A Tsallis entropy-based redundancy measure for water distribution networks

• Tsallis entropy is employed for deriving a redundancy measure for water distribution networks.
• The Tsallis entropy-based redundancy measure is found to have a one-to-one relation with the Shannon entropy-based measure.
• Tsallis entropy-based measure can be employed for design of water distribution systems.
• The Tsallis entropy-based redundancy values show that the redundancy increases with increasing number of loops in the network.

A measure of redundancy inherent in the layouts of water distribution networks is developed using the Tsallis entropy. Both the local redundancy at a node and the global redundancy due to the redundancies at adjacent nodes are derived. The redundancy measure is applied to layouts reported in the literature and is compared with the Shannon entropy-based measure. Using the values reported in the literature, it is shown that there is almost a one-to-one relation between the Shannon entropy and the Tsallis entropy-based redundancy and reliability and this relation allows to specify the reliability of a network whose redundancy is known. Hence, the redundancy measure can also be employed in the water distribution network design.