Optimal Design of Water Distribution Network Considering the Uncertainty and Correlation of Nodal Demands

In the least-cost design of water distribution network (WDN), it is crucial to consider the uncertainty in nodal demands to improve the reliability and robustness of the design. Meanwhile, the nodal demands with similar consumption pattern may have notable correlations. This paper proposes a multi-objective optimal design model of WDN considering the uncertainty and correlation of nodal demands, which takes pipe diameter as the decision variable aiming to maximize the service reliability of WDN and minimize the design cost of pipes. To deal with the probabilistic problem in the optimization model, the reliability of WDN is expressed as the probability of all user nodes in the WDN simultaneously satisfying the minimum water pressure. The reliability is evaluated by the Monte Carlo method, where the independent uncertain samples of nodal demands are firstly generated by Latin hypercube sampling according to their probabilistic characteristics, then the correlated uncertain samples are transformed from the independent samples through the inverse-Orthogonal and inverse-Nataf transformation. The influence of uncertainty and correlation of nodal demands on the optimal design schemes is investigated by its application in two WDN cases. Compared with the independent uncertain cases, the correlation of uncertain nodal demands results in a greater increment of design cost by 8%~15%. In addition, the correlations of nodal demands do not always result in higher design costs. The cost corresponding to the partial intra-group correlation among user nodes with similar water demand pattern is less than that corresponding to independent cases.