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4.4 Modeling Model-Based Fault Diagnosis
//input is assumed to be correct
correct_w = true;
}
// Connect the 3 inverters
invA ( correct_w, hA, correct_x);
invB ( correct_x, hB, correct_y);
invC ( correct_x, hC, correct_z);
The user of the diagnostic system should be able to determine whether a specific output is
correct or not. These are the observables.
Weak Fault Model This model only defines the nominal behavior of the system. The description
of the 3-inverters in Section 4.2 is a weak model; it does not define how an inverter behaves if
something has been broken (if h=0).
Strong Fault Model Description of the system that defines all modes of operation. A mode of
operation is a state of a component in which it obeys an unique behavioral rule. The nominal
behavior of a weak model could specify more than one nominal modes of operation. A strong
fault model also defines all known false modes of operation. The corresponding LYDIA code
follows the form !h => s. Examples are stuck-at-zero, stuck-at-one, etc. This way, it is
possible in MBD to define an abductive model [18], as discussed in Chapter 3. A strong
model of the 3-inverters is:
system inverter(bool i, h, o) {
h => (i = !o); // If healthy, output equals inverse of the input
!h => (o = 0); // If unhealthy, the output is stuck-at-zero
}
Model that is not from First Principles It might be that it is practically impossible, for certain
parts of the system, to define the correct behavioral rules. In these cases it is possible to
include mappings of symptoms on broken components (of the form ’s → f ’). MBD diagnosis
does not forbid to use these explicitly specified statements, that are abductively or deductively
derived by humans. A (partial) model that is not based on first principles, and that is equal to
the weak model of the 3-inverter example is:
// mapping of symptom (y=0, z=1) on diagnosis
((y=0) and (z=1)) => (
!hB
or (!hA and !hC)
)
In theory, the expressive power of rules that are not based on first principles is the same. After
all, the rules are equivalent to a consistency-based model (’s → f ’ corresponds to ’¬ f → ¬s’).
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