Variational multi-harmonic mode extraction for characterising impulse envelope of bearing failures

The envelope shape of a failure-induced impulse response reflects the strike procedure of the bearing failure area and provides information on the size and contour of the defective area. Because the impulse envelope is a broad-bandwidth component severely affected by in-band noise, it is difficult to separate from the vibration signals. To eliminate the in-band noise and obtain diagnostic information from the full-band envelope, a novel method, called variational multi-harmonic mode extraction (VMHME), is proposed to extract the impulse envelope component and characterise the envelope shape. First, a multi-harmonic mode function (MHMF) is constructed to define a harmonic assembly, which is generally has a broad-bandwidth property, but each harmonic is narrow-bandwidth. A variational model is then established to optimally decompose the mode with explicit MHMF from the analysed signal. Only one specific mode is extracted at a time and adopted to efficiently satisfy the demand for failure-induced impulse envelope extraction. Essentially, VMHME provides an optimal band-pass filter bank just with a local narrow bandwidth at failure characteristic harmonics. Utilising​ the narrow-bandwidth harmonic assembly eliminates the in-band noise, whereas the failure characteristics in the envelope shape are retained The effectiveness of the proposed method was verified using both simulated and experimental bearing failure signals. The results prove that VMHME can make in-depth use of the envelope shape information for bearing failure diagnosis.