Fault Detection and Diagnostics for Rooftop Air Conditioners

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faults’ features
( j ≠ i
z
j
’s ( j ≠ i ), its feature z i
would be contaminated by another fault j
). For example, the condenser air flow rate can be estimated from an energy
balance with refrigerant mass flow rate estimated from a compressor performance map.
However, the air flow rate estimate can be corrupted by a compressor valve leakage fault.
Therefore, only the coupling from i to j is broken while the one from j to i is not. The
worse case which can be handled is described in equation (1-9), in which the feature z
i
would be impacted by faults j ’s ( < i ) but not by those ( > i ).
Z = LX
⎡l
⎢
⎢
l
=
⎢ M
⎢
⎣ln
11
21
1
l
l
22
M
n2
O
L
l
nn
⎤⎡x1⎤
⎥⎢
⎥
⎥⎢
x2⎥
⎥⎢
M ⎥
⎥⎢
⎥
⎦⎣xn⎦
(1-9)
A sequential FDD method, which is contrasted with the above simultaneous FDD
technique, can be used to solve this case.
Step 1 Do FDD on fault 1. Because feature z 1
is independent of any other faults, fault
1 can be detected and diagnosed independently. If fault 1 does not exist, go to the
next step. Otherwise, don’t go to the next step until either fault 1 is fixed if it is
severe enough or the features, which have been corrupted by this fault, are modified
according to this diagnosed fault in the virtual sensor.
z1
sign _ stat(
z1)
z1
= l11x1
⇒ x1
= ⇒ x1,
sign
=
l
sign(
l )
11
Step 2 Do FDD on fault 2 . After step 1 has been done, either x
1
= 0 (if fault 1 does
not exist or is fixed) or l
21
= 0 (after modification according to fault 1) can be
guarantied. So,
z2
sign _ stat(
z2)
z2
= l21x1
+ l
22x2
= l22x2
⇒ x2
= ⇒ x2,
sign
=
l
sign(
l )
22
If it exists, fix fault 2 if it is severe enough, or otherwise modify the infected
features.
M
M
11
22
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