Exploring Topological Effects on Water Distribution System Performance Using Graph Theory and Statistical Models

AbstractWater distribution system (WDS) pipe networks can vary widely in topological layout. The variations in branch and loop combinatorics across large pipe network data sets are ideal for exploring graph-based structural patterns and linkages with engineered performance. To facilitate this exploration, a library of 10,001 lattice-like pipe networks is developed. Each network is equipped with hydraulic, water quality, and diurnal demand information for extended period simulations. Results show strong correlations exist among graph theory metrics (e.g., geodesic, spectral, and combinatorics-based) and performance measures (e.g., maximum hourly unit headloss, average water age, and average chemical concentration). These trends are extended with performance predictions using parametric and semiparametric statistical models. Predictive accuracies are evident for processes that follow diffusion-like behaviors, indicating coupled applications of graph theory and statistical methods may have strong abilities to characterize WDSs at lower computational and analytical costs. Evidence also reveals features from percolation theory, with sharp phase transitions in WDS performance at certain probabilistic thresholds of pipe network connectivity. This may support future probabilistic studies on WDS performance with percolation-like transitions.