Decomposition of gear vibration signals by the generalised S transform

This paper describes the generalised S transform, a variant of the wavelet transform which allows calculation of the instantaneous phase of a signal, and its application to the decomposition of vibration signals from mechanical systems such as gearboxes for the early detection of failure. It is shown that the original S transform is in essence the same as existing forms of the wavelet transform, except that it may be implemented in a way which allows the easy recovery of information about the phase of components of a signal. However, the definition of the original S transform places unnecessary restrictions on the form of the window function used. A new distribution, called the generalised S transform, is proposed which avoids these restrictions. A procedure is described for the automatic identification of the amplitude, phase, frequency, time and shape of components within a signal and for their step-by-step removal. Provided the components are sufficiently well separated so that significant interference does not occur in time or in frequency, perfect or near-perfect decomposition can be achieved. By considering the energy of the component, the window parameters can be optimised for each component to obtain the best match. Monitoring the total energy of the removed components and the remaining signal helps ensure the integrity of the decomposition. Several window functions are considered, including two forms of exponential functions, amplitude modulation by a cosine function and phase modulation by a cosine function. Decomposition using the generalised S transform and the new window functions is demonstrated using a numerically generated test signal and experimentally measured gear vibration data. (C) 1999 Academic Press.