Methodologies for hybrid systems diagnosis based on the hybrid automaton framework
Authors:   , Vento Maldonado Jorge 
Published: July 2023

Hybrid systems play an important role in the modeling of complex systems since they take into account the interaction between both continuous dynamics and discrete events. Complex systems are subject to changes in the dynamics due to several factors such as nonlinearities, changes in the parameters, disturbances, faults, discrete events and controller actions among others. These facts lead to the need to develop a diagnostic system for hybrid systems improving the diagnostic precision. Hybrid systems allow to combine the classic fault detection and isolation approaches and a diagnoser based on discrete event models. Hence, a design methodology and implementation architecture for diagnosers in the
framework of hybrid systems is proposed.
The design methodology is based on the hybrid automaton model that represents the system behavior by means of the interaction of continuous dynamics and discrete events. The architecture is composed of modules which carry out mode recognition and diagnostic tasks interacting each other, since the diagnosis module adapts accordingly to the current hybrid system mode. The mode recognition task involves detecting and identifying a mode change by determining the set of residuals that are consistent with the current hybrid system mode. On the other hand, the diagnostic task involves detecting and isolating two type of faults: structural and non-structural faults. In the first case, structural faults are represented by a dynamic model as in the case of nominal modes. Hence they are identified by consistency checking through the set of
residuals. In the second case, non-structural faults do not change the structure of the model, therefore, they are identified by a proper residual pattern. %the set of of residuals that can explain this inconsistency.
Discernibility is the main property used in hybrid systems diagnosis. Through the concept of discernibility it is possible to predict whether modes changes (faulty or nominal) in the hybrid model can be detected and isolated properly. This concept can be applied in practice, evaluating a set of mathematical properties derived from residual expressions, which can be obtained from input-output models or parity space equations. General properties are derived to evaluate the discernibility between modes in the hybrid automaton model.
The diagnoser is built through propagation algorithms developed for discrete models represented by automata. The automaton employed to build the diagnoser for a hybrid system is named behaviour automaton. It gathers all information provided by discernibility properties between modes and observable events in the system, increasing the system diagnosability. % in the system.
Diagnosis for hybrid systems can be divided in two stages: offline and online. Moreover, it can be carried out twofold: in a non-incremental and an incremental form. In the non-incremental form, algorithms are executed taking into account global models, unlike incremental form that leads to building the useful parts of the diagnoser, only developing the branches that are needed to explain the occurrence of incoming events. The resulting diagnoser adapts to the system operational life and it is much less demanding in terms of memory storage than building the full diagnoser offline. The methodology is validated by the application to a case study based on a representative part of the Barcelona sewer network by means of a tool
implemented in Matlab.