Post-disaster damage detection for pipeline networks by Matrix-based System Reliability analysis

![CDATA[After a natural or man-made hazard occurs, it is essential to detect damaged components in lifeline networks to enable rapid recovery of the utility service in the impacted areas. However, inspections of individual network components such as buried pipes are often impractical due to exceedingly large costs and time. This paper aims to develop new system reliability methods for identifying network components with higher conditional probabilities of damage given post-disaster network flow monitoring data. First, the matrix-based system reliability (MSR) method (Song & Kang 2009, Lee et al. 2010) is further developed for quantifying the uncertainties in the flow quantities of a lifeline network with a large number of component damage scenarios. In order to overcome the computational challenge in using the MSR method for large system problems, this paper introduces a new procedure to construct the vectors of the system state probabilities efficiently by selectively searching elements that correspond to the system states with higher likelihoods. Using the convenient matrix-based framework, one can obtain the probability distributions and statistical parameters of network flow quantities efficiently. Second, a Bayesian method is proposed to compute the conditional probability that a component is damaged given post-disaster network flow monitoring data. This method achieves an optimal matrix-based representation of the problem for efficient damage detection. The developed methods are demonstrated by a water pipeline network consisting of 15 pipelines. The uncertainty in the outflow at a location is quantified using the MSR method with a selective expansion scheme. The conditional probabilities of damage in 15 pipelines given post-disaster network flow observations are obtained by the Bayesian method for damage detection purpose. The results of the methods are compared to those by Monte Carlo simulations and by the MSR method without selective expansion scheme in order to demonstrate the accuracy and efficiency of the proposed methods.]]