• CN:11-2187/TH
  • ISSN:0577-6686

机械工程学报 ›› 2018, Vol. 54 ›› Issue (7): 97-106.doi: 10.3901/JME.2018.07.097

• 机械动力学 • 上一篇    下一篇

基于K-SVD字典学习算法的稀疏表示振动信号压缩测量重构方法

郭俊锋, 石斌, 魏兴春, 李海燕, 王智明   

  1. 兰州理工大学机电工程学院 兰州 730050
  • 收稿日期:2017-04-18 修回日期:2017-09-12 出版日期:2018-04-05 发布日期:2018-04-05
  • 通讯作者: 石斌(通信作者),男,1990年出生,硕士研究生。主要研究方向为机械振动信号处理。E-mail:18919852073@163.com
  • 作者简介:郭俊锋,男,1978年出生,博士,副教授。主要研究方向为现代测试技术及故障诊断。E-mail:junf_guo@163.com
  • 基金资助:
    国家自然科学基金资助项目(51465034)。

A Method of Reconstruction of Compressed Measuring for Mechanical Vibration Signals Based on K-SVD Dictionary-training Algorithm Sparse Representation

GUO Junfeng, SHI Bin, WEI Xingchun, LI Haiyan, WANG Zhiming   

  1. School of Mechanical and Electronic Engineering, Lanzhou University of Technology, Lanzhou 730050
  • Received:2017-04-18 Revised:2017-09-12 Online:2018-04-05 Published:2018-04-05

摘要: 针对目前机械振动信号频带越来越宽,依据传统香农-内奎斯特采样定理进行数据采集时,将会得到巨量振动数据,对存储、传输和处理带来困难的问题,提出了基于K-SVD字典学习算法的稀疏表示振动信号压缩测量重构方法。首先分析了振动信号在基于K-奇异值分解(K-Singular value decomposition,K-SVD)字典学习算法得到的过完备字典上的近似稀疏性,即可压缩性;然后利用高斯随机矩阵对振动信号进行压缩测量;最后基于压缩测量值采用正交匹配追踪算法对原始振动信号进行重构。仿真测试结果表明,当振动信号压缩率在60%~90%时,基于K-SVD字典学习算法构造的过完备字典比基于离散余弦过完备字典压缩感知重构相对误差小。该方法既可以得到较高的信号压缩比又有着精确的信号重构性能,在不丢失振动信息的情况下,大大减少了原始振动数据量。

关键词: 过完备字典, 精确重构, 稀疏表示, 压缩感知, 振动信号

Abstract: With the band of mechanical vibration signals getting wider, traditional Shannon-Nyquist sampling theorem is used for data collection, which will bring a huge amount of data and produce difficult problems of storage, transmission and processing. Hence, a method of reconstruction of compressed measuring for mechanical vibration signal based on K-SVD dictionary-training algorithm sparse representation is proposed in this research. Firstly, the sparsity(also called compressibility) of the vibration signal based on over-complete dictionary by the developed K-Singular value decomposition(K-SVD) dictionary-training algorithm is analyzed; Then, Gaussian random matrix is used as the sensing matrix to measure the vibration signal; Finally, orthogonal matching pursuit algorithm is utilized to reconstruct the original vibration signal, which is based on the compression measurements. The test results of simulated data demonstrate that the relative error of the compressed sensing reconstruction of vibration signal based on over-complete dictionary by the developed K-SVD dictionary-training algorithm is smaller than that of the method using over-complete dictionary of discrete cosine when the vibration signal compression rate is at 60%~90%. In the case of without losing vibration information, the proposed method not only obtains high compression rate of vibration signal and accuracy of signal reconstruction, but also reduces the original amount of vibration data.

Key words: accurate reconstruction, compressed sensing, over-complete dictionary, sparse representation, vibration signal

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