Bearing fault detection using second-order moment spectrum and adaptive time-varying morphological filtering

Abstract

The second-order moment spectrum is a method designed to simplify the complex shape of the spectrum, thus facilitating its interpretation for the identification and localization of defects based on peak frequency. Generally used as a final step in defect detection methods, this method offers the advantage of a more easily interpretable spectral shape. Compared to the shape of the spectrum of the vibration signal defined by the Fourier transform, which includes sidebands composed of peaks of large amplitude at different frequencies, the spectrum generated by the second-order moment spectrum method stands out for its simplicity. Starting from the mean and standard deviation of the vibration signal, the second-order moment can be defined as the power of the ratio between the standard deviation and the difference between the signal and the mean. Next, the Fourier transform is applied to express the second-order moment spectrum. The performance of the second-order moment spectrum is evaluated using the principle of comparison with the envelope spectrum obtained by the Hilbert transform. Vibration signals are analyzed using two methods: adaptive time-varying morphological filtering and second-order moment spectrum. After applying these methods to the signals from the database, we observe high-amplitude peaks at the frequencies corresponding to inner ring and ball defects. The second-order moment spectrum gives similar results to those obtained with the Hilbert transform envelope.