Higher-order spectral techniques for machine vibration condition monitoring

Abstract

The vibration signals measured from rotating machinery can be very complex and a number of machine malfunctions can create complicated modulation patterns which are sometimes difficult to detect and to understand. Conventional linear spectral analysis will be of limited use in particular instances when frequency components interact together to form new spectral components due to some non-linear process. Under these circumstances, various signal processing tools are available for performing sophisticated analysis of the measured vibration to detect the non-linear interaction of frequency components and hence changes in machine performance and condition. This paper presents two higher-order spectral analysis techniques, the bispectrum and the trispectrum, and demonstrates how they can be used to detect phase coherence between various frequency components. The theoretical relationship of the higher-order spectral techniques to the power spectrum is given along with the derivation of the normalized bispectrum and trispectrum using the Fourier series of phase- related signals to show that the higher-order spectral analysis techniques can detect various forms of phase coupling between frequency components as well as the strength of the phase coupling. The particular case of modulation is investigated to show the applicability of the higher-order spectral techniques to detect amplitude and phase modulation.