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Analytical probability propagation method for reliability analysis of general complex networks

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  • 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
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    References listed on IDEAS

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    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    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.
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    Cited by:

    1. 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).
    2. 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).
    3. 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).
    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).

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