Vibration data recovery based on compressed sensing

Abstract

A missing data recovery method based on compressed sensing is proposed for vibration data of rotating machinery. Firstly, the incomplete signal is transformed into lossy signal by setting the data values corresponding to the time without input as zeros. According to the indices of zero elements in lossy signal, the observation matrix in the frame of compressed sensing is constructed based on identity matrix. Secondly, the dictionary matrix with which the vibration signal can be represented sparsely is chosen or constructed according to the signal needed to be recovered and other prior knowledge. Finally, the original complete signal is recovered based on the lossy signal, observation matrix and dictionary matrix by using an effective and steady pursuit algorithm. The efficiency of the proposed method is validated with simulation data and practical bearing vibration data. Recovery results are discussed by comparing the characteristic values corresponding to the complete signal, lossy signal and recovered signal in time domain and frequency domain. The test results show that the proposed method can well achieve the missing data recovery, and from the view of statistical characteristics, the recovery signal can describe the complete vibration signal more accurately than the lossy signal.