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This paper investigates the problem of optimal placement and operation of valves and chlorine boosters in water networks. The objective is to minimize average zone pressure while penalizing deviations from target chlorine concentrations. The problem formulation includes nonconvex quadratic terms within constraints representing the energy conservation law for each pipe, and discretized differential equations modeling advective transport of chlorine concentrations. Moreover, binary variables model the placement of valves and chlorine boosters. The resulting optimization problem is a nonconvex mixed integer nonlinear program, which is difficult to solve, especially when large water networks are considered. We develop a new convex heuristic to optimally place and operate valves and chlorine boosters in water networks, while estimating the optimality gaps for the computed solutions. We evaluate the proposed heuristic using case studies with varying sizes and levels of connectivity and complexity, including two large operational water networks. The convex heuristic is shown to generate good-quality feasible solutions in all problem instances with bounds on the optimality gap comparable to the level of uncertainty inherent in hydraulic and water quality models. [ABSTRACT FROM AUTHOR]

Issue 2(b) "The discusser has made the argument that when head loss is low, pressure data are not only useless but can be misleading because the algorithms essentially end up calibrating noise in the field data ([9]). However, it is much better to determine head loss using a handful of data points with significant head loss than with data based on a large number of useless head loss values." For large pipes, it is necessary to collect calibration data at times of high flow (although such large pipes generally have higher head loss than smaller pipes)." The large data sets we acquire for model calibration make it infeasible and cost prohibitive for a person to observe the acquired hydraulic data and conduct "detective work", which has little input from "hydraulic theory" and state-of-the-art optimization methods. [Extracted from the article]

An accurate hydraulic model of a water distribution network (WDN) is a critical prerequisite for a multitude of operational, optimization, and planning tasks. The accuracy of a hydraulic model can only be maintained through its periodic calibration and validation with acquired pressure and flow data from a WDN. It is important that this process be robust and computationally efficient. This paper describes the regularization of an inverse problem to deal with data uncertainties and ill-posedness of parameter estimation problems in WDNs. A novel data-driven strategy is presented for tuning the regularization hyperparameter for the inverse problem and also for validating the results on an independent set of operational hydraulic data. A limited-memory quasi-Newton method (L-BFGS-B) is implemented to solve the resulting regularized nonlinear inverse problem. Furthermore, the implemented method utilizes either the Darcy-Weisbach or Hazen-Williams head loss formulas and is investigated both with and without pipe grouping. An extensive experimental program was carried out to acquire unique hydraulic data from an operational WDN in order to investigate the robustness of the proposed parameter estimation method. The hydraulic model of the operational WDN and the acquired hydraulic data are provided as supplementary data to enable the comparison of hydraulic model calibration methods with operational data and encourage reproducible research. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The optimal placement and operation of pressure control valves in water distribution networks is a challenging engineering problem. When formulated in a mathematical optimization framework, this problem results in a nonconvex mixed integer nonlinear program (MINLP), which has combinatorial computational complexity. As a result, the considered MINLP becomes particularly difficult to solve for large-scale looped operational networks. We extend and combine network model reduction techniques with the proposed optimization framework in order to lower the computational burden and enable the optimal placement and operation of control valves in these complex water distribution networks. An outer approximation algorithm is used to solve the considered MINLPs on reduced hydraulic models. We demonstrate that the restriction of the considered optimization problem on a reduced hydraulic model is not equivalent to solving the original larger MINLP, and its solution is therefore sub-optimal. Consequently, we investigate the trade-off between reducing computational complexity and the potential sub-optimality of the solutions that can be controlled with a parameter of the model reduction routine. The efficacy of the proposed method is evaluated using two large scale water distribution network models. [ABSTRACT FROM AUTHOR]