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Reduction of Petri net maintenance modeling complexity via Approximate Bayesian Computation

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  • Chiachío, Manuel
  • Saleh, Ali
  • Naybour, Susannah
  • Chiachío, Juan
  • Andrews, John

Abstract

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.

Suggested Citation

  • Chiachío, Manuel & Saleh, Ali & Naybour, Susannah & Chiachío, Juan & Andrews, John, 2022. "Reduction of Petri net maintenance modeling complexity via Approximate Bayesian Computation," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    • Handle: RePEc:eee:reensy:v:222:y:2022:i:c:s0951832022000436
    DOI: 10.1016/j.ress.2022.108365
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    1. Lee, Juseong & Mitici, Mihaela, 2020. "An integrated assessment of safety and efficiency of aircraft maintenance strategies using agent-based modelling and stochastic Petri nets," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    2. Bian, Chong & Yang, Shunkun & Huang, Tingting & Xu, Qingyang & Liu, Jie & Zio, Enrico, 2019. "Degradation state mining and identification for railway point machines," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 432-443.
    3. Zhang, Haoyuan & Marsh, D. William R, 2021. "Managing infrastructure asset: Bayesian networks for inspection and maintenance decisions reasoning and planning," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
    4. Compare, M. & Martini, F. & Zio, E., 2015. "Genetic algorithms for condition-based maintenance optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 244(2), pages 611-623.
    5. Zio, E., 2009. "Reliability engineering: Old problems and new challenges," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 125-141.
    6. Latsou, Christina & Dunnett, Sarah J. & Jackson, Lisa M., 2019. "A new methodology for automated Petri Net generation: Method application," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 113-123.
    7. Chen, Yiming & Liu, Yu & Jiang, Tao, 2021. "Optimal maintenance strategy for multi-state systems with single maintenance capacity and arbitrarily distributed maintenance time," Reliability Engineering and System Safety, Elsevier, vol. 211(C).
    8. Taleb-Berrouane, Mohammed & Khan, Faisal & Amyotte, Paul, 2020. "Bayesian Stochastic Petri Nets (BSPN) - A new modelling tool for dynamic safety and reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    9. Paul Fearnhead & Dennis Prangle, 2012. "Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(3), pages 419-474, June.
    10. Andrews, John & Fecarotti, Claudia, 2017. "System design and maintenance modelling for safety in extended life operation," Reliability Engineering and System Safety, Elsevier, vol. 163(C), pages 95-108.
    11. Sheng, Jingyu & Prescott, Darren, 2019. "Using a novel hierarchical coloured Petri net to model and optimise fleet spare inventory, cannibalisation and preventive maintenance," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    12. Li, Xiao-Yang & Liu, Yue & Lin, Yan-Hui & Xiao, Liang-Hua & Zio, Enrico & Kang, Rui, 2021. "A generalized petri net-based modeling framework for service reliability evaluation and management of cloud data centers," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
    13. Yianni, Panayioti C. & Neves, Luis C. & Rama, Dovile & Andrews, John D., 2018. "Accelerating Petri-Net simulations using NVIDIA Graphics Processing Units," European Journal of Operational Research, Elsevier, vol. 265(1), pages 361-371.
    14. Izquierdo, J. & Crespo Márquez, A. & Uribetxebarria, J., 2019. "Dynamic artificial neural network-based reliability considering operational context of assets," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 483-493.
    15. Chahrour, Nour & Nasr, Mohamad & Tacnet, Jean-Marc & Bérenguer, Christophe, 2021. "Deterioration modeling and maintenance assessment using physics-informed stochastic Petri nets: Application to torrent protection structures," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
    16. Mark A. Beaumont & Jean-Marie Cornuet & Jean-Michel Marin & Christian P. Robert, 2009. "Adaptive approximate Bayesian computation," Biometrika, Biometrika Trust, vol. 96(4), pages 983-990.
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    Cited by:

    1. Saleh, Ali & Chiachío, Manuel & Salas, Juan Fernández & Kolios, Athanasios, 2023. "Self-adaptive optimized maintenance of offshore wind turbines by intelligent Petri nets," Reliability Engineering and System Safety, Elsevier, vol. 231(C).
    2. Andrews, John & Tolo, Silvia, 2023. "Dynamic and dependent tree theory (D2T2): A framework for the analysis of fault trees with dependent basic events," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    3. Saleh, Ali & Remenyte-Prescott, Rasa & Prescott, Darren & Chiachío, Manuel, 2024. "Intelligent and adaptive asset management model for railway sections using the iPN method," Reliability Engineering and System Safety, Elsevier, vol. 241(C).

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