PhD Thesis

On the fault diagnosis of dynamic system using set-based approaches

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  • Started: 17/04/2015
  • Finished: 12/04/2019


Model-based Fault Detection and Isolation (FDI) is a major theoretical topic that is
becoming increasingly to one of the most signi cant key features to increase safety and
reliability of complex automatic control systems. Basically, model-based FDI relies on
the use of a mathematical model to describe the system behavior. However, uncertainty
remains always present when modelling a system since its ef ect is non-negligible
even if there are no process faults. One way to deal with uncertainty is to assume
its unknown-but-bounded description. Generally speaking, the uncertainty in so-called
set-based approaches is represented by a set that is unknown-but-bounded at each time
instant. Set-based approaches can be classi ed into three main paradigms: interval observer
approach, set-membership approach and set-invariance approach. In this thesis,
the influence of the uncertainty is addressed using the set-based approaches considering
a zonotopic representation. Moreover, this thesis presents both analysis and comparison
of the set-based approaches for the state estimation and FDI frameworks with the goal
of establishing the advantages and disadvantages of each approach, and also, to find
out their relationship in a formal mathematical framework. However, the mentioned
set-based approaches implicitly assume time-varying uncertainty. In the set-based approach,
the propagation of the state set is a ected by several problems such as the
wrapping ef ect, temporal variance on uncertain parameters (or uncertain parameter
time dependency) and range evaluation of an interval function, especially in the case of
using the interval hull of the set at each iteration. Therefore, conservative and unstable
results may be obtained (for even a stable system) when using the set-based approach
in the simulation of the system with parametric time-invariant uncertainties. On the
other hand, the approximated state set can be computed based on a set of point-wise
trajectories. This type of approach is called trajectory-based approach. Therefore, the
uncertain parameter time dependency is preserved if the set of point-wise trajectories is
generated using the mentioned trajectory-based approach.

The work is under the scope of the following projects:

  • DEOCS: Monitorización, diagnostico y control tolerante a fallos de sistemas ciberfísicos con métodos basados en datos (web)