System for estimating water flows at the boundaries of a sub-network of a water distribution network

A method for estimating, for a water distribution network composed of nodes and arcs, one or more water flow rates at boundaries of a sub-network of the water distribution network, the water distribution network being modeled as a graph, and the sub-network being defined as a connected subgraph of the graph, the method comprising:

• defining parameters of a hydraulic model of the water distribution network with a set of values of control variables characterizing a prediction of an input of the water distribution network and an output of the water distribution network at the nodes over a set of time references;
• using sensors on a subset of the nodes and/or the arcs of the water distribution network to acquire observations of a subset of state variables of the water distribution network at the subset of the nodes and arcs at successive time references, the state variables characterizing a physical parameter and/or a physical value at the arcs and/or at the nodes at the successive time references, the sensors comprising at least one sensor of pressure, at least one sensor of flow rate, or at least one sensor of water level of water tanks, the sub-network being any sub-network of the water distribution network, wherein at least one arc at boundaries of the sub-network and at least one of the nodes at boundaries of the sub-network do not belong to the subset of the nodes and/or the arcs;
• calculating predicted values of the state variables of the network according to the hydraulic model;
• calculating a difference between the observations of a subset of state variables of the water distribution network and the predicted values of the state variables of the network;
• determining the set of values of control variables which minimize differences between the prediction and the observations of the subset of state variables by applying an optimization procedure, wherein the optimization procedure comprises a stepwise adjustment of the set of values of control variables;
• and
• calculating, using the hydraulic model parameterized with the determined set of values of control variables which minimize the differences between the prediction and the observations of the subset of state variables, the one or more water flow rates at boundaries of the sub-network, for a period of time.