Entropy-based Serviceability Assessment of Water Distribution Networks, Subjected to Natural and Man-Made Hazards

In this study a modified entropy-based measure is presented for evaluating the serviceability level of water distribution networks in which the hydraulic uncertainties (flow rates in pipes) as well as the uncertainties due to mechanical parameters (failure probabilities of links) are considered simultaneously. In the proposed entropy calculation method, the connectivity order of the network demand nodes is incorporated in the entropy calculations by defining a factor based on the ratio of the nodal demand to the total flow rates of all links of the network. The failure probability of the network links has been incorporated by using a penalty function based on their failure probability in any specified hazard scenario. Then, this penalty function is inserted satisfactorily in the existing hydraulic entropy function (defined by previous researchers) of the network. In this way, the effect of mechanical behavior of links is also taken into account in the hydraulic entropy function of the network, while keeping its simplicity and applicability. By calculating the entropy values of some sample networks, it has been shown that the proposed entropy-based index is an efficient tool to find the optimum hydraulic layout for designing a new system, or to make decision on the best mitigation plan for an existing network subjected to different natural and man-made hazards.