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4.4 Modeling Model-Based Fault Diagnosis
still be able to produce accurate diagnoses. Discretization is the process of mapping variables in a
many-valued domain to variables in a few-valued domain.
Some terminology regarding to this topic is useful. Note that this terminology is defined for this
thesis, and might not correspond to terminology in other literature. Suppose there is a system that
has 4 components, and logs 5 signals to a log file. Three of those signals are in the floating point
domain (f1, f2 and f3), and two are in the boolean domain (b1, b2). Instances of the tuple (f1, f2, f3,
b1, b2) are called system data, and this term is generally defined as:
System Data: All unprocessed digital data that the target system produces.
Each instance of the system data, for example (500, 400, 50, true, true), is part of a fault scenario,
and the definition of this term is:
Fault scenario: A particular failure of the system. It is characterized by the system data that is
logged at the moment a failure occurs, in addition with the actual broken component.
Often, the system data is hard to interpret, and its values should be discretized to a domain with few
members. The term discretization is defined as follows:
Discretization: A mapping of variables within the system data, that are in a many-valued domain,
on observables, that are in a few-valued domain.
Thus, discretization maps the variables in the system data to a domain with a finite number of
members. It could be that the source domain of system data variables is unknown. Preferable, the
few-valued domain has as few as possible members, say 2, 3, or 4. Each observable is a derivative
of the system data. For example, suppose the system data (f1, f2, f3, b1, b2) is mapped on the two
observables (o1, o2) by a discretization D. D defines two derivatives of the system data, say o1 =
f1 - f2 - f3 > 10 and o2 = b1 ∨ b2. The result of the discretization for a fault scenario with values
(500, 400, 50, true, true) is then (true, true).
Because of the many-to-few mapping it is very likely that various fault scenarios are not different
in the conclusions that could be drawn. These are said to correspond to the same fault category. A
definition is:
Fault category: A set of fault scenarios that have the same values for (a subset of) the observables.
Suppose the system data of two fault scenarios is resp. (500, 400, 50, true, true) and (50, 20, 10,
false, true). Discretization D maps the system data of both fault scenarios to the observables (o1,
o2) = (true, true). Consequently, the MBD engine infers the same diagnoses. Therefore, these fault
scenarios belong to the same fault category.
The system data of the 3-inverter example, as well as the example of Section 4.6, only consists
of variables that are already in the boolean domain. The next chapter presents a complex example
that shows how a discretization simplifies modeling. It uses the concepts system data, discretization,
fault scenario and fault category.
4.4.4 Compositional Subsystems
Another important issue is to make subsystem entities compositional. This is one of the characteristics
of model-based computing. The 3-inverter example presented above is specified in a
compositional model. A non-compositional model would be:
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