Optimal design of water distribution network considering the uncertainty and correlation of nodal demands

Abstract In the least-cost design of water distribution network (WDN), it is crucial to consider the uncertainties in nodal demands to improve the reliability and robustness of the design. Meanwhile, the nodal demands with similar consumption pattern may behaves 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 design 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 WDNs. In comparison with the result of 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 inter-group correlation among user nodes with similar pattern of water demands is lower than that corresponding to independent cases.