Pressure-driven modelling of water distribution systems

This paper presents a novel method to model water distribution systems (WDS) with insufficient pressure. Methods for the prediction of the performance of a WDS with pressure deficiencies are reviewed. The influence of imposed relationships between nodal heads and outflows is assessed and numerical results are given. A Newton-Raphson technique plus line search is employed for solving the governing equations. It is demonstrated that the approach offers superior results for the hydraulic performance of networks under abnormal operating conditions compared to demand-driven analysis-based models

Reliability assessment of water distribution systems with statistical entropy and other surrogate measures

There is ever increasing commercial and regulatory pressure to minimise the cost of water distribution networks even as the demand for them keeps on growing. But cost minimizing is only one of the demands placed on network design. Satisfactory networks are required to operate above a minimum level even if they experience failure of components. Reliable hydraulic performance can be achieved if sufficient redundancy is built in the network. This has given rise to various water distribution system optimization methods including genetic algorithms and other evolutionary computing methods. Evolutionary computing approaches frequently assess the suitability of enormous numbers of potential solutions for which the calculation of accurate reliability measures could be computationally prohibitive. Therefore, surrogate reliability measures are frequently used to ease the computational burden. The aim of this paper is to assess the correlation of surrogate reliability measures in relation to more accurate measures. The surrogate measures studied are statistical entropy, network resilience, resilience index and modified resilience index. The networks were simulated with the prototype software PRAAWDS that produces more realistic results for pressure-deficient water distribution systems. Statistical entropy outperformed resilience index in this study. The results also demonstrate there is a strong correlation between entropy and failure tolerance

Reliability-based optimal design of water distribution networks

A considerable amount of research has been carried out on the reliability analysis and optimal design of water distribution systems, and it has been reported that each of the above problems is very difficult to solve (Eiger et al. 1994; Wagner et al. 1988). The authors are therefore to be commended for their work, which directly incorporated a sophisticated probabilistic reliability model into an optimization routine. The paper had other interesting and useful aspects, which, unfortunately, will not be elaborated upon here

Some reflections on the building and calibration of useful network models

Over the past 10 years or so in the UK much effort has gone into the construction of computerised network models of water supply and distribution networks. At best such models offer an approximation of reality, their performance in simulation being constrained, in many cases, by the uncertainties present in the data upon which they were compiled. Most notable are the problems of demand specification, including leakage evaluation. In the UK this exercise is compounded by the unmetered nature of most domestic consumption. Reconciliation of the output of this process is invariably and inextricably linked to such matters as flow-meter accuracy, network and district metered area (DMA) connectivity, and monitored pressure regime, as well as precision in property allocation and quality of billing records. For large networks the task of the modeller is most arduous since the exercise of pipe calibration, leading to production of the 'verified' model, is itself highly dependent upon the distribution of flows generated in the network. The paper elaborates on these problems and introduces outlines for systematic treatments of the data reconciliation processes, with the aim of producing usable models which 'best' represent reality from the information available

Multiobjective evolutionary optimization of water distribution systems : exploiting diversity with infeasible solutions

This article investigates the computational efficiency of constraint handling in multi-objective evolutionary optimization algorithms for water distribution systems. The methodology investigated here encourages the co-existence and simultaneous development including crossbreeding of subpopulations of cost-effective feasible and infeasible solutions based on Pareto dominance. This yields a boundary search approach that also promotes diversity in the gene pool throughout the progress of the optimization by exploiting the full spectrum of non-dominated infeasible solutions. The relative effectiveness of small and moderate population sizes with respect to the number of decision variables is investigated also. The results reveal the optimization algorithm to be efficient, stable and robust. It found optimal and near-optimal solutions reliably and efficiently. The real-world system based optimisation problem involved multiple variable head supply nodes, 29 fire-fighting flows, extended period simulation and multiple demand categories including water loss. The least cost solutions found satisfied the flow and pressure requirements consistently. The cheapest feasible solutions achieved represent savings of 48.1% and 48.2%, for populations of 200 and 1000, respectively, and the population of 1000 achieved slightly better results overall

Investigation into the pressure-driven extension of the EPANET hydraulic simulation model for water distribution systems

Several hydraulic modelling approaches have been proposed previously to simulate pressure deficient operating conditions in water distribution networks more realistically. EPANET-PDX is an extension of EPANET 2 that has an embedded logistic nodal head-flow function. The EPANET-PDX algorithm was investigated to address the weaknesses uncovered under conditions of extremely low pressure. It was observed that, under certain circumstances, the norm of the system of equations increased from one iteration to the next. A criterion that detects false convergence was included. In general, in the examples considered, the formulation proposed had more consistent computational properties, required fewer iterations of the global gradient algorithm, and application of the line minimization procedure was frequent. The formulation proposed is significantly faster in conditions of extremely low pressure. The hydraulic and water quality modelling functionality of EPANET 2 was preserved. For the operating conditions with satisfactory pressure, where direct comparisons with EPANET 2 were possible, EPANET 2 was consistently faster

Integration of hydraulic and water quality modelling in distribution networks : EPANET-PMX

Simulation models for water distribution networks are used routinely for many purposes. Some examples are planning, design, monitoring and control. However, under conditions of low pressure, the conventional models that employ demand-driven analysis often provide misleading results. On the other hand, almost all the models that employ pressure-driven analysis do not perform dynamic and/or water quality simulations seamlessly. Typically, they exclude key elements such as pumps, control devices and tanks. EPANET-PDX is a pressure-driven extension of the EPANET 2 simulation model that preserved the capabilities of EPANET 2 including water quality modelling. However, it cannot simulate multiple chemical substances at once. The single-species approach to water quality modelling is inefficient and somewhat unrealistic. The reason is that different chemical substances may co-exist in water distribution networks. This article proposes a fully integrated network analysis model (EPANET-PMX) (pressure-dependent multi-species extension) that addresses these weaknesses. The model performs both steady state and dynamic simulations. It is applicable to any network with various combinations of chemical reactions and reaction kinetics. Examples that demonstrate its effectiveness are included

Practical Application Of Pressure-Dependent EPANET Extension

Hydraulic models have been widely used in the design and operation of water distribution system (WDSs). The models enable planning for possible changes in the system under a wide range of conditions. Under abnormal operating condition, for instance, WDSs become pressure deficient and unable to satisfy demand fully. In such circumstances, pressure dependent models are suitable to quantify the shortfall in flow and pressure accurately for crucial decision-making. Most recently, a pressure dependent extension of the renowned EPANET hydraulic simulator was developed to enable modelling of pressure deficient networks. The model has an integrated pressure dependent demand (i.e. nodal flow) function coupled with a line search and backtracking procedure to facilitate convergence. Extensive verifications were conducted on the model using benchmark and real life networks and good modelling performances were accomplished. The model was combined with multi-objective genetic algorithm for optimisation of design, rehabilitation and operation of WDSs. It generated superior results for benchmark as well as real life networks in terms of cost, hydraulic performance and computational time in reference to previous solutions. It has also been utilised for water quality modelling of real life networks. Overall, the model has not experienced convergence problems when executing the various simulations. Having demonstrated the robustness and benefits of the model previously including seamless integration in genetic algorithms, it would be greatly beneficial on investigating ways of improving the algorithm further. In this work, the line search and backtracking procedure of the algorithm has been improved. This has improved the robustness further by enhancing greatly the computational properties for low flow conditions and increasing the algorithm’s consistency over a wider range of operating conditions. Extended period simulations were executed on real life network considering source head variations and pipe closure conditions

Evolutionary multi-objective optimal control of combined sewer overflows

This paper presents a novel multi-objective evolutionary optimization approach for the active control of intermittent unsatisfactory discharges from combined sewer systems. The procedure proposed considers the unsteady flows and water quality in the sewers together with the wastewater treatment costs. The distinction between the portion of wastewater that receives full secondary treatment and the overall capacity of the wastewater treatment works (including storm overflow tanks) is addressed. Temporal and spatial variations in the concentrations of the primary contaminants are incorporated also. The formulation is different from previous approaches in the literature in that in addition to the wastewater treatment cost we consider at once the relative polluting effects of the various primary contaminants in wastewater. This is achieved by incorporating a measure of the overall pollution called the effluent quality index. The differences between two diametrically opposed control objectives are illustrated, i.e. the minimization of the pollution of the receiving water or, alternatively, the minimization of the wastewater treatment cost. Results are included for a realistic interceptor sewer system that show that the combination of a multi-objective genetic algorithm and a stormwater management model is effective. The genetic algorithm achieved consistently the frontier optimal control settings that, in turn, revealed the trade-offs between the wastewater treatment cost and pollution of the receiving water

Multi-directional maximum-entropy approach to the evolutionary design optimization of water distribution systems

A new multi-directional search approach that aims at maximizing the flow entropy of water distribution systems is investigated. The aim is to develop an efficient and practical maximum entropy based approach. The resulting optimization problem has four objectives, and the merits of objective reduction in the computational solution of the problem are investigated also. The relationship between statistical flow entropy and hydraulic reliability/failure tolerance is not monotonic. Consequently, a large number of maximum flow entropy solutions must be investigated to strike a balance between cost and hydraulic reliability. A multi-objective evolutionary optimization model is developed that generates simultaneously a wide range of maximum entropy values along with clusters of maximum and near-maximum entropy solutions. Results for a benchmark network and a real network in the literature are included that demonstrate the effectiveness of the procedure