Fault Detection and Diagnostics for Rooftop Air Conditioners

efficiency and performance for the simulated data that he studied. These methods,
however, have not been compared using real operating data. Breuker (1997) compared the
performance of the methods using actual transient data recorded for the FDD
demonstration shown in figure 4.8.
Each of the methods has design parameters that affect its performance. For the slope and
variance methods based on measurements in a fixed-length sliding window of recent
values, the number of measurements in the fixed-length window, the frequency with which
new measurements are taken, and the steady-state detector threshold are the design
parameters. Instead of using a fixed window length, the exponentially weighted variance
method uses a forgetting factor to reduce the contribution of successively older
measurements on the variance calculated at each step.
In order to compare the performance of the three methods, each was applied to a transient
start-up profile for hot gas temperature from a rooftop air conditioning unit. This analysis
used a fixed window length of 10 measurements and a forgetting factor of 0.7 with
measurements being taken from the test unit every 5 seconds. The forgetting factor of 0.7
was chosen to give similar outputs between the variance calculated from the sliding
window and the exponentially weighted variance. The first observation which can be made
about the slope method with the two variance methods is that the slope can assume both
positive and negative values, while the variance is only positive. This could lead to a
problem with the slope method, since an overshoot could be interpreted as steady-state
operation. For this reason, the methods which utilize variance rather than slope are more
reliable. Figure 4.8 shows that the two methods which utilize variance as an indicator of
steady-state operation have almost identical outputs during their transient startup. Since
the exponentially weighted method is more computationally efficient than the fixedwindow
method, this method was selected for further study.
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