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Vibration signals of a machine always contain abundant feature components. In this paper, a novel method for fault feature components extraction based on redundant lifting scheme and independent component analysis is proposed. Redundant prediction operator and update operator which adapt to the dominant structure of the signal are constructed, and the thresholds at different scales are selected according to the noise characteristics. The signal is de-noised and recovered, and independent component analysis is used on the de-noised signal to separate the fault feature components that are hidden in the signal. Practical vibration signals acquired from a generator set with rub impact fault are analyzed with the proposed method, and the failure symptom is extracted successfully. The results show that the proposed method is superior to independent component method in extracting the fault feature components from heavy background noise.