In complex working conditions, the monitoring signals of mechanical equipment are easily disturbed by multi-vibration sources and background noise, making weak fault features and strong coupling. It brings a great challenge to fault diagnosis. Therefore, a generalized minimax-concave enhanced convolutional sparse mechanical fault features resolution method based on the vibration characteristics atom is proposed to analyze weak features and strong-coupling faults. Firstly, an auto-adapted single-side fading wavelet framework is constructed to obtain the optimal feature atoms. The optimal feature atoms are increased in dimension to match the fault periodic to get the vibration feature atoms with periodic characteristics. Secondly, a convolutional sparse coding method based on GMC enhancement is proposed, which combines vibration feature atoms to obtain the sparse coefficients optimally. In addition, a processing parameter optimal selection method based on the ratio of average kurtosis to harmonic energy is designed, which overcomes the dilemma of selecting key parameters. Finally, the main features of the envelope spectrum are extracted and compared with theoretical fault feature frequencies to determine fault type. The effectiveness and superiority of the proposed method are verified by simulated and real test-bed signals. The spectrum kurtosis and tunable Q-factor wavelet transform Generalized Minimax-concave sparse enhancement method are set as comparison groups. The results demonstrate that different fault features are better decoupled, and the sparse component amplitudes are well improved compared to the comparison method.