Research On Compression Sampling And Measurement Matrix Of Mechanical Vibration Signal

Mechanical vibration signals contain diversified information in equipment operation.Real-time acquisition of mechanical vibration signals is one of the core technologies in the field of fault diagnosis.However,the frequency band of vibration signals is becoming wider and wider,and a huge amount of data will be collected according to the Nyquist sampling theorem,which is not conducive to transmission and storage.Based on Compressive Sensing theory,measurement matrix of data compression of mechanical vibration signals is studied in this paper.The main research results are as follows:(1)In-depth analysis of the adaptability of common measurement matrix to mechanical vibration signals.Based on the sparsity of mechanical vibration signal on Discrete Cosine Transform basis,the performance of random measurement matrix(i.e.,Gaussian random matrix and Bernoulli random matrix),partial random measurement matrix(i.e.,partial Fourier matrix and partial Hadamard matrix)and deterministic measurement matrix(i.e.,the Toeplitz matrix and cyclic matrix)applied to the compression measurement of mechanical vibration signals are analyzed respectively.The experimental results show that the reconstruction error of random measurement matrix is the smallest,the computational complexity is the highest,and the amount of storage is the largest;the reconstruction errors of the deterministic measurement matrix and partial random matrix measurement matrix are basically equivalent and relatively large,but the deterministic matrix's structure is the simplest and easy to implement in hardware.(2)An Orthogonal Symmetric Toeplitz(for short OST)measurement matrix suitable for mechanical vibration signals is designed.Considering the problem of engineering realization,the deterministic measurement matrix suitable for vibration signal is studied based on the construction principle of the Toeplitz measurement matrix.Firstly,the first element of OST square matrix is obtained by inverse Fourier transform.then the first line's last element is shifted to the right and other rows are formed in turn;after that,according to the compression ratio,a certain number of rows of the OST square matrix are randomly selected and standardized,and the OST matrix can be obtained,which has the property of orthogonal symmetry;finally from the theoretical point of view,the OST matrix is analyzed to meet the Restricted Isometry Property.The experiments show that The performance of the OST measurement matrix for the mechanical vibration signal is better than that of the original Toeplitz matrix,and the performance of the Gaussian random measurement matrix is basically the same.This study is of great significance to the application of compressed sensing to practicality.(3)A method for data compression of vibration signals based on optimal deterministic measurement matrix is proposed.From the point of incoherence,the performance of the mechanical vibration signal of OST measurement matrix is still to be improved.So,firstly the threshold iterative shrinking algorithm is used to the matrix to reduce the mutual coherence between the OST matrix and the sparse basis.Then,the singular value decomposition algorithm is used to optimize the matrix,for improving the column independence of the OST matrix,thus the optimal OST measurement matrix is obtained.The experimental results show that the performance of the optimal OST matrix on compressing and measuring mechanical vibration signal is better than OST matrix and Gaussian random measurement matrix.Meanwhile,the complexity of OST matrix is much lower than that of the random matrix,which lays a foundation for engineering research.Finally,based on the optimal OST deterministic measurement matrix,a data compression method for collecting mechanical vibration signals is proposed.This method can greatly reduce the number of sampling without losing the original vibration information,which provides a new direction for solving the problem of mass data transmission and storage pressure.