针对目前机械振动信号频带越来越宽，依据奈奎斯特采样定律进行数据采集时，会得到海量的振动数据，对存储、传输和处理带来困难的问题，结合压缩感知理论，提出了一种基于最优型确定性测量矩阵的振动信号数据压缩采集方法。该方法的核心内容为测量矩阵的设计：首先，以托普利兹（Toeplitz）矩阵为基础，建立正交对称托普利兹（Orthogonal Symmetric Toeplitz, OST）测量矩阵模型；其次，为了降低测量矩阵与稀疏基之间的互相干性，应用阈值迭代收缩算法对该矩阵进行迭代，得到改进的OST矩阵；最后，为了提高OST矩阵自身列独立性，采用奇异值分解（Singular Value Decomposition, SVD）算法继续优化OST矩阵，从而得到最优型确定性矩阵。仿真实验结果显示，提出的最优型测量矩阵与Toeplitz矩阵、高斯矩阵及优化前的OST矩阵相比，在重建振动信号时，重建精度较高，并且易于工程实现。
Abstract
Aiming at frequency bandwidth of mechanical vibration signals being getting wider and wider,when using Nyquist sampling theorem for data collection,a huge amount of vibration data are acquired to bring difficulties of storage,transmission and processing. Here,combining the compression sensing theory,a data compression collecting method for vibration signals based on optimal deterministic measurement matrix was proposed. The core of this method was to design a measurement matrix. Firstly,based on Toeplitz matrix,an orthogonal symmetric Toeplitz (OST) measurement matrix model was established. Secondly,in order to reduce the mutual coherence between the measurement matrix and sparse bases,the threshold iterative contraction algorithm was used for OST matrix iteration to get a modified OST matrix. Finally,to improve the column independence of the OST matrix,the singular value decomposition (SVD) algorithm was used to optimize the OST matrix to acquire the optimal deterministic measurement matrix. The simulation results showed that compared with Toeplitz matrix,Gaussian one and the OST one before optimization,the proposed optimal deterministic measurement matrix has higher reconstruction accuracy when reconstructing vibration signals,and it is easy to implement in engineering.
关键词
振动信号 /
压缩采集 /
测量矩阵 /
互相干性 /
阈值收缩 /
奇异值分解
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Key words
vibration signal /
compressed sampling /
measurement matrix /
mutual coherence /
threshold contraction /
SVD
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