The stochastic modeling of water demand requires knowledge of the statistical features of the demand time series at different spatial and temporal aggregations. The observation of real data has revealed the presence of a nontrivial scaling of the second-order moments with the number of customers. The main objective of this paper is to analyze the spatial and temporal features of the demand at different spatial aggregation scales and sampled with different temporal resolutions, deriving appropriate scaling laws for the first- and second-order moments. In this context the analytical expressions of the scaling laws are first derived, pointing out the role of the space–time correlation. Then the scaling laws are empirically derived for two data sets of real indoor water demand data of two different case studies, sampled with different metering techniques. This enables the evaluation of the relevance of this effect on real data. A further analysis is carried out to understand how the sampling time affects the ...

The knowledge of the simultaneous nodal pressure values in a water distribution network (WDN) can favor its correct management, with advantages for both water utilities and end users, and guarantee higher sustainability in the use of the water resource. However, monitoring pressure in all the nodes is not feasible, so it can be useful to develop methods that allow us to estimate the whole pressure field based on data from a limited number of nodes. For this purpose, the work employed an artificial neural network (ANN) as a machine-learning regression algorithm. Uncertainty of water demand is modeled through scaling laws, linking demand statistics to the number of users served by each node. Three groups of demand scenarios are generated by using a Latin Hypercube Random Sampling with three different cross-correlations matrices of the nodal demands. Each of the corresponding groups of pressure scenarios is employed for the training of an ANN, whose performance parameter is preliminarily used to solve the sampling design for the WDN. Most of the so-derived monitoring nodes coincide in the three cases. The performance of each ANN appears to be strongly influenced by cross-correlation values, with the best results provided by the ANN relating to the most correlated demands.

A numerical approach for generating a limited number of water demand scenarios and estimating their occurrence probabilities in a water distribution network (WDN) is proposed. This approach makes use of the demand scaling laws in order to consider the natural variability and spatial correlation of nodal consumption. The scaling laws are employed to determine the statistics of nodal consumption as a function of the number of users and the main statistical features of the unitary user’s demand. Besides, consumption at each node is considered to follow a Gamma probability distribution. A high number of groups of cross-correlated demands, i.e., scenarios, for the entire network were generated using Latin hypercube sampling (LHS) and the numerical procedure proposed by Iman and Conover. The Kantorovich distance is used to reduce the number of scenarios and estimate their corresponding probabilities, while keeping the statistical information on nodal consumptions. By hydraulic simulation, the whole number of generated demand scenarios was used to obtain a corresponding number of pressure scenarios on which the same reduction procedure was applied. The probabilities of the reduced scenarios of pressure were compared with the corresponding probabilities of demand.

Submerged vanes are low-height flow-training structures emerging from the riverbed with a suitable angle of attack to the incoming flow. These structures redirect the stream flow and modify erosion and depositional rates in the bottom and in the banks of a river as a result of the secondary currents generated by their installation. For this reason they have many applications in river hydraulics for controlling river bed morphology. An experimental investigation is carried out to compare the efficiency of sheet-piling vanes versus thin plane ones in controlling sediment redistribution in the channel bed. In particular, experimental tests were carried out within a straight water channel, in conditions of bed load motion. The morphology of the river bed both in the area close to the structure and in the far field was examined at different angles of attack of the vane to the incoming flow and at different values of the submergence parameter, which is the ratio between the height of the water above the structure and the water level. The experimental results show that both the shape of the vanes as well as the angle of attack affect their performance in terms of the effects on the bed morphology, especially for greater submergence parameters. Specifically, plane and sheet-piling vanes produce comparable remodelings of the channel bed in the downstream region, but when the attack angle is increased, the thin plane vane causes deeper scour holes close to the structure. This last effect is probably due to the increased erosive capacity of the horseshoe vortex associated with the plane vane, while the uneven surface of the sheet-piling vane mitigates the erosive strength of that vortex.

Water demand scenarios are defined assuming that the samples are complete. On the other hand, consumption measurements are often affected by a considerable number of missing data. This paper explores the problem of missing data and proposes an example of a data pre-processing technique. Afterwards, a deconstruction of the time series, without being influenced by the presence of gaps, is presented. For this purpose, the fast Fourier transform for nonuniform sampling is developed. This analysis allows us to generate ergodic and stationary samples, useful for pursuing the generation of water demand scenarios. An application is provided on a water consumption time series recorded in a suburban area of Naples, Italy.