Analysis of Hydraulic Stress Effects on the Performance of Water Distribution Networks Using Interval Analysis and Optimization Approach

Hydraulic analysis of pipe networks is generally done considering certain values for independent parameters of the system such as roughness of pipes, nodal demands, etc. Such analysis would inevitably lead to certain hydraulic responses of the system, i.e. nodal pressures, etc. This is while, inherent uncertainties associated with independent parameters as expected stresses, spread over the system and result in hydraulic stress in nodal pressure heads as dependent uncertainties. Using optimization tools, this study presents a reliable approach based on interval analysis to deal with these uncertain hydraulic stresses. In the proposed approach, the optimization problem is formulated in a manner that the nodal demands, roughness of pipes and water levels in elevated tanks would be the decision variables while extreme nodal pressures for unknown intervals are explored as the objectives functions. The large number of junctions in the case of real pipe networks, leads to inefficient iterative use of single objective optimization engine. In order to this problem, this study exploits a many-objective approach with an appropriate performance. Applying the proposed approach on a real pipe network shows that ±15% variation in nodal demands and pipes’ roughness in addition to ±1m in water levels might produce hydraulic stress in pressure heads from -13.7% to +10.2% with regard to the crisp values. In such a condition, it is possible for 125 junctions out of 128, to fail in satisfying the minimum required pressure head. It is demonstrated that the proposed approach has acceptable accuracy for analyzing hydraulic stress in real water distribution networks.