Wavelet-based spatiotemporal sparse quaternion dictionary learning for reconstruction of multi-channel vibration data

Abstract

Accurate reconstruction of multi-source data information plays an essential role in remote intelligent operation, and prognostic and health maintenance (RIO-PHM) of industrial systems. However, traditional signal reconstruction methods such as compressed sensing fail to capture the spatio-temporal characteristics and coupling nature of the multi-source or multi-channel data. To alleviate this bottleneck, in this paper, a new wavelet-based spatiotemporal sparse quaternion dictionary learning (WSTS-QDL) algorithm is formulated for the reconstruction of multi-channel vibration data for the first time. Specifically, the wavelet-based spatiotemporal sparse low-rank matrix (SLRM) algorithm is elaborated and the sparse coefficient matrix of the multi-channel signals can be estimated using the split Bregman iteration (SBI) technique. Then, quaternion-based dictionary learning is introduced for multi-channel data reconstruction according to the updated sparse coefficient matrix during quaternion dictionary learning. Eventually, two equipmental scenarios including run-to-failure data of rolling bearing in bearing test bench and vibration signal of the failured bearing in corn thresher, are utilized for verification. The experimental results demonstrate that the highest recovery accuracy performance with scoring function and the lowest errors are achieved by the proposed method in contrast with the state-of-the-art benchmarks such as orthogonal matching pursuit (OMP) method and spatiotemporal sparse Bayesian learning (SSBL), and the waveform of phase space trajectory and points cloud distribution of the Poincare section in the original signal are similar/same to that obtained by the proposed method.