Stochastic Discrete Event Systems Research Articles

Asynchronous Fault Diagnosis of Stochastic Discrete-Event Systems in Industrial Applications

Asynchronous Fault Diagnosis of Stochastic Discrete-Event Systems in Industrial Applications

Bounded Synthesis and Reinforcement Learning of Supervisors for Stochastic Discrete Event Systems With LTL Specifications

Bounded Synthesis and Reinforcement Learning of Supervisors for Stochastic Discrete Event Systems With LTL Specifications

Identification of unobservable behavior in stochastic discrete event systems with a low number of sensors

Dynamic discrete event systems (DDES) are systems that evolve from the asynchronous occurrence of discrete events. Their versatility has become a critical modeling tool in different applications. Finding models that define the behavior of DES is a topic that has been addressed from different approaches, depending on the type of system to be modeled and the model's objective. This article focuses on the identification of timed models for stochastic discrete event systems. The identified model includes both observable and unobservable behavior. The objective of the method is achieved through the following steps:•Identifying the sequences of events observed at different time instances during the closed-loop operation of the system (observed language),•Inferring the stochastic behavior of time between events and modeling the observable behavior as a stochastic timed Interpreted Petri Net (st-IPN),•and finally, inferring the non-observable behavior using the language projection operation between the observed language and the language generated by the st-IPN.This method has novel aspects because it uses timed events, can be applied to systems with a low number of sensors and can infer unobservable behavior for any sequence of events.

Online prognosis of stochastic discrete event systems with guaranteed performance bound

In this paper, we consider the online prognosis of stochastic discrete event systems. Even though it is easy to predict the occurrence of faults in advance accurately for a prognosable discrete event system, it is much more difficult to do so for systems that are not prognosable. In this paper, we solve the online prognosis problem in a stochastic discrete event system framework. Our idea is to calculate the probability of the occurrence of faults in the future when a no-fault observable string is observed. We say an observable string is no-fault if no faults have occurred when it is observed. We then compare the probability with a pre-set threshold to decide whether to issue an alert or not. We develop a method to calculate the lower bound for possible thresholds, which has the fewest false alerts and no missed alerts of faults. For a given threshold, we use the rate of missed fault alerts and the rate of false fault alerts to evaluate the performance of fault prognosis. We formally define these two rates and develop algorithms to calculate them. These results can guide us in choosing a proper threshold to achieve the best trade-off between false fault alerts and missed alerts of faults.

Probabilistic verification of diagnosability for a certain class of timed stochastic systems

This paper addresses diagnosability for a class of timed stochastic discrete event systems that are modeled with labeled continuous time Markov models. A large variety of fault patterns is considered and the paper aims to define and propose conditions for weak notions of diagnosability of fault patterns in a time stochastic framework. The proposed approach is based on a state isolation perspective. Logical and probabilistic verifiers that result by first taking the product of the system with the fault pattern, followed by the parallel composition of the resulting structure with its logical observer are designed in this perspective. The advantage of this schema is to separate explicitly the system from the pattern we are interested in, as well as from the sensoring and observational aspects. Consequently, the verifiers allow the explicit tracking of the information about the first occurrence of a fault pattern and the preservation of not only the logical information provided by the labeling function but also the timing aspects imposed by the dynamics of the system.

Robustness Evaluation Process for Scheduling under Uncertainties

Scheduling production is an important decision issue in the manufacturing domain. With the advent of the era of Industry 4.0, the basic generation of schedules becomes no longer sufficient to face the new constraints of flexibility and agility that characterize the new architecture of production systems. In this context, schedules must take into account an increasingly disrupted environment while maintaining a good performance level. This paper contributes to the identified field of smart manufacturing scheduling by proposing a complete process for assessing the robustness of schedule solutions: i.e., its ability to resist to uncertainties. This process focuses on helping the decision maker in choosing the best scheduling strategy to be implemented. It aims at considering the impact of uncertainties on the robustness performance of predictive schedules. Moreover, it is assumed that data upcoming from connected workshops are available, such that uncertainties can be identified and modelled by stochastic variables This process is supported by stochastic timed automata for modelling these uncertainties. The proposed approach is thus based on Stochastic Discrete Event Systems models and model checking techniques defining a highly reusable and modular process. The solution process is illustrated on an academic example and its performance (generecity and scalability) are deeply evaluated using statistical analysis. The proposed application of the evaluation process is based on the technological opportunities offered by the Industry 4.0.

Sufficiency for diagnosability of stochastic discrete‐event systems and a polynomial‐time verification

AbstractThe notion of diagnosability of stochastic discrete‐event systems (SDESs) was introduced in the literature, but the method for verifying the diagnosability of SDESs was exponential. However, is there a sufficient condition of diagnosability of SDESs that can be tested with polynomial method? In this paper, we present a sufficient condition of diagnosability of SDESs based on a constructive testing automaton, and a polynomial method is proposed to test the condition.

Decentralized Failure Prognosis of Stochastic Discrete-Event Systems and a Test Algorithm

Recently, the study of fault diagnosis and prognosis of discrete-event systems (DESs) has received considerable attention. This article aims to investigate the decentralized fault prognosis of stochastic DESs (SDESs). The notion of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> -step stochastic-coprognosability, called <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S_{m} $ </tex-math></inline-formula> -coprognosability, is formalized to capture the capability of stochastic systems to predict a fault at least <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> steps in advance under the decentralized framework. The verifier is constructed from the stochastic decentralized system, in which <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> local prognosers are deployed to send the local prognostic decisions to a coordinator for calculating the final prognostic decision. In particular, a necessary and sufficient condition of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S_{m}$ </tex-math></inline-formula> -coprognosability of stochastic systems is derived, and an algorithm for testing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S_{m} $ </tex-math></inline-formula> -coprognosability is given, which is polynomial to the number of states and events but exponential to the number of local sites. Furthermore, the maximum number of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> for making the given SDES to be <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S_{m} $ </tex-math></inline-formula> -coprognosable is discussed. Note to Practitioners—This article extends the fault prognosis methods of SDESs from centralized framework to decentralized framework, such that for many technologically complex systems whose information collection is scattered in physically separated different sites, every local site makes decision based on information collected by own sensors, without communicating with other local sites, which is more appropriate than the centralized method.

Robust predictability of stochastic discrete-event systems and a polynomial-time verification

The purpose of fault prediction of discrete-event systems (DESs) is to predict the occurrence of fault in advance such that some protective actions can be taken before the occurrence of the fault. The robust predictability issue under the framework of stochastic DESs (SDESs) with model uncertainty is studied. First, the notions of (ϵ,m)−robust predictability and robust predictability of SDESs are formalized. In general, a set of stochastic systems being robustly predictable can predict the occurrences of faults in the sense of probability. Then the robust predictor and robust verifier for performing the robust prediction are constructed from the given possible stochastic systems. Particularly, the necessary and sufficient conditions for (ϵ,m)−robust predictability and robust predictability of SDESs are proposed, and an approach is presented to verify the robust predictability of SDESs with polynomial-time complexity both in the state space and in the number of all possible models.

Reliable Co-Prognosability of Decentralized Stochastic Discrete-Event Systems and a Polynomial-Time Verification.

Fault prognosis of discrete-event systems (DESs) aims to predict the occurrence of fault beforehand such that certain protective measures may be adopted before the fault occurs. This article investigates the reliable coprognosability issue for decentralized stochastic DESs (SDESs) facing the possible unavailability of some local agents. The main contributions are as follows. First, we formalize the notion of r -reliable coprognosability for SDESs. In general, an r -reliably coprognosable SDES with n local sites (1 ≤ r ≤ n) can predict the occurrences of faults even though n-r local agents are invalid. Second, we construct a reliable coprognoser from the given stochastic system and present a necessary and sufficient condition for testing r -reliable coprognosability by the reliable coprognoser. Third, due to the exponential complexity of testing r -reliable coprognosability by reliable coprognoser, a reliable coverifier is constructed and an alternate necessary and sufficient condition for verifying r -reliable coprognosability of SDESs by the reliable coverifier is proposed, which is polynomial time.

Synthesis of Optimal Multiobjective Attack Strategies for Controlled Systems Modeled by Probabilistic Automata

In this article, we study the security of control systems in the context of the supervisory control layer of stochastic discrete-event systems. Control systems heavily rely on correct communication between the plant and the controller. In this article, we consider that such communication is partially compromised by a malicious attacker. The attacker has the ability to modify a subset of the sensor readings and mislead the supervisor, with the goal of inducing the system into an unsafe state. We consider this problem from the attacker’s viewpoint and investigate the synthesis of an attack strategy for systems modeled as probabilistic automata. Specifically, we investigate the synthesis of attack functions constrained by multiple objectives. We proceed in two steps. First, we quantify each attack strategy based on the likelihood of successfully reaching an unsafe state. Based on this quantification, we study the problem of synthesizing attack functions with the maximum likelihood of successfully reaching an unsafe state. Second, we consider the problem of synthesizing attack functions that have the maximum likelihood of successfully reaching an unsafe state while minimizing a cost function, i.e., the synthesis of attack functions is constrained by multiple objectives. Our solution methodology is based on mapping these problems to optimal control problems for Markov decision processes, specifically, a probabilistic reachability problem and a stochastic shortest path problem.

Diagnosability of fault patterns with labeled stochastic Petri nets

This paper is about the diagnosability of fault patterns in timed stochastic discrete event systems. For this purpose, the diagnosability problem is formulated with labeled stochastic Petri net models and pure logical fault pattern nets. A particular composition of a labeled stochastic Petri net with a fault pattern net is proposed and is shown to characterize in an explicit way the fault patterns, including the timing and probabilistic aspects of the underlying system. Logical and probabilistic verifiers are derived, and used to establish a set of conditions to check not only the strong diagnosability property but also weaker notions of diagnosability.

Abstract executions of stochastic discrete event systems

Stochastic discrete event systems play a steadily increasing role in reliability engineering and beyond in systems engineering. Designing stochastic discrete event systems presents however well-known difficulties: models are hard to debug and to validate because of the existence of infinitely many possible executions, itself due to stochastic delays, which are possibly intertwined with deterministic ones. In this article, revisiting ideas introduced in the framework of model-checking of timed and hybrid systems, we show that it is possible to abstract the time in stochastic discrete event systems. More specifically, we show that schedules of transitions can be abstracted into systems of linear inequalities and that abstract and concrete executions are bisimilar. The result presented in this article represents thus a very important step forward in quality assurance of stochastic models of complex technical systems. We illustrate the potential of the proposed approach by means of AltaRica 3.0 models.

Stochastic Timed Discrete-Event Systems: Modular Modeling and Performance Evaluation Through Markovian Jumps

We are interested in a scalable, flexible, and modular methodology, for modeling and performance analysis of stochastic discrete-event systems (SDES). In this sense, we propose a modular approach for timing non-markovian SDES expressed as a parallel composition of modules that interacts with each other through events. We show how general distribution for event lifetimes can be implemented systematically by coupling timing modules to the system model. As a result, this coupling mechanism preserves modularity, leading to a compact markovian model expressed in terms of flexible modules. Therefore the methodology allows us to write the whole SDES model as a composition of the system model and the timing one, giving flexibility and scalability in modeling design, as we can modify the modules individually according to the designer’s interests. In addition, from the whole markovian SDES model, we show how to perform the model analysis through the analytic approach, as well as through Monte Carlo computer simulation. As an application, we present a numerical example of computing the abandonment rate for a service network with general service time employing both analytical and computer-simulation models.

Abstract executions of stochastic discrete event systems

Abstract executions of stochastic discrete event systems

Exposure and Revelation Times as a Measure of Opacity in Timed Stochastic Discrete Event Systems

Opacity is a security notion that focuses on determining whether a given system's behavior is kept secret to intruders. Various notions of opacity have received significant attention during the last decade including current state opacity and initial state opacity, which have been studied for deterministic and probabilistic systems in untimed contexts. In timed systems, opacity requirements may vary with time and one could also be interested in knowing the time duration for which opacity requirements are violated or preserved. The main contribution of this article is to introduce and analyze opacity exposure and opacity revelation times as measures of vulnerability in timed discrete event system (DES) that behave according to Markovian dynamics (i.e., at any given time, all enabled events are independent and distributed in time with exponential probability density functions). Labeled stochastic Petri nets (LSPNs) are used to model timed stochastic DESs, and appropriate constructions (involving current and initial state observers) are used to evaluate exposure and revelation times for a given LSPN.

Diagnosis of Structural and Temporal Faults for $k$ -Bounded Non-Markovian Stochastic Petri Nets

This paper concerns the diagnosis of faults for stochastic discrete event systems that behave according to non-Markovian dynamics. ${k}$ -bounded partially observed Petri nets are used to model the system structure and the sensors. Stochastic processes with probability density functions (pdf) of finite support define the dynamics. Structural and temporal faults are considered. Structural faults correspond to specific sequences of events that should satisfy precedence conditions defined with patterns. Temporal faults are defined with time constraints that must be fulfilled by the firing durations. The probabilities of consistent trajectories are computed with a numerical scheme from the collected timed measurements. The advantage of the proposed scheme is that it can be used for a large variety of pdf that may be defined either with an analytical or a numerical description. It works also for various time semantics. Diagnosis in terms of probability for faulty patterns and temporal constraints is established as a consequence.

Verification of safe diagnosability of stochastic discrete-event systems

Safe diagnosability of discrete-event systems (DESs) is viewed as the first necessary step of fault-tolerant supervision in the literature. For safe diagnosable systems, it is required that not only failures occurring in systems can be detected within a finite delay, but also the detection should be completed before running any unsafe operation. In this paper, we present a novel approach to deal with the safe diagnosis issue for stochastic DESs by constructing a nondeterministic automaton called the safe verifier, and the necessary and sufficient condition for safe diagnosability of stochastic DESs is presented. It is worth noting that the proposed approach has lower complexity than the existing approach based on safe diagnoser as far as the number of states.

Privacy and safety analysis of timed stochastic discrete event systems using Markovian trajectory-observers

Various aspects of privacy and safety in many application domains can be assessed based on proper analysis of successive measurements that are collected about a given system. This work is devoted to such issues in the context of timed stochastic discrete event systems (DES) that are modeled with partially observed timed stochastic Petri net models. The first contribution is to introduce a k-step trajectory-observer, which is a construction that captures all possible k-suffixes of the trajectories that are consistent with a given sequence of measurements that has been recorded. When the system behaves according to Markovian dynamics (i.e., all event occurrences are distributed in time with exponential probability density functions), a parallel-like composition of the timed system with the resulting observer is proposed that leads to a Markovian process. The second contribution is to take advantage of the Markovian analysis to compute certain important characteristic times during which the underlying system should satisfy a given property (based on the suffixes of length k of a given trajectory). To illustrate the approach, we consider two particular properties, namely k-suffix language opacity and k-diagnosability, which can be studied in a stochastic timed context using the Markovian trajectory observer.

Pattern diagnosis for stochastic discrete event systems

In this paper, pattern diagnosis problem in stochastic discrete event system (SDES) is investigated. In a system, an abnormal state may be caused by the occurrence of several normal events. This kind of fault is called fault pattern. The diagnosis problem of fault pattern is defined as pattern diagnosis. Based on the notions of A-diagnosability and AA-diagnosability in SDES, the definitions of PA-diagnosability and PAA-diagnosability for pattern diagnosability in SDES are presented in this paper. In addition, a necessary and sufficient condition for an SDES to be PA-diagnosable is proposed. The goal of this paper is diagnosing fault pattern in the real systems. Three-Tank Water Level Control System and Heating, Ventilation, and Air-conditioning System are described to illustrate our algorithm. Experimental results demonstrate that pattern diagnosability in SDES is more accurate than that in DES.