Weighted Cyclic Harmonic-to-Noise Ratio for Rolling Element Bearing Fault Diagnosis

A novel index termed weighted cyclic harmonic-to-noise ratio (WCHNR) is proposed to directly evaluate the quality and quantity of harmonics of bearing characteristic frequency (BCF) in the squared envelope spectrum (SES). There are four steps to construct the proposed index. First, cyclic harmonic-to-noise ratio (CHNR) is defined to evaluate the prominence of harmonic, which is inspired by harmonic-to-noise ratio (HNR) and ratio of cyclic content (RCC). Interestingly, it is showed in this paper that a special case of CHNR is a local $L\infty /L1$ norm, which bridges the proposed index with other indexes such as spectral Gini index and spectral kurtosis. Second, a local 0-dB threshold and a global threshold derived from a statistical hypothesis test are utilized to decide the detection of prominent harmonic. Third, if two consecutive harmonics are not prominent, the following higher order harmonics would not be considered, which helps avoid large gap between prominent harmonics and reduce the influence of random cyclic frequency noise. Finally, the sum of each type of CHNR is weighted based on the number of detected harmonics. The proposed index is compared with the spectral Gini index and spectral kurtosis in three case studies, which indicates that the proposed index is less sensitive to outliers and more effective in bearing fault diagnosis. It is also found that the number of detected harmonics can be potentially used in bearing fault classification easily and practically.