When fault such as pit failure arises in the rolling element bearing the vibration signal of which will take on periodic characteristics, and the abrupt failure of rotating machinery can be avoided effectively if the weak periodic characteristics of the early fault stage is extracted timely. However, the periodic characteristics of bearing’ early weak fault is hard to be extracted usually and the reasons can be boiled to as following: Firstly, the weak periodic signal of rolling element bearing’ early fault stage is buried by the strong background noise. Secondly, the weak fault cannot show the complete shock attenuation impulsive characteristic due to its weak energy, so the traditional wavelet transform would not work effectively if a proper wavelet basis function fitting for analyzing the impulsive characteristics is not selected. To solve the above two problems, a feature extraction method of the weak periodic signal of rolling element bearing’ early fault based on Shift Invariant Sparse Coding (SISC) originating from sparse representation is proposed in the paper. To capture the underlying structure of machinery fault signal, SICS provides an effective basis functions learning scheme by solving the flowing two convex optimization problems iteratively: 1) L1-regularized least squares problem. 2) L2-constrained least squares problem. The fault feature can be probably contained and extracted if optimal latent component is filtered among these basis functions. The feasibility and effectiveness of the proposed method are verified through the corresponding simulation and experiment
