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

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 3,200+ scientific posters on ePosters
  • More Than 4,700+ 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 TechnologyNetworks.com 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
Open Source Seed Initiative – A Welcome Boost to Global Crop Breeding
A team of plant breeders, farmers, non-profit agencies, seed advocates, and policymakers have created the Open Source Seed Initiative.
ASMS 2016: Targeting Mass Spectrometry Tools for the Masses
The expanding application range of MS in life sciences, food, energy, and health sciences research was highlighted at this year's ASMS meeting in San Antonio, Texas.
A New Way Out for Stem Cells
Researchers at North Carolina State University have discovered that therapeutic stem cells exit the bloodstream in a different manner than was previously thought.
One Giant Leap for the Future of Safe Drug Delivery
Sheffield engineers make major breakthrough in developing silk ‘micro-rockets’ that can be used safely in biological environments.
Designing Potential AIDS Vaccine Candidates
Findings represent ‘big accomplishment’ in biomedical engineering and design.
Anticancer Drug Stops Ebola Virus Molecule in its Tracks
A team of scientists from the University of Oxford have successfully mapped the structure of the Ebola virus molecule that drives the attack strategy and leads to fatal infections in humans.
Assessing the Effectiveness of Genome-Editing Technologies
Researchers have developed a cost-effective and rapid method for assessing edits generated by CRISPR-Cas9 and other genome-editing technologies.
Anthrax Proteins Might Help Treat Cancerous Tumors
Studies in mice reveal novel treatment regimen.
New Cancer Drug Target Found in Dual-Function Protein
Findings from a study from TSRI have shown that targeting a protein called GlyRS might help to halt cancer growth.
Key to Chronic Fatigue Syndrome is in Your Gut, Not Head
Researchers report they have identified biological markers of the disease in gut bacteria and inflammatory microbial agents in the blood.
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
3,200+ scientific and medical posters
A library of 2,500+ scientific videos on LabTube
4,700+ scientific videos
Close
Premium CrownJOIN TECHNOLOGY NETWORKS PREMIUM FOR FREE!