Fault Detection and Diagnostics for Rooftop Air Conditioners

Table 3.4 Contrast of Black-box modeling approaches
Characteristics Advantages Disadvantages
Polynomials Assume polynomial Easy to build
functional form of the
Low-order model has
model
reasonable extrapolating
performance
Conflict between
interpolation and
extrapolation
GRNN
Memory-based
network
One-pass learning
algorithm
Parallel structure
Free from the
necessity of assuming
a specific functional
form of the model;
Very fast training
Very good interpolating
performance
No conflict between
interpolation and extrapolation
Parallel ANN-like structure,
not iterative, able to operate in
parallel
Takes noise and disturbances
into account
Easy to be adaptive
Every additional output needs
only two additional units
Need to cluster the data to
reduce nodes and memory
when data are large
Poor extrapolating
performance
Back- Weights and biases
Propagation are moved in the
direction of
minimizing the
network error
Radial basis Use radial basis
interpolation function as basis
function to
interpolate
Very good interpolating
performance;
Very good interpolating
performance
Need long time to train
Poor extrapolating
performance
Poor extrapolating
performance;
Strictly speaking, most real systems are nonlinear and can be expanded by Taylor series.
Wide use of the first order approximation of Taylor series in engineering shows that most
real systems have a low-order dominant component, so low-order polynomials which
capture the system performance will have reasonable extrapolating performance far outside
their training data range while high-order polynomials will extrapolate very poorly.
However, the interpolating performance is normally proportional to the polynomial order.
26