Weighted envelope spectrum based on the spectral coherence for bearing diagnosis

The key idea behind demodulation analysis for bearing diagnosis is to determine the fault-induced frequency band and directly detect the potential bearing fault characteristic frequency (FCF) in the demodulated spectrum. Till now, most demodulation methods are based on the optimal selection of only one informative frequency band. However, the unwanted in-band noise will be retained or some fault information may be ignored in the case of the discrete resonant frequency band or multiple informative frequency bands. To address the issue, a FCF-oriented criterion is proposed to determine all the informative frequency bands rather than only one specified frequency band. A new weighting vector is obtained to control the contribution of each spectral frequency in the demodulated spectrum. Subsequently, a weighted envelope spectrum (WES) is introduced by integrating the spectral correlation over the full spectral frequency band and assigning the new weighting vector on each spectral frequency. In this way, all frequency components with fault information are enhanced while other components are inhibited. Furthermore, expanded to the diagnosis of compound-fault, the FCF-oriented criterion can provide the different weighting vectors relevant to the different potential faults, and the separated fault features can be identified directly in the generated WESs. Finally, the advantages of WES over the traditional methods are testified by the simulated signal and experimental data.