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Efficient and automatic fault feature extraction of rotating machinery, especially for 
incipient faults is a challenging task of great significance. In this article, an optimal periodicity-enhanced group sparse method is proposed. Firstly, a period sequence determination method without 
any prior information is proposed, and the amplitude is calculated by the numerical characteristics 
of the vibration signal to obtain period square waves. Secondly, the periodic square waves are
embedded into the group sparse algorithm, to eliminate the influence of random impulses, and 
intensify the periodicity of the acquisition signal. Thirdly, a fault feature indicator reflecting both 
signal periodicity and sparsity within and across groups is proposed as the fitness of the marine 
predator algorithm for parameter automatic selection. In addition, the method proposed is evaluated 
and compared by simulation and experiment. The results show that it can effectively extract 
incipient fault features and outperforms traditional overlapping group shrinkage and Fast Kurtogram

Incipient faults features are often extremely weak and susceptible to heavy noise, making it challenging to obtain the concentrated faulty energy ridges in the time-frequency domain. Thus, a novel impulse-enhanced sparse time-frequency representation (IESTFR) method is proposed in this paper. First, the time-rearranged multisynchrosqueezing transform is utilized to produce a time-frequency representation with a high energy concentration for faulty impulses. Next, a new non-convex penalty function is constructed by the hyperbolic tangent function, which can enhance the periodic impulsivity of sparse time-frequency representation for more obvious fault characteristic frequency. Moreover, the time-frequency transform is evaluated and compared by simulated signals and a selection strategy for the regularization parameter is designed. Simulated signals and two experimental signals are applied to verify the effectiveness of IESTFR, and the results show that IESTFR is effective and superior in bearing incipient fault feature extraction.

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