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Automated Fault Diagnosis
3.1 Overview Techniques
by a sequence of states [4]. The structure is what enables the system to generate the behavior [4].
One of the ideas in system theory is that the structure is as important for implementing the function
of a system as the individual behavior of components. The reason for this is that the interaction
between individual components results in the intended behavior of the whole. These relations between
structure and behavior are important to understand, because when creating an approach to
fault diagnosis, various viewpoints on these concepts can be used. Two very important viewpoint
types are black box and white box. The definitions of these concepts that are used in this thesis are:
Black Box: A model that describes the externally observable behavior, but does not state anything
about the structure of the system, or behavior of internal components of the system.
White Box: A model that describes the internally non-observable behavior as well as externally
observable behavior. The behavior of the whole system is defined by the structure and the
behavior of internal components.
Many views on a system include more information than just system input and output, but do not
provide a complete behavioral, or structural description of the system. These views are sometimes
referred to as grey boxes, but terms like these are not well established. The problem with these
terms is that it is not clear what is considered to be a ’complete’ white box, because a model is
never complete. For this reason, in this thesis a model is called white box whenever it uses some
structural or internal behavioral information. Otherwise, it is a black box model.
3.1.4 Abductive Model versus Consistency-based Models
The distinction between black box and white box models determines what information is used in
the model. Another distinction determines how the information is stated. A distinction between a
consistency-based and an abductive approach to fault diagnosis [18], is as follows:
Abductive model: A model that defines a diagnosis as a set of abnormality assumptions that covers
(or, in terms of logic, implies) the observations. [18, 24]
Consistency-based model: A model that defines a diagnosis as a set of assumptions about a system
component’s abnormal behavior such that observations of one component’s misbehavior are
consistent with the assumption that all the other components are acting correctly [11, 25].
The important difference between the two is that the former, an abductive model, defines effectto-cause
relations between observables, while that latter defines cause-to-effect relations between
observables (also called first principles). This requires different kinds of reasoning schemes.
3.1.5 Effect-to-Cause versus Cause-to-Effect Reasoning
In effect-to-cause reasoning, the effect ”there is no light” can be explained by the cause ”the light
bulb is broken”, knowing that that when a light bulb is broken there is no light. In cause-to-effect
reasoning, the fact ”the light bulb is broken” is the only cause that is consistent with the effect ”there
is no light”. Let s be a symptom and f be a fault (e.g., the fault f denotes the cause ”the light bulb is
broken”, and the symptom s denotes the effect ”there is no light”). In logic, the basic inference rule
of abductive reasoning can be characterized by the following reasoning pattern [8]:
s
f → s
⊢ f (3.1)
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