Comparison of four reliability surrogate measures for water distribution systems design

Water distribution system (WDS) design naturally involves a trade-off between the cost and reliability or robustness of a design. Traditionally, WDS reliability quantification schemes have employed graph theoretic techniques or probabilistic schemes such as Monte Carlo simulation. In recent decades there has been increased interest in the application of so-called reliability surrogate measures, such as flow entropy, the resilience index, and network resilience, because of their ease of use and dramatically reduced computational burden. In this paper, these surrogate measures (as well as a mixed reliability surrogate) are employed in the multiobjective evolutionary design of a set of WDS benchmarks from the literature. The resulting Pareto-optimal sets in cost-reliability space for each surrogate measure are analyzed in terms of their ability to handle demand uncertainty and pipe failure, and a regression analysis is conducted in order to determine whether the surrogate measures are correlated to stochastic reliability and failure reliability as expressed by demand satisfaction measures. It is found that the resilience index demonstrates the best performance under pure stochastic demand variation. However, it lags when compared to the network resilience and mixed reliability measures in terms of reliability under pipe failure conditions. These are recommended as the most practical reliability surrogate measures for use in general WDS design, since they also produce designs that minimize size discontinuities between adjacent pipes. Flow entropy performs relatively poorly in terms of correlation to both stochastic reliability and failure reliability.