Adaptability Analysis of Common Measurement Matrices for Mechanical Vibration Signal

Ab stract—In this paper, the construction method of common measurement matrices is studied, adaptability of common measurement matrices for mechanical vibration signal is analyzed. Typical measurement matrices are selected from commonly used measurement matrices, Gaussian random measurement matrix and Bernoulli random measurement matrix are chosen from totally random measurement matrices, Circulant measurement matrix and Toeplitz measurement matrix are selected from deterministic matrices, partially random Fourier measurement matrix and Hadamard matrix are chosen from deterministic measurement matrices. The sensing performance of common measurement matrices for mechanical vibration signal is evaluated from the two perspective of reconstruction error and memory space. The simulation results show that two kinds of complete random matrices, Gaussian and Bernoulli matrices, can exactly reconstruct original vibration signal, but they occupy large memory space; deterministic matrices, Circulant and Toeplitz matrices, although need fewer memory space, obtained measurements which do not have information of global vibration signal lead to lower reconstruction results; partially random Fourier matrix is extremely coherent with sparse transforming base of vibration signal, so it has not exact result in the process of reconstructing original vibration signal, the requirement of Exponentiation of 2 seriously restrict its application.