Multi‐scale system reliability analysis of lifeline networks under earthquake hazards

Abstract

SUMMARYRecent earthquake events evidenced that damage of structural components in a lifeline network may cause prolonged disruption of lifeline services, which eventually results in significant socio-economic losses in the affected area. Despite recent advances in network reliability analysis, the complexity of the problem and various uncertainties still make it a challenging task to evaluate the post-hazard performance and connectivity of lifeline networks efficiently and accurately. In order to overcome such challenges and take advantage of merits of multi-scale analysis, this paper develops a multi-scale system reliability analysis method by integrating a network decomposition approach with the matrix-based system reliability (MSR) method. In addition to facilitating system reliability analysis of large-size networks, the multi-scale approach enables optimizing the level of computational effort on subsystems; identifying the relative importance of components and subsystems at multiple scales; and providing a collaborative risk management framework. The MSR method is uniformly applied for system reliability analyses at both the lower-scale (for link failure) and the higher-scale (for system connectivity) to obtain the probability of general system events, various conditional probabilities, component importance measures, statistical correlation between subsystem failures and parameter sensitivities. The proposed multi-scale analysis method is demonstrated by its application to a gas distribution network in Shelby County of Tennessee. A parametric study is performed to determine the number of segments during the lower-scale MSR analysis of each pipeline based on the strength of the spatial correlation of seismic intensity. It is shown that the spatial correlation should be considered at both scales for accurate reliability evaluation. The proposed multi-scale analysis approach provides an effective framework of risk assessment and decision support for lifeline networks under earthquake hazards

Bayesian network modeling of correlated random variables drawn from a Gaussian random field

“…The constraint functions are based on (4). The use of nonlinear constrained optimization to determine the terms of an approximate transformation matrix was earlier suggested by Song and Ok [18] and Song and Kang [17]. Hereafter, construction of the approximate transformation matrix by use of the optimization scheme in (13) is referred to as the nodebased optimization approach (NOA).…”

“…Alternatively, the transformation matrix may be determined approximately via numerical optimization [17,18], as described later in this paper. The BN corresponding to the above transformation is shown in Figure 3, where the latent -nodes are introduced as parents of the -nodes.…”

“…We note that the addition of thenodes does not significantly increase the computational complexity of the BN. As suggested by Song and Kang [17] and Song and Ok [18], the transformation in (3) may be regarded as a generalization of the Dunnett-Sobel (DS) class of Gaussian random variables [19]. This class of random variables is defined by * * , 1 … (6) where and are independent standard normal random variables and and are variable-specific coefficients satisfying the conditions 1 / and 1 1.…”

Bayesian Network Methods for Modeling and Reliability Assessment of Infrastructure Systems

“…The resulting analyses of these two expanded systems demonstrates how the proposed algorithms perform compared to existing algorithms for systems of increasing size. We note that, as pointed out by Der Kiureghian and Song (2008), Song and Ok (2010) and Bensi et al (2013), the above systems can be more efficiently represented as a system of three supercomponents, each supercomponent representing a series or parallel subsystem. However, here we disregard this advantage in order to investigate the system size effect.…”

Methodologies for Simplified Lifeline System Risk Assessments

“…This is of special concern for systems like rail that cross large faults that could require continual re-straightening of tracks for years after an earthquake. (Kameda, 2000;Song, 2009). Soil and structure interaction has had a drastic effect on performance.…”