Fault Detection and Diagnostics for Rooftop Air Conditioners

solution procedure involves the non-linear solution of three residual equations in the cycle.
The effect of all five of the operating faults which are being studied can be simulated with
ACMODEL.
Except for Rossi and Braun, the problem of developing a physical model for a rooftop air
conditioning unit for FDD purposes has not been specifically addressed in the literature.
Stylianou and Nikanpour (1996) considered two different models for a reciprocating chiller
to use with a model-based FDD technique. For the problem of fault detection, a gray-box
model was used. This model, developed from first principles and first introduced by
Gordon and Ng (1994), correlated the equipment COP with the condenser and evaporator
inlet water temperatures. This performance index is used to decide when the impact of a
fault is significant enough to warrant repair. The other model is a black-box model which
will be discussed in the next section.
2.2 Black-box modeling
Since black-box models are easy to develop, accurately fit training data, and are
computationally simple, they are popular for engineering use. Several kinds of black-box
modeling approaches will be discussed here.
2.2.1 Polynomials
Linear regression polynomials are the easiest and most frequently used black-box
models. Grimmelius et al. (1995) used steady-state linear models with three input
variables to predict a number of output states of a vapor compression chiller. The
predicted variables included the temperatures and pressures at the inlet and outlet of
each component in the refrigeration cycle, suction superheat, liquid subcooling, oil
pressure, temperature, and level, the pressure ratio across the compressor, temperature
changes of the water across the evaporator and condenser, filter pressure drop, and
compressor power. The three input variables were the chiller water inlet temperature,
the cooling water temperature into the condenser, and the number of compressor
cylinders in operation. The model form which was used is
y = β + β T + β T + β Z + β Z + β Z + β log( T )
i o, i 1, i chwi 2, i cwi 3, i 1 4, i 2 5, i 3 6,
i chwi
−1
+ β ( T ) + β log( T ) + β ( T )
−1
7, i chwi 8, i cwi 9,
i cwi
8