Two new approaches for the stochastic least cost design of water distribution systems

2004 ◽  
Vol 4 (5-6) ◽  
pp. 355-363 ◽  
Author(s):  
Z. Kapelan ◽  
A.V. Babayan ◽  
D.A. Savic ◽  
G.A. Walters ◽  
S.T. Khu
Keyword(s):  
New York ◽  
Distribution System ◽  
Distribution Systems ◽  
Water Distribution ◽  
Demand Uncertainty ◽  
Integration Method ◽  
Pressure Head ◽  
Problem Formulation ◽  
Independent Random Variables ◽  
System Robustness

The problem of stochastic (i.e. robust) water distribution system (WDS) design is formulated and solved here as an optimisation problem under uncertainty. The objective is to minimise total design costs subject to a target level of system robustness. System robustness is defined as the probability of simultaneously satisfying minimum pressure head constraints at all nodes in the network. The decision variables are the alternative design options available for each pipe in the WDS. The only source of uncertainty analysed is the future water consumption uncertainty. Uncertain nodal demands are assumed to be independent random variables following some pre-specified probability density function (PDF). Two new methods are developed to solve the aforementioned problem. In the Integration method, the stochastic problem formulation is replaced with a deterministic one. After some simplifications, a fast numerical integration method is used to quantify the uncertainties. The optimisation problem is solved using the standard genetic algorithm (GA). The Sampling method solves the stochastic optimisation problem directly by using the newly developed robust chance constrained GA. In this approach, a small number of Latin Hypercube (LH) samples are used to evaluate each solution's fitness. The fitness values obtained this way are then averaged over the chromosome age. Both robust design methods are applied to a New York Tunnels rehabilitation case study. The optimal solutions are identified for different levels of robustness. The best solutions obtained are also compared to the previously identified optimal deterministic solution. The results obtained lead to the following conclusions: (1) Neglecting demand uncertainty in WDS design may lead to serious under-design of such systems; (2) Both methods shown here are capable of identifying (near) optimal robust least cost designs achieving significant computational savings.

Risk- and robustness-based solutions to a multi-objective water distribution system rehabilitation problem under uncertainty

2006 ◽  
Vol 53 (1) ◽  
pp. 61-75 ◽  
Author(s):  
Z. Kapelan ◽  
D.A. Savic ◽  
G.A. Walters ◽  
A.V. Babayan
Keyword(s):  
New York ◽  
Distribution System ◽  
Water Distribution ◽  
Water Distribution System ◽  
Sampling Technique ◽  
Latin Hypercube Sampling ◽  
Pressure Head ◽  
Total Risk ◽  
Fitness Evaluation ◽  
Multi Objective

The water distribution system (WDS) rehabilitation problem is defined here as a multi-objective optimisation problem under uncertainty. Two alternative problem formulations are considered. The first objective in both approaches is to minimise the total rehabilitation cost. The second objective is to either maximise the overall WDS robustness or to minimise the total WDS risk. The WDS robustness is defined as the probability of simultaneously satisfying minimum pressure head constraints at all nodes in the network. Total risk is defined as the sum of nodal risks, where nodal risk is defined as the product of the probability of pressure failure at that node and consequence of such failure. Decision variables are the alternative rehabilitation options for each pipe in the network. The only source of uncertainty is the future water consumption. Uncertain demands are modelled using any probability density functions (PDFs) assigned in the problem formulation phase. The corresponding PDFs of the analysed nodal heads are calculated using the Latin Hypercube sampling technique. The optimal rehabilitation problem is solved using the newly developed rNSGAII method which is a modification of the well-known NSGAII optimisation algorithm. In rNSGAII a small number of demand samples are used for each fitness evaluation leading to significant computational savings when compared to the full sampling approach. The two alternative approaches are tested, verified and their performance compared on the New York tunnels case study. The results obtained demonstrate that both new methodologies are capable of identifying the robust (near) Pareto optimal fronts while making significant computational savings.

scholarly journals A fast approach for multiobjective design of water distribution networks under demand uncertainty

2010 ◽  
Vol 13 (2) ◽  
pp. 143-152 ◽  
Author(s):  
S. Sun ◽  
S.-T. Khu ◽  
Z. Kapelan ◽  
S. Djordjević
Keyword(s):  
New York ◽  
Distribution System ◽  
Water Distribution ◽  
Demand Uncertainty ◽  
Model Simulation ◽  
Computational Cost ◽  
Distribution Networks ◽  
Point Of View ◽  
Computational Time ◽  
Computationally Efficient

Water distribution system (WDS) design has received much attention lately from the point of view of uncertainties. Designers are generally interested in the Pareto optimal cost-robustness trade off curve. This paper aims to find a solution to the multiobjective problem in a computationally time-efficient way in comparison to previous methods from the literature. A parameter θ, which is linked to the system robustness through a derived analytic formula, is introduced. The robustness of the WDS can be approximated by one single model simulation; consequently a large amount of computational time is saved compared to using a sampling-based technique. The application of the method to the New York tunnels problem demonstrates that, although the resulting design is conservative on cost, the proposed method is very computationally efficient. This is of importance when high computational cost is the major obstacle for some real-world problems.

scholarly journals Flexible and deterministic household water saving under water demand uncertainty: existing water distribution system and sanitary sewer perspectives

2021 ◽  
Author(s):  
Innocent Basupi
Keyword(s):  
Water Demand ◽  
Distribution System ◽  
Distribution Systems ◽  
Water Distribution ◽  
Demand Uncertainty ◽  
Water Distribution System ◽  
Water Saving ◽  
Sustainable Solutions ◽  
Sanitary Sewer ◽  
Household Water

Abstract An integrated method that evaluates conflicting hydraulic performances of water distribution systems (WDSs) and sanitary sewers (SSs) considering water-saving schemes (WSSs) under fixed (deterministic) or uncertain water demands was formulated. WSSs considered include household water-saving fixtures and appliances whose water flows impact water distribution system (WDS) and sanitary sewer (SS) hydraulic performances in different ways. In the proposed flexible approach, a multi-objective optimisation problem was formulated and solved considering trade-offs of three objectives: (1) maximisation of the average cost savings (2) maximisation of the average WDS resilience index and (3) minimisation of the average SS self-cleansing velocity deficit factor. The decision variables include water-saving fixture and appliance capacities that are applied in a deterministic or flexible manner at a household level. The constraints include WDS and SS hydraulic requirements together with decision bounds of the available water-saving scheme capacities. The non-dominated sorting genetic algorithm was used to obtain trade-off solutions. This method was demonstrated in the corresponding WDS and SS network subsystems of Tsholofelo extension in Gaborone, Botswana. The results indicate that WSSs lead to visibly conflicting WDS and SS hydraulic performances. Moreover, considering uncertainty inherent in water demand and the corresponding planning and management of WDSs and SSs provides more sustainable solutions as demand uncertainties unveil.

Biological stability of drinking water in new York City

1998 ◽  
Vol 38 (6) ◽  
pp. 181-190 ◽  
Author(s):  
D. Jolis ◽  
W. W. Faber ◽  
V. Diyamandoglu
Keyword(s):  
New York ◽  
New York City ◽  
Drinking Water ◽  
Biological Activity ◽  
York City ◽  
Distribution System ◽  
Distribution Systems ◽  
Water Distribution ◽  
Quality Parameters ◽  
Drinking Water Distribution Systems

A study was carried out to determine the degree of biological activity in the drinking water supplied to New York City by the Croton and Catskill/Delaware systems, as measured by the Attached Growth Rate Estimate (AGRE) method. Also, possible relationships between AGRE results and standard water quality parameters were examined. The AGRE results for both the systems ranged between 0 and 0.5 d−1, indicative of biologically stable water. These results suggest that excessive bacterial growth in the New York City distribution system would be rare. The Croton results were temperature and alkalinity dependent. The Catskill/Delaware results revealed that growth rates decreased with travel time in the distribution system. These differences emphasize the complexity of biological activity monitoring in drinking water distribution systems.

Application of linear programming for looped water supply pipe network design

2013 ◽  
Vol 13 (5) ◽  
pp. 1195-1201 ◽  
Author(s):  
A. K. Sharma ◽  
P. K. Swamee
Keyword(s):  
Linear Programming ◽  
Water Supply ◽  
Distribution System ◽  
Distribution Systems ◽  
Water Distribution ◽  
Problem Formulation ◽  
Supply Networks ◽  
Supply Pipe ◽  
Final Design ◽  
Basic Purpose

It has been indicated in the literature that looped water distribution systems designed with the linear programming (LP) optimisation technique are converted into tree-like structures resulting in the disappearance of the original geometry in the final design. Looped networks are provided for system reliability, thus such a design approach will defeat the basic purpose of looped systems provision. Such a limitation has hindered the application of LP for the design of looped water supply networks. A method for the design of a looped water distribution system has been developed such that the loop configuration of the network is maintained by bringing all the pipes of the network into the optimisation problem formulation using the LP optimisation method.

scholarly journals Application of genetic programming to modeling pipe failures in water distribution systems

2010 ◽  
Vol 13 (3) ◽  
pp. 419-428 ◽  
Author(s):  
Qiang Xu ◽  
Qiuwen Chen ◽  
Weifeng Li
Keyword(s):  
Genetic Programming ◽  
Distribution System ◽  
Distribution Systems ◽  
Water Distribution ◽  
Pipe Failure ◽  
Beijing City ◽  
Failure Data ◽  
Processing Strategies ◽  
Gis Data ◽  
Failure Models

The water loss from a water distribution system is a serious problem for many cities, which incurs enormous economic and social loss. However, the economic and human resource costs to exactly locate the leakage are extraordinarily high. Thus, reliable and robust pipe failure models are demanded to assess a pipe's propensity to fail. Beijing City was selected as the case study area and the pipe failure data for 19 years (1987–2005) were analyzed. Three different kinds of methods were applied to build pipe failure models. First, a statistical model was built, which discovered that the ages of leakage pipes followed the Weibull distribution. Then, two other models were developed using genetic programming (GP) with different data pre-processing strategies. The three models were compared thereafter and the best model was applied to assess the criticality of all the pipe segments of the entire water supply network in Beijing City based on GIS data.

scholarly journals A Head Formulation for the Steady-State Analysis of Water Distribution Systems Using an Explicit and Exact Expression of the Colebrook–White Equation

Water ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1163
Author(s):  
Mengning Qiu ◽  
Avi Ostfeld
Keyword(s):  
Steady State ◽  
Distribution System ◽  
Distribution Systems ◽  
Water Distribution ◽  
Solution Method ◽  
Water Distribution System ◽  
Academic Research ◽  
Exact Expression ◽  
Contamination Source

Steady-state demand-driven water distribution system (WDS) solution is the bedrock for much research conducted in the field related to WDSs. WDSs are modeled using the Darcy–Weisbach equation with the Swamee–Jain equation. However, the Swamee–Jain equation approximates the Colebrook–White equation, errors of which are within 1% for ϵ/D∈[10−6,10−2] and Re∈[5000,108]. A formulation is presented for the solution of WDSs using the Colebrook–White equation. The correctness and efficacy of the head formulation have been demonstrated by applying it to six WDSs with the number of pipes ranges from 454 to 157,044 and the number of nodes ranges from 443 to 150,630. The addition of a physically and fundamentally more accurate WDS solution method can improve the quality of the results achieved in both academic research and industrial application, such as contamination source identification, water hammer analysis, WDS network calibration, sensor placement, and least-cost design and operation of WDSs.

scholarly journals Cyber—Physical Attack Detection in Water Distribution Systems with Temporal Graph Convolutional Neural Networks

Water ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1247
Author(s):  
Lydia Tsiami ◽  
Christos Makropoulos
Keyword(s):  
Neural Networks ◽  
Distribution System ◽  
Distribution Systems ◽  
Water Distribution ◽  
Attack Detection ◽  
Convolutional Network ◽  
Irreversible Damage ◽  
Physical Attack ◽  
Temporal Graph ◽  
Graph Neural Networks

Prompt detection of cyber–physical attacks (CPAs) on a water distribution system (WDS) is critical to avoid irreversible damage to the network infrastructure and disruption of water services. However, the complex interdependencies of the water network’s components make CPA detection challenging. To better capture the spatiotemporal dimensions of these interdependencies, we represented the WDS as a mathematical graph and approached the problem by utilizing graph neural networks. We presented an online, one-stage, prediction-based algorithm that implements the temporal graph convolutional network and makes use of the Mahalanobis distance. The algorithm exhibited strong detection performance and was capable of localizing the targeted network components for several benchmark attacks. We suggested that an important property of the proposed algorithm was its explainability, which allowed the extraction of useful information about how the model works and as such it is a step towards the creation of trustworthy AI algorithms for water applications. Additional insights into metrics commonly used to rank algorithm performance were also presented and discussed.

scholarly journals Comparison of Searching Behaviour of Three Evolutionary Algorithms Applied to Water Distribution System Design Optimization

Water ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 695 ◽  
Author(s):  
Weiwei Bi ◽  
Yihui Xu ◽  
Hongyu Wang
Keyword(s):  
Evolutionary Algorithms ◽  
Real Time ◽  
Distribution System ◽  
Optimization Design ◽  
Distribution Systems ◽  
Water Distribution ◽  
Optimal Solutions ◽  
Great Ability ◽  
Searching Behaviour ◽  
Run Time

Over the past few decades, various evolutionary algorithms (EAs) have been applied to the optimization design of water distribution systems (WDSs). An important research area is to compare the performance of these EAs, thereby offering guidance for the selection of the appropriate EAs for practical implementations. Such comparisons are mainly based on the final solution statistics and, hence, are unable to provide knowledge on how different EAs reach the final optimal solutions and why different EAs performed differently in identifying optimal solutions. To this end, this paper aims to compare the real-time searching behaviour of three widely used EAs, which are genetic algorithms (GAs), the differential evolution (DE) algorithm and the ant colony optimization (ACO). These three EAs are applied to five WDS benchmarking case studies with different scales and complexities, and a set of five metrics are used to measure their run-time searching quality and convergence properties. Results show that the run-time metrics can effectively reveal the underlying searching mechanisms associated with each EA, which significantly goes beyond the knowledge from the traditional end-of-run solution statistics. It is observed that the DE is able to identify better solutions if moderate and large computational budgets are allowed due to its great ability in maintaining the balance between the exploration and exploitation. However, if the computational resources are rather limited or the decision has to be made in a very short time (e.g., real-time WDS operation), the GA can be a good choice as it can always identify better solutions than the DE and ACO at the early searching stages. Based on the results, the ACO performs the worst for the five case study considered. The outcome of this study is the offer of guidance for the algorithm selection based on the available computation resources, as well as knowledge into the EA’s underlying searching behaviours.

scholarly journals Modelling both the continual erosion and regeneration of discolouration material in drinking water distribution systems

2013 ◽  
Vol 14 (1) ◽  
pp. 81-90 ◽  
Author(s):  
W. R. Furnass ◽  
R. P. Collins ◽  
P. S. Husband ◽  
R. L. Sharpe ◽  
S. R. Mounce ◽  
...  
Keyword(s):  
Distribution System ◽  
Distribution Systems ◽  
Water Distribution ◽  
Transport Model ◽  
Water Distribution Systems ◽  
Sensitivity Analyses ◽  
Drinking Water Distribution Systems ◽  
Proactive Management ◽  
Drinking Water Distribution ◽  
Mass Transport Model

The erosion of the cohesive layers of particulate matter that causes discolouration in water distribution system mains has previously been modelled using the Prediction of Discolouration in Distribution Systems (PODDS) model. When first proposed, PODDS featured an unvalidated means by which material regeneration on pipe walls could be simulated. Field and laboratory studies of material regeneration have yielded data that suggest that the PODDS formulations incorrectly model these processes. A new model is proposed to overcome this shortcoming. It tracks the relative amount of discolouration material that is bound to the pipe wall over time at each of a number of shear strengths. The model formulations and a mass transport model have been encoded as software, which has been used to verify the model's constructs and undertake sensitivity analyses. The new formulations for regeneration are conceptually consistent with field and laboratory observed data and have potential value in the proactive management of water distribution systems, such as evaluating change in discolouration risk and planning timely interventions.

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