A Novel Method for Repairing Missing Data of Bearing Vibration Signals Based on Compressed Sensing

The theory of compressed sensing is introduced to solve the repairing of missing data collected in PHM monitoring. An improved measurement matrix is proposed to optimize the conventional measurement matrix to increase the uncorrelation between the observation matrix and the sparse basis. Then a sparse representation of the vibration signal through discrete cosine transform (DCT) is utilized to sparse the noisy vibration signal. Finally, the orthogonal matching pursuit (OMP) algorithm is employed to reconstruct the missing signal. The method validation results show that the signal repaired by the proposed method agrees well with the original signal in the time domain, and the signal reconstructed by the optimized observation matrix has higher accuracy than the signal reconstructed by the initial observation matrix. Under different missing rates, the reconstruction error of the proposed method is smaller than other comparison methods. This shows the effectiveness and advantages of the proposed missing data recovery method.