Estimating Risk Measures for Water Distribution Systems using Metamodels

Recent developments in the field of optimization of Water Distribution Systems (WDS) have focused on incorporating uncertainty into the analysis, recognizing that variables such as demand should be considered as stochastic variables. As a result hydraulic reliability must be considered as a constraint, rather than pressure heads. The most common method of quantifying reliability is to use a Monte Carlo Simulation (MCS). However, this is a very computationally expensive process. In this research, a metamodeling approach was used to reduce this computational intensity. A metamodel is an approximation of an existing model, which takes less time to run, making it much more computationally efficient upon repeated use, such as in a MCS or during optimisation with a Genetic Algorithm. The specific type of metamodel used in this research was an Artificial Neural Network (ANN), as it is capable of approximating any function without specifying the form it will take. Two metamodeling scenarios are used in this research to approximate reliability. First, a metamodel was developed that approximated pressure heads and chlorine residuals for an adaptation of the New York Tunnels problem, from which reliability was calculated. Second, reliability was approximated directly with a metamodel, thus eliminating the need of a MCS completely. The results in this paper have shown that ANN metamodels can be used to accurately approximate common risk measures used to evaluate WDS performance, such as hydraulic and water quality reliability and vulnerability, while offering considerable savings in computational time. It was found that it was more computationally efficient to use ANNs to approximate pressure heads and chlorine residuals than to approximate reliability directly. This was due to the fact that it took a significant amount of time to generate training data for the latter case.