Exhaustive search of residuals computation schemes using macro-graphs and invertibility constraints
Résumé
In this paper, a structural analysis of a model is performed with the objective to design fault indicators, i.e. residuals, which are used for Fault Detection and Isolation. The invertibility constraints of the relations are considered at the early stage of the method, which gives some information on the calculability of the residuals. The set of all possible residuals is obtained by determining exhaustively the matchings in the structural model. A matching gives a computation path for the residual. In this article, we search for all realizable computation paths for all possible residuals. Even if the structural analysis is known to be a powerful method, this exhaustive search may be very expensive in computational time for high-dimensional models. The key element of this paper is the use of a reduced graph, called macro-graph, in order to reduce the complexity of the exhaustive residuals search. Our method is compared with the classical one and the complexity gain is proven. An academic example is taken to illustrate our method.