LMD与非凸罚最小化L q正则子压缩传感的轴承振动信号重建

摘要

Considering the high speed transmission and long-term online storage of mechanical vibration signals, a hybrid reconstruction approach to bearing fault vibration signal based on local mean decomposition (LMD) and nonconvex penalized Lqminimization compressed sensing was proposed. This method adopts an ideology that sampling and compression for vibration signal was carried out simultaneously. First, each complicated signal was decomposed into a number of stable single component product functions by using LMD method, and then the best sparse matrix was sought for different frequency components, and the underdetermined equations were built based on Gaussian random matrix. Meanwhile, the appropriate compression ratio was solved by the reconstruction results of each single product function component, and the original vibration signals were obtained by the combination of each signal component reconstruction signals with the nonconvex penalizedLq(q=0.5) minimization. The results show that the method of LMD and nonconvex penalizedLq minimization compressed sensing can not only improve compression accuracy and reduce the reconstruction computational complexity, but also enhance the speed of process and operational efficiency.%针对机械振动信号高速传输、大容量长期实时存储问题，提出一种局部均值分解(LMD)与非凸罚最小化L q正则子压缩传感(CS)相结合的轴承故障振动信号重建方法。该方法利用振动系统信号采样、压缩合并进行的思想，首先通过LMD把振动信号分解为若干个不同频率分量的乘积函数平稳信号，对不同的频段分量寻求最佳的稀疏基，构建基于随机高斯矩阵的高度欠定方程；然后求解合适的压缩比，应用非凸罚最小化L q正则子(q=0.5)算法重构，对所有重构信号组合得到原始振动信号。研究结果表明：LMD与非凸罚最小化L q正则子压缩传感相结合的方法提高了轴承振动信号的重构精度，降低了重构计算复杂度，具有更高的处理速度和运行效率。