Instantaneous frequency of a transient mechanical signature and its estimation by a moving window; applicability and physical interpretation

Abstract

Instantaneous frequency often indicates the occurrence of specific events which could indicate a change in the action of machinery. It is therefore useful to find a way to utilise instantaneous frequency on the characterisation of transient actions of mechanical components. This can also be based on conventional signal processing techniques such as amplitude--time domain data and Fourier analysis. In this paper, we look at the possibility of applying instantaneous frequency to analyse transient mechanical signatures. We found that instantaneous frequency is quite sensitive to signal to noise ratio and therefore to utilise this measure an improved estimator which can minimise the effect of noise on the estimation is needed. The suggested method is a moving window in the time domain, which essentially averages out the noise effect for the prescribed window length. The proposed method reduces the noise effect on the instantaneous frequency estimation but is not satisfactory for signals which have quite low signal to noise ratios. To deal with this, we proposed an 'instantaneous frequency histogram' which shows the number of occurrences of instantaneous frequency and can thus be used to grade the meaningful instantaneous frequency components. The non-linear characteristics of the instantaneous frequency which produce the additional component of the signal which in general has frequencies which differ from the original signals is discussed in terms of its applicability and limitations for mechanical signature analysis.