Resumen
We have constructed a stochastic model of a water supply network with leaks, which, compared to the previously proposed models (excluding leaks), more adequately describes the processes of transportation and water distribution in water supply systems. Mathematical modeling of water supply networks is associated with difficulties related to the huge dimensionality of actual water supply networks, limited information resources and operational data, which does not make it possible to assess parameters of the technological equipment and structure of a water supply network adequately enough. Therefore, an equivalent scheme is built for an actual water supply network based on its dictation points, which is then used for subsequent calculations. The task on building a scheme for an equivalent water supply network consists of three problems: identification of the structure, parameters, and state of a water supply network. The proposed method for leaks detection is based on the comparison of change in the magnitude of head at pumping stations and at the dictation points of a water supply network. Based on the stochastic model of a water supply network with leaks, we have constructed a method for calculating the magnitude of leaks, which implies the following: by knowing the head of water at the nodes of an equivalent water supply network and the approximate diameters of leaks at nodes, new values of heads at nodes of the equivalent water supply network are calculated. Then we again compute the magnitude of a leak by knowing the new head at the node and the diameter of the leaks. Upon completion of several such iterations, a conclusion is drawn on that starting at a certain step the magnitude of leaks and the heads at the nodes of the equivalent water supply network stop changing. By knowing the magnitude of leaks and head at each node within the equivalent water supply network, we determine the actual diameter of fistulas at each node. The proposed method for calculating the magnitude of leaks does not require financial costs or the use of additional equipment; it could be used by water utilities to detect and calculate the magnitude of leaks