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

摘要

In this paper a simple recurrent neural network (NN) is used asuda basis for constructing an integrated system capable of findingudthe state estimates with corresponding confidence limits for wateruddistribution systems. In the first phase of calculations a neuraludlinear equations solver is combined with a Newton-Raphsonuditerations to find a solution to an overdetermined set of nonlinearudequations describing water networks.udThe mathematical model of the water system is derived usingudmeasurements and pseudomeasurements consisting certainudamount of uncertainty. This uncertainty has an impact on theudaccuracy to which the state estimates can be calculated. Theudsecond phase of calculations, using the same NN, is carried out inudorder to quantify the effect of measurement uncertainty onudaccuracy of the derived state estimates. Rather than a singleuddeterministic state estimate, the set of all feasible statesudcorresponding to a given level of measurement uncertainty isudcalculated. The set is presented in the form of upper and lowerudbounds for the individual variables, and hence provides limits onudthe potential error of each variable.udThe simulations have been carried out and results are presentedudfor a realistic 34-node water distribution network.