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Model-Based Fault Diagnosis
4.4 Modeling
The only difference is the way how relevant information is specified. As explained in Chapter
3, this effects the time to create the model, is error-prone, and inflexible in case of a design
change. But is some cases there is no other possibility.
4.4.2 Granularity
The first step of making a model is deciding the granularity, in other words ’level of detail’, of the
model. Granularity has two dimensions; depth and breadth.
If you consider depth in granularity, it is possible to tune the level of abstraction. For each
system, there is an infinite number of levels of abstraction. Consider the 3-inverter example again.
On the highest level of granularity the 3-inverter system has one entity; the 3-inverter system. In
this case, the LYDIA model has one health variable, and the only outcome of the diagnostic engine is
whether or not the system is broken. This means that, in case of malfunctioning, a supervisory controller
would have to replace the entire system with a healthy one. In this case, the costs to recover
the system are higher than when a model that specifies the system at a lower level of granularity is
used. On one lower level, the model distinguishes 3 entities, namely the 3 inverters, as shown in Figure
4.1. The results of these diagnoses state for each inverter if it has to be replaced with a healthy
one, or that it could be preserved. Going another step lower could be that the model also specifies
the transistor and resistor that (could) implement the inverter. But usually these components cannot
be replaced, and diagnosing this level of detail is of no added value.
If you consider breadth in granularity, it is possible to include or exclude certain components
from being modeled. Given a certain level of granularity, what components should, and which
should not be specified by the model? For example, the 3-inverter system might include a casing
that protects the system from the outside. Should this component be included? Maybe the casing
gets easily damaged, and is the cause for the breaking down of inverters in the first place. If the
casing never breaks, adding it, would only unnecessarily increase complexity. The particular considerations
greatly depend on the specific system, the environment, and the motives of the modeler.
As said before in this thesis, modeling of a system is not a trivial activity. Although modeling
is a divergent activity without general procedures, this thesis considers three possible approaches to
modeling:
1. Modeling the entire system. The modeler chooses its granularity, based on domain-dependent
and general considerations (e.g. Could the supervisory controller use the correct or incorrect
functioning of this component for recovering the system? Does this component ever brake
down? Is it possible to, directly or indirectly, observe the state?)
2. Modeling to cover faults. The modeler composes a list of all known faults (things that could
brake down). Only those components that could reveal a fault are included in the model.
3. Modeling based on log data. Most existing systems log values of certain parameters to allow
for monitoring the state of the system. Experts, mostly developers of the system, know what
to conclude about the system state given a set of parameters. The modeler chooses the granularity
of the system in order to reproduce the same diagnosis for a certain set of parameters.
Of course, a modeler could use more approaches in parallel, in order to achieve a high quality model.
4.4.3 Discretization of Observations
The output of sensors, or other sources of data in a system, usually contains much resolution. Most
sensor output is continuous. It is hard to use variables with high levels of resolution in a model, and
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