Fault Detection and Diagnostics for Rooftop Air Conditioners

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In order to extend the easily-implemented SRB fault diagnosis idea to handle
multiple-simultaneous faults, Deliverable 2.1.5 proposed a decoupling-based method,
which decouples the interactions between the transformed FDD features Z and faults X
(see Equation (4-1)). That is, it makes each entry of the feature vector Z only correspond
to unique fault entries of the fault vector X and vice versa.
⎡λ1
⎢
Z = ⎢
⎢
⎢
⎣
λ
2
O
⎤
⎥
⎥ X
⎥
⎥
λn
⎦
(4-1)
Based on the decoupled features, the SRB FDD technique can be applied to
handle multiple-simultaneous faults. That is, the
decoupled to be n
n − dimensional
FDD problem has been
1 − dimensional
SRB FDD problems. In addition, the decouplingbased
diagnosis method simplifies fault detection from a high-D problem to n 1-D ones.
Equation (3-1) boils down to the following n 1-D equations,
ω1:
normal
2
( − µ ) ≤
1
z i
σ
i,
normal
2
i,
normal
>
ω2:
faulty
or
2 −
( χ ) {(1
− α ),1}
(4-2A)
z
i
− µ
σ
i,
normal
i,
normal
ω1:
normal
≤
>
ω2:
faulty
N
−1
{(1
− α ),0,1}
(4-2B)
2 −1
−1
where, ( χ ) {} , is the inverse chi-square cumulative distribution function, N {} , is the
inverse normal cumulative distribution function, α is the false alarm rate, and
i = 1,2,
L,n
.
Fault diagnosis automatically is achieved without any extra computation
immediately after fault detection is finished, so the fault diagnosis classifier is not
required.