Modeling risks in dependent systems: A Copula-Bayesian approach

Yue Pan, Shenwei Ou, Limao Zhang, Wenjing Zhang, Xianguo Wu, Heng Li

Research output: Journal article publicationJournal articleAcademic researchpeer-review

78 Citations (Scopus)


This paper develops a hybrid Copula–Bayesian-based approach to model the structural health of an operational metro tunnel in a dependent system, where risk factors interact with each other. Aiming to rectify drawbacks of discrete Bayesian networks, the Gaussian copula and different marginal distributions are involved to build up complicated interactions among possible risk factors and structural health state more precisely and rationally. To achieve systematic and real-time decision support for safety insurance during the entire life cycle of risk-prone systems, model analytics is conducted to perform correlation analysis, forward reasoning, and backward reasoning. For demonstrating the effectiveness of the method, it is applied to a realistic cross-river tunnel, the Wuhan Yangtze Metro Tunnel in China, where all the concerning risk factors are water-related rooting in water leakage, poor construction quality, exterior load, and others. Due to the availability of vault displacement by sensors, it can herein represent the structural health to explore the impacts of risk factors. Larger vault displacement implies higher risk in the overall safety condition of the tunnel structure. This research contributes to (a) the state of knowledge by integrating Bayesian networks with copula, contributing to a more robust risk assessment by accurately modeling the complex dependence structure of risk factors; (b) the state of practice by providing guidelines of the whole-life-cycle safety control for complex systems under uncertainty and randomness, which not only prevent structural failure in advance but also control risk after accident occurrence.

Original languageEnglish
Pages (from-to)416-431
Number of pages16
JournalReliability Engineering and System Safety
Publication statusPublished - Aug 2019


  • Bayesian networks
  • Copula theory
  • Dependent systems
  • Operational tunnels
  • Risk assessment

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Industrial and Manufacturing Engineering


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