pdf download - Software and Computer Technology - TU Delft

Model-Based Fault Diagnosis
4.5 Entropy Gain
system inverter3 ()
{
// Define a priori probabilities for all health variables
probability ( hA = false ) = 0.01;
probability ( hB = false ) = 0.01;
probability ( hC = false ) = 0.01;
}
// Define the behavioral rules for the 3 inverters
hA => (w = !x);
hB => (x = !y);
hC => (x = !z);
By the way, this is an intermediate step within the LYDIA compiler. It does not change the semantics
of the model. Compositional models improve maintainability, allow for reuse, and improve
readability. Suppose the inverters are implemented by resistive-drain (that is, using one transistor
and one resistor). For some reason, the supervisory controller is interested in the health of these
transistors and resistors. The only code that requires to be updated is the specification of a single
inverter.
4.5 Entropy Gain
This section discusses a metric that can be used to estimate the diagnostic performance of a specific
MBD implementation, namely entropy. Entropy can be used as a feedback mechanism to improve
the quality of a model, or decide which measurements are best. Entropy is a heuristic, introduced
by Shannon [26], to quantify information. De Kleer and Williams suggested to use entropy as a
heuristic for quantifying the uncertainty of diagnosis [11]. The idea is as follows. The outcome of
the diagnostic engine has some uncertainty. If no information about a system is available, anything
can be broken, and the uncertainty is at its maximum. A stronger model, or more observations
upon the physical system, can shorten the list of possible diagnoses; the uncertainty decreases.
The extent to which a specific MBD implementation decreases uncertainty is called entropy gain
(although entropy loss seems to make more sense, this thesis follows the convention to use the
term entropy gain). Entropy is measurable in bits. This enables the comparison of various MBD
implementations. In other words, entropy in MBD could be used to optimize models, and as a mean
to decide the best measurements on the target system.
Below, entropy is used to determine the best measurement points of a classical diagnosis example,
namely a digital circuit of 4 inverters.
4.5.1 Best Next Measurements
As explained before, a list of diagnoses is consistent with a certain set of observations. Additional
measurement could decrease the number of possibilities, thus improve diagnostic resolution. This is
called sequential fault diagnosis [23]. In industry, doing an additional measurement increases costs.
Entropy outcomes can be used to decide which measurements are best to be done first. Consider
Figure 4.2. It shows a simple digital circuit of 4 inverters, A, B, C and D, in a pipeline structure.
This section uses entropy to decide the best points to measure in this circuit. The input and output
43