Sensitivity analysis of entropy-constrained designs of water distribution systems

A study of the relationship between the statistical entropy and hydraulic reliability of water distribution systems (WDS) was carried out by assessing the effects of layout, flow direction, and pipe costs. Because of an invariance property of the entropy function, different WDS layouts can have identical maximum entropy values. The properties of designs that have identical maximum entropy values were also compared. The results reinforce previous observations that entropy is a potential surrogate measure for hydraulic reliability and suggest that any influences due to the design factors mentioned above are negligible. Maximum entropy designs are shown to be more reliable than other designs, while designs with different layouts but equal maximum entropy values have very similar levels of reliability. The head-dependent analysis method was used and revealed the correlation between entropy and reliability more clearly than hitherto achieved using demand-driven analysis.