E. Downey Brill

Adaptive Contamination Source Identification in Water Distribution Systems Using an Evolutionary Algorithm-based Dynamic Optimization Procedure

Accidental drinking water contamination has long been and remains a major threat to water security throughout the world. Consequently, contamination source identification is an important and difficult problem in the managing safety in water distribution systems. This problem involves the characterization of the contaminant source based on observations that are streaming from a set of sensors in the distribution network. Since contamination spread in a water distribution network is relatively quick and unpredictable, rapid identification of the source location and related characteristics is important to take contaminant control and containment actions. As the contaminant event unfolds, the streaming data could be processed over time to adaptively estimate the source characteristics. This provides an estimate of the source characteristics at any time after a contamination event is detected, and this estimate is continually updated as new observations become available. We pose and solve this problem using a dynamic optimization procedure that could potentially provide a real-time response. As time progresses, additional data is observed at a set of sensors, changing the vector of observations that should be predicted. Thus, the prediction error function is updated dynamically, changing the objective function in the optimization model. We investigate a new multi population-based search using an evolutionary algorithm (EA) that at any time represents the solution state that best matches the available observations. The set of populations migrates to represent updated solution states as new observations are added over time. At the initial detection period, non-uniqueness is inherent in the source-identification due to inadequate information, and, consequently, several solutions may predict similarly well. To address nonuniqueness at the initial stages of the search and prevent premature convergence of the EA to an incorrect solution, the multiple populations in the proposed methodology are designed to maintain a set of alternative solutions representing different non-unique solutions. As more observations are added, the EA solutions not only migrate to better solution states, but also reduce the number of solutions as the degree of non-uniqueness diminishes. This new dynamic optimization algorithm adaptively converges to the best solution(s) to match the observations available at any time. The new method will be demonstrated for a contamination source identification problem in an illustrative water distribution network.

Modeling to generate alternatives: A fuzzy approach

Modeling to generate alternatives (MGA) has been proposed as a framework for dealing with complex problems for which there are important unmodeled issues. MGA techniques are designed to provide the analyst (or decision maker) with a set of alternatives that are good with respect to modeled objectives and different from each other. Some of these alternatives may be better than others with respect to the unmodeled issues. Furthermore, by examining a set of different alternatives the analyst may gain insight and understanding. The concept of fuzziness is demonstrated here to be applicable to the MGA framework. The fuzzy approach can increase the flexibility of targets on modeled objectives as well as the flexibility of the original constraints of the model. Illustrations are provided using a linear programming model of a land use planning problem and a mixed integer programming model of a regional wastewater treatment system planning problem.

Evaluating environmental quality management programmes in which dischargers are grouped

Abstract A method is presented for evaluating management programmes in which the dischargers are divided into groups. Analogous non-linear mathematical formulations are presented for direct regulation and effluent charge programmes, and a non-linear branch-and-bound solution procedure is described. A detailed algorithm is described for the effluent charge case; it is shown to be very practical in an application to data for the Delaware estuary.

Parallel Evolutionary Algorithm for Designing Water Distribution Networks to Minimize Background Leakage

AbstractLeaks in water distribution systems waste energy and water resources, increase damage to infrastructure, and may allow contamination of potable water. This research develops an evolutionary algorithm-based approach to minimize the cost of water loss, new infrastructure, and operations that reduce background leakage. A new design approach is introduced that minimizes capital and operational costs, including energy and water loss costs. Design decisions identify a combination of infrastructure improvements, including pipe replacement and valve installment, and operation rules for tanks and pumps. Solution approaches are developed to solve both a single-objective and multiobjective problem formulation. A genetic algorithm and a nondominated sorting genetic algorithm are implemented within a high-performance computing platform to select tank sizes, pump placement and operations, placement of pressure-reducing valves, and pipe diameters for replacing pipes. The evolutionary algorithm approaches identif...

ADDRESSING NON-UNIQUENESS IN A WATER DISTRIBUTION CONTAMINANT SOURCE IDENTIFICATION PROBLEM

The source of contamination in a water distribution system may be identified through a simulation-optimization approach. The optimization method searches for the contaminant source characteristics by iteratively estimating the contaminant plume concentrations until they match observations at sensors. The amount of information available for characterizing the source depends on the number and spatial locations of the sensors, as well as on the temporally varying stream of sensed data. The accuracy of the source characterization depends on the amount of observations available. A major factor affecting this accuracy is the degree of non-uniqueness present in the problem, which may cause misidentification of the source characteristics. As more sensors are added to the network, the non-uniqueness may be reduced and a unique solution may be identified. Thus, a key consideration when solving these problems is to assess whether the solution identified is unique, and if not, what other possible solutions are present. A systematic search for a set of alternatives that are maximally different in solution characteristics can be used to address and quantify non-uniqueness. For example, if the most different set of solutions that are identified by a search procedure are very similar, then that solution will be considered as the unique solution with a higher degree of certainty. Alternatively, identification of a set of maximally different solutions that vary widely in solution characteristics will indicate that nonuniqueness is present in the problem, and the range of solutions can be used as a general representation of the amount of non-uniqueness. This paper investigates the use of evolutionary algorithm (EA)-based alternatives generation procedures to quantify and address non-uniqueness present in a contaminant source identification problem for a water distribution network. As additional sensors may decrease the amount of non-uniqueness, several sensor configurations will be tested to investigate and quantify the improvement in uniqueness as more information is used in the source characterization.

A Hybrid Heuristic Search Approach for Contaminant Source Characterization

The rapid discovery of the contaminant source and its mass loading characteristics in a water distribution system (WDS) is vital for generating an efficient control strategy during a contamination event. Previous work on the Adaptive Dynamic Optimization Technique (ADOPT), which was developed as an Evolution Strategy (ES) based procedure, presents an approach to estimate the source characteristics adaptively, given dynamically updated observation data. Although this simulation-optimization approach is promising, it is computationally expensive, which poses challenges in the context of real-time solutions. This paper reports the findings of an investigation that builds upon the prior work by introducing a hybrid heuristic search method for the real-time characterization of a contaminant source. This new method integrates the ES-based ADOPT with a logistic regression (LR) analysis and a local improvement method to expedite the convergence and possibly solve the problem quickly. As a prescreening technique, a LR analysis step is performed prior to ADOPT; this step reduces the search space by eliminating unnecessary source nodes as potential source locations. Then, a local search (LS) approach is embedded into some of the algorithmic steps in ADOPT to serve as a postscreening step that potentially speeds up the convergence in localized regions in the solution space. Numerical experiments for the proposed hybrid approach are performed on an example water distribution network, and the results are compared with those of the standard implementation of ADOPT.

Characterizing reactive contaminant sources in a water distribution system

Accurate knowledge of the characteristics of the contamination source during a contamination event is necessary for development of any mitigation and control strategy. Contaminant injected in a system is most likely to be reactive with chlorine; however, it is impractical for water quality monitoring systems to be able to monitor for the presence of all possible contaminants. In any distribution system, chlorine levels and other water quality parameters (pH, conductance, etc.) are routinely monitored to maintain the prescribed disinfection capacity. Any reactive contaminant would affect the chlorine levels resulting in deviations in the expected chlorine levels from those expected under normal operating conditions. Anomalies in the chlorine concentration from that of the expected value can be used as a surrogate to characterize the contaminant source in the system. In the absence of knowing the reactive characteristics of the contaminants, the location of injection, and injection pattern, source identification becomes a difficult problem to solve. Source identification can be posed as an inverse problem. In earlier work authors investigated the effect of the order of reaction kinetics of the contaminant with chlorine and its impact on source identification problem assuming the reaction kinetics to be known. That work is extended to investigate a methodology to address the source identification problem based on chlorine measurements, and the effects of different uncertain contamination conditions. Findings from a range of scenarios will be presented and discussed.

Generation of alternative optima for nonlinear programming problems

Many nonlinear optimization problems are not unimodal, and only local optima can be obtained using gradient algorithms. A heuristic method, Modeling to Generate Alternatives (MGA), is introduced as a method for use in searching for a good local optimum for a highly nonlinear problem. The purpose of the MGA approach in this context is to produce easily a set of points which are feasible and maximally different from each other. By using this set as starting points for a nonlinear programming algorithm, the likelihood of locating more local optima is increased, and thus the likelihood of locating the global optimum or a good local optimum is also increased. Several problems, having multiple local optima and therefore difficult to optimize globally, were obtained from the literature and were used to demonstrate the approach. Two problems are described here: a wastewater treatment plant design model and a facility location model.