针对压缩采集在机械振动信号采集的过程中，现有随机测量矩阵不易硬件实现、确定性测量矩阵重构误差较大的问题。将高斯序列的优点和循环原理的优点相结合，提出一种高斯分布循环测量矩阵，其是一种结构化随机测量矩阵。首先，高斯分布循环测量矩阵的第一行元素由服从高斯分布的序列生成，通过循环移位生成剩余的所有行向量；然后，随机取出除第一行的其他所有行的部分元素，每个元素再乘不同的随机数或者同一个随机数，并放回原位置；最后，基于高斯分布循环测量矩阵得到的机械振动信号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。高斯分布循环测量矩阵的所有元素的随机性可以满足测量矩阵对随机性的要求，循环原理的内在确定性又可以满足测量矩阵硬件实现的要求。仿真表明：高斯分布循环测量矩阵的感知性能略优于与高斯矩阵的性能，整体上基本相当。
Abstract
When the compressed sampling theory is applied in mechanical vibration signal acquisition,the existing random measurement matrix occupies a large storage space,the process of compression acquisition and reconstruction need to handle a large amount of computation problems.Here,Gaussian distribution cycle measurement matrix (GCMM) was proposed by integrating advantages of Gaussian sequences and the circulant theory.Firstly,the first row elements of GCMM were generated with a row vector obeying Gaussian distribution,all the remaining row vectors were generated through circular shift.Then part elements of all rows except the 1st row were taken out,each element was multiplied by the same random number or different ones,they were put back at the original position.Finally,the compressed measurement values of mechanical vibration signals obtained based on GCMM were used to reconstruct the original vibrating signals using the orthogonal matching pursuit algorithm.All the elements of GCMM satisfied he randomness requirements of the measurement matrix,the intrinsic certainty of the circulant principle also met the requirement of hardware implementation of the measurement matrix.Simulation results showed that the perception performance of GCMM is similar to that of Gaussian matrix,but the required storage space of GCMM is less than that of Gaussian matrix.
关键词
振动信号 /
压缩采集 /
高斯序列 /
循环原理 /
结构化随机测量矩阵
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Key words
vibration signal /
compressed sampling /
Gauss sequence /
cycle principle /
structured random measurement matrix
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