Edo Abraham

Edo Abraham, Ivan Stoianov

Null space Newton algorithms are efficient in solving the nonlinear equations arising in hydraulic analysis of water distribution networks. In this article, we propose and evaluate an inexact Newton method that relies on partial updates of the network pipes' frictional headloss computations to solve the linear systems more efficiently and with numerical reliability. The update set parameters are studied to propose appropriate values. Different null space basis generation schemes are analysed to choose methods for sparse and well-conditioned null space bases resulting in a smaller update set. The Newton steps are computed in the null space by solving sparse, symmetric positive definite systems with sparse Cholesky factorizations. By using the constant structure of the null space system matrices, a single symbolic factorization in the Cholesky decomposition is used multiple times, reducing the computational cost of linear solves. The algorithms and analyses are validated using medium to large-scale water network models.

D. B. Steffelbauer, E. J. M. Blokker, S. G. Buchberger et al.

Socio-economic characteristics are influencing the temporal and spatial variability of water demand - the biggest source of uncertainties within water distribution system modeling. Improving our knowledge on these influences can be utilized to decrease demand uncertainties. This paper aims to link smart water meter data to socio-economic user characteristics by applying a novel clustering algorithm that uses dynamic time warping on daily demand patterns. The approach is tested on simulated and measured single family home datasets. We show that the novel algorithm performs better compared to commonly used clustering methods, both, in finding the right number of clusters as well as assigning patterns correctly. Additionally, the methodology can be used to identify outliers within clusters of demand patterns. Furthermore, this study investigates which socio-economic characteristics (e.g. employment status, number of residents) are prevalent within single clusters and, consequently, can be linked to the shape of the cluster's barycenters. In future, the proposed methods in combination with stochastic demand models can be used to fill data-gaps in hydraulic models.