In this paper a simple recurrent neural network (NN) is used as
a basis for constructing an integrated system capable of finding
the state estimates with corresponding confidence limits for water
distribution systems. In the first phase of calculations a neural
linear equations solver is combined with a Newton-Raphson
iterations to find a solution to an overdetermined set of nonlinear
equations describing water networks.
The mathematical model of the water system is derived using
measurements and pseudomeasurements consisting certain
amount of uncertainty. This uncertainty has an impact on the
accuracy to which the state estimates can be calculated. The
second phase of calculations, using the same NN, is carried out in
order to quantify the effect of measurement uncertainty on
accuracy of the derived state estimates. Rather than a single
deterministic state estimate, the set of all feasible states
corresponding to a given level of measurement uncertainty is
calculated. The set is presented in the form of upper and lower
bounds for the individual variables, and hence provides limits on
the potential error of each variable.
The simulations have been carried out and results are presented
for a realistic 34-node water distribution network
