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4.1 Fundamentals Model-Based Fault Diagnosis
Figure 4.1: 3-inverter example
This chapter starts by introducing the fundamentals of MBD by means of a classical diagnosis
example. Section 4.2 uses this example to introduce the LYDIA approach to MBD. Section 4.3
presents the assumptions of MBD. Section 4.4 discusses issues related to constructing the model of
a system. Section 4.5 introduces a metric that can be used to estimate the diagnostic performance
of a model-based approach. The final section of this chapter shows how MBD works on a real
example.
4.1 Fundamentals
MBD is the process of finding differences between behavior predicted by a model, and behavior
observed during runtime operation. The model is assumed to be correct, so the differences should
be explained by faulty components.
Consider Figure 4.1. It shows a simple digital circuit, consisting of 3 inverters: A, B and C.
This classical diagnosis example is commonly used to introduce the basic notions of MBD. This
text does so likewise. Let w = 1, then y and z should be 1 as well. If observations during runtime
indicate that y=0 and z=1, there is a discrepancy between observed and predicted behavior. Any
discrepancy is called a symptom, and in this case the symptom is that y=0 while y=1 is predicted.
This symptom could be explained by the malfunctioning of inverter B. However, it could also be
that both inverter A and inverter C are broken. No subset of {B} or {A, C} is able to explain the
symptom, and therefore {B}, {A,C} is called the minimal fault set. Another possible candidate is
that all inverters are broken. Actually, all supersets of {B} or {A,C} are candidates, although with
lower probability.
The question is, how could MBD automate the reasoning of above? The model-based approach
requires two artifacts: a model, and a diagnostic engine that operates on that model. These two
ingredients of MBD are described now.
Model
The model of the MBD approach describes the behavior and structure of the components. Let h
indicate the health of a component. If h=1, the component is ”healthy” and obeys certain behavior
rules. For a combinational system, such as the 3 inverters example, the behavioral rules can be
formalized to propositional logic:
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h A ⇒ (x ⇔ ¬w)