Envelope calculation of the multi-component signal and its application to the deterministic component cancellation in bearing fault diagnosis

• The envelope of the multi-component signal is calculated by the Hilbert transform.
• A novel deterministic component cancellation method is proposed.
• The proposed method is performed by the iterative calculation of the envelope.
• Simulations and experiments are used to validate the theoretical calculation.
• The proposed method is more efficient than the available methods including CPW.

Commonly presented as cyclic impulse responses with some degrees of randomness, the vibrations induced by bearing faults are multi-component signals and usually overwhelmed by other deterministic components, which may degrade the efficiency of the traditional envelope analysis used for bearing fault feature extraction. In this paper, the envelope of the multi-component signal, including both discrete frequency components and cyclic impulse responses, is theoretically calculated by the Hilbert transform in both time and frequency domains at first. Then, a novel deterministic component cancellation method is proposed based on the iterative calculation of the signal envelope. Finally, simulations and experiments are used to validate the theoretical calculation and the proposed deterministic component cancellation method. It is indicated that the oscillation part of the envelope is dominated by the cross-terms of the multi-component signal, and that the cross-terms between a discrete frequency component and cyclic impulse responses present as new cyclic impulse responses, which retain the cyclic feature of the original ones. Furthermore, the deterministic component can be canceled by iteratively subtracting the direct current (DC) offset of the envelope. Compared with the cepstrum pre-whiten (CPW) method, used to separate the deterministic (discrete frequency) component from the random component (vibration induced by the bearing fault), the proposed method is more efficient to the shifting of the cyclic impulse responses from the powerful deterministic component with little disruption, and is more suitable for the real time signal processing owing to the high efficient calculation of the Hilbert transform.