Journal of Water Resources Planning and Management

The potential threats to U.S. water supply systems have changed fundamentally in the past 4 years. Prior to 2001, the major threats were natural causes, accidents, and some malicious behavior by a small group of individuals. Against these threats, water supply agencies have done a truly remarkable job of ensuring a safe, dependable supply. However, threats posed by an organized group of actors may represent a new and different challenge to the security of water supplies. A tool to assist in identifying possible attacks has been developed. Knowledge of these attack scenarios may help in designing countermeasures. The tool uses evolutionary computation as the optimization method, and EPANET as the system simulator. Examples of its use to identify effective physical attacks against a realistic but hypothetical pipe network and initial corresponding countermeasures are presented.

We present a mixed-integer programming (MIP) formulation for sensor placement optimization in municipal water distribution systems that includes the temporal characteristics of contamination events and their impacts. Typical network water quality simulations track contaminant concentration and movement over time, computing contaminant concentration time series for each junction. Given this information, we can compute the impact of a contamination event over time and determine affected locations. This process quantifies the benefits of sensing contamination at different junctions in the network. Ours is the first MIP model to base sensor placement decisions on such data, compromising over many individual contamination events. The MIP formulation is mathematically equivalent to the well-known $p$ -median facility location problem. We can exploit this structure to solve the MIP exactly or to approximately solve the problem with provable quality for large-scale problems.

A mixed-integer linear program is proposed to identify optimal sensor locations for early warning against accidental and intentional contaminations in drinking water distribution systems. The general model can be applied to unsteady hydraulic conditions. Furthermore, it may accommodate different design objectives whose problem formulations vary only by the cost function coefficients while decision variables and linear constraints remain identical. Such a feature is very important since several requirements may be factors for practical design of warning systems. Linear constraint matrix properties show that the solution may often be found at the root (no branching). If not, a procedure is proposed to identify a significant set of discrete decision variables whose integrality constraints can be always relaxed. This result is coupled with good data preprocessing to minimize auxiliary continuous variables and constraints, allowing for efficient computation and increasing model applicability to large problems. The methodology is illustrated on a small and a midsize network.

A Bayesian belief network (BBN) methodology is proposed for combining evidence to better characterize contamination events and reduce false positive sensor detections in drinking water distribution systems. A BBN is developed that integrates sensor data with other validating evidence of contamination scenarios. This network is used to graphically express the causal relationships between events such as operational changes or a true contaminant release and consequent observable evidence in an example distribution system. In the BBN methodology proposed here, multiple computer simulations of contaminant transport are used to estimate the prior probabilities of a positive sensor detection. These simulations are run over multiple combinations of possible source locations and initial mass injections for a conservative solute. This approach provides insight into the effect of uncertainties in source mass and location on the detection probability of the sensors. In addition, the simulations identify the upstream nodes that are more likely to result in positive detections. The BBN incorporates the probabilities that result from these simulations, and the network is updated to reflect three demonstration scenarios—a false positive and two true positive sensor detections.

This paper addresses the problem of contamination source determination in municipal drinking water networks. In previous work, the authors introduced a large-scale nonlinear programming approach for identifying both the time and location of contamination sources given concentration information from a limited number of sensors. Due to the sparseness of the sensor grid, this problem inherently has nonunique solutions. The problem was therefore regularized, and the regularized solution provided an approximate linear combination of possible injection scenarios. In this paper, a mixed-integer quadratic program is presented to refine the solution provided by the nonlinear programming formulation. We introduce a two-phase approach. In the n-phase, the number of likely injection locations is estimated. Using this information, the $e$ -phase is performed to extract the likely injection scenarios from the family of nonunique solutions. This two-phase approach is tested on a realistic municipal water network model with approximately 400 nodes, simulating five different injection scenarios. In all five examples, the approach was able to determine the correct number of injection locations and identify a set of possible injection scenarios containing the actual simulated injections.

In this paper, the authors propose a new approach, the simulation–optimization method, to solve a nonlinear contaminant-source and release-history identification problem for a complex water distribution system. This approach is based on optimization analysis, using the EPANET water distribution system model as a simulator. In this approach, EPANET is used to generate concentrations at arbitrarily selected monitoring locations by specifying release histories of potential contaminant sources that are arbitrarily located within the water distribution system. This information is used in a continuous optimal predictor–corrector algorithm to identify the sources and their release histories. Throughout the simulation sequence, the water distribution system being studied is assumed to operate under known hydraulic operational patterns. The optimization model that is used as a corrector to estimate the release histories of the contaminant sources is designed to identify the similarity between the simulation response and measured data at monitoring locations. This information exchange is developed as a closed-loop system resulting in a convergent algorithm. Three scenarios, derived from the publicly documented Dover Township (Toms River), N.J., water-distribution system are tested using the proposed approach. Results show that the approach is effective, efficient, and robust in identifying locations and release histories of contaminant sources.

This paper presents a new approach for contamination source identification in water distribution systems through a coupled model trees–linear programming algorithm. Model trees are an extension of regression trees (regression trees: tree-based models used to solve prediction problems in which the response variable is a numerical value) in the sense that they associate leaves with multivariate linear models. The model trees replace EPANET through learning (i.e., training and cross validation) after which a linear programming formulation uses the model trees linear rule classification structure to solve the inverse problem of contamination source identification. The use of model trees represents forward modeling (i.e., from root to leaves). The implementation of linear programming on the linear tree structure allows backward (inverse) modeling (i.e., from leaves to root) where the contamination injections characteristics are the problem unknowns. The proposed methodology provides an estimation of the time, location, and concentration of the contamination injection sources. The model is demonstrated using two example applications.

Vulnerability assessments may be used to help identify components of water distribution systems that require strengthening against possible attacks, including physical destruction and/or chemical contamination. Numerous recent research efforts have focused on the placement of sensor systems to aid vulnerability assessments associated with contamination events. A related issue is the probability of isolating a contaminant following sensor detection. In this current effort, we utilize three optimization techniques: (1) an unconstrained first-order reliability method (FORM); (2) a constrained FORM; and (3) parameter estimation (PEST), to determine the optimal demand to reduce contaminant concentration. This aids in consequence management of contamination events by supplying water distribution system operators with additional information to remediate contaminated sections. Application of these techniques to a relatively simple network and a moderately complex network demonstrates the usefulness of optimization methods in determining optimal demands in order to reduce contaminant concentration. Although each of the techniques performed well for this example, PEST illustrated greater capabilities in determining the most optimal solution.

This paper presents a two-part investigation of the response of municipal water distribution systems to contamination events. In Part I of the investigation, a contamination event was modeled as a steady $6\text{-}\mathrm{h}$ injection of a soluble conservative substance into a single node. The injection was repeated node by node at all 89 nodes in the pipe network. In each case, the fraction of the population at risk of contaminant exposure was estimated at the end of a $72\text{-}\mathrm{h}$ simulation period. A dimensionless exposure index (EI) was introduced as a simple global measure of network response, ranging from $\mathrm{EI}=0$ (no consumers are exposed) to $\mathrm{EI}=100\%$ (all consumers are at risk of exposure). Simulation results were used to construct a zone of influence (ZOI) map, which categorizes network injection nodes on the basis of their potential to expose downstream consumers. In Part II of the investigation, a generalized sensitivity analysis was performed to determine the sensitivity of network response to four dynamic network variables (base demand, storage capacity, injection mass, and injection duration). Latin hypercube sampling was used to set up 1,152 contamination event simulations at two injection nodes. Both nodes were selected on the basis of their exposure potential (one high, one low) as determined from the ZOI map. Based on the Kolmogorov-Smirnov $d$ statistic, exposure levels in the example network were found to be most sensitive to variations in base demand and injection mass. Tank storage capacity was important in certain cases, while injection duration tended to be least important.

Disease transmission models predict the spread of disease over time through susceptible, infected, and recovered populations, and are commonly used to design public health intervention strategies. A modified disease model is linked to flow and transport models for water distribution systems in order to predict the health risks associated with use of contaminated water. The proposed framework provides information about the spatial and temporal distribution of health risks in distribution systems and is useful for understanding the vulnerability of drinking water systems to contamination events, as well as for designing public health and water utility strategies to reduce risks.

Red team–blue team exercises are methods of evaluating security by creating a “game” where one team (the red team) attempts to “attack” a target and the other team (the blue team) tries to defend it. This paper describes a computer exercise where the red team simulates the contamination of a water distribution system and the blue team defends the system by installing monitors to detect the presence of the contaminant. This exercise was developed and has been used as part of several demonstrations on the effectiveness of contamination monitoring systems for distribution systems. For comparison, a mathematical model is applied to the same network to select monitor locations that provide the optimal solution in terms of a set of objectives.

Real-time water quality sensors are becoming commonplace in water distribution systems. However, field deployable, contaminant-specific sensors are still in the development stage. As development proceeds, the necessary operating parameters of these sensors must be determined to protect consumers from accidental and malevolent contamination events. This objective can be quantified in several different ways including minimization of: the time necessary to detect a contamination event, the population exposed to contaminated water, the extent of the contamination within the network, and others. We examine the ability of a sensor set to meet these objectives as a function of both the detection limit of the sensors and the number of sensors in the network. A moderately sized distribution network is used as an example and different sized sets of randomly placed sensors are considered. For each combination of a certain number of sensors and a detection limit, the mean values of the different objectives across multiple random sensor placements are calculated. The tradeoff between the necessary detection limit in a sensor and the number of sensors is evaluated. Results show that for the example problem examined here, a sensor detection limit of 0.01 of the average source concentration is adequate for maximum protection. Detection of events is dependent on the detection limit of the sensors, but for those events that are detected, the values of the performance measures are not a function of the sensor detection limit. The results of replacing a single sensor in a network with a sensor having a much lower detection limit show that while this replacement can improve results, the majority of the additional events detected had performance measures of relatively low consequence.

Protecting the water systems of the United States from terrorist attacks has become a federal and local priority. Routine sampling and analysis has been proposed as a potential monitoring approach that could be used to provide early detection of contamination events in drinking water systems. Using the threat ensemble vulnerability assessment computational framework, an evaluation of the benefits of three routine sampling programs is compared to a real-time monitoring program. The results are illustrated by tradeoff curves that demonstrate the benefits provided by a sensor network given an intentional biological or chemical attack. Further, the results show that response time is critical and physical sampling-based monitoring with sample collection frequencies of 24 h or longer are much less effective than real-time monitoring.