Skip to main content

Diagnosability verification using LTL model checking

Abstract

One of the challenges of fault diagnosis is to verify diagnosability of systems with huge state space efficiently. Model checking approaches have the potential to analyze such systems efficiently. In this work, we propose a model checking approach to deal with the problem of the diagnosability verification. We define the diagnosability property in the transition system framework. To check this property, we describe it by using an unique linear temporal logic (LTL) formula. Our approach can be carried out in model checker tools for formal verification of models, such as SPIN and NuSMV. To illustrate the efficiency of our approach we perform some experiments. First, we consider a railway level crossing benchmark, comparing the results of our approach in SPIN and NuSMV with the results found using DESLab and Supremica tools. Then, we perform an exploratory statistical analysis comparing the average size of verifiers computed with our approach in SPIN with the average size of verifiers (it number of states plus transitions) computed with DESLab, which is a tool for diagnosability verification of Discrete Event Systems (DES) that uses the same foundation idea.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Notes

  1. In this paper we always consider that x0Xcoac

  2. http://projects.laas.fr/tina/home.php

References

  • Alves LVR, Martins LRR, Pena PN (July 2017) UltraDES – a library for modeling, analysis and control of discrete event systems. In: Proceedings of the 20th World Congress of the International Federation of Automatic Control, Toulose, France, pp 5996–2001

  • Athanasopoulou E, Li L, Hadjicostis CN (July 2006) Probabilistic failure diagnosis in finite state machines under unreliable observations. In: 2006 8th international workshop on discrete event systems. IEEE, Ann Arbor, MI, USA, pp 301–306

  • Baier C, Katoen J-P (2008) Principles of model checking. MIT Press, Cambridge

    MATH  Google Scholar 

  • Basile F, De Tommasi G, Sterle C, Boussif A, Ghazel M (2018) Efficient diagnosability assessment via ilp optimization: a railway benchmark. In: 2018 IEEE 23rd international conference on emerging technologies and factory automation (ETFA), vol 1, pp 441–448

  • Basilio JC, Lafortune S (2009) Robust codiagnosability of discrete event systems. In: Proc. American control conference, St. Louis, MO, USA, pp 2202–2209

  • Basilio JC, Lima STS, Lafortune S, Moreira MV (2012) Computation of minimal event bases that ensure diagnosability. Discret Event Dyn Syst 22(3):249–292

    MathSciNet  Article  Google Scholar 

  • Bassino F, David J, Nicaud C (2009) Enumeration and random generation of possibly incomplete deterministic automata. Pure Math Appl 19:1–16

    MathSciNet  MATH  Google Scholar 

  • Bassino F, Nicaud C (2007) Enumeration and random generation of accessible automata. Theor Comput Sci 381:86–104

    MathSciNet  Article  Google Scholar 

  • Bermeo LE, Basilio JC, Carvalho LK (2012) DESLAB: a scientific computing program for analysis and synthesis of discrete-event systems. In: Preprints of the 11th international workshop on discrete event systems, Guadalajara, Mexico, pp 349–355

  • Berthomieu B, Ribet P-O, Vernadat F (2004) The tool TINA – construction of abstract state spaces for Petri nets and time Petri nets. Int J Prod Res 42(14)

  • Boussif A, Ghazel M (2015) Diagnosability analysis of input/output discrete-event systems using model-checking. IFAC-PapersOnLine 48(7):71–78. 5th IFAC International Workshop on Dependable Control of Discrete Systems

    Article  Google Scholar 

  • Boussif A, Ghazel M (2016) Using model-checking techniques for diagnosability analysis of intermittent faults-a railway case-study.. In: VECOS 2016-10th international workshop on verification and evaluation of computer and communication systems, Tunis, Tunisia, p 11p

  • Boussif A, Ghazel M (2018) Formal verification of intermittent fault diagnosability of discrete-event systems using model-checking. Int J Crit Comput-Based Syst 8(2):193–213

    Article  Google Scholar 

  • Cabasino MP, Giua A, Seatzu C (2010) Fault detection for discrete event systems using Petri Nets with unobservable transitions. Automatica 46 (9):1531–1539

    MathSciNet  Article  Google Scholar 

  • Carvalho LK, Basilio JOC, Moreira MV (2012) Robust diagnosis of discrete event systems against intermittent loss of observations. Automatica 48 (9):2068–2078

    MathSciNet  Article  Google Scholar 

  • Cassandras CG, Lafortune S (2008) Introduction to discrete event systems, 2nd edn. Springer, Massachussets

    Book  Google Scholar 

  • Cassez F (2012) The complexity of codiagnosability for discrete event and timed systems. IEEE Trans Autom Control 57(7):1752–1764

    MathSciNet  Article  Google Scholar 

  • Cimatti A, Clarke EM, Giunchiglia E, F Giunchiglia MP, M Roveri RS, Tacchella A (2002) NuSMV 2: An opensource tool for symbolic model checking. In: Proceeding of international conference on computer-aided verification

  • Cimatti A, Pecheur C, Cavada R (2003) Formal verification of diagnosability via symbolic model checking. In: Workshop on model checking and artificial intelligence (MoChArt-2002), Lyon, France, pp 363–369

  • Clarke EM, Henzinger TA, Veith H, Bloem R (2018) Handbook of model checking, 1st edn. Springer International Publishing, New York

    Book  Google Scholar 

  • Clavijo LB, Basilio JC (2017) Empirical studies in the size of diagnosers and verifiers for diagnosability. Discret Event Dyn Syst 27:701–739

    MathSciNet  Article  Google Scholar 

  • Debouk R, Lafortune S, Teneketzis D (2000) Coordinated decentralized protocols for failure diagnosis of discrete event systems. Discret Event Dyn Syst 20(1-2):33–86

    MathSciNet  Article  Google Scholar 

  • Genc S, Lafortune S (2006) Predictability in discrete-event systems underpartial observation. In: Proc. 6th IFAC safeprocess symposium

  • Genc S, Lafortune S (2003) Distributed diagnosis of discrete-event systems using Petri nets. In: Applications and theory of Petri nets. Springer, Berlin, Heidelberg, pp 316–336

  • Ghazel M, Liu B (2016) A customizable railway benchmark to deal with fault diagnosis issues in DES. In: Proc. of the 13th international workshop on discrete event systems (WODES’16), Xi’an, China, pp 177–182

  • Gougam H-E, Pencolé Y, Subias A (2017) Diagnosability analysis of patterns on bounded labeled prioritized Petri nets. Discret Event Dyn Syst 27:143–180

    MathSciNet  Article  Google Scholar 

  • Grastien A (2009) Symbolic testing of diagnosability. In: 20th international workshop on principles of diagnosis (DX-09), Stockholm, Sweden, pp 131–138

  • Grastien A, Anbulagan A (2013) Diagnosis of discrete event systems using satisfiability algorithms: A theoretical and empirical study. IEEE Trans Autom Control 58(12):3070–3083

    MathSciNet  Article  Google Scholar 

  • Hermann M, Pentek T, Otto B (2016) Design principles for industrie 4.0 scenarios. In: 2016 49th Hawaii international conference on system sciences (HICSS), pp 3928–3937

  • Holzmann GJ (1997) The model checker spin. IEEE Trans Softw Eng 23(5)

  • Holzmann GJ (2004) The spin model checker: Primer and reference manual. Addison-Wesley

  • Jiang S, Huang Z, Chandra V, Kumar R (2001) A polynomial algorithm for testing diagnosability of discrete-event systems. IEEE Trans Autom Control 46(8):1318–1321

    MathSciNet  Article  Google Scholar 

  • Jiang S, Kumar R (2004) Failure diagnosis of discrete-event systems with linear-time temporal logic specifications. IEEE Trans Autom Control 49 (6):934–945

    MathSciNet  Article  Google Scholar 

  • Jiang S, Kumar R (2006) Diagnosis of repeated failures for discrete event systems with linear-time temporal-logic specifications. IEEE Trans Autom Control 3(1):47–58

    Google Scholar 

  • Kumar R, Takai S (2010) Decentralized prognosis of failures in discrete event systems. IEEE Trans Autom Control 55(1):48–59

    MathSciNet  Article  Google Scholar 

  • Lin F (1994) Diagnosability of discrete event systems and its applications. J Discret Event Dyn Syst 4(197-212)

  • Malik R, Åkesson K, Flordal H, Fabian M (2017) Supremica – an efficient tool for large-scale discrete event systems. IFAC-PapersOnLine 50 (1):5794–5799

    Article  Google Scholar 

  • Marangé P, Philippot A, Pétin JF, Gellot F (2015) Diagnosability evaluation by model-checking. IFAC-PapersOnLine 48(21):308–313

    Article  Google Scholar 

  • McGrath N (2018) Verification of the diagnosability of discrete-event systems in waters. Tech. Rep. 04, Department of Computer Science The University of Waikato

  • Moreira MV, Jesus TC, Basilio JC (2011) Polynomial time verification of decentralized diagnosability of discrete event system. IEEE Trans Autom Control 56(7):1679–1684

    MathSciNet  Article  Google Scholar 

  • Pencolé Y, Subias A (2021) Diagnosability of event patterns in safe labeled time Petri Nets: A model-checking approach. IEEE Trans Autom Sci Eng :1–12

  • Ramadge PJG, Wonham WM (1989) The control of discrete event systems. Proc IEEE 77(1):81–98

    Article  Google Scholar 

  • Ramirez-Trevino A, Ruiz-Beltran E, Rivera-Rangel I, Lopez-Mellado E (2007) Online fault diagnosis of discrete event systems. a Petri Net-based approach. IEEE Trans Autom Sci Eng 4(1):31–39

    Article  Google Scholar 

  • Reis R, Moreira N, Almeida M (2005) On the representation of finite automata. In: Proceedings of the 7th international workshop on descriptional complexity of formal systems, pp 269–276

  • Ricker L, Lafortune S, Genc S (2006) DESUMA: A tool integrating GIDDES and UMDES. In: 2006 8th international workshop on discrete event systems, pp 392–393

  • Rudie K (2006) The integrated discrete-event systems tool. In: 2006 8th international workshop on discrete event systems, Michigan, US, pp 394–395

  • Sampath M, Sengupta R, Lafortune S, Sinnamohideen K, Teneketzis D (1995) Diagnosability of discrete-event systems. IEEE Trans Autom Control 40(9):1555–1575

    MathSciNet  Article  Google Scholar 

  • Sampath M, Lafortune S, Teneketzis D (1998) Active diagnosis of discrete-event systems. IEEE Trans Autom Control 43(7):908–929

    MathSciNet  Article  Google Scholar 

  • Sampath M, Sengupta R, Lafortune S, Sinnamohideen K, Teneketzis DC (March 1996) Failure diagnosis using discrete-event models. IEEE Trans Control Syst Technol 4(2):105–124

  • Su R, Wonham WM (2005) Global and local consistencies in distributed fault diagnosis for discrete-event systems. IEEE Trans Autom Control 50 (12):1923–1935

    MathSciNet  Article  Google Scholar 

  • Thorsley D, Yoo T-S, Garcia H E (2008) Diagnosability of stochastic discrete-event systems under unreliable observations. In: 2008 American control conference. IEEE, Seattle, WA, USA, pp 1158–1165

  • Tuxi T (2020) Experiment files. https://gthub.com/TuxiThiago/SPIN_FDIAGNOSIS

  • Tuxi TM, Carvalho LK, Nunes EVL, da Cunha AEC (November 2020) Is LTL model-checking effective for diagnosability verification?. In: Proc. of the 15th international workshop on discrete event systems (WODES’20), Rio de Janeiro, Brazil, pp 256–262

  • Vardi MY, Wolper P (1986) An automata-theoretic approach to automatic program verification. In: Proceedings of the first symposium on logic in computer science, IEEE Computer Society, pp 322–331

  • Yoo T-S, Lafortune S (2002) Polynomial-time verification of diagnosability of partially observed discrete-event systems. IEEE Trans Autom Control 47 (9):1491–1495

    MathSciNet  Article  Google Scholar 

  • Zaytoon J, Lafortune S (2013) Overview of fault diagnosis methods for discrete event systems. Annu Rev Control 37(2):308–320

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Thiago M. Tuxi.

Ethics declarations

Conflict of Interests

The authors declare that they have no conflict of interest.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This article belongs to the Topical Collection: Topical Collection on Control 2022 Guest Editors: Joerg Raisch, Carla Seatzu and Shigemasa Takai

This work is financed in part by CNPq, CAPES Finance Code 001, FAPERJ and the Brazilian Army Force.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Tuxi, T.M., Carvalho, L.K., Nunes, E.V.L. et al. Diagnosability verification using LTL model checking. Discrete Event Dyn Syst (2022). https://doi.org/10.1007/s10626-022-00360-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10626-022-00360-w

Keywords

  • Diagnosability
  • Model-checking
  • Linear temporal logic
  • Statistical analysis
  • Tools