IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v189y2019icp21-30.html
   My bibliography  Save this article

Analytical probability propagation method for reliability analysis of general complex networks

Author

Listed:
  • Tong, Yanjie
  • Tien, Iris

Abstract

Reliability analysis of complex networks is often limited by large and exponentially increasing computational requirements with system size. In this paper, a new approximated analytical method the authors call the probability propagation method (PrPm) is proposed to calculate the reliability of general complex networks. The proposed method originates from the idea of belief propagation for inference in network graphs to pass a joint probability distribution between nodes in the network. At each step, the distribution is updated and passed as the message to its direct neighbors. After the message passes to the terminal node, an approximation of the network reliability is found. In this paper, the derived updating rules for message passing are provided, as well as a precise formulation of the error compared to the exact solution. The method is applied to three test applications: an example from a previous study on network reliability, a power distribution network, and a general grid network. Results from these applications show high accuracy for the proposed method compared to exact solutions where possible for comparison. In addition, the authors show orders of magnitude increases in computational efficiency of PrPm compared to existing approaches. This includes reducing the computational cost for analyses from an exponential increase in computation time with the size of the system to a quartic increase. The proposed PrPm enables accurate and computationally tractable reliability assessments of larger, complex networks.

Suggested Citation

  • Tong, Yanjie & Tien, Iris, 2019. "Analytical probability propagation method for reliability analysis of general complex networks," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 21-30.
    • Handle: RePEc:eee:reensy:v:189:y:2019:i:c:p:21-30
    DOI: 10.1016/j.ress.2019.04.013
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832017309109
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2019.04.013?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Iris Tien, 2017. "Bayesian Network Methods for Modeling and Reliability Assessment of Infrastructure Systems," Springer Series in Reliability Engineering, in: Paolo Gardoni (ed.), Risk and Reliability Analysis: Theory and Applications, pages 417-452, Springer.
    2. Shields, Michael D. & Teferra, Kirubel & Hapij, Adam & Daddazio, Raymond P., 2015. "Refined Stratified Sampling for efficient Monte Carlo based uncertainty quantification," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 310-325.
    3. Tien, Iris & Der Kiureghian, Armen, 2016. "Algorithms for Bayesian network modeling and reliability assessment of infrastructure systems," Reliability Engineering and System Safety, Elsevier, vol. 156(C), pages 134-147.
    4. Cheng, Lei & Lu, Zhenzhou & Zhang, Leigang, 2015. "Application of Rejection Sampling based methodology to variance based parametric sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 9-18.
    5. Der Kiureghian, Armen & Song, Junho, 2008. "Multi-scale reliability analysis and updating of complex systems by use of linear programming," Reliability Engineering and System Safety, Elsevier, vol. 93(2), pages 288-297.
    6. Cheng, Wen-Ju & Cox, Jim & Whitlock, Paula, 2017. "Random walks on graphs and Monte Carlo methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 135(C), pages 86-94.
    7. Kim, Youngsuk & Kang, Won-Hee, 2013. "Network reliability analysis of complex systems using a non-simulation-based method," Reliability Engineering and System Safety, Elsevier, vol. 110(C), pages 80-88.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wu, Yipeng & Chen, Zhilong & Zhao, Xudong & Liu, Ying & Zhang, Ping & Liu, Yajiao, 2021. "Robust analysis of cascading failures in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).
    2. Mohajer, Amin & Bavaghar, Maryam & Farrokhi, Hamid, 2020. "Mobility-aware load Balancing for Reliable Self-Organization Networks: Multi-agent Deep Reinforcement Learning," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    3. Wang, Rongxi & Li, Yufan & Xu, Jinjin & Wang, Zhen & Gao, Jianmin, 2022. "F2G: A hybrid fault-function graphical model for reliability analysis of complex equipment with coupled faults," Reliability Engineering and System Safety, Elsevier, vol. 226(C).
    4. Ling, Chunyan & Lu, Zhenzhou & Zhang, Xiaobo, 2020. "An efficient method based on AK-MCS for estimating failure probability function," Reliability Engineering and System Safety, Elsevier, vol. 201(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zheng, Xiaohu & Yao, Wen & Xu, Yingchun & Chen, Xiaoqian, 2020. "Algorithms for Bayesian network modeling and reliability inference of complex multistate systems: Part I – Independent systems," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    2. Medeiros, C.P. & Alencar, M.H. & de Almeida, A.T., 2017. "Multidimensional risk evaluation of natural gas pipelines based on a multicriteria decision model using visualization tools and statistical tests for global sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 268-276.
    3. Chiron, Marie & Genest, Christian & Morio, Jérôme & Dubreuil, Sylvain, 2023. "Failure probability estimation through high-dimensional elliptical distribution modeling with multiple importance sampling," Reliability Engineering and System Safety, Elsevier, vol. 235(C).
    4. Rodríguez, Joanna & Lillo, Rosa E. & Ramírez-Cobo, Pepa, 2015. "Failure modeling of an electrical N-component framework by the non-stationary Markovian arrival process," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 126-133.
    5. Bistouni, Fathollah & Jahanshahi, Mohsen, 2015. "Evaluating failure rate of fault-tolerant multistage interconnection networks using Weibull life distribution," Reliability Engineering and System Safety, Elsevier, vol. 144(C), pages 128-146.
    6. Dharmaraja, S. & Vinayak, Resham & Trivedi, Kishor S., 2016. "Reliability and survivability of vehicular ad hoc networks: An analytical approach," Reliability Engineering and System Safety, Elsevier, vol. 153(C), pages 28-38.
    7. Di Maio, Francesco & Pettorossi, Chiara & Zio, Enrico, 2023. "Entropy-driven Monte Carlo simulation method for approximating the survival signature of complex infrastructures," Reliability Engineering and System Safety, Elsevier, vol. 231(C).
    8. Mrinal Kanti Sen & Subhrajit Dutta & Golam Kabir, 2021. "Flood Resilience of Housing Infrastructure Modeling and Quantification Using a Bayesian Belief Network," Sustainability, MDPI, vol. 13(3), pages 1-24, January.
    9. Bibartiu, Otto & Dürr, Frank & Rothermel, Kurt & Ottenwälder, Beate & Grau, Andreas, 2021. "Scalable k-out-of-n models for dependability analysis with Bayesian networks," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
    10. Costa, Rodrigo & Haukaas, Terje & Chang, Stephanie E. & Dowlatabadi, Hadi, 2019. "Object-oriented model of the seismic vulnerability of the fuel distribution network in coastal British Columbia," Reliability Engineering and System Safety, Elsevier, vol. 186(C), pages 11-23.
    11. Kawahara, Jun & Sonoda, Koki & Inoue, Takeru & Kasahara, Shoji, 2019. "Efficient construction of binary decision diagrams for network reliability with imperfect vertices," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 142-154.
    12. Bensi, Michelle & Kiureghian, Armen Der & Straub, Daniel, 2013. "Efficient Bayesian network modeling of systems," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 200-213.
    13. Thalles Vitelli Garcez & Helder Tenório Cavalcanti & Adiel Teixeira de Almeida, 2021. "A hybrid decision support model using Grey Relational Analysis and the Additive-Veto Model for solving multicriteria decision-making problems: an approach to supplier selection," Annals of Operations Research, Springer, vol. 304(1), pages 199-231, September.
    14. Cai, Wei & Zhao, Jingyi & Zhu, Ming, 2020. "A real time methodology of cluster-system theory-based reliability estimation using k-means clustering," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    15. Kim, Dong-Seok & Ok, Seung-Yong & Song, Junho & Koh, Hyun-Moo, 2013. "System reliability analysis using dominant failure modes identified by selective searching technique," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 316-331.
    16. Bistouni, Fathollah & Jahanshahi, Mohsen, 2014. "Analyzing the reliability of shuffle-exchange networks using reliability block diagrams," Reliability Engineering and System Safety, Elsevier, vol. 132(C), pages 97-106.
    17. Casado, Ramon Swell Gomes Rodrigues & Alencar, Marcelo Hazin & de Almeida, Adiel Teixeira, 2022. "Combining a multidimensional risk evaluation with an implicit enumeration algorithm to tackle the portfolio selection problem of a natural gas pipeline," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    18. Li, Jian & Dueñas-Osorio, Leonardo & Chen, Changkun & Shi, Congling, 2016. "Connectivity reliability and topological controllability of infrastructure networks: A comparative assessment," Reliability Engineering and System Safety, Elsevier, vol. 156(C), pages 24-33.
    19. Shields, Michael D. & Zhang, Jiaxin, 2016. "The generalization of Latin hypercube sampling," Reliability Engineering and System Safety, Elsevier, vol. 148(C), pages 96-108.
    20. Shields, Michael D., 2018. "Adaptive Monte Carlo analysis for strongly nonlinear stochastic systems," Reliability Engineering and System Safety, Elsevier, vol. 175(C), pages 207-224.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:reensy:v:189:y:2019:i:c:p:21-30. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.