Online Fault Diagnosis in Petri Net Models of Discrete-Event Systems Using Fourier-Motzkin

Published on Nov 1, 2018
· DOI :10.1109/CONTROL.2018.8516748
Ahmed Al-Ajeli (College of Information Technology), Ahmed Al-Ajeli2
Estimated H-index: 2
(College of Information Technology),
David Parker72
Estimated H-index: 72
(University of Birmingham)
Sources
Abstract
This paper presents a new approach for the fault diagnosis problem in partially observable discrete-event systems modelled with Petri nets. Our approach is based on the use of the Integer Fourier-Motzkin Elimination (IFME) method. The fault diagnosis problem is solved by first creating an initial set of inequalities from the state equation of a Petri net. The occurrence or absence of faults can also be expressed by inequalities. After adding these inequalities to the initial set, we apply the IFME method to eliminate the variables corresponding to unobservable transitions. The resulting set of inequalities is used for the purpose of diagnosis. We prove the correctness of our approach for both bounded and unbounded Petri nets with no cycles of unobservable transitions.
📖 Papers frequently viewed together
7 Citations
2006
15 Citations
References15
Newest
#1Ahmed Al-Ajeli (University of Birmingham)H-Index: 2
#2Behzad Bordbar (University of Birmingham)H-Index: 21
This paper presents a new technique for failure diagnosis in partially observable discrete event systems modelled as Petri nets. In this new technique we adopt Integer Fourier-Motzkin Elimination (IFME) method. We start with a Petri net and produce the state equations. The state equations are a set of integer valued inequalities in variables that represent number of firing of transitions. Occurrences of failure can also be expressed by inequalities. Then we extend the set of inequalities obtaine...
7 CitationsSource
#1Mariagrazia DotoliH-Index: 29
#2Maria Pia FantiH-Index: 31
Last. Walter Ukovich (UniTS: University of Trieste)H-Index: 25
view all 4 authors...
The paper addresses the fault detection problem for discrete event systems in a Petri Net (PN) framework. Assuming that the structure of the PN model and the initial marking are known, faults are modelled by unobservable transitions. Moreover, we assume that there may be additional unobservable transitions associated with the system legal behaviour and that the marking reached after the firing of any transition is unknown. The proposed diagnoser works on-line: it waits for the firing of an obser...
121 CitationsSource
A novel approach to fault diagnosis of discrete event systems is presented in this paper. The standard approach is based on the offline computation of the set of fault events that may have occurred at each reachable state, providing a fast online diagnosis at a price of excessive memory requirements. A different approach is here adopted, which is based on the online computation of the set of possible fault events required to explain the last observed event. This is efficiently achieved by modell...
141 CitationsSource
#1George Jiroveanu (Transelectrica)H-Index: 3
#2René Boel (UGent: Ghent University)H-Index: 22
Last. Behzad Bordbar (University of Birmingham)H-Index: 21
view all 3 authors...
We consider a Petri Net model of the plant. The observation is given by a subset of transitions whose occurrence is always and immediately sensed by a monitoring agent. Other transitions not in this subset are silent (unobservable). Classical on-line monitoring techniques, which are based on the estimation of the current state of the plant and the detection of the occurrence of undesirable events (faults), are not suitable for models of large systems due to high spatial complexity (exponential i...
48 CitationsSource
#1Francesco BasileH-Index: 20
#2Pasquale ChiacchioH-Index: 27
Last. G. De TommasiH-Index: 23
view all 3 authors...
Sufficient conditions for diagnosability of DES modeled as Petri net are given in this paper. In proposed framework we refer to the concept of diagnosability given by Sampath et al. for finite state automata; as far as the fault events are concerned, they are modeled as unobservable transitions. The results here presented are based on the mathematical representation of PNs, and their complexity does not depend on the initial marking of the net. Hence the proposed approach does not suffer of the ...
15 CitationsSource
This paper studies online fault detection and isolation of modular dynamic systems modeled as sets of place-bordered Petri nets. The common places among the set of Petri nets modeling a system capture coupling of various system components. The transitions are labeled by events, some of which are unobservable (i.e., not directly recorded by the sensors attached to the system). The events whose occurrence must be diagnosed have unobservable transition labels. These events model faults or other sig...
120 CitationsSource
Dec 12, 2005 in CDC (Conference on Decision and Control)
#1Alessandro Giua (University of Cagliari)H-Index: 53
#2Carla Seatzu (University of Cagliari)H-Index: 36
In this paper we present an efficient approach for the fault detection of 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. We prove that the set of all possible firing sequences corresponding to a given observation can be described as follows. First a set of basis markings corresponding to the observation are computed together with the minimal set of transitions firings that j...
248 CitationsSource
#1Meera Sampath (UM: University of Michigan)H-Index: 8
#2Raja Sengupta (UM: University of Michigan)H-Index: 57
Last. Demosthenis Teneketzis (UM: University of Michigan)H-Index: 43
view all 5 authors...
Fault detection and isolation is a crucial and challenging task in the automatic control of large complex systems. We propose a discrete-event system (DES) approach to the problem of failure diagnosis. We introduce two related notions of diagnosability of DES's in the framework of formal languages and compare diagnosability with the related notions of observability and invertibility. We present a systematic procedure for detection and isolation of failure events using diagnosers and provide nece...
1,346 CitationsSource
#1Kohkichi Tsuji (UIUC: University of Illinois at Urbana–Champaign)H-Index: 3
#2T. Murata (UIUC: University of Illinois at Urbana–Champaign)H-Index: 2
By using the state equation of a Petri net, the authors derive a sufficient condition for reachability of Petri nets. Then, from this sufficient condition, they show that necessary and sufficient conditions can be derived for reachability of subclasses of a Petri net. The results presented are useful for analyzing many behavioral properties of Petri nets. >
7 CitationsSource
#1William Pugh (UMD: University of Maryland, College Park)H-Index: 51
The Omega test is an integer programming algorithm that can determine whether a dependence exists between two array references, and if so, under what conditions. Conventional wisdom holds that integer programming techniques are far too expensive to be used for dependence analysis, except as a method of last resort for situations that cannot be decided by simpler methods. We present evidence that suggests this wisdom is wrong, and that the Omega test is competitive with approximate algorithms use...
717 CitationsSource
Cited By1
Newest
#1Ahmed Al-Ajeli (College of Information Technology)H-Index: 2
#2David Parker (University of Birmingham)H-Index: 72
Abstract null null We propose techniques for fault diagnosis in discrete-event systems modelled by labelled Petri nets, where fault events are modelled as unobservable transitions. The proposed approach combines an offline and an online algorithm. The offline algorithm constructs a diagnoser in the form of sets of inequalities that capture the legal, normal and faulty behaviour. To implement the offline algorithm, we adopt the Fourier–Motzkin method for elimination of variables from these sets o...
Source