经验模态分解的方法改进研究

发布时间：2018-04-16 22:20

本文选题：经验模态分解 + 单调性一致　；参考：《湖南科技大学》2016年硕士论文

【摘要】：经验模态分解(Empirical Mode Decomposition,EMD)是处理非线性和非平稳信号的有效方法。该方法根据自身信号的特点,将信号分解成若干个本征模态函数IMF之和,弥补了短时傅里叶、小波分解和Wigner-Ville分布的不足。目前,EMD广泛应用于机械故障诊断、生物医学信号分析和通讯信号分析等领域。本文对EMD的理论进行了分析,以算法本身固有的缺点为突破口,对EMD中的端点效应问题和模态混叠问题进行了研究,并给出了相应的解决方案。研究的主要内容如下:(1)针对用的机械故障信号时频分析方法,如短时Fourier变换、Wigner-Ville分布、小波变换等,总结这些方法的特点及不足,在此基础上引出Hilbert-Huang变换(HHT),指出EMD分解算法中有几个问题需要解决,如端点效应、模态混叠。(2)利用信号波形单调性一致来处理信号端点效应问题。经验模态分解需通过极值点描述信号上下包络线,但是信号两端边界的极大值和极小值不好估计,包络线就存在着变数,这样经验模态分解过程就会产生边界误差,随着分解进行边界误差会向内传播,从而污染内部数据,导致分解结果不合理。通过分析几种典型的抑制端点效应的方法,把单调性一致法引入EMD,以获得信号端点极值点,这种方法简单而且可以有效地抑制端点效应。(3)提出奇异值分解去噪法来抑制EMD过程中的事件性模态混叠问题和提出了基于能量分离的方法(SEMD)避免了非事件性模态混叠现象。事件性模态混叠首先通过联合平稳度的自适应模态解混叠方法筛选出异常信号区间,再利用奇异值分解去噪消除异常事件,使异常事件不再那么明显,从而使信号包络更自然,可以有效抑制模态混叠现象,提高EMD的整体分解效果,并与传统的EMD方法对比,改进的方法能有效抑制模态混叠问题。非事件性模态混叠采用奇异值分解将能量高的信号重新聚合,能量低的重新聚合,再进行EMD分解,并进行了模拟验证,结果表明SEMD方法能有效的分离出信号成分,与直接进行EMD分解相比较,该方法具有明显优越性。(4)基于以上的研究,提出了基于单调性一致和奇异值分解的EMD方法(MSEMD),并选用美国凯斯西储大学轴承数据中心的数据进行分析,对MSEMD和经验模态分解进行故障频率识别对比分析,得出了MSEMD分解效果优于经验模态分解,可以有效的识别轴承故障。
[Abstract]:Empirical Mode decomposition (EMD) is an effective method for dealing with nonlinear and non-stationary signals.According to the characteristics of the signal, the method decomposes the signal into the sum of several intrinsic mode functions (IMF), which makes up for the shortage of short-time Fourier transform, wavelet decomposition and Wigner-Ville distribution.At present, EMD is widely used in mechanical fault diagnosis, biomedical signal analysis and communication signal analysis.In this paper, the theory of EMD is analyzed, and the endpoints effect and modal aliasing in EMD are studied with the inherent shortcomings of the algorithm as the breakthrough point, and the corresponding solutions are given.The main contents of this paper are as follows: (1) aiming at the time-frequency analysis methods of mechanical fault signals, such as short time Fourier transform Wigner-Ville distribution, wavelet transform and so on, the characteristics and shortcomings of these methods are summarized.On this basis, the Hilbert-Huang transform is introduced, and several problems need to be solved in the EMD decomposition algorithm, such as endpoint effect, mode aliasing.Empirical mode decomposition (EMD) is required to describe the upper and lower envelope of the signal through extreme points. However, the maximum and minimum of the two ends of the signal are difficult to estimate, and the envelope exists variables, so the empirical mode decomposition process will produce boundary errors.The boundary error will propagate inward with the decomposition, which pollutes the internal data and leads to unreasonable decomposition results.By analyzing several typical methods to suppress the endpoint effect, the monotonic consistency method is introduced into the EMD to obtain the extreme point of the signal endpoint.This method is simple and effective to suppress the endpoint effect. (3) the singular value decomposition (SVD) denoising method is proposed to suppress the event-mode aliasing in the EMD process and the energy seperation-based method (SEMD-based) is proposed to avoid the non-event-mode aliasing.Event mode aliasing first selects the interval of abnormal signals by combining the adaptive mode de-aliasing method of stationary degree, and then uses singular value decomposition to remove the abnormal events, which makes the abnormal events less obvious, thus making the envelope of the signals more natural.It can effectively suppress the phenomenon of mode aliasing and improve the overall decomposition effect of EMD. Compared with the traditional EMD method, the improved method can effectively suppress the modal aliasing problem.Non-event mode aliasing uses singular value decomposition (SVD) to reaggregate high-energy signals, low-energy reaggregates, and then EMD decomposition. The simulation results show that the SEMD method can effectively separate the signal components.Compared with direct EMD decomposition, this method has obvious advantages. Based on the above research, a EMD method based on monotonicity uniformity and singular value decomposition is proposed, and the data from the Cass Western Reserve University bearing data Center are selected for analysis.Comparing the fault frequency identification between MSEMD and empirical mode decomposition, it is concluded that the effect of MSEMD decomposition is better than that of empirical mode decomposition, and it can effectively identify bearing faults.
【学位授予单位】：湖南科技大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TH17

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