Integrated Neural Based System for State Estimation and Confidence Limit Analysis in Water Networks.

Abstract

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.