Integrating Bond Graph and Interval Models in Fault Detection and Isolation
A. Stancu?? , B. Ould Bouamama? , J. Quevedo?, V.Puig?
? Polytech’Lille. L.A.I.L. Bat. Eudil 59655
Cité Scientifique Villeneuve d’Ascq Cedex France
belkacem.bouamama@univ-lille1.fr
? Automatic Control Department - Campus de Terrassa
Universidad Politécnica de Cataluña (UPC)
Rambla Sant Nebridi, 10. 08222 Terrassa (Spain)
{Joseba.Quevedo, Vicenc.Puig, Alexandru.Stancu}@upc.es
Abstract - This paper deals with model based fault
detection and isolation considering the effect of model
uncertainty. Fault detection test relies on checking
discrepancy between the measurements obtained from
a monitored process and its model by generating a
residual that should be zero in the ideal case when
there is no fault and different of zero otherwise.
However, when building a model of a complex system
to monitor its behaviour, there is always a mismatch
between the predicted and real behaviour. The
predicted behaviour will be obtained using an
observer. An approach to deal with this model
uncertainty is to propagate parameter uncertainty to
the residual obtaining an interval. While measured
residual is inside this interval no fault can be
indicated, on the contrary a fault should be indicated.
On the other hand, fault isolation requires a set of
those residuals provided by a set of analytical
redundancy relations (ARRs) that could be easily
generated combining bond graph model with
structural analysis. The evaluation of those residuals
in real time and their contrast with a fault signature
matrix will allow isolating faults. And, finally, this
approach will be tested pinpointing their benefits and
drawbacks in the context of a complex industrial
system: an intelligent servo-actuator proposed as a
benchmark in the context of the DAMADICS
European project.
I. INTRODUCTION
This paper deals with fault detection and isolation using
analytical models represented using bond graphs and
interval models. A bond graph is a graphical
representation which highlights the power transfer
through junction structures [Thoma, 1975]. The bond
graph model is a very powerful tool used for modeling
the dynamical systems since it is suitable for modeling
multidisciplinary systems because of the universality of
the language which is based on a few basic elements.
However, when building an analytical model of a
complex system to monitor its behaviour, there is always
a mismatch between the modelled and real behaviour due
to some effects are neglected, some non-linearities are
linearised in order to simplify the model, some parameters
have tolerance when compared between several unit of
the same component, some errors in parameters or in the
structure of the model are introduced in the calibration
process, etc. One possible approach to take into account
modelling uncertainty is to include all the uncertainty in
system parameters during the calibration process using
new set-membership identification algorithms producing
not just nominal values but instead a confidence interval
for every parameter of the model [Ploix et al., 1999]. A
dynamic model with parameters with their values
bounded in intervals is called an interval model.
Model based fault isolation does not require a global
model of the system but instead partial models that relate
the available measurements. Each partial model
represents relations between measured variables of the
system and it is known as an analytical redundancy
relation (ARR). These relations are satisfied (validated)
in fault-free situation and not satisfied (invalidated) when
a fault occurs. This allows us to detect faults on a process.
However, an ARR can be invalidated not due to a fault
but because of the modelling errors. This unexpected
situation will generate many false alarms in our
monitoring system. Then, any model based fault detection
algorithm should take care of the modelling uncertainty in
order to not confusing a fault with a modelling error, i.e.
must be robust. ARR containing dynamic relations could
be evaluated using a prediction or observer approach. In
this paper, the observer approach is followed and
combined with interval models using the so called
interval observers [Puig et al., 2003a].
And, finally, this combined interval bond-graph model
will be used to detect and isolate faults in an intelligent
servo-actuator proposed as a benchmark in the context of
the DAMADICS European project.
II. BOND GRAPH MODELLING AND ARR
GENERATION
A. Monitoring system architecture
A monitored system can be represented as shown in
Fig.1.
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