Calculating Failure Probabilities of Water Distribution Systems through Subset Simulation

Thomas Catanach, California Institute of Technology

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Subset simulation is an established technique in structural reliability for calculating the failure probability of a system model in situations where failure is unlikely and simulating the system is computationally intensive, making traditional Monte Carlo techniques impractical. Recently, this approach has been used to study the robustness of network systems, which we further develop in this work. We analyze a simplified water distribution network where we consider sources, pipes, and sinks arranged in a network with varying topology and size. We address uncertainties in the supply, capacity and demand of water in the system, replicating uncertainties caused by climatic fluctuations, infrastructure degradation, and population growth. Further, these uncertainties are allowed to be correlated, thus letting us to more accurately model the behavior of real systems. With this model and the subset simulation method, we explore the potential for system failure to see how robust a water system can be to these uncertainties and to help improve urban planning and infrastructure development. This work is not only important because it’s applicable to studying the robustness of infrastructure networks, but also because it demonstrates how the subset simulation algorithm can benefit from parallel computing. In order to ensure that the highly multidimensional parameter space is adequately explored to find all possible failure domains, we evolve several independent Markov chains. These chains can easily be distributed among multiple cores with little overhead, hence allowing the algorithm to reap the full benefits of parallelism.

Abstract Author(s): T.A. Catanach, J.L. Beck, S. Wu, K.M. Zuev