Fault Detection and Diagnostics for Rooftop Air Conditioners

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⎛ ⎡n⎤⎞
⎜ ⎢ ⎥⎟
⎜ T
⎢
n ⎟
X
⎥
sign
= sign⎜
J
sign
Ysign
−
⎢ ⎥⎟
(1-5)
⎜
M
⎟
⎢ ⎥
⎝ ⎣n⎦⎠
By determining which entry of vector X
sign
is 1, the fault diagnosis classifier can
make a decision. The advantages of this method are that:
1. It is very easy to infer the J sign
accurately by n simple tests or from experience,
compared to
2
n well- designed tests to estimate J roughly.
2. Although this method is derived from a linearization operation and drivingcondition-independence
assumption, it applies without these two assumptions.
Actually there is no linearization approximation necessary for the sign of J
sign
.
3. J
sign
is generic at least for the same type of system, compared to different J ’s for
different systems.
4. This diagnosis method cleverly uses direction change pattern (sign) to convert an
infinite classification problem (infinite number of fault levels for an individual type
of fault) into a multiple classification one.
The drawback is that it can only handle individual faults.
It also should be pointed out that the above deduction only involves a matrix
transposition operation instead of a matrix inverse operation, so the conclusion can be
obtained without the assumption of
m = n . This is because the SRB fault diagnosis
method uses “sign” to do fault diagnosis qualitatively instead of quantitatively. The
“possible inconsistencies” in the case of
m > n are impossible. Mathematically the
maximum number of faults can be diagnosed by m state variables is up to
m
n = 2 , which
can be either larger or smaller than m . Practically, in order to simplify the process of
extracting rules, more state variables ( m > n) are often adopted. For example, Rossi and
Braun (1997) use seven state variables to deal with five faults.
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