Stochastic DES Fault Diagnosis with Coloured Interpreted Petri Nets

Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2015, Article ID 303107, 13 pages http://dx.doi.org/10.1155/2015/303107 Research Article Stochastic DES Fault Diagnosis with Coloured Interpreted Petri Nets Doyra Mariela Muñoz,1 Antonio Correcher,2 Emilio García,2 and Francisco Morant2 1 Grupo de Automática Industrial, Universidad del Cauca, Popayán, Colombia Instituto de Automática e Informática Industrial, Universitat Politècnica de València, Camino de Vera, s/n, 46022 Valencia, Spain 2 Correspondence should be addressed to Doyra Mariela Muñoz; Received 22 October 2014; Revised 3 February 2015; Accepted 4 February 2015 Academic Editor: Hiroyuki Mino Copyright © 2015 Doyra Mariela Muñoz et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This proposal presents an online method to detect and isolate faults in stochastic discrete event systems without previous model. A coloured timed interpreted Petri Net generates the normal behavior language after an identification stage. The next step is fault detection that is carried out by comparing the observed event sequences with the expected event sequences. Once a new fault is detected, a learning algorithm changes the structure of the diagnoser, so it is able to learn new fault languages. Moreover, the diagnoser includes timed events to represent and diagnose stochastic languages. Finally, this paper proposes a detectability condition for stochastic DES and the sufficient and necessary conditions are proved. 1. Introduction Fault diagnosis has a major role in industrial systems since it allows the fault detection as soon as possible to avoid serious damages of the system or the injury of an operator. Fault diagnosis of Discrete Event Systems (DES) is an issue that has been addressed from different approaches. A fault is a deviation of the normal or required behavior. Fault diagnosis is the process of detecting and identifying such deviations of the system by using the information available on system variables [1]. According to [2], fault diagnosis aims to achieve three complementary tasks: fault detection, fault isolation, and fault identification. Fault detection is a functionality that decides whether the system works in normal conditions or whether a fault has occurred. If a fault has occurred, fault isolation aims to locate the component(s) causing the fault. Fault identification is concerned with identifying the specific nature of the fault (its size, criticality, importance, etc.). This problem has been addressed by many researchers related with developing new models, new properties, new algorithms, and efficient solutions to fault diagnosis of DES. Model based diagnosis techniques can be divided into two groups. The first group uses models which include fault-free and faulty behaviors. The second group only uses fault-free models. The work of [3, 4] has provided a formal foundation of fault diagnosis and diagnosability analysis of DES that has been the base for many approaches of diagnosis. They use an automaton which generates all the possible event sequences in nominal and faulty operation. Petri Nets (PNs) have been recognized as a suitable model to describe DES, particularly when a system is asynchronous [5, 6]. PN has been used for fault diagnosis starting from [7–9] who presented diagnosis proposals of estimating faulty states. In [10] a net unfolding approach to online asynchronous diagnosis is presented. This proposal avoids the state explosion problem that typically results from having concurrent components interacting asynchronously in a distributed system, but the computing cost of performing the online diagnosis increases for offline diagnosis. In [11], the authors extend the proposal of [3] to online fault diagnosis of modeled systems by PN. Some years later, these authors in [12] present two new algorithms to deal with the case of multiple modules and real-time communication requirements. In [13] the authors not only model faults by unobservable transitions but also include other transitions representing legal unobservable behaviors as well. They prove that all possible firing sequences corresponding to a given observation can be characterized and based on the notion of basis markings and justifications. The authors use a basis reachability tree to 2 compute the set of basis markings; [6] changes the concept of basis marking and enumerates only a subset of the reachability space. This approach includes a different characterization in terms of new original notions such as justifications and minimal explanations. The work of [14] considers the system modeled as an interpreted PN (IPN) with partially observable states and events; the model includes the possible faults that may happen. Reference [15] proposes an online fault detection technique to avoid the redesign and the redefinition of the diagnoser when the structure of the system changes. The diagnoser waits for an observable event and an algorithm decides whether the system behavior is normal or may exhibit some possible faults. The solution of an integer linear programming (ILP) problem provides a sequence of unobservable transitions containing the faults that may have occurred. The system is modeled by IPN where fault events are modeled as unobservable transitions. It associates a different label to each transition, so it models the regular behavior. In [16] the authors started from the results of [15]. They extend the work by considering a new source of nondeterminism (different observable transitions sharing the same label) and by considering distributed systems. To conclude [17] builds an online diagnoser based on PN approach, using the ILP definition and resolution. The advantage of this class of methods lies in the possibility to give guarantees about the diagnosability of faults; moreover, if certain conditions hold, modeled faults can be precisely localized. An inherent disadvantage is that only faults explicitly considered in the system model can be detected and localized. Diagnosis methods without fault model avoid this disadvantage; moreover, they build straightforward models since no special knowledge of system fault behavior is necessary. Nevertheless, the main drawback of these approaches is how to locate the fault since the models have less knowledge. Moreover, diagnosability of a given set of faults usually cannot be guaranteed. These methods are based on comparing the system outputs with model nominal outputs. In [18, 19] the proposed method compares the observed and the expected behavior, a fault can be detected, and a set of fault candidates is determined. Inspired by residuals known from diagnosis in continuous systems, different set operations are introduced to generate the fault candidate set. After fault detection and (...truncated)