There is a wide variety of condition monitoring techniques currently in use for the diagnosis
and prediction of machinery faults, but little attention has been paid to the occurrence and
detection of chaotic behaviour in time series vibration signals. This paper introduces some of
the basic concepts of chaos theory, then details a method for quantifying a fractal dimension
from a time series, the correlation dimension. Some of the practical difficulties encountered
in measuring the correlation dimension from the correlation integral algorithm are also …

Determination of the correlation dimension from experimental chaotic time series data
involves two steps. First, reconstruction of the attractor using the time delay method from the
raw time series, followed by computation of the correlation dimension from the phase space
vectors. We demonstrate how this process has been performed experimentally on bearing
vibration acceleration times series. The effects on the correlation dimension were noted as
each of the relevant parameters was individually varied and the optimum values for each …