704 research outputs found
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
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
Reduction of Petri net maintenance modeling complexity via Approximate Bayesian Computation
This paper is part of the ENHAnCE ITN project (https://www.h2020-enhanceitn.eu/) funded by the European Union's Horizon 2020 research and innovation programme under the Marie SklodowskaCurie grant agreement No. 859957. The authors would like to thank the Lloyd's Register Foundation (LRF), a charitable foundation in the U.K. helping to protect life and property by supporting engineeringrelated education, public engagement, and the application of research. The authors gratefully acknowledge the support of these organizations which have enabled the research reported in this paper.The accurate modeling of engineering systems and processes using Petri nets often results in complex graph
representations that are computationally intensive, limiting the potential of this modeling tool in real life
applications. This paper presents a methodology to properly define the optimal structure and properties of
a reduced Petri net that mimic the output of a reference Petri net model. The methodology is based on
Approximate Bayesian Computation to infer the plausible values of the model parameters of the reduced model
in a rigorous probabilistic way. Also, the method provides a numerical measure of the level of approximation
of the reduced model structure, thus allowing the selection of the optimal reduced structure among a set
of potential candidates. The suitability of the proposed methodology is illustrated using a simple illustrative
example and a system reliability engineering case study, showing satisfactory results. The results also show
that the method allows flexible reduction of the structure of the complex Petri net model taken as reference,
and provides numerical justification for the choice of the reduced model structure.European Commission 859957Lloyd's Register Foundation (LRF), a charitable foundation in the U.K
A survey on efficient diagnosability tests for automata and bounded Petri nets
This paper presents a survey and evaluation of the efficiency of polynomial diagnosability algorithms for systems modeled by Petri nets and automata. A modified verification algorithm that reduces the state space by exploiting symmetry and abstracting unobservable transitions is also proposed. We show the importance of minimal explanations on the performance of diagnosability verifiers.
Different verifiers are compared in terms of state space
and elapsed time. It is shown that the minimal explanation
notion involved in the modified basis reachability
graph, a graph presented by Cabasino et al. [3] for diagnosability analysis of Petri nets, has great impact also
on automata-based diagnosability methods. The evaluation
often shows improved computation times of a factor
1000 or more when the concept of minimal explanation is
included in the computation
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Steady State Analysis of Flexible Nets
The modeling and analysis of complex dynamic
systems, such as those in manufacturing, logistics and biology,
require powerful analysis methods for their study and optimization.
A significant modeling and analysis challenge posed by
both, artificial and natural systems, is the existence of uncertain
parameters. Flexible Nets is a novel modeling formalism, inspired
by Petri nets, that can handle different types of uncertain
parameters in a natural way. This paper develops an efficient
method to analyse the evolution of a system modeled by a Flexible
Net in the long run. More precisely, the method focuses on the
computation of steady state bounds for an objective function of
interest. The method makes use of a set of constraints, expressed
as linear inequalities, that the state variables must satisfy in
the steady state. In order to account for systems that do not
reach a constant steady state, the developed constraints allow
the system state to switch among different values, i.e. the steady
state variables are not forced to be constant.European Commission: FormalBio Contract No: 623995,
Call reference: FP7-PEOPLE-2013-IE
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Flexible Nets: a modeling formalism for dynamic systems with uncertain parameters
Funder: FP7 People: Marie-Curie Actions; doi: https://doi.org/10.13039/100011264; Grant(s): 623995Abstract: The modeling of dynamic systems is frequently hampered by a limited knowledge of the system to be modeled and by the difficulty of acquiring accurate data. This often results in a number of uncertain system parameters that are hard to incorporate into a mathematical model. Thus, there is a need for modeling formalisms that can accommodate all available data, even if uncertain, in order to employ them and build useful models. This paper shows how the Flexible Nets (FNs) formalism can be exploited to handle uncertain parameters while offering attractive analysis possibilities. FNs are composed of two nets, an event net and an intensity net, that model the relation between the state and the processes of the system. While the event net captures how the state of the system is updated by the processes in the system, the intensity net models how the speed of such processes is determined by the state of the system. Uncertain parameters are accounted for by sets of inequalities associated with both the event net and the intensity net. FNs are not only demonstrated to be a valuable formalism to cope with system uncertainties, but also to be capable of modeling different system features, such as resource allocation and control actions, in a facile manner
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
Handling variability and incompleteness of biological data by flexible nets: a case study for Wilson disease.
Mathematical models that combine predictive accuracy with explanatory power are central to the progress of systems and synthetic biology, but the heterogeneity and incompleteness of biological data impede our ability to construct such models. Furthermore, the robustness displayed by many biological systems means that they have the flexibility to operate under a range of physiological conditions and this is difficult for many modeling formalisms to handle. Flexible nets (FNs) address these challenges and represent a paradigm shift in model-based analysis of biological systems. FNs can: (i) handle uncertainties, ranges and missing information in concentrations, stoichiometry, network topology, and transition rates without having to resort to statistical approaches; (ii) accommodate different types of data in a unified model that integrates various cellular mechanisms; and (iii) be employed for system optimization and model predictive control. We present FNs and illustrate their capabilities by modeling a well-established system, the dynamics of glucose consumption by a microbial population. We further demonstrate the ability of FNs to take control actions in response to genetic or metabolic perturbations. Having bench-marked the system, we then construct the first quantitative model for Wilson disease-a rare genetic disorder that impairs copper utilization in the liver. We used this model to investigate the feasibility of using vitamin E supplementation therapy for symptomatic improvement. Our results indicate that hepatocytic inflammation caused by copper accumulation was not aggravated by limitations on endogenous antioxidant supplies, which means that treating patients with antioxidants is unlikely to be effective
Updating Probabilistic Knowledge on Condition/Event Nets using Bayesian Networks
The paper extends Bayesian networks (BNs) by a mechanism for dynamic changes to the probability distributions represented by BNs. One application scenario is the process of knowledge acquisition of an observer interacting with a system. In particular, the paper considers condition/event nets where the observer\u27s knowledge about the current marking is a probability distribution over markings. The observer can interact with the net to deduce information about the marking by requesting certain transitions to fire and observing their success or failure.
Aiming for an efficient implementation of dynamic changes to probability distributions of BNs, we consider a modular form of networks that form the arrows of a free PROP with a commutative comonoid structure, also known as term graphs. The algebraic structure of such PROPs supplies us with a compositional semantics that functorially maps BNs to their underlying probability distribution and, in particular, it provides a convenient means to describe structural updates of networks
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