Recovering the Timing of Impulsive Forces From Noisy Vibration Transients

A transient vibration signal can be processed to extract information about impulsive forces within a machine, by removing the effects of dispersion and reverberation. These source waveform signatures, like the timing and strength of valve impact forces within a reciprocating air compressor, can then be used to diagnose machine faults. Stable and causal inverse filters are guaranteed through the use of minimum-phase processing. Unfortunately, the timing of the impulsive source waveform is lost in this manner. A technique to accurately recover the timing is highly desirable. The time of occurrence of the force input can be robustly obtained from the frequency-averaged group delays of the transfer function and vibration response once the nonminimum-phase behavior of the signals, except that due to pure delay, has been removed. This is best done with the allpass components of the signals because, in addition to the nonminimum-phase inherently present in a structure due to reverberation, additional nonminimum-phase zeros can be artificially introduced by data truncation. Since only the phase is of interest, the nonminimum-phase behavior can be removed by electronically damping the signals with exponential windows, effectively de-reverberating them. In some instances the timing of the impulsive source events that we aim to recover will change as faults develop; also, in any machine there will be some normal random variation in the timing of internal events like valve impacts. The correct timing can be determined in the presence of this inherent variability through the use of a sliding exponential window and statistical curve fitting.