Sufficient Conditions For Diagnosability Research Articles

On the Decidability and Complexity of Diagnosability for Labeled Petri Nets

In this paper, we investigate the decidability and complexity of the fault diagnosis problem in unbounded labeled Petri nets. First, we show that checking diagnosability for unbounded Petri nets is decidable. We present a new necessary and sufficient condition for diagnosability, which can be reduced to a model checking problem for unbounded Petri nets. Then, we show that checking diagnosability for unbounded Petri nets is EXPSPACE-complete. This complexity result is further extended to various subclasses of Petri nets. To the best of our knowledge, this is the first paper that establishes decidability and complexity results for diagnosability of unbounded Petri nets.

On‐the‐Fly and Incremental Technique for Fault Diagnosis of Discrete Event Systems Modeled by Labeled Petri Nets

AbstractIn this paper, we develop an on‐the‐fly and incremental technique for fault diagnosis of discrete event systems modeled by labeled Petri nets, in order to tackle the combinatorial explosion problem. K‐diagnosability, diagnosability, Kmin (the minimum K ensuring diagnosability) and on‐line diagnosis are solved on the basis of the on‐the‐fly and incremental building of two structures, called respectively fault marking graph and fault marking set graph, in parallel. We build on existing results, namely those establishing necessary and sufficient conditions for diagnosability, but we bring mechanisms to make the checking of such conditions potentially more efficient. We show that, in general, analyzing or even building the whole reachability graph is unnecessary to analyze diagnosability and build an on‐line diagnoser. Our technique was implemented in a prototype tool called OF‐PENDA, and a railway level crossing benchmark is used to make a comparative discussion pertaining to efficiency in terms of time and memory relative to some existing approaches.

Diagnosability of Petri nets with observation graphs

This paper addresses the problem of diagnosability for dynamic discrete event systems modeled with bounded or unbounded Petri nets that are deadlock-free and monitored with sensor configurations with marking and event measurements. The proposed method gives necessary and sufficient conditions for diagnosability. It is based on the transformation of the coverability graph into an observation graph that encodes all observation sequences of measured markings and events with respect to the sensor configuration. This graph also encodes all sequences of transitions that may fire from any reachable marking of the Petri net. Diagnosability is determined by analyzing the paths and circuits in the observation graph. The method is illustrated with several examples of bounded or unbounded Petri nets.

Diagnosability of Discrete-Event Systems Using Labeled Petri Nets

In this paper, we focus on labeled Petri nets with silent transitions that may either correspond to fault events or to regular unobservable events. We address the problem of deriving a procedure to determine if a given net system is diagnosable, i.e., the occurrence of a fault event may be detected for sure after a finite observation. The proposed procedure is based on our previous results on the diagnosis of discrete-event systems modeled with labeled Petri nets, whose key notions are those of basis markings and minimal explanations, and is inspired by the diagnosability approach for finite state automata proposed by Sampath in 1995. In particular, we first give necessary and sufficient conditions for diagnosability. Then, we present a method to test diagnosability that is based on the analysis of two graphs that depend on the structure of the net, including the faults model, and the initial marking.

Optimal sensor selection for ensuring diagnosability in labeled Petri nets

This paper studies the problem of optimal static sensor selection for ensuring diagnosability in labeled bounded and unbounded Petri nets. Starting from a non-diagnosable labeled Petri net system, we present a systematic procedure to design a new labeling function that makes the system diagnosable and optimizes a given objective function. This procedure employs a particular net, called Verifier Net, that is built from the original Petri net and provides necessary and sufficient conditions for diagnosability. We exploit the system structure captured in the verifier net to guide the search for the desired new labeling function. The search is performed over an unfolding of the reachability/coverability tree of the verifier net and follows a set of rules that capture the relabeling strategy. We allow for unobservable transitions that cannot be labeled as well as for multiple fault classes. We formulate an integer linear programming problem that finds an optimal labeling function when numerical costs are associated with transition relabeling.

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 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> steps, where the detection must occur within a fixed bound of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> 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 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> steps, we give a procedure to compute the bound <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> . To the best of our knowledge, this is the first time that necessary and sufficient conditions for diagnosability and diagnosability in <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> steps of labeled unbounded Petri nets are presented.

Structural Diagnosability of DES and Design of Reduced Petri Net Diagnosers

This paper deals with diagnosis of permanent and operational faults of partially observed discrete event systems modeled by interpreted Petri nets capturing both normal and faulty behaviors. Two main results are presented: a structural characterization of the diagnosability property and a method for designing reduced model diagnosers for online fault detection and location. Sufficient conditions for diagnosability are provided based on the analysis of the influence area of every fault fi in the model and the relative distance between pairs of transitions; polynomial algorithms are proposed for determining diagnosability. The diagnoser includes two reduced models that monitor the system; one for tracking the actual behavior and the other for establishing the expected behavior; the difference of markings in such models, called residue, provides enough information for the immediate location of faults, even if they occur simultaneously.

Optimal Sensor Selection for Ensuring Diagnosability in Labeled Bounded Petri Nets

This paper studies the problem of optimal static sensor selection for ensuring diagnosability in labeled bounded Petri nets. Starting from a non-diagnosable labeled Petri net system, we present a systematic procedure to design a new labeling function that makes the system diagnosable and optimizes a given objective function. This procedure employs a particular net, called Verifier Net, that is built from the original Petri net and provides necessary and sufficient conditions for diagnosability. We exploit the system structure captured in the verifier net to guide the search for the desired new labeling function. The search is performed over an unfolding of the reachability tree of the verifier net.

Diagnosis of delay–deadline failures in real time discrete event models

In this paper a method for fault detection and diagnosis (FDD) of real time systems has been developed. A modeling framework termed as real time discrete event system (RTDES) model is presented and a mechanism for FDD of the same has been developed. The use of RTDES framework for FDD is an extension of the works reported in the discrete event system (DES) literature, which are based on finite state machines (FSM). FDD of RTDES models are suited for real time systems because of their capability of representing timing faults leading to failures in terms of erroneous delays and deadlines, which FSM-based ones cannot address. The concept of measurement restriction of variables is introduced for RTDES and the consequent equivalence of states and indistinguishability of transitions have been characterized. Faults are modeled in terms of an unmeasurable condition variable in the state map. Diagnosability is defined and the procedure of constructing a diagnoser is provided. A checkable property of the diagnoser is shown to be a necessary and sufficient condition for diagnosability. The methodology is illustrated with an example of a hydraulic cylinder.

EFFICIENT DIAGNOSABILITY TEST FOR STATE-BASED DIAGNOSIS OF DISCRETE EVENT SYSTEMS

State-based fault diagnosis of discrete event systems is considered. The concept of resonating state cycles is introduced, which is used to develop a necessary and sufficient condition for diagnosability. An algorithm to test diagnosability is presented, and is shown to have polynomial complexity. Extensions of the algorithm to include a priori state estimates are discussed.

Diagnosability of Semiconductor Manufacturing Equipment

Diagnosis of discrete event systems such as complex semiconductor manufacturing equipment has become more and more difficult such that it cannot be performed based on experience. Systematic approaches for the diagnosis problem are urgently needed. In this paper, we present an algorithm of polynomial complexity in the number of nodes for computing a sufficient condition of diagnosability of semiconductor manufacturing equipment modeled by Petri nets. Our algorithm is more efficient than previous ones since no state enumeration is necessary. This gives us an advantage to solve large real-world problems. Our algorithm is formulated as a linear programming problem, which is well-known to be of polynomial complexity in the worst case. We use a Metal-Organic Vapor Phase Epitaxy system that is simplified from real-world semiconductor manufacturing equipment applications to illustrate our proposed approach.

Failure diagnosis using discrete-event models

Detection and isolation of failures in large, complex systems is a crucial and challenging task. The increasingly stringent requirements on performance and reliability of complex technological systems have necessitated the development of sophisticated and systematic methods for the timely and accurate diagnosis of system failures. We propose a discrete-event systems (DES) approach to the failure diagnosis problem. This approach is applicable to systems that fall naturally in the class of DES; moreover, for the purpose of diagnosis, continuous-variable dynamic systems can often be viewed as DES at a higher level of abstraction. We present a methodology for modeling physical systems in a DES framework and illustrate this method with examples. We discuss the notion of diagnosability, the construction procedure of the diagnoser, and necessary and sufficient conditions for diagnosability. Finally, we illustrate our approach using realistic models of two different heating, ventilation, and air conditioning (HVAC) systems, one diagnosable and the other not diagnosable. While the modeling methodology presented here has been developed for the purpose of failure diagnosis, its scope is not restricted to this problem; it can also be used to develop DES models for other purposes such as control.

Diagnosability of discrete-event systems

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 necessary and sufficient conditions for a language to be diagnosable. The diagnoser performs diagnostics using online observations of the system behavior; it is also used to state and verify off-line the necessary and sufficient conditions for diagnosability. These conditions are stated on the diagnoser or variations thereof. The approach to failure diagnosis presented in this paper is applicable to systems that fall naturally in the class of DES's; moreover, for the purpose of diagnosis, most continuous variable dynamic systems can be viewed as DES's at a higher level of abstraction.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>