Corporate Banner
Satellite Banner
Scientific Communities
Become a Member | Sign in
Home>News>This Article

Math Detects Contamination in Water Distribution Networks

Published: Friday, November 30, 2012
Last Updated: Friday, November 30, 2012
Bookmark and Share
The identification of contaminants in a water distribution network in considered as an optimal control problem within a networked system.

None of us want to experience events like the Camelford water pollution incident in Cornwall, England, in the late eighties, or more recently, the Crestwood, Illinois, water contamination episode in 2009 where accidental pollution of drinking water led to heart-wrenching consequences to consumers, including brain damage, high cancer risk, and even death. In the case of such catastrophes, it is important to have a method to identify and curtail contaminations immediately to minimize impact on the public.

A paper published earlier this month in the SIAM Journal on Applied Mathematics considers the identification of contaminants in a water distribution network as an optimal control problem within a networked system.

“Water supply networks are an essential part of our infrastructure. Sometimes the water in such a network can be contaminated, often by human error, causing the use of polluted water for drinking water production. In the case of such a situation, it is important to have a method to identify the location of the pollution source,” says the paper’s author, Martin Gugat, explaining the significance of his work.
The paper considers a water distribution network with a finite number of nodes where contamination can occur in the pipes.

“The contamination spreads dynamically through the network with time. So, in order to model the system, a model of the evolution in time is necessary,” explains Gugat. “In our approach, we use a partial differential equation (PDE) to model how pollution spreads in the network.”

By using a PDE model for transport of contaminants, the problem of identifying the source becomes an optimal control problem. The solution is calculated using equidistant time grids, which allows one to determine the values of contamination at all potential sources on the time grid. Available data on pollution and network flow is incorporated into the model.

Employing certain assumptions for travel times through the pipes, the author uses a least-squares method to solve the problem. The least squares method provides approximate solutions to optimization problems that are relatively efficient to compute using the tools of numerical linear algebra.

This provides a fast method to identify possible contamination sources, explains Gugat. “For a really accurate model, however, a full system of three-dimensional PDEs is necessary. But with three-dimensional PDEs, simulation is only possible for small networks,” he says. “This illustrates that to solve real life problems on real networks, there is a trade-off between the accuracy of the model and its utility.”

While the method is tested numerically in the paper, additional work would involve testing the system with an existing water network to demonstrate its workability in practice.

Another future direction is toward elimination of the contaminant. “The second step after the identification of the contamination source is a strategy to flush the polluted water out of the network as fast as possible with acceptable operational cost. The development of an optimal strategy for such a rehabilitation of the water supply is an interesting question for future research,” says Gugat.

“For a more detailed model of the process, more complex nonlinear PDEs could be used,” he continues. “The cost of the numerical treatment of complex PDEs for large networks is prohibitive. Applied mathematics has to offer models that can be used according to the problem requirements to solve problems with network graphs of a realistic size.”

Further Information

Join For Free

Access to this exclusive content is for Technology Networks Premium members only.

Join Technology Networks Premium for free access to:

  • Exclusive articles
  • Presentations from international conferences
  • Over 3,500+ scientific posters on ePosters
  • More Than 5,100+ scientific videos on LabTube
  • 35 community eNewsletters

Sign In

Forgotten your details? Click Here
If you are not a member you can join here

*Please note: By logging into you agree to accept the use of cookies. To find out more about the cookies we use and how to delete them, see our privacy policy.

Scientific News
Integrated Omics Analysis
Studying multi-omics promises to give a more holistic picture of the organism and its place in its ecosystem, however despite the complexities involved those within the field are optimistic.
Unravelling the Role of Key Genes and DNA Methylation in Blood Cell Malignancies
Researchers from the University of Nebraska Medical Center have demonstrated the role of Dnmt3a in safeguarding normal haematopoiesis.
Salford Lung Study - The First Real World Clinical Trial
In this podcast, we learn about the Salford Lung Study and its potential to revolutionize the way we assess new drugs and treatments around the world.
Point of Care Diagnostics - A Cautious Revolution
Advances in molecular biology, coupled with the miniaturization and improved sensitivity of assays and devices in general, have enabled a new wave of point-of-care (POC) or “bedside” diagnostics.
Mass Spec Technology Drives Innovation Across the Biopharma Workflow
With greater resolving power, analytical speed, and accuracy, new mass spectrometry technology and techniques are infiltrating the biopharmaceuticals workflow.
Structure of Primary Cannabinoid Receptor is Revealed
The findings provide key insights into how natural and synthetic cannabinoids including tetrahydrocannabinol —a primary chemical in marijuana—bind at the CB1 receptor to produce their effects.
Overlooked Molecules Could Revolutionise our Understanding of the Immune System
Researchers have discovered that around one third of all the epitopes displayed for scanning by the immune system are a type known as ‘spliced’ epitopes.
Illumina Contributes to ClinVar Database
The contribution includes variants of all classifications, from pathogenic to benign, identified during interpretation of whole genome sequences generated in the CLIA-certified, CAP-accredited Illumina Clinical Services Laboratory.
Agilent Presents Early Career Professor Award to Dr. Roeland Verhaak
JAX professor recognized for the development and implementation of workflows for the analysis of big-data from transcriptomics to next generation sequencing approaches.
NIH Study Determines Key Differences between Allergic and Non-Allergic Dust Mite Proteins
Researchers at NIH have uncovered factors that lead to the development of dust mite allergy and assist in the design of better allergy therapies.
Scroll Up
Scroll Down
Skyscraper Banner

Skyscraper Banner
Go to LabTube
Go to eposters
Access to the latest scientific news
Exclusive articles
Upload and share your posters on ePosters
Latest presentations and webinars
View a library of 1,800+ scientific and medical posters
3,500+ scientific and medical posters
A library of 2,500+ scientific videos on LabTube
5,100+ scientific videos