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