Water Distribution Networks (WDN) are complex and highly interconnected systems. To maintain operation under failure conditions, WDNs should have built-in resilience based on topological and energy redundancy. There are various methods for analysing the resilience of WDNs based on either hydraulic models or surrogate network measures; however, not a single universally accepted method exists. Hydraulic modeling of disruptive operational scenarios suffer from combinatorial restrictions and uncertainties. Methods that rely on surrogate network measures do not take into account the complex interactions between topological and energy redundancy. To bridge this gap, the presented work introduces a hydraulically informed surrogate measure of pipe criticality for the resilience analysis of WDNs, called Water Flow Edge Betweenness Centrality (WFEBC). The WFEBC combines the random walk betweenness centrality with hydraulic (energy) loss principles in pipes. The proposed network resilience estimation method is applied to a case study network and an operational network. Furthermore, a network decomposition approach is proposed to complement the network estimation method and facilitate its scalability to large operational networks. The described resilience analysis method is benchmarked against a hydraulic model-based analysis of WDN reserve capacity. WFEBC is also applied to assess the improvement in resilience allowed by the implementation of a dynamically adaptive topology in an operational network. The benefits and limitations of the proposed method are discussed.

This paper investigates control and design-for-control strategies to improve the resilience of sectorized water distribution networks (WDN), while minimizing pressure induced pipe stress and leakage. Both evolutionary algorithms (EA) and gradient-based mathematical optimization approaches are investigated for the solution of the resulting large-scale non-linear (NLP) and bi-objective mixed-integer non-linear programs (BOMINLP). While EAs have been successfully applied to solve discrete network design problems for large-scale WDNs, gradient-based mathematical optimization methods are more computationally efficient when dealing with large search spaces associated with continuous variables in optimal network control problems. Considering the advantages of each method, we propose a sequential hybrid method for the optimal design-for-control of large-scale WDNs, where a refinement stage relying on gradient-based mathematical optimization is used to solve continuous optimal control problems corresponding to design solutions returned by an initial EA search. The proposed method is applied to compute the Pareto front of a bi-objective design-for-control problem for the operational network BWPnet, where we consider reopening closed connections between isolated supply areas. The results show that the considered design-for-control strategy increases the resilience of BWPnet while minimizing pressure induced leakage. Moreover, the refinement stage of the proposed hybrid method efficiently improves the coarse approximation computed by the initial EA search, returning a continuous and even Pareto front approximation.

The resilience of a water distribution system is defined as its ability to maintain continuous customer supply, and can be improved by increasing its redundancy in energy and/or connectivity. This can, however, negatively impact other aspects of network performance, such as leakage management. In this article, we consider the design-for-control (DfC) problem of adding new connections (from a predefined set of candidate pipes) to water supply systems to improve their resilience to failure events while minimizing the impact on leakage management under normal operating conditions. We present a mixed-integer nonlinear programming (MINLP) formulation of the problem of optimal link addition for the minimization of average zone pressure (AZP), a surrogate measure of pressure dependent leakage. We implement a method based on spatial branch-and-bound to solve the problem on a case study network from the literature and an operational network part of an urban water system in the U.K. Finally, we validate the improvement in network resilience resulting from the addition of new connections by performing an a posteriori critical link analysis, using the hydraulic resilience measure of reserve capacity.

This manuscript investigates the design-for-control (DfC) problem of minimizing pressure induced leakage and maximizing resilience in existing water distribution networks. The problem consists in simultaneously selecting locations for the installation of new valves and/or pipes, and optimizing valve control settings. This results in a challenging optimization problem belonging to the class of non-convex bi-objective mixed-integer non-linear programs (BOMINLP). In this manuscript, we propose and investigate a method to approximate the non-dominated set of the DfC problem with guarantees of global non-dominance. The BOMINLP is first scalarized using the method of \(\epsilon \)-constraints. Feasible solutions with global optimality bounds are then computed for the resulting sequence of single-objective mixed-integer non-linear programs, using a tailored spatial branch-and-bound (sBB) method. In particular, we propose an equivalent reformulation of the non-linear resilience objective function to enable the computation of global optimality bounds. We show that our approach returns a set of potentially non-dominated solutions along with guarantees of their non-dominance in the form of a superset of the true non-dominated set of the BOMINLP. Finally, we evaluate the method on two case study networks and show that the tailored sBB method outperforms state-of-the-art global optimization solvers.

This paper investigates an adaptive control strategy which takes advantage of remotely actuated pumps and valves to improve the performance of water distribution networks (WDN) during burst incidents. The proposed strategy relies on model predictive control (MPC) to switch between problem formulations corresponding to normal operating conditions and burst conditions. The optimal control problems are formulated as non-convex non-linear programs (NLP), where the action of fixed-speed pumps and control valves (non-return and bi-directional) is modeled exactly and burst remedial interventions are represented using time-dependent connectivity matrices. We propose an efficient solution method based on reformulations and approximations of the non-convex objectives and constraints and apply the proposed strategy to the adaptive control of an operational WDN during a burst incident. The numerical experiments show that the computed burst control settings allow to partially or completely restore customer supply following the detection of a burst while maintaining minimum water levels in the network tanks and without increasing the cost of pumping operations. The results suggest that the proposed adaptive control strategy can be implemented alone, to mitigate the impact of bursts incidents in WDNs at minimum cost, or to complement traditional remedial interventions.