### ASA 127th Meeting M.I.T. 1994 June 6-10

## 3aSAa11. Effect of spectral notches on robust waveform recovery methods
for machinery diagnostics.

**David L. Bowen
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*RH Lyon Corp, 691 Concord Ave., Cambridge, MA 02138
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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 2(pi) 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 (pi) 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.]