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The compressive sensing (CS) theory provides a new slight to the big-data problem led by the Shannon sampling theorem in rolling element bearings condition monitoring, where the measurement matrix of CS tends to be designed by the random matrix (RM) to preserve the integrity of signal roughly. However, when the signal to be analyzed is infected with strong noise, not only does the signal become insufficiently sparse, but the randomness of the measurement matrix will bring down the sensing efficiency, resulting in the loss of fault feature. Thus, a sensing-enhanced CS scheme based on a series of modes after VMD decomposition is proposed under this paper. The core of this scheme is as follows: (1) the principal mode of VMD with better sparsity replaces the raw signal for compressive sensing; (2) all these modes contain the time-frequency characteristics of the raw signal; (3) a new measurement matrix called mode-circulant matrix (MCM) is defined by circulating the mode matrix, and when the amount of samples is shrunk, the sensing efficiency can be enhanced greatly. Besides, considering the fault signal of rolling bearings under variable speed, there is a need to use order tracking to overcome the nonstationarity of the signal before applying CS theory. The analysis results of simulation and experiment prove that the VMD- and MCM-based CS can successfully extract the weak fault feature of rolling bearings with operating speed changing.

An MCM-Enhanced Compressive Sensing for Weak Fault Feature Extraction of Rolling Element Bearings under Variable Speeds