Global Gradient Algorithm Extension to Distributed Pressure Driven Pipe Demand Model

The analysis of a looped water distribution network, operating under pressure and in steady flow conditions, can be accomplished once the topology of the network, the geometry of the pipes, the water demands at the nodes and the head value of at least one node are known. In a water distribution network (WDN), water demands are assigned to the nodes, although in reality they are distributed along the pipes converging at such nodes. This classic assumption represents the total demand along a pipe as two lumped withdrawals at its terminal nodes. This paper demonstrates that the above approximation is wrong because it generates head loss errors which may be significant when network analysis is performed for calibration, system design, real-time operations, rehabilitation strategies, optimal operation studies, reliability analyses, etc. Therefore, an extension of the global gradient algorithm (GGA) for network analysis is proposed which entails a modified GGA permitting the effective introduction of the lumped nodal demands, and without forfeiting a correct physical representation of head losses, by means of a pipe hydraulic resistance correction.

Water Distribution Networks (WDNs) are crucial for meeting current and future urban water demands. Knowledge of future water demand at different time scales is fundamental for optimal WDN design and operations. Various predictive models of water demand have been proposed in the literature, ranging from traditional time series analysis to cutting-edge machine learning and deep learning techniques. However, the task of forecasting urban water demand remains mostly decoupled from the design of the optimal control of the related WDN. Current performance assessment of demand predictive models focuses predominantly on forecast accuracy, overlooking their practical implications on WDN operations. Meanwhile, the existing research on WDN management often assumes either perfect knowledge of future water demands or employs empirical approximations and aggregate statistics to estimate future water needs. This study bridges this gap by scrutinizing the actual operational value of water demand forecasts in designing optimal operations of WDNs.Here, we develop a forecast-informed optimal WDN control framework to evaluate the operational value of water demand forecasts for WDN operations. Our framework comprises two main modules. The first module computes water demand forecasts. We comparatively evaluate a suite of different forecasting models —including Seasonal Auto-Regressive Integrated Moving Average with eXogenous factors, Multilayer Perceptron, Convolutional Neural Network, and Long Short-Term Memory (a network augmented with an attention mechanism) —across various forecast horizons (1/6/12 hours and 1/3/7/14 days ahead). The most accurate forecasts are integrated into the second module, an economic nonlinear Model Predictive Control (MPC) algorithm designed to optimize WDN operations. Within this module, an Artificial Neural Network (ANN) – based surrogate model encapsulates the hydraulics of the physical WDN, enhancing the optimization process while reducing complexity.We demonstrate our forecast-informed optimal WDN control framework on a real WDN of a rural town with approximately 10,000 inhabitants. Water demand data collected in the Netherlands for a period of 10 years (2007-2017) at 5-minute resolution and corresponding meteorological data are used to train the water demand forecasting models. The MPC module computes the optimal control sequence for 7 pumps and 1 valve in the WDN to minimize pump energy costs while meeting water demands and ensuring safety storage in 5 tanks. Initial findings reveal that the ANN-based surrogate model can accurately incorporate the WDN characteristics (R2 > 0.85), facilitating its integration into the MPC for an efficient and simplified representation of a real-world WDN. Further, MPC fed by 24-hour ahead water demand forecasts achieves potential energy savings of approximately 18% compared to a benchmark rule-based control strategy. Our framework yields a versatile simulation-based optimization tool for evaluating the impact of demand forecasts on WDN management. Future research efforts will aim at refining and comparing deterministic and stochastic water demand forecasts within the MPC framework, under diverse operational objectives.

Drinking water distribution networks are important because they provide water to meet basic human needs, and to protect humans in the event of fires and other public emergencies. With aging infrastructure, there is an urgent need to design water distribution networks to ensure safety and reliability of service in the future. The uncertainty that surrounds future scenarios of climate-induced drought, population levels, and urbanization patterns – all factors that influence water demand – means that a system design chosen today may be inadequate to meet future demands in a water distribution network. Water utilities often have to plan the design of their water distribution network with only limited information on future water demand levels. For example, if water demand in the future is higher than the level predicted at the time of design, then a municipality will eventually have to retrofit the system, perhaps at great expense, to meet the unanticipated water demand. Thus, there is a need for methods to design networks to minimize the need for future system retrofit under uncertain demands, and to make networks economically robust. In this paper a new framework is presented to design water distribution networks for economic robustness. Economic robustness supplements the least-cost optimality criterion by providing a measure of the variability involved in retrofit costs of a system under uncertain future conditions. In the new framework, water demand projected at the end of a 20-year planning period is treated as an uncertain quantity and modeled as a random variable with an error probability density function (PDF). In the proposed framework, new criteria such as the expected value and standard deviation of retrofit cost are developed to evaluate the economic robustness of water distribution networks. The framework is applied to a simple network, with comparison of design alternatives done on the basis of pipe cost and expected retrofit cost. The results obtained indicate that surplus hydraulic capacity lowers the uncertainty of future retrofit costs and increases confidence of retrofit cost estimates. Consequently, the results substantiate the intuitive understanding of the benefits of surplus hydraulic capacity in a system.

While operating a water distribution network (WDN), it is essential to prepare the system to face with intentional (e.g., cyber-physical attack) or unintentional (e.g., pipe leakage/burst) adverse events or other drivers such as the effects of climate change. Increasing the network’s preparedness to deal with anomalous events is an effective manner to improve the system’s resilience, reducing the negative impacts of events. In this paper, leakage/burst events, and ordinary network operation, are captured by both sensors and expert knowledge in a WDN in Spain. Event-driven and data-driven approaches are used to characterise the system behaviour, in particular when it is operating under the effects of an anomalous event, based on the resilience phases (i.e., absorptive, adaptive, restorative) for the collected dataset. The relationship of clustering pressure head time series based on their potential state in a particular resilience phase, in three random cases of short-term leakage events, was explored. This paper focuses on capturing the behaviour of the system, through the exploration of the hydraulic parameters of WDNs (in particular the pressure head) before, during, and after a leakage event, by means of a spatial-temporal analysis. It was observed that the network behaviour could be categorised into 1) ordinary operation and 2) during the event, which would allow to characterise the system behaviour when influenced by leakage/burst event and also explore its adaptability to resilience phases. The results show that it is possible to extract relevant patterns (i.e., feature maps) and generate an anomaly indicator from the pressure head heatmaps that facilitate the characterisation of anomalous events for WDNs.

Future water demands and pipe roughness coefficients used in the design of water distribution networks (WDNs) have a high degree of uncertainty. Fuzzy analysis of WDNs provide how the uncertainties in independent or basic parameters (such as nodal demands and pipe roughness coefficients) are propagated to dependent or derived parameters (such as pipe flows, pipe velocities, and available pressure heads). Usually demand dependent analysis is used for such analysis. A WDN may be pressure deficient or may become pressure deficient because of high pipe roughness or inadequate pump pressure and may not be able to meet desired demands at all nodes. Thus, it is desirable to consider the nodal outflows as unknown and as a function of available pressure heads under pressure-deficient conditions. An approach for fuzzy analysis of a WDN that takes into account pressure-deficient condition using node flow analysis is presented in this paper. The proposed methodology is illustrated with an example network taken from literature. The methodology is useful in identifying vulnerable zones in WDNs and can be extended for reliability analysis under uncertainty of nodal demands and pipe roughness coefficients. Comparison of results with usual demand-dependent analysis shows that proposed method is better for identifying vulnerable zones.

In water distribution networks (WDNs), the classic pressure control valves (PCVs) are mechanical/hydraulic devices aimed at maintaining the target pressure just downstream or upstream of the PCV pipe, namely pressure reduction or sustaining valves. From a modelling standpoint, the major drawback of such local control is that classic PCVs may require target pressure varying over time with the pattern of delivered water because the controlled node is not strategic for the optimal WDN pressure control. Current information and communication technology allows transferring streams of pressure data from any WDN node to the PCV. Thus, remotely real-time control (RRTC) permits real-time electric regulation of PCVs to maintain a fixed target pressure value in strategic critical nodes, resulting in optimal control of pressure and background leakages. This paper shows three strategies for the electric regulation of RRTC PCVs, which use as control variables the shutter opening degree (SD), the valve hydraulic resistance (RES) and the valve head loss (HL). The Apulian network is used to compare the three strategies, while the application on the real Oppegård WDN yields further discussions. Results show that HL and RES strategies outperform SD; constraining the maximum shutter displacement helps SD stability although it still needs calibration.

A hydraulic model was developed in order to evaluate the potential energy recovery from the use of centrifugal pumps as turbines (PATs) in a water distribution network characterized by the presence of private tanks. The model integrates the Global Gradient Algorithm (GGA), with a pressure-driven model that permits a more realistic representation of the influence on the network behaviour of the private tanks filling and emptying. The model was applied to a real case study: a District Metered Area in Palermo (Italy). Three different scenarios were analysed and compared with a baseline scenario (Scenario 0 – no PAT installed) to identify the system configuration with added PATs that permits the maximal energy recovery without penalizing the hydraulic network performance. In scenarios involving PAT on service connections, the specification of PAT operational parameters was also evaluated by means of Monte Carlo Analysis. The centralized solution with a PAT installed downstream of the inlet node of the analysed district, combined with local PATs on the larger service connections, proves to be the most energy-efficient scenario.

Pipe re-sizing of water distribution networks (WDNs) aims at improving the service performance to the required level, while minimizing the cost of replacing pipes in the network. The main challenge comes from the identification of the most effective pipes to re-size from a large number of interacting components. Performing a global search over all pipes in large WDNs does not guarantee a feasible and efficient solution due to the enormous search space, even by employing advanced algorithms, e.g., evolutionary algorithms. This paper proposes a novel method to reduce the search space for optimal re-sizing based on topological metrics from Complex Network Theory and hydraulic metrics, while providing suboptimal solutions comparable to the full search solutions, i.e., considering all pipes as candidates. The topological metrics are based on the edge-betweenness tailored for WDN analysis. Hydraulic metrics are unit head loss and flow rates of pipes computed based on simulation of the WDN in the current configuration. The optimal re-sizing plans obtained, particularly those using edge betweenness, were tested on a real WDN. The results are comparable with the full search solutions but they are much more efficient to obtain and require replacing mostly contiguous pipes, i.e., easier for practical fieldwork.

In the first place, this paper presents an examination of the effects of missing cadastral information on the modeling and calibration of water distribution networks (WDN). For this purpose, cadastral errors were artificially introduced to the hydraulic models of the WDN of three cities of the province of Valle del Cauca (Colombia), with population in the range of 15,000–30,000 inhabitants. The cadastral errors were introduced by eliminating some pipes from the unaltered models using the resilience index as selection criterion. From this examination, typical responses observed during the calibration process were associated to specific topological and hydraulic errors and it was also noted that there is a direct relation between the resilience index and the effect of the removal of a certain pipe on the hydraulic performance of the model. In the second place, after identifying the effects of missing and erroneous cadastral and hydraulic information on the calibration of WDN models, the inverse procedure was carried out: the calibration process was used as a tool for detecting missing and erroneous cadastral and hydraulic information. This methodology was successfully applied to the WDN of Sector Estadio (250,000 inhabitants), which is a complex area of the city of Bucaramanga (Colombia); through the calibration of this WDN, errors such as failing water meters, pipes and valves that existed in the real system but were not in the model, significant errors in pipe diameters in the model, among others, were identified.

Water distribution networks (WDN) model optimization is an important part of smart water systems to achieve optimal strategies. WDN optimization focuses on the nonlinearity of the discharge head loss equation, the availability of discrete properties of pipe sizes, and the conservation of constraints. Multi-objective evolutionary algorithms (MOEAs) have been proposed and successfully applied in the field of WDN design optimization. Previous studies have focused on comparing the optimization effects of algorithms in water distribution networks, ignoring the problems of unbalanced pressure distribution and water hammer at the nodes of the pipe network caused by the complex terrain in mountainous areas. In this paper, a multi-objective water supply optimization model that integrated cost, reliability, and water quality was established for a mountainous WDN in real engineering. The method of traversing the nodes to solve the water age was introduced to find a more scientific and practical water age solution model, with setting the weight function to evaluate the water age of the water supply model comprehensively. Strength Pareto Evolutionary Algorithm II (SPEA-II) and Non-dominated Sorting Genetic Algorithm II (NSGA-II) were adopted to optimize the WDN design model in the mountainous complex terrain. The significance levels of the number of Pareto solutions (NOPS) and running time are 0.029 and 0.001, respectively, indicating that the two algorithms have significant differences. Compared to NSGA-II, SPEA-II has a better convergence rate and running time in multi-objective water supply optimization design. The solution set distribution of SPEA-II is more concentrated than that of NSGA-II, also the numerical value is better. The number of SPEA-II optimization schemes is larger and the scheme is more effective. Among them, the Pareto solution set of SPEA-II can obtain more desirable optimization results on cost, reliability index (RI) and water age. In summary, the study provides valuable information for decision makers in WDN with complex terrain.

Control of water distribution networks (WDNs) can be represented by an optimization problem with hydraulic models describing the nonlinear relationship between head loss, water flow, and demand. The problem is difficult to solve due to the non-convexity in the equations governing water flow. Previous methods used to obtain WDN controls (i.e., operational schedules for pumps and valves) have adopted simplified hydraulic models. One common assumption found in the literature is the modification of WDN topology to exclude loops and assume a known water flow direction. In this paper, we present a new geometric programming-based model predictive control approach, designed to solve the water flow equations and obtain WDN controls. The paper considers the nonlinear difference algebraic equation (DAE) form of the WDN dynamics, and the GP approach amounts to solving a series of convex optimization problems and requires neither the knowledge of water flow direction nor does it restrict the water network topology. A case study is presented to illustrate the performance of the proposed method.

Hydraulic analysis of pipe networks is generally done considering certain values for independent parameters of the system such as roughness of pipes, nodal demands, etc. Such analysis would inevitably lead to certain hydraulic responses of the system, i.e. nodal pressures, etc. This is while, inherent uncertainties associated with independent parameters as expected stresses, spread over the system and result in hydraulic stress in nodal pressure heads as dependent uncertainties. Using optimization tools, this study presents a reliable approach based on interval analysis to deal with these uncertain hydraulic stresses. In the proposed approach, the optimization problem is formulated in a manner that the nodal demands, roughness of pipes and water levels in elevated tanks would be the decision variables while extreme nodal pressures for unknown intervals are explored as the objectives functions. The large number of junctions in the case of real pipe networks, leads to inefficient iterative use of single objective optimization engine. In order to this problem, this study exploits a many-objective approach with an appropriate performance. Applying the proposed approach on a real pipe network shows that ±15% variation in nodal demands and pipes’ roughness in addition to ±1m in water levels might produce hydraulic stress in pressure heads from -13.7% to +10.2% with regard to the crisp values. In such a condition, it is possible for 125 junctions out of 128, to fail in satisfying the minimum required pressure head. It is demonstrated that the proposed approach has acceptable accuracy for analyzing hydraulic stress in real water distribution networks.

A gradient algorithm based method is presented for analyzing gradually varied unsteady flow in water distribution networks. Using a Newton-Raphson solution technique, the algorithm simultaneously computes piezometric heads at nodes and flow rates in pipes for all points within the network. Comparisons are made with steady-state extended period simulations to show the robust behavior of the model for a complex water distribution network. The benefits of using a gradient algorithm are its flexibility in coding, versatility in operational conditions, and its application to complicated water distribution networks. The computer program implementing the method is general, easy to use, and allows a dynamic analysis of complex looped and open water distribution networks.

Hydraulic performance benchmarking for effective management of water distribution networks: An innovative composite index-based approach

The weighted-least-squares method based on the Gauss-Newton minimization technique is used for parameter estimation in water distribution networks. The parameters considered are: element resistances (single and/or group resistances, Hazen-Williams coefficients, pump specifications) and consumptions (for single or multiple loading conditions). The measurements considered are: nodal pressure heads, pipe flows, head loss in pipes, and consumptions/inflows. An important feature of the study is a detailed consideration of the influence of different choice of weights on parameter estimation, for error-free data, noisy data, and noisy data which include bad data. The method is applied to three different networks including a real-life problem.