带有同步变迁的有界Petri网系统的建模及可达性分析

由于存在可达标识集的爆炸性问题,大型Petri网系统的建模及可达性分析等问题的研究存在难度.文章利用矩阵的半张量积工具,研究了带有同步变迁的有界Petri网系统的建模及可达性问题.一方面,由于该类Petri网系统可以看作是由若干个子Petri网系统组成,所以可以用半张量积工具表述得到整个Petri网系统的矩阵表示.另一方面,在得出的矩阵表示的基础上,研究了两个标识之间可达性的充要判据,并给出了求可达变迁序列的算法.最后,文章用实例验证了该算法的正确性.所提出的方法在一定程度上解决了状态空间爆炸问题,并易于计算机实现.     

部分状态可见的隐马尔可夫模型的Viterbi算法

本文研究了隐马尔可夫模型的Viterbi算法,在已知隐马尔可夫模型的部分状态、初始概率分布、状态转移概率矩阵和观测概率矩阵的条件下,由此Viterbi算法给出最优状态序列的估计.相对于已有的算法,本文的算法考虑了部分可见状态对初始条件和递推公式的影响,并且本文的算法能保证预测的状态序列是整体最优的.最后,我们将本文的算法应用于故障识别,从而验证所设计算法的可行性.     

有界Petri网的可逆性和活性的STP判别方法

基于矩阵半张量积(the semi-tensor product,STP)方法研究了有界Petri网系统的可逆性和活性问题.首先,利用先前所建立的有界Petri网系统的状态演化方程,分别给出了有界Petri网系统的可逆性和活性判别的充要条件.文章的结果是基于矩阵形式的,利用Matlab的STP工具箱,可将Petri网系统的可逆性和活性判别问题转化为简单直接的矩阵计算问题.所提出的方法不仅形式简单、计算方便,而且易于计算机实现.其次,两个实例说明了文章所提出方法的可行性和有效性.     

模式识别技术在泵源系统故障诊断中的应用

本文介绍采用自回归模型参数作故障特征,用模式识别中的 Perceptron 算法求解的线性判定函数对各故障状态进行分类的方法,介绍 Perceptron 算法的具体过程,讨论结束学习过程的条件.用这种方法对简单泵源系统故障诊断模拟试验研究表明,这种诊断方法原理正确、效果良好、具有工程应用价值.     

一类含时间因素的 Petri 网及其在工程上的应用

Petri 网是一种用于描述系统的动态行为和分析系统的动态性质的数学模型.一个Petri 网实质上是一个带标识的有向偶图.有向偶图描述系统的静态结构,而标识指出系统所处的状态.当一个 Petri 网的标识按一定规律发生变化时,就形象地模拟了系统的动态行为.自1962年被提出以来,Petri 网理论得到了迅速的发展和广泛的应用.如今,Petri网已被用作对大型操作系统、分布式数据库、通讯协议、并行程序以及许多计算机系统进行分析和设计的手段.此外,在化学、工程技术、法律及其他领域里,也不乏 Petri 网应用的实例.     

基于SVM极点分类的故障诊断与可靠控制

利用SVM分类技术,针对系统故障极点进行分类,利用网格搜寻法,实现对不同故障极点的分类进而实现对系统故障的检测和诊断,为了实现对系统极点变化的实时监测,给出了通过系统状态估计系统极点的新方法.在给出故障诊断的基础上,同时给出了针对相应故障的可靠控制器的设计.最后通过数例验证极点观测器对极点估计的准确性和故障诊断的准确性及可靠控制的有效性.     

有界Petri网的进程表达式

提出了有界Petri网的进程表达式的概念,并给出了求有界Petri网进程表达式的一个算法.一个有界Petri网的进程表达式是以该网的基本子进程集为字母表的正规表达式.它所表示的正规集是该Petri网全体满进程的集合.所谓满进程,是指每个s切对应着Petri网的一个可达标识的那类进程.     

一种基于随机森林的备件预测模型研究

对舰船零部件发生故障问题进行故障诊断,并对故障诊断结果进行分析,建立舰船零部件备件需求模型,给出零部件之间的发生故障概率的关系与备件需求特征;将随机森林回归原理应用到了舰船零部件的备件需求预测领域,构建了基于随机森林的预测模型,以及预测结果准确率的评价。用诊断结果数据对算法进行验证,结果表明,将随机森林算法运用到舰船的备件预测领域可以为舰船装备在一次海上任务期内备件配置问题提供参考价值。     

K(0,1)-TPN方法在三防系统安全性分析应用

三防系统软件是坦克装甲车辆防护系统中的安全关键软件,对其安全性分析是十分必要的.定义了k(0,1)—时间Petri网(K(0,1)-TPN),该网是对时间Petri网的一种扩展,对于输入不同、运行过程相同及其控制机构相同或不同的系统分析建模具有普遍的应用价值.应用k(0,1)—时间Petri网及其动态的运行规则,并采用合成技术建立起了三防系统的模型.通过对运行时序、状态转移等的分析,得出了若干个三防软件系统存在的危险状态,并对软件及其系统的修改提出了建议.     

基于模拟退火算法的船用核动力装置故障诊断研究北大核心

针对核动力装置故障诊断存在的诊断精度低等问题,提出了一种基于模拟退火算法和概率因果模型相结合的故障诊断方法.首先根据故障样本集和概率因果理论建立动态多故障诊断模型,将复杂系统的多故障诊断转换成非线性规划问题.利用模拟退火算法对该问题进行求解,并建立了诊断测试系统.测试结果表明,方法能有效避免误诊、漏诊现象,可用于复杂核动力装置的动态多故障诊断.     

Some contributions with Petri nets for the modelling, analysis and control of HDS

Petri nets (PN) are useful for the modelling, analysis and control of hybrid dynamical systems (HDS) because PN combine in a comprehensive way discrete events and continuous behaviours. On one hand, PN are suitable for modelling the discrete part of HDS and for providing a discrete abstraction of continuous behaviours. On the other hand, continuous PN are suitable for modelling the continuous part of HDS and for working out a continuous approximation of the discrete part in order to avoid the complexity associated with the exponential growth of discrete states. This paper focuses on the advantages of PN as a modelling tool for HDS. Investigations of such models for diagnosis and control issues are detailed.

Taking inspiration from the discrete event approach, sensor selection for diagnosis is discussed according to the structural analysis of the PN models. Faults are represented with fault transitions and a faulty behaviour occurs when a sequence of transitions is fired that contains at least one fault transition. Minimal sets of observable places are defined for detecting and isolating faulty behaviours.

Taking inspiration from the continuous time approach, flow control of HDS modelled with continuous PN is also investigated. Gradient-based controllers are introduced in order to adapt the firing speeds of some controllable transitions according to a desired trajectory of the marking. The equilibria and stability of the controlled system are studied with Lyapunov functions.     

About the stochastic and continuous Petri nets equivalence in the long run

Reliability analysis is often based on stochastic discrete event models like stochastic Petri nets (SPNs). For large dynamical systems with numerous components, the analytical expression of the SPNs steady state is full of complexities because of the combinatory explosion with discrete models. Moreover, the estimation of mean markings thanks to simulations is time consuming in case of rare events. For these reasons, Petri net fluidification may be an interesting alternative to provide a reasonable estimate of the asymptotic behavior of stochastic processes. Unfortunately, the steady states of SPNs and timed continuous Petri nets (contPNs) with the same structure, same initial marking and same firing rates are mainly often different. The region of SPN steady states (when firing rates are defined in a polyhedral area) contrasts with that of contPN ones. The purpose of this paper is to illuminate this issue in taking advantage of the piecewise-affine hybrid structure of contPNs. Regions and critical regions are defined in the marking space in order to characterize this structure. Based on this characterization, the main contribution is to propose a transformation of the considered SPN into a contPN with the same structure, modified firing rates and homothetic initial marking so that the corrected contPN converges partially to the same mean marking than the SPN. Consequently, a global understanding of an SPN steady state can be obtained according to the corrected contPN.     

Scheduling of piecewise constant product flows: A Petri net approach

Scheduling a manufacturing system is usually an NP-hard problem. This means that only heuristic algorithms can be used to provide near-optimal schedules. In this paper, we show that a manufacturing system can be modeled using a particular type of Petri nets, called Controllable-Output nets, or CO nets for short. These Petri net models are then used to introduce a two-stage scheduling algorithm for problems in which the product flows can be considered as piecewise constant. The first stage consists of distributing the workload among the resources. The second stage derives a schedule from the resource workload. The deterministic case is considered. Numerical results are proposed.     

Removing dead transitions in timed-arc Petri nets

Timed-arc Petri nets (TAPNs) are a timed extension of Petri nets where tokens are assigned an age indicating the time elapsed from its creation, and PT-arcs (place to transition arcs) are labelled with time intervals that are used to restrict the age of the tokens that can be used to fire the adjacent transition. This is a rather pathological model, as reachability is undecidable, whereas some other known properties of Petri nets, like boundedness, coverability and even termination, are decidable. This article focuses on the problem of detecting dead transitions, i.e. transitions that can be removed from the model since they can never become enabled. We prove that this problem is decidable for TAPNs with natural times, and we present an algorithm that can be used to find dead transitions in the particular case of 1-safe TAPNs.     

Modeling,analysis and performance evaluation for fault diagnosis and Fault Tolerant Control in bottle-filling plant modeled using Hybrid Petri nets

In this paper, an approach to achieve fault diagnosis and Fault Tolerant Control in a typical bottle-filling plant using event based techniques is discussed. For this purpose, the plant is modeled using Hybrid Petri nets which enable study and analysis with regard to the working of the plant. Once effective modeling is done based on two different case studies considered, new algorithms are proposed to achieve fault diagnosis and Fault Tolerant Control on the models developed. Finally, performance measures with regard to the models proposed are evaluated to check the correctness of the models developed. Both analytical and numerical results are obtained which are highly useful to understand plant behavior.     

A comprehensive approach of planning and scheduling based on petri nets

The main results available on the use of black-and-white Petri nets for modelling, planning and scheduling manufacturing systems are presented. In the first part of the paper, the basics of Petri nets necessary to understand the subsequent presentation are introduced. Particular attention is paid to event graphs, a particular type of Petri nets used for modelling and evaluating ratio-driven systems. The second part of the paper is devoted to ratio-driven systems, their modelling and their scheduling. Job-shops, assembly systems, and KANBAN systems are used to illustrate this section. Finally, the general case is investigated of manufacturing systems subject to changing demands. An approach based on conflict-free Petri nets with input and output transitions is proposed for planning and scheduling this type of system.     

Stochastic cyclic flow lines: non-blocking,Markovian models

In this paper we consider stochastic cyclic flow lines where identical sets of jobs are repeatedly produced in the same loading and processing sequence. Each machine has an input buffer with enough capacity. Processing times are stochastic. We model the shop as a stochastic event graph, a class of Petri nets. We characterise the ergodicity condition and the cycle time. For the case where processing times are exponentially distributed, we present a way of computing queue length distributions. For two-machine cases, by the matrix geometric method, we compute the exact queue length distributions. For general cases, we present two methods for approximately decomposing the line model into two-machine submodels, one based on starvation propagation and the other based on transition enabling probability propagation. We experiment our approximate methods for various stochastic cyclic flow lines and discuss performance characteristics as well as accuracy of the approximate methods. Finally, we discuss the effects of job processing sequences of stochastic cyclic flow lines.     

Mathematical programming approach to the Petri nets reachability problem

This paper focuses on the resolution of the reachability problem in Petri nets, using the mathematical programming paradigm. The proposed approach is based on an implicit traversal of the Petri net reachability graph. This is done by constructing a unique sequence of Steps that represents exactly the total behaviour of the net. We propose several formulations based on integer and/or binary linear programming, and the corresponding sets of adjustments to the particular class of problem considered. Our models are validated on a set of benchmarks and compared with standard approaches from IA and Petri nets community.     

Analysis of strong and strong periodic detectability of bounded labeled Petri nets

Detectability describes the property of a system to uniquely determine, after a finite number of observations, the current and the subsequent states. Different notions of detectability have been proposed in the literature. In this paper, we formalize and analyze strong detectability and strong periodic detectability for systems that are modeled as labeled Petri nets with partial observation on their transitions. We provide three new approaches for the verification of such detectability properties using three different structures. The computational complexity of the proposed approaches is analyzed and the three methods are compared. The main feature of all the three approaches is that they do not require the calculation of the entire reachability space or the construction of an observer. As a result, they have lower computational complexity than other methods in the literature.