Featured Research

from universities, journals, and other organizations

Mathematics used to identify contamination in water distribution networks

Date:
November 28, 2012
Source:
Society for Industrial and Applied Mathematics
Summary:
New research considers the identification of contaminants in a water distribution network 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."


Story Source:

The above story is based on materials provided by Society for Industrial and Applied Mathematics. Note: Materials may be edited for content and length.


Journal Reference:

  1. Martin Gugat. Contamination Source Determination in Water Distribution Networks. SIAM Journal on Applied Mathematics, 2012; 72 (6): 1772 DOI: 10.1137/110859269

Cite This Page:

Society for Industrial and Applied Mathematics. "Mathematics used to identify contamination in water distribution networks." ScienceDaily. ScienceDaily, 28 November 2012. <www.sciencedaily.com/releases/2012/11/121128143541.htm>.
Society for Industrial and Applied Mathematics. (2012, November 28). Mathematics used to identify contamination in water distribution networks. ScienceDaily. Retrieved July 26, 2014 from www.sciencedaily.com/releases/2012/11/121128143541.htm
Society for Industrial and Applied Mathematics. "Mathematics used to identify contamination in water distribution networks." ScienceDaily. www.sciencedaily.com/releases/2012/11/121128143541.htm (accessed July 26, 2014).

Share This




More Earth & Climate News

Saturday, July 26, 2014

Featured Research

from universities, journals, and other organizations


Featured Videos

from AP, Reuters, AFP, and other news services

Virginia Governor Tours Tornado Aftermath

Virginia Governor Tours Tornado Aftermath

AP (July 25, 2014) Virginia Gov. Terry McAuliffe toured the Cherrystone Family Camping and RV Resort on the Chesapeake Bay today, a day after it was hit by a tornado. The storm claimed two lives and injured dozens of others. (July 25) Video provided by AP
Powered by NewsLook.com
Europe's Highest Train Turns 80 in French Pyrenees

Europe's Highest Train Turns 80 in French Pyrenees

AFP (July 25, 2014) Europe's highest train, the little train of Artouste in the French Pyrenees, celebrates its 80th birthday. Duration: 01:05 Video provided by AFP
Powered by NewsLook.com
Goma Cheese Brings Whiff of New Hope to DRC

Goma Cheese Brings Whiff of New Hope to DRC

Reuters - Business Video Online (July 24, 2014) The eastern region of the Democratic Republic of Congo, mainly known for conflict and instability, is an unlikely place for the production of fine cheese. But a farm in the village of Masisi, in North Kivu is slowly transforming perceptions of the area. Known simply as Goma cheese, the Congolese version of Dutch gouda has gained popularity through out the region. Ciara Sutton reports. Video provided by Reuters
Powered by NewsLook.com
Bill Gates: Health, Agriculture Key to Africa's Development

Bill Gates: Health, Agriculture Key to Africa's Development

AFP (July 24, 2014) Health and agriculture development are key if African countries are to overcome poverty and grow, US software billionaire Bill Gates said Thursday, as he received an honourary degree in Ethiopia. Duration: 00:36 Video provided by AFP
Powered by NewsLook.com

Search ScienceDaily

Number of stories in archives: 140,361

Find with keyword(s):
Enter a keyword or phrase to search ScienceDaily for related topics and research stories.

Save/Print:
Share:

Breaking News:
from the past week

In Other News

... from NewsDaily.com

Science News

Health News

Environment News

Technology News



Save/Print:
Share:

Free Subscriptions


Get the latest science news with ScienceDaily's free email newsletters, updated daily and weekly. Or view hourly updated newsfeeds in your RSS reader:

Get Social & Mobile


Keep up to date with the latest news from ScienceDaily via social networks and mobile apps:

Have Feedback?


Tell us what you think of ScienceDaily -- we welcome both positive and negative comments. Have any problems using the site? Questions?
Mobile: iPhone Android Web
Follow: Facebook Twitter Google+
Subscribe: RSS Feeds Email Newsletters
Latest Headlines Health & Medicine Mind & Brain Space & Time Matter & Energy Computers & Math Plants & Animals Earth & Climate Fossils & Ruins