A novel reliability analysis method for a dependent system by copula model: a case study in operation tunnels maintenance

Liu Wenli, Li Ang, Chen Elton J., Luo Hanbin, Wang Yanyu

Abstract

To effectively minimize structural risk and forestall the system failure, a structural performance evaluation approach based on the copula model is proposed. This approach could provide resilient predictions and diagnose safety performance under complex structural systems with multiple interdependent uncertainties. Specifically, the proposed copula model establishes the joint distribution of multiple parameters through their actual marginal distributions and coefficient. The reliability analysis is a typical method for calculating structural performance based on various identified failure modes. However, the traditional reliability analysis possesses three significant deficiencies, namely, (1) reliability analysis usually adopts the Gaussian-dependent (Nataf model) or independent assumption that ignores the dependent diversity relationships among different failure modes; (2) previous research lacked an integrated and universal framework for evaluating the potential uncertainties of different dependent structures for different copulas; (3) the algorithms in most of the previous copula models failed to provide an efficient estimation of copula parameters with high accuracy and less bias. For addressing those limitations, we establish a novel probabilistic reliability analysis framework based on copula theory and then verify the proposed approach by a subway tunnel project in Wuhan, China. The results indicate that the proposed approach could represent the complex interdependent relationships between monitored parameters through the best-fit copula model. The results of the proposed reliability analysis could guide the tunnel operators to design an efficient maintenance schema.

Keywords: Operation tunnel, Copula model, MCMC algorithms, Parameters estimation, Reliability analysis

https://link.springer.com/article/10.1007/s13349-022-00581-5