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UBC Theses and Dissertations

Hydraulic network analysis and model calibration with artificial neural nets Fayegh, David A.


Computation of steady-state flow rates and the pressure distribution in a hydraulic network of given topology, pipe carrying capacities, and nodal demand discharges plays an essential role in the design, analysis, and operation of water and other fluid distribution systems. When accurate estimates of the hydraulic network model parameters (namely, pipe resistances and demand discharges) are available, the pipe segment flow rates and nodal energy heads can be easily calculated by means of a number of efficient algorithms that iteratively solve the basic non-linear system of hydraulic equations. For existing networks, however, reliable estimates of model parameters are rarely available since the nodal demands are in a continual state of change and the pipe segment carrying capacities gradually change with time. Artificial neural networks1 have recently emerged as general problem-solving tools whose potential has only begun to be exploited in engineering. The objectives of this dissertation are three fold: first, to identify the most appropriate class of ANN architectures and learning algorithms suitable for modeling two key problems associated with the design and operation of water distribution systems, namely, hydraulic network analysis and model calibration; secondly, to develop a relatively general framework for representing arbitrarily complex hydraulic networks by means of multilayered feedforward ANNs; and finally, to experimentally investigate the convergence and performance behavior of a number of feedforward networks trained by error back propagation for hydraulic network analysis and model calibration under typical operating conditions. Specifically, several sets of input/output2 training and testing vector pairs were generated and used to train and test the convergence and performance of a number of feedforward networks used to represent three characteristically different classes of hydraulic network problems. *ANNs henceforth. 2I/O henceforth. Convergence behavior was observed to improve after the appropriate preprocessing of the I/O training vector pairs generated by the hydraulic network model simulator. In part, this process involved application of linear and non-linear fuzzy transformation functions to the various groups of variables and parameters in the input and output vector pairs followed by the algebraic normalization of the input to the feedforward networks. The effects on convergence and performance as a result of variations in a number of experimental parameters such as the choice of transformation functions, changes in the underlying probability distribution from which seed hydraulic network data were drawn, the presence of noise in training and testing data, choice of the activation and output functions and their parameters, the size of training I/O data pairs, and the number of layers used in the feedforward network have also been investigated. Examination of the results indicates that the standard error back propagation algorithm converges relatively slowly for even medium-sized distribution systems although the number of training cycles required to learn an assigned class of tasks remains relatively invariant of the number of variables and parameters of the hydraulic network under investigation. The success of any particular feedforward network was largely dependent on the representation of the hydraulic networks (such as identification of the I/O, number of layers and nodes/layer in the ANN) and the choice of the transformation functions applied to I/O vector pairs. The techniques developed for transformation and normalization of the 1/0 training and testing data in addition to the appropriate ANN representation of the hydraulic network were observed to result in significant improvements in performance both during training, as measured in terms of the cycles required to achieve a desired root mean square error3 computed with both the training and testing data sets. 3RMSE henceforth.

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