ground motion signal is also a kind of typical nonlinear signal. Based on the analysis of the characteristics of blasting ground motion signal, the measured blasting ground motion signal is analyzed by using EMD algorithm, and its velocity characteristics and millisecond time are studied, which provides a new way for the study of ground motion signal. The research in this paper provides a useful theoretical basis for the improvement of EMD algorithm, and expands the application field of EMD algorithm.
【学位授予单位】：北京理工大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TN911.7

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