An efficient null space inexact Newton method for hydraulic simulation of water distribution networks

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.Comment: 15 pages, 9 figures, Preprint extension of Abraham and Stoianov, 2015 (https://dx.doi.org/10.1061/(ASCE)HY.1943-7900.0001089), September 2015. Includes extended exposition, additional case studies and new simulations and analysi

Chlorine decay under steady and unsteady-state hydraulic conditions

AbstractThis paper describes a simulation framework for the scale-adaptive hydraulic and chlorine decay modelling under steady and unsteady-state flows. Bulk flow and pipe wall reaction coefficients are replaced with steady and unsteady-state reaction coefficients. An unsteady decay coefficient is defined which depends upon the absolute value of shear stress and the rate of change of shear stress for quasi-unsteady and unsteady-state flows. A preliminary experimental and analytical investigation was carried out in a water transmission main. The results were used to model monochloramine decay and these demonstrate that the dynamic hydraulic conditions have a significant impact on water quality deterioration and the rapid loss of disinfectant residual

Graph-theoretic Surrogate Measures for Analysing the Resilience of Water Distribution Networks

AbstractHydraulic resilience can be formulated as a measure of the ability of a water distribution network to maintain a minimum level of service under operational and failure conditions. This paper explores a hybrid approach to bridge the gap between graph-theoretic and hydraulic measures of resilience. We extend the concept of geodesic distance of a pipeline by taking into account energy losses associated with flow. New random-walk algorithms evaluate hydraulically feasible routes and identify nodes with different levels of hydraulic resilience. The nodes with the lowest scores are further analysed by considering the availability and capacity of their supply routes

Continuous chlorine detection in drinking water and a review of new detection methods

Chlorination is necessary to prevent epidemics of waterborne disease however excess chlorination is wasteful, produces harmful disinfection byproducts, exacerbates corrosion and causes deterioration in aesthetic qualities, leading to consumer complaints. Residual chlorine must be continuously monitored to prevent both under- and over-chlorination and factors including pH, temperature and fouling must be considered as these also affect the disinfectant strength of residual chlorine. Standard methods used by water utility companies to determine residual chlorine concentration in drinking water distribution systems are appraised and found to be unsuitable for continuous monitoring. A selection of newly developed methods for residual chlorine analysis are evaluated against performance criteria, to direct research towards the development of chlorine sensors that are suitable for use in water systems. It is found that fouling tolerance in particular is generally not well understood for these selected sensor technologies and that long-term trials in real systems is recommended

Dynamically adaptive networks for integrating optimal pressure management and self-cleaning controls

This paper investigates the problem of integrating optimal pressure management and self-cleaning controls in dynamically adaptive water distribution networks. We review existing single-objective valve placement and control problems for minimizing average zone pressure (AZP) and maximizing self-cleaning capacity (SCC). Since AZP and SCC are conflicting objectives, we formulate a bi-objective design-for-control problem where locations and operational settings of pressure control and automatic flushing valves are jointly optimized. We approximate Pareto fronts using the weighted sum scalarization method, which uses a previously developed convex heuristic to solve the sequence of parametrized single-objective problems. The resulting Pareto fronts suggest that significant improvements in SCC can be achieved for minimal trade-offs in AZP performance. Moreover, we demonstrate that a hierarchical design strategy is capable of yielding good quality solutions to both objectives. This hierarchical design considers pressure control valves first placed for the primary AZP objective, followed by automatic flushing valves placed to augment SCC conditions. In addition, we investigate an adaptive control scheme for dynamically transitioning between AZP and SCC controls. We demonstrate these control challenges on case networks with both interconnected and branched topology.Comment: 26 pages, 7 figures, published paper in Annual Reviews in Contro

Sparse null space algorithms for hydraulic analysis of large scale water supply networks

In this article, a comprehensive review of existing methods is presented and computationally efficient sparse null space algorithms are proposed for the hydraulic analysis of water distribution networks. The linear systems at each iteration of the Newton method for nonlinear equations are solved using a null space algorithm. The sparsity structure of these linear equations, which arises from the sparse network connectivity, is exploited to reduce computations. A significant fraction of the total flops in the Newton method are spent in computing pipe head losses and matrix-matrix multiplications involving flows. Because most flows converge after a few iterations, a novel partial update of head losses and matrix products is used to further reduce computational complexity. Convergence analyses are also presented for the partial-update formulas. A new heuristic for reducing the number of pressure head computations of a null space method is proposed. These savings enable fast near-real-time control of large-scale water networks. It is often observed that the linear equations that arise in solving the hydraulic equations become ill-conditioned due to hydraulic solutions with very small and zero flows. The condition numbers of the Newton equations are bounded using a regularization technique with insignificant computational overheads. The convergence properties of all proposed algorithms are analyzed by posing them as an inexact-Newton method. Small-scale to large-scale models of operational water networks are used to evaluate the proposed algorithms

Decreasing the Discolouration Risk of Drinking Water Distribution Systems through Optimised Topological Changes and Optimal Flow Velocity Control

In this paper, a new mathematical framework is proposed for maximizing the self-cleaning capacity (SCC) of drinking water distribution systems by controlling the diurnal peak flow velocities in the pipes under normal operation. This is achieved through an optimal change of the network connectivity (topology). This paper proposes an efficient algorithm for the network analysis of valve closures, which allows enforcing favorable changes in the flow velocities for maximizing the SCC by determining an optimal set of links to isolate in the forming of a more branched network, while concurrently satisfying the hydraulic and regulatory pressure constraints at the demand nodes. Multiple stochastic demands from an end-use demand model are generated to test the robustness in the improved SCC for the modified network connectivity under changing demand. An operational network model is used to demonstrate the efficacy of the proposed approach

CCWI2017: F143 'Fault Detection and Diagnosis for Pressure Control Valves in Water Supply Networks'

The control of water supply networks is becoming more advanced and complex, and it is therefore increasingly important to continuously monitor and optimise the performance of automatic control valves. This paper investigates a method for early fault detection and diagnosis (FDD) of pressure control valves in water supply networks. Potential faults are categorised, and different process variables and residuals are defined from continuous measurements and model-based simulations of the operation of a diaphragm actuated globe valve in order to detect a fault and diagnose its likely cause. We generate and utilise experimental data from controlled laboratory conditions and an operational network together with numerically simulated data to validate the performance of the proposed FDD method.<br