Resumen de Detección robusta de fallos utilizando análisis intervalar

Sebastián Tornil Sin

• Model-based fault detection methods rely on analytical redundancy, defined as the existence of two or more ways of determining a given variable using the model and the observations. If the model provides redundancy on n variables, the fault detection task can be interpreted as the comparison of n-dimensional values, searching for differences that are indicative of faults.

  In practice, is not possible to obtain an accurate and complete model of the system.

  When the values of the system parameters are not exactly known but bounded, intervals appear as a natural framework to represent this uncertainty. Using this modeling approach, the model provides the set of feasible behaviors in normal system operation on the basis of the existing uncertainty. Extending the concept of analytical redundancy, the detection is formalized on the intersection between Rn sets that correspond to different ways of estimating the same n variables. The main property of this approach is that the obtained methods eliminate the false alarms.

  The counterpart is that the uncertainty masks the effect of some faults that will remain undetected.

  This thesis studies the problem of fault detection using models in presence of bounded uncertainty. This uncertainty is given as intervals for the model parameters and for the observations of the system inputs and outputs. In this context, the efforts have been made in two main directions. The first one is the study and implementation of computational tools for the representation and manipulation of bounded uncertainty. The second one corresponds to the development of strategies for the suitable use of the model and the observations in order to minimize the effects of its uncertainty on the fault detection task.

  Two different type of sets are studied for the representation of bounded uncertainty: n-dimensional boxes and subpavings. Boxes are directly obtained when the joint representation of variables and parameters known as intervals is considered.

  Subpavings are unions of non-overlapping boxes that allow a more precise representation of the arbitrary uncertainty sets that are obtained from the use of the model, although its manipulation needs a higher computational effort. This leads to a trade-off between detectability a real-time applicability in its application to the fault detection task.

  The first studied fault detection strategy is simulation, which estimates the system output feeding the model only with the system inputs. Next, prediction is studied.

  Prediction uses the observations of previous system outputs, which allows to reduce the uncertainty in the actual output estimation. In its application to fault detection, prediction provides fast but non-persistent detectors. Using the results from the study of simulation and prediction, several combined strategies are proposed to improve the detection performance. Finally, the last studied strategy involves a totally different approach. In this approach, the set of model parameters that are consistent with the uncertain observations is calculated and compared with the initial set, indicating a fault when an empty intersection is obtained.

  Finally, the application of the algorithms for uncertainty manipulation and the strategies for detection to three case studies is shown. The first example corresponds to an industrial gas turbine, the second is a d.c. motor and the last one is a sewer network.