Fault Detection and Diagnostics for Rooftop Air Conditioners

So the interpolating performance of polynomials conflicts with their extrapolating
performance.
Other black box modeling approaches such as GRNN, RBF and BP ANN can have very
good interpolating performance and but can not be expected to extrapolate very well far
outside the training data range.
3.3 Polynomial plus GRNN model
Low-order polynomials have good extrapolating ability but poor interpolating ability,
whereas, GRNN, BP ANN and RBF have very good interpolating ability, so the
combination of polynomials with one of GRNN, BP or RBF modeling approaches could
have both good interpolating ability and good extrapolating ability. The result can be seen
from the table 3.5.
GRNN was selected in ombination with polynomials since GRNN is easy to adapt. Nodes
can be added to or deleted from the network to improve the accuracy.
First, a low-order polynomial model is regressed with the training data and then the
residuals between the polynomial output and the training data are fit with a GRNN as
shown in figure 3.7. After training, the model can be used to generalize as shown in figure
3.8.
The order of the low-order polynomial model depends on the characteristic of the system
modeled. Different systems and different variables of the same system have a different
“dominant order”. Usually the “dominant order” is not greater than two. Before modeling,
the “dominant order” of the system is not known so the “dominant order” is determined
by evaluating the extrapolating performance. Table 3.5 shows that first-order for
Tevap
cond dis sh sc Tca
,T ,T and T and second-order for T ,
∆ and ∆Tea
work well and are
best for polynomial models. The purpose of the low-order polynomial model is to
optimize the extrapolating performance, whereas the GRNN compensates and improves
the interpolating performance, which is sacrificed by the choice of a low-order polynomial
model. The GRNN may improve also the extrapolating performance somewhat (figure
3.9). The interpolating and extrapolating performance of the various approaches are
summarized in table 3.6.
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