Identification of Stochastic Timed Discrete Event Systems with st-IPN

This paper presents a method for the identification of stochastic timed discrete event systems, based on the analysis of the behavior of the input and output signals, arranged in a timeline. To achieve this goal stochastic timed interpreted Petri nets are defined. These nets link timed discrete event systems modelling with stochastic time modelling. The procedure starts with the observation of the input/output signals; these signals are converted into events, so that the sequence of events is the observed language. This language arrives to an identifier that builds a stochastic timed interpreted Petri net which generates the same language. The identified model is a deterministic generator of the observed language. The identification method also includes an algorithm that determines when the identification process is over.

[1]  Alessandro Giua,et al.  Fault detection for discrete event systems using Petri nets with unobservable transitions , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[2]  H.-M. Hanisch,et al.  Net condition/event systems with multiple condition outputs , 1995, Proceedings 1995 INRIA/IEEE Symposium on Emerging Technologies and Factory Automation. ETFA'95.

[3]  A. M. Mangini,et al.  On-line identification of Petri Nets with unobservable transitions , 2008, 2008 9th International Workshop on Discrete Event Systems.

[4]  Vicenç Puig,et al.  Diagnosis of timed automata: Theory and application to the DAMADICS actuator benchmark problem , 2006 .

[5]  Antonio Ramírez-Treviño,et al.  Geometrical characterization of observability in Interpreted Petri Nets , 2005, Kybernetika.

[6]  Antonio Ramírez-Treviño,et al.  Structural Diagnosability of DES and Design of Reduced Petri Net Diagnosers , 2012, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[7]  Rüdiger Valk,et al.  Petri nets for systems engineering - a guide to modeling, verification, and applications , 2010 .

[8]  J. Fleiss Statistical methods for rates and proportions , 1974 .

[9]  Edward H Livingston,et al.  Statistical power and estimation of the number of required subjects for a study based on the t-test: a surgeon's primer. , 2005, The Journal of surgical research.

[10]  P. Supavatanakula,et al.  Diagnosis of timed automata : Theory and application to the DAMADICS actuator benchmark problem , 2004 .

[11]  E. Lopez-Mellado,et al.  Required event sequences for identification of Discrete Event Systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[12]  Antonio Ramírez-Treviño,et al.  Online Fault Diagnosis of Discrete Event Systems. A Petri Net-Based Approach , 2007, IEEE Transactions on Automation Science and Engineering.

[13]  Chi Ma,et al.  Fault Detection of Non-Gaussian Processes Based on Model Migration , 2013, IEEE Transactions on Control Systems Technology.

[14]  Kunihiko Hiraishi,et al.  Analysis and control of discrete event systems represented by petri nets , 1988 .

[15]  Karen Hernández,et al.  Fault Diagnosis Using Petri Nets. A case study , 2012 .

[16]  B.H. Krogh,et al.  Petri Net based Models for Condition/Event Systems , 1991, 1991 American Control Conference.

[17]  Feng Lin,et al.  Detectability of Discrete Event Systems , 2007, IEEE Transactions on Automatic Control.

[18]  James E. Bartlett,et al.  Organizational research: Determining appropriate sample size in survey research , 2001 .

[19]  Kunihiko Hiraishi Construction of a Class of Safe Petri Nets by Presenting Firing Sequences , 1992, Application and Theory of Petri Nets.

[20]  Mariagrazia Dotoli,et al.  Real time identification of discrete event systems using Petri nets , 2008, Autom..

[21]  Olfa Mosbahi,et al.  Design of a Maximally Permissive Liveness- Enforcing Petri Net Supervisor for Flexible Manufacturing Systems , 2011, IEEE Transactions on Automation Science and Engineering.

[22]  Walter Ukovich,et al.  Fault Detection by Labeled Petri Nets in Centralized and Distributed Approaches , 2013, IEEE Transactions on Automation Science and Engineering.

[23]  Ernesto López-Mellado,et al.  A Comparative Analysis of Recent Identification Approaches for Discrete-Event Systems , 2010 .

[24]  C. Seatzu,et al.  Identification of deterministic Petri nets , 2006, 2006 8th International Workshop on Discrete Event Systems.

[25]  Valeriy Vyatkin,et al.  Formal verification of Intelligent Mechatronic Systems with decentralized control logic , 2012, Proceedings of 2012 IEEE 17th International Conference on Emerging Technologies & Factory Automation (ETFA 2012).

[26]  D. Ruppert Statistics and Data Analysis for Financial Engineering , 2010 .

[27]  Christos G. Cassandras,et al.  Introduction to Discrete Event Systems , 1999, The Kluwer International Series on Discrete Event Dynamic Systems.

[28]  Mariagrazia Dotoli,et al.  On Line Identification of Discrete Event Systems via Petri Nets: an Application to Monitor Specification , 2007, 2007 IEEE International Conference on Automation Science and Engineering.

[29]  Jean-Jacques Lesage,et al.  An FDI Method for Manufacturing Systems Based on an Identified Model , 2009 .

[30]  MengChu Zhou,et al.  Supervisor Optimization for Deadlock Resolution in Automated Manufacturing Systems With Petri Nets , 2011, IEEE Transactions on Automation Science and Engineering.

[31]  H. Toutenburg Fleiss, J. L.: Statistical Methods for Rates and Proportions. John Wiley & Sons, New York‐London‐Sydney‐Toronto 1973. XIII, 233 S. , 1974 .

[32]  MengChu Zhou,et al.  An Optimization Approach to Improved Petri Net Controller Design for Automated Manufacturing Systems , 2013, IEEE Transactions on Automation Science and Engineering.

[33]  Donald E. Jarvis An identification technique for timed event systems , 2010, WODES.

[34]  M. Emiliano Mathematical Problems in Engineering , 2014 .

[35]  W. Ukovich,et al.  Fault detection by labeled Petri nets and time constraints , 2011, 2011 3rd International Workshop on Dependable Control of Discrete Systems.

[36]  Christoforos N. Hadjicostis,et al.  Least-Cost Transition Firing Sequence Estimation in Labeled Petri Nets With Unobservable Transitions , 2011, IEEE Transactions on Automation Science and Engineering.

[37]  Jean-Jacques Lesage,et al.  FAULT DETECTION OF DISCRETE EVENT SYSTEMS USING AN IDENTIFICATION APPROACH , 2005 .

[38]  A. Winsor Sampling techniques. , 2000, Nursing times.

[39]  M. Dotoli,et al.  An Optimization Approach for Identification of Petri Nets , 2006, 2006 8th International Workshop on Discrete Event Systems.

[40]  Tadao Murata,et al.  Petri nets: Properties, analysis and applications , 1989, Proc. IEEE.

[41]  Francesco Basile,et al.  Identification of Petri nets using timing information , 2011, 2011 3rd International Workshop on Dependable Control of Discrete Systems.