斜拉索振动信号的包络线稀疏复原算法

Envelope sparse recovery algorithm for stay cable vibration signals

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。将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,结果表明本算法不仅可以提高提取信号包络线的精度,还可以有效的抑制端点效应。

Empirical mode decomposition（ EMD） has extensive applications in a lot of fields,such as,fault diagnosis,signal de-noising,trend prediction and trend elimination. The key of EMD technique is to extract the signal envelope,it directly affects the effects of decomposition results. Current envelope analysis methods in signal processing are Hilbert transformation,generalized detection and filtering,cubic spline interpolation and modeling of partial differential equations,etc. However,the disadvantages of these methods are the lower accuracy for envelope extraction and the end effects,etc,especially,the jitter effect of ends leads to a larger envelope extraction error. Here,the extreme points of a signal were regarded as spare sampling points of its envelope signal in a certain transformation domain,the sparse optimization algorithms were introduced to do envelope sparse optimal recovery for these extreme points. Firstly,the steady change characteristics of the envelope were studied to construct a DCT sparse base with varying frequency; secondly,the extreme points of the signal were solved and the extreme points of the signal were taken as observation values for sparse optimization algorithms; then,the orthogonal matching pursuit algorithm was used to do solving envelope sparse recovery.Finally,the actual stay cable vibration signals were employed for algorithm testing and applications. Through a comparative analysis with the cubic spline interpolation method,the results showed that the proposed algorithm can not only improve the accuracy of extracting signal envelope but also can effectively inhibit the end effect.