Frequency band selection based on the kurtosis of the squared envelope spectrum and its application in bearing fault diagnosis

Selection of a suitable frequency band for envelope analysis is a key step towards successful diagnosis of rolling element bearing faults. The band selection requirements include: (a) effectively avoiding the frequency range which contains irrelevant periodic impulses, and (b) keeping the feature of impulsiveness for bearing signals. Popular frequency band selection approaches often aim at searching for the band which maximizes the envelope kurtosis or the kurtosis of the envelope spectrum, and thus may not satisfy those requirements simultaneously when weak bearing signals are masked by strong noisy impulses. To resolve this issue, the energy of envelope signal and its energy distribution in the spectrum were taken into consideration in the proposed approach. It was shown that, for weak impulsive signals, the kurtosis of squared envelope spectrum (KSES) decreases as the bandwidth increases provided that the initial band is wide enough to contain most of the signal energy. The decreasing trend of KSES was then used to determine bandwidths for predefined center frequencies. From the obtained narrow bands, the one with a large bandwidth and a low KSES was selected for further analysis by comparing the value of a quality index. The bandwidth determination method and the final band selection criterion effectively excluded irrelevant periodic impulses in the selected band and ensured the high impulsiveness of the extracted signal. The proposed method was validated using experimental data obtained from a bearing rig and a planetary gearbox test rig, and its advantages were highlighted by comparing with fast kurtogram and protrugram.