Neural networks for hydraulic analysis of water distribution systems

A new approach to solving hydraulic networks using recurrent neural network concepts is proposed. The network equilibrium flow problem is first formulated in this new approach as an optimisation problem which minimises a modified content function subject to constraints on flow continuity at each node. This constrained optimisation is then transformed into an unconstrained optimisation using the Augmented Lagrange Multiplier method. The derivation of the cost function enables the minimisation problem to be transformed into a set of ordinary differential equations which can be implemented using artificial neural networks (ANNs), namely Gradient-type Hopfield neural networks. The performance of the neural network-based hydraulic solver is demonstrated by computer simulation of an example network.