On Fault Diagnosis of random Free-choice Petri Nets

This paper presents an on-line diagnosis algorithm for Petri nets where a priori probabilistic knowledge about the plant operation is available. We follow the method developed by Benveniste, Fabre, and Haar to assign probabilities to configurations in a net unfolding thus avoiding the need for randomizing all concurrent interleavings of transitions. We consider different settings of the diagnosis problem, including estimating the likelihood that a fault may have happened prior to the most recent observed event, the likelihood that a fault will have happened prior to the next observed event. A novel problem formulation treated in this paper considers deterministic diagnosis of faults that occurred prior to the most recent observed event, and simultaneous calculation of the likelihood that a fault will occur prior to the next observed event

A new approach for diagnosability analysis of Petri nets using Verifier Nets

In this paper, we analyze the diagnosability properties of labeled Petri nets. We consider the standard notion of diagnosability of languages, requiring that every occurrence of an unobservable fault event be eventually detected, as well as the stronger notion of diagnosability in K steps, where the detection must occur within a fixed bound of K event occurrences after the fault. We give necessary and sufficient conditions for these two notions of diagnosability for both bounded and unbounded Petri nets and then present an algorithmic technique for testing the conditions based on linear programming. Our approach is novel and based on the analysis of the reachability/coverability graph of a special Petri net, called Verifier Net, that is built from the Petri net model of the given system. In the case of systems that are diagnosable in K steps, we give a procedure to compute the bound K. To the best of our knowledge, this is the first time that necessary and sufficient conditions for diagnosability and diagnosability in K steps of labeled unbounded Petri nets are presented

Diagnosis on a sliding window for partially observable Petri nets

summary:In this paper, we propose an algebraic approach to investigate the diagnosis of partially observable labeled Petri nets based on state estimation on a sliding window of a predefined length $h$. Given an observation, the resulting diagnosis state can be computed while solving integer linear programming problems with a reduced subset of basis markings. The proposed approach consists in exploiting a subset of $h$ observations at each estimation step, which provides a partial diagnosis relevant to the current observation window. This technique allows a status update with a "forgetfulness" of past observations and enables distinguishing repetitive and punctual faults. The complete diagnosis state can be defined as a function of the partial diagnosis states interpreted on the sliding window. As the analysis shows that some basis markings can present an inconsistency with a future evolution, which possibly implies unnecessary computations of basis markings, a withdrawal procedure of these irrelevant basis markings based on linear programming is proposed

Fault detection for discrete event systems using Petri nets with unobservable transitions

In this paper we present a fault detection approach for discrete event systems using Petri nets. We assume that some of the transitions of the net are unobservable, including all those transitions that model faulty behaviors. Our diagnosis approach is based on the notions of basis marking and justification, that allow us to characterize the set of markings that are consistent with the actual observation, and the set of unobservable transitions whose firing enable it. This approach applies to all net systems whose unobservable subnet is acyclic. If the net system is also bounded the proposed approach may be significantly simplified by moving the most burdensome part of the procedure off-line, thanks to the construction of a graph, called the basis reachability graph

Stochastic DES Fault Diagnosis with Coloured Interpreted Petri Nets

[EN] 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.This work was supported by a grant from the Universidad del Cauca, Reference 2.3-31.2/05 2011.Muñoz-Añasco, DM.; Correcher Salvador, A.; García Moreno, E.; Morant Anglada, FJ. (2015). Stochastic DES Fault Diagnosis with Coloured Interpreted Petri Nets. 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Fault Detection by Labeled Petri Nets in Centralized and Distributed Approaches. IEEE Transactions on Automation Science and Engineering, 10(2), 392-404. doi:10.1109/tase.2012.2203596Basile, F., Chiacchio, P., & De Tommasi, G. (2009). An Efficient Approach for Online Diagnosis of Discrete Event Systems. IEEE Transactions on Automatic Control, 54(4), 748-759. doi:10.1109/tac.2009.2014932Roth, M., Lesage, J.-J., & Litz, L. (2011). The concept of residuals for fault localization in discrete event systems. Control Engineering Practice, 19(9), 978-988. doi:10.1016/j.conengprac.2011.02.008Roth, M., Schneider, S., Lesage, J.-J., & Litz, L. (2012). Fault detection and isolation in manufacturing systems with an identified discrete event model. International Journal of Systems Science, 43(10), 1826-1841. doi:10.1080/00207721.2011.649369Chung-Hsien Kuo, & Han-Pang Huang. (2000). Failure modeling and process monitoring for flexible manufacturing systems using colored timed Petri nets. 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Supervisory Control and Analysis of Partially-observed Discrete Event Systems

Nowadays, a variety of real-world systems fall into discrete event systems (DES). In practical scenarios, due to facts like limited sensor technique, sensor failure, unstable network and even the intrusion of malicious agents, it might occur that some events are unobservable, multiple events are indistinguishable in observations, and observations of some events are nondeterministic. By considering various practical scenarios, increasing attention in the DES community has been paid to partially-observed DES, which in this thesis refer broadly to those DES with partial and/or unreliable observations. In this thesis, we focus on two topics of partially-observed DES, namely, supervisory control and analysis. The first topic includes two research directions in terms of system models. One is the supervisory control of DES with both unobservable and uncontrollable events, focusing on the forbidden state problem; the other is the supervisory control of DES vulnerable to sensor-reading disguising attacks (SD-attacks), which is also interpreted as DES with nondeterministic observations, addressing both the forbidden state problem and the liveness-enforcing problem. Petri nets (PN) are used as a reference formalism in this topic. First, we study the forbidden state problem in the framework of PN with both unobservable and uncontrollable transitions, assuming that unobservable transitions are uncontrollable. For ordinary PN subject to an admissible Generalized Mutual Exclusion Constraint (GMEC), an optimal on-line control policy with polynomial complexity is proposed provided that a particular subnet, called observation subnet, satisfies certain conditions in structure. It is then discussed how to obtain an optimal on-line control policy for PN subject to an arbitrary GMEC. Next, we still consider the forbidden state problem but in PN vulnerable to SD-attacks. Assuming the control specification in terms of a GMEC, we propose three methods to derive on-line control policies. The first two lead to an optimal policy but are computationally inefficient for large-size systems, while the third method computes a policy with timely response even for large-size systems but at the expense of optimality. Finally, we investigate the liveness-enforcing problem still assuming that the system is vulnerable to SD-attacks. In this problem, the plant is modelled as a bounded PN, which allows us to off-line compute a supervisor starting from constructing the reachability graph of the PN. Then, based on repeatedly computing a more restrictive liveness-enforcing supervisor under no attack and constructing a basic supervisor, an off-line method that synthesizes a liveness-enforcing supervisor tolerant to an SD-attack is proposed. In the second topic, we care about the verification of properties related to system security. Two properties are considered, i.e., fault-predictability and event-based opacity. The former is a property in the literature, characterizing the situation that the occurrence of any fault in a system is predictable, while the latter is a newly proposed property in the thesis, which describes the fact that secret events of a system cannot be revealed to an external observer within their critical horizons. In the case of fault-predictability, DES are modeled by labeled PN. A necessary and sufficient condition for fault-predictability is derived by characterizing the structure of the Predictor Graph. Furthermore, two rules are proposed to reduce the size of a PN, which allow us to analyze the fault-predictability of the original net by verifying that of the reduced net. When studying event-based opacity, we use deterministic finite-state automata as the reference formalism. Considering different scenarios, we propose four notions, namely, K-observation event-opacity, infinite-observation event-opacity, event-opacity and combinational event-opacity. Moreover, verifiers are proposed to analyze these properties