Effect of spectral notches on robust waveform recovery methods for machinery diagnostics

Abstract

Recovery of pulselike waveforms from vibration response measurements is often a goal in reciprocating machinery diagnostics. One such method, which makes use of inverse filtering, uses cepstral windowing in an attempt to make the procedure ‘‘robust.’’ It has been observed that, under certain conditions, the timing of the (cepstrally windowed) waveforms recovered from several consecutive machine cycles may occur at one of two distinct values. This behavior stems from a zero lying close to the unit circle in the response spectrum. Small changes in the measured response will cause such a zero to fluctuate between minimum and nonminimum phase conditions, resulting in corresponding phase differences of 2π between cycles. Subsequent cepstral windowing (smoothing) of the phase curves tends to ‘‘smear’’ this difference out over a broader frequency range, causing the recovered waveforms to be grouped into two distinctly different times, depending on whether π was added or subtracted at the frequency of the zero. The timing differences between these two groups is a function of the frequency of the zero, the characteristics of the transfer function, and the cepstral window width. Waveform recovery procedures that try to take this behavior into account have been investigated, and will be discussed. [Work supported by Robert Bosch GmbH.]