Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:


Math detects contamination in water distribution networks

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.”

Source Article:
Contamination Source Determination in Water Distribution Networks
Martin Gugat, SIAM Journal on Applied Mathematics, 72(6), 1772–1791 (Online publish date: 5 November 2012)
The source article is available for free access at the link above until February 28, 2013.

About the Author:
Martin Gugat is a researcher at the University of Erlangen-Nuremberg, Lehrstuhl f¨ur angewandte Mathematik 2, in Erlangen, Germany. This work was supported by DFG research cluster 1253: Optimization with Partial Differential Equations, grant GU 376/7-1.

About SIAM
The Society for Industrial and Applied Mathematics (SIAM), headquartered in Philadelphia, Pennsylvania, is an international society of over 14,000 individual members, including applied and computational mathematicians and computer scientists, as well as other scientists and engineers. Members from 85 countries are researchers, educators, students, and practitioners in industry, government, laboratories, and academia. The Society, which also includes nearly 500 academic and corporate institutional members, serves and advances the disciplines of applied mathematics and computational science by publishing a variety of books and prestigious peer-reviewed research journals, by conducting conferences, and by hosting activity groups in various areas of mathematics. SIAM provides many opportunities for students including regional sections and student chapters. Further information is available at

Karthika Muthukumaraswamy | EurekAlert!
Further information:

More articles from Ecology, The Environment and Conservation:

nachricht Minimized water consumption in CSP plants - EU project MinWaterCSP is making good progress
05.12.2017 | Steinbeis-Europa-Zentrum

nachricht Jena Experiment: Loss of species destroys ecosystems
28.11.2017 | Technische Universität München

All articles from Ecology, The Environment and Conservation >>>

The most recent press releases about innovation >>>

Die letzten 5 Focus-News des innovations-reports im Überblick:

Im Focus: Towards data storage at the single molecule level

The miniaturization of the current technology of storage media is hindered by fundamental limits of quantum mechanics. A new approach consists in using so-called spin-crossover molecules as the smallest possible storage unit. Similar to normal hard drives, these special molecules can save information via their magnetic state. A research team from Kiel University has now managed to successfully place a new class of spin-crossover molecules onto a surface and to improve the molecule’s storage capacity. The storage density of conventional hard drives could therefore theoretically be increased by more than one hundred fold. The study has been published in the scientific journal Nano Letters.

Over the past few years, the building blocks of storage media have gotten ever smaller. But further miniaturization of the current technology is hindered by...

Im Focus: Successful Mechanical Testing of Nanowires

With innovative experiments, researchers at the Helmholtz-Zentrums Geesthacht and the Technical University Hamburg unravel why tiny metallic structures are extremely strong

Light-weight and simultaneously strong – porous metallic nanomaterials promise interesting applications as, for instance, for future aeroplanes with enhanced...

Im Focus: Virtual Reality for Bacteria

An interdisciplinary group of researchers interfaced individual bacteria with a computer to build a hybrid bio-digital circuit - Study published in Nature Communications

Scientists at the Institute of Science and Technology Austria (IST Austria) have managed to control the behavior of individual bacteria by connecting them to a...

Im Focus: A space-time sensor for light-matter interactions

Physicists in the Laboratory for Attosecond Physics (run jointly by LMU Munich and the Max Planck Institute for Quantum Optics) have developed an attosecond electron microscope that allows them to visualize the dispersion of light in time and space, and observe the motions of electrons in atoms.

The most basic of all physical interactions in nature is that between light and matter. This interaction takes place in attosecond times (i.e. billionths of a...

Im Focus: A transistor of graphene nanoribbons

Transistors based on carbon nanostructures: what sounds like a futuristic dream could be reality in just a few years' time. An international research team working with Empa has now succeeded in producing nanotransistors from graphene ribbons that are only a few atoms wide, as reported in the current issue of the trade journal "Nature Communications."

Graphene ribbons that are only a few atoms wide, so-called graphene nanoribbons, have special electrical properties that make them promising candidates for the...

All Focus news of the innovation-report >>>



Event News

Innovative strategies to tackle parasitic worms

08.12.2017 | Event News

AKL’18: The opportunities and challenges of digitalization in the laser industry

07.12.2017 | Event News

Blockchain is becoming more important in the energy market

05.12.2017 | Event News

Latest News

Making fuel out of thick air

08.12.2017 | Life Sciences

Rules for superconductivity mirrored in 'excitonic insulator'

08.12.2017 | Information Technology

Smartphone case offers blood glucose monitoring on the go

08.12.2017 | Information Technology

More VideoLinks >>>