Assignment # 5 - Sensor Placement

Article Review

Berry, J., Fleisher, L, Hart, W. Phillips, C. and Watson, J.-P. (2005) “Sensor Placement in Municipal Water Networks”, Journal of Water Resources Planning and Management, 131(3) pp. 237-243

This article addresses the issue contaminant events in water distribution systems. The motivation is higher vulnerabilities in water networks due its distributed geography. An approach for determining an optimal sensor configuration in water distribution systems is presented. The optimization method minimizes the expected fraction of population exposed to a contaminant event. Integer programming techniques was used. Four assumptions were used:

1) An attack occurs at a single point in the network
2) Total population exposed
3) Sensors protect downstream populations
4) Transitions between periods are ignored

Three data sets were evaluated. Data set 1 and 2 were test set from EPANET and one real network. A sensitivity analysis was performed in the model. It was evaluated how optimal solution would change considering changes in population densities and attack risks.

The article concludes that the optimization approach proposed can effectively solve large-scale sensor-placement problems. However, different modeling structures exists considering different performance objectives, alternative placement locations, temporal effects, and sensor costs.

Discussion

The aspect that called my attention is this article and that I think it is a great contribution to this kind of problem is the use of sensitivity analysis. Due the uncertainties presented in some datasets, especially in water distribution systems, which obtaining data from water utilities is usually difficult, performing sensitivity analysis helps in validating the results. Future research could incorporate different temporal patterns and mobility data to better understand the variation in water demand during the day or even year.

Assignment #4

Article Review

Lee, B. H. and Deininger, R. A. (1992) “Optimal Locations of Monitoring Stations in Water Distribution Systems”, Journal of Environmental Engineering, 118(1) pp. 4-16

The subject of this article is defining locations of sampling water quality in water distribution systems. The motivation of this problem is that U.S. EPA requires water quality monitoring prescribing sampling frequency and water-quality parameters. The sampling stations must be representative, but regulation doesn’t specify direct criteria on representativeness in water distribution system.

The authors bring the concept of coverage. Consider a water distribution network composed of nodes and pipes. Pipes convey water for demands in the nodes. For a specific node “i” there is a pathway that define upstream nodes. It is assumed that the water quality in upstream nodes can be inferred by the water quality of the node “i”. So, for a demand-fraction, the most downstream node used for sampling would represent better the water quality of the network.

A small example of network with 7 nodes is used to illustrate the concept and optimization model formulated. Using a integer programming code, the optimization model maximize coverage, for a specific number of sampling station, a water-fraction criterion and a demand pattern. Two study cases are analyzed: Flint, Michigan, and Cheshire, Connecticut. In this last case, different patterns on demand were considered, since demand is highly variable during a day. The coverage for this last example increased from 29.7 % to 45 %, considering 3 stations.

Discussion

The article presents a very interesting case of integer optimization model in water distribution systems, because it’s application in real systems. The formulation is very simple to understand, making the article an easy reading. Future applications, however could consider more refine water quality modeling.

Assignment # 3 - The Tragedy of the Commons

Article Review

Garrett Hardin, “The Tragedy of the Commons,” Science, 162(1968):1243-1248.

Hardin begins his article with the idea that there is no technical solution for certain kinds of problems. The problem here is the “population problem” and the main idea is that it cannot be solved in a technical way. The followings paragraphs state that a finite world can support only a finite population, that the optimum population is not the maximum population possible and would it be the maximum good per person the right question, but what is good?

Then, Hardin brings the picture first sketched by a mathematical William Forster Lloyd, of a pasture shared by herdsmen, called “commons”. This example is used to exemplify how rational beings seeking to maximize its gains bring systematic negative effects that ruin all society. The article addresses some other interconnected issues like pollution and regulation.

Discussion:

Despite the article is a important reference in science in general, bringing into discussion the relevant issue of population growth and finite resources, I have some critics related to how the author have addressed the issue. The article states that the common doesn’t have rules and that anyone was free to do whatever it wants. This is not exactly correct with the concept of common according with economic science. Even if not formally defined, a society sharing a common will have cultural and habits that would characterize the behavior of the resources in a commons. Besides that, it seems to me unrealistic with the present world that a common could be exploited without any regulation.

Another issue apparently neglected by the author is the fact that human society is in evolution and development of new technology is constantly solving new problems. I do believe that in future, human societies can achieve a state of sustainability of human demands and natural resources.

Assignment # 2 - Ground Water contaminant removal

Article Review in Linear Programming

Atwood, D. F. & Gorelick S. M. (1985). "Hydraulic gradient control for groundwater contaminant removal." Journal of Hydrology, 76. 85 - 106.

The article addresses the problem of contaminant ground water plume and proposes a two stage planning procedure to select the best wells and schedules to contain the contaminant plume, while a second system of wells removes the contaminated water. The study contemplates the use of linear programming, groundwater flow and solute transport simulation.

The study case is located in Rocky Mountain Arsenal near Denver, Colorado. The contaminated ground water is result of military and industrial uses. The groundwater modeling was based in previous studies (Konikow, 1975, 1977, and Trescott et. al. 1976), which considered the two-dimensional flow in a heterogeneous isotropic aquifer. The solute transport was combined with groundwater simulation flow, based on the advection-dispersion equation. The objective of the modeling was to compute the field velocity in order to locate the plume boundary relative to the potential gradient control wells.

The stage II of the procedure is select best wells and rates of pumping/recharge, which was done by a linear programming approach combined with ground water flow simulation. The optimization framework minimizes the total pumping/recharge over time subject to hydraulic constraints that force the gradient to be toward the center contaminant removal well. The objective function and constraints are:

where [R] = matrix of gradient response coefficients at gradient check locations; {u} pumpage vector; uc = pumping rate at central removal well; {v} = recharge vector; {e}T= row vector of 1’s; and {g} = known right-hand-side vector reflecting the target gradients.

The main important results are the developed of a procedure for aquifer restoration. The procedure is general and can be applied in other situations. The author outlines two methodologies contributions: “the manner in which the problem is linearized and the extension of the concept of drawdown responses to hydraulic gradients responses”. The linearization was possible due the division of the problem into two parts.

Assignment # 1b

Article Review in Linear Programming

Ilich, N. (2008). "Shortcomings of linear programming in optimizing river basin allocation." Water Resour. Res. 44.

The article has identified possible failures to solve a simple allocation problem using network flow algorithm (NFA). Two applications were tested. The first one was a reservoir with multiple outflows and the second one related to modeling of hydrologic channel routing.
The NFA searches a minimum cost flow in a network, which is represented by:

where cij, lij, and uij are the cost per unit of flow, lower bound, flow and upper bound on flow along an arc(i, j). Constraints represent the mass balance at each node.

The test problem 1 “demonstrates breakdown of an iterative scheme on modeling a reservoir with two distinct outflow structures”. The outflow capacity is a function of water elevation in the reservoir. The water elevation, however is determined by the mass balance occurred in a time step. Therefore, the “NFA-based model must “guess” the final elevation for a time step in order to numerically integrate the average outflow capacity and thus estimate the upper bound on reservoir outflow”. The iterative procedure to converge to a guessed value may not achieve a good solution in complex systems with multiple reservoir and multiple outlet structures. The author proposes a method for linearization of reservoir outflow constrains in order to improve the described issues.

The test problem 2 addresses two issues related to use of LP and a hydrologic routing. “Hydrologic channel routing cannot be included in the LP-based models for a single time step optimization without violating the assumption of “demand driven reservoir releases”, which is the basic premise on which these models were built and on which they operate on a steady-state basis”. The second issue is the “inclusion of channel routing in multiple time step optimization framework may often require nonlinear representation of routing coefficients, since routing coefficients should be updated when channel flows change from low- to high- flow season”.
The author claims that none of the previous problems discussed can be overcome in a satisfactory way using LP framework, despite the fact that a suggestion of linearization was proposed for the first problem.

Discussion

Despite the fact that the article addresses specific issues related to the use of LP-framework, the article is interesting in the sense that brings awareness to the use of LP. Specifically, it discusses two important and common modeling procedures in water resources management studies, the first one a reservoir and the second one the inclusion of hydrologic channel routing. The article doesn’t propose definitive solutions for the problems, but well identified them and stimulate future research to better deal with them.

Future research would be the comparison analysis of these problems with different types of optimization frameworks, like for example, dynamic programming or evolutionary algorithm.