经验模态分解算法在故障诊断、信号去噪、趋势预测和趋势消除等很多领域具有广泛的应用价值。信号包络线提取是经验模态分解算法的核心关键技术，直接影响分解结果的效果。目前在信号处理中常用的包络分析法有Hilbert变换、广义检波滤波、三次样条插值法和偏微分方程建模等，但是这些方法存在提取包络线精度不高、端点效应等不足，尤其是端点抖动效应导致很大的包络线提取误差。本文把信号的极值点看成是包络线信号的某一变换域上稀疏采样点，引入了稀疏优化算法对这些极值点进行包络线的稀疏优化复原。首先研究分析包络线的平稳变化特性，以此构建变频的DCT稀疏基；其次求解信号的极值点，以信号的极值点集用于稀疏优化算法的观测值；然后采用正交匹配追踪算法进行包络线的稀疏复原求解；最后对实际斜拉索振动信号进行算法测试和应用，通过与三次样条插值法进行比较分析，结果表明本文的算法不仅可以提高提取信号包络线的精度，而且可以有效的抑制端点效应。
Abstract
Empirical mode decomposition in a lot of fields has extensive application value,such as in fault diagnosis, signal de-noising and trend prediction and trend to eliminate.The key of empirical mode decomposition technique is to extract the envelope,which directly affects the result of the effect of decomposition.Currently used envelopment analysis in the signal processing with Envelopment analysis has Hilbert transform,generalized detection filtering,cubic spline interpolation and modeling of partial differential equations,etc.However,the disadvantages of these methods are the low accuracy the envelope and the end effect,etc,especially the effects of jitter end leads to large envelope extraction error.The paper regards the extreme points of the signal as sampling points of sparse signal on a transform domain,introduces sparse optimization algorithms to extract the envelope.First,study the smooth change characteristics of the envelope,to construct a variable frequency DCT sparse base;secondly solving extreme points of the signal and treating the extreme points of the signal as observations sparse optimization,then using orthogonal matching pursuit algorithm for sparse recovery to extract the signal envelope.Finally,the actual stay cable vibration signal algorithm testing and applications,through a comparative analysis with the cubic spline interpolation method,the results show that the proposed algorithm can not only improve the accuracy of extracting signal envelope but also can effectively inhibit the end effect.
关键词
经验模态分解 /
Hilbert变换 /
三次样条插值 /
稀疏复原 /
端点效应
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Key words
Empirical Mode Decomposition /
Hilbert transform /
cubic spline interpolation /
sparse recovery /
end effect
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参考文献
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