کوپلینگ از تجزیه و تحلیل رگرسیون لجستیک و روش های جستجوی محلی برای بررسی خصوصیات منبع آلاینده سیستم توزیع آب

Accidental or intentional drinking water contamination has long been and remains a major threat to water security throughout the world. An inverse problem can be constructed, given sensor measurements in a water distribution system (WDS), to identify the contaminant source characteristics by integrating a WDS simulation model with an optimization method. However, this approach requires numerous compute-intensive simulation runs to evaluate potential solutions; thus, determining the best source characteristic within a reasonable computational time is challenging. In this paper, we describe the development of a WDS contamination characterization algorithm by coupling a statistical model with a heuristic search method. The statistical model is used to identify potential source locations of contamination and a local search aims at further refining contaminant source characteristics. Application of the proposed approach to two illustrative example water distribution networks demonstrates its capability of adaptively discovering contaminant source characteristics as well as evaluating the degree of non-uniqueness of solutions. The results also showed that the local search as an optimizer has better performance than a standard evolutionary algorithm (EA).

Water distribution systems (WDSs) are highly vulnerable to various threat attempts. Intentional biochemical contamination has become a major concern recently due to the potential hazard to human health and the inherent complexities of the contaminants as well as the system. The installation of well-designed monitoring stations is necessary to detect the contamination and enhance the response capability. Rapid and accurate characterization of contaminant sources, once detected, is critical for managing an accidental or intentional WDS contamination event. The process of contaminant source determination involves not only the rapid identification of the injection locations but also the characterization of start time, duration and magnitude of contaminants to effectively control the spread of contamination as well as remediating the contaminated area. However, insufficient data and countless possible contamination scenarios can pose challenge to the characterization process in terms of both accuracy and efficiency. Various optimization based approaches for WDS source identification problems have been recommended by several researchers. The approaches reported previously can be classified into two categories. The first one employs direct sequential and simultaneous methods (e.g., Van Bloemen Waanders et al., 2003, Laird et al., 2005 and Laird et al., 2006). The second category couples a search procedure with a WDS hydraulic and water quality simulation package. One such approach, introduced by Guan et al. (2006), links the reduced gradient method with the WDS simulation to identify contaminant sources. Another simulation-optimization approach, proposed by Liu et al. (2006), uses a multiple population-based EA to search for a set of contaminant source characteristics that may result in similar sensor observations. Preis and Ostfeld, 2007 and Preis and Ostfeld, 2008 described a straightforward approach for contaminant source identification by coupling EPANET simulator with a genetic algorithm. Zechman and Ranjithan (2009) investigated evolution strategy (ES)-based approach and suggested ways to best structure the algorithm to solve this class of problem. Overall, increasing attention has recently been attracted to heuristic search methods due to the complexity of such a problem, such as discreteness, nonlinearity, non-convexity as well as non-uniqueness. More recently, some new methods have been reported to enhance the solution efficiency and allow practical application, such as Perelman and Ostfeld (2010), Shen and McBean (2010), etc. Heuristic search methods have their potential in tackling such complex optimization problems by incorporating simulation models. However, such a method results in increased computational burden because of a large number of time-consuming simulation runs needed to evaluate potential solutions. In particular, it poses challenges to a large network in terms of the identification time as well as the solution quality, even using parallel or distributed computing implementations. Computational requirements may be reduced by using a prescreening technique that eliminates infeasible solutions to reduce a priori the decision space in which the heuristic procedure must search. One such prescreening method is the back-tracking algorithm reported by De Sanctis et al., 2006 and De Sanctis et al., 2010, with the aim of identifying all possible locations and times that explain contamination incidents detected by water quality sensors. Di Cristo and Leopardi (2008) proposed an approach using the pollution matrix concept to determine a group of candidate nodes that could explain discrete solute concentration measurements. Another approach, proposed by Neupauer et al. (2010), identifies the probability density functions of possible prior times when the observed contamination was at any upgradient node. Logistic regression model (LRM) is another potential prescreening approach that shows promise, which has been investigated by Liu et al. (2011) to estimate the probability of each node being a candidate source node. The use of LR analysis would provide a more suitable tool due to its computational efficiency and the ability to describe source characteristics allowing for various uncertainties associated with the contamination event. Although the knowledge of potential source locations from the LRMs assists decision makers in isolating the source hydraulically from larger network, estimation of release history is required to identify potential extent of contamination, thus reducing public exposure in the contaminated area (De Sanctis et al., 2006 and De Sanctis et al., 2010). Therefore, subsequent to the LR analysis, heuristic search methods (e.g., EAs) could be considered to further refine the identification solutions. EAs discover global optima independently of initial guesswork through a population-based scheme and particular operators (e.g., crossover, mutation); however, as the population gradually moves towards optimal solutions, the efficiency of EAs typically decreases due to the stochastic property of the search process (Gen and Chen, 1997 and Xu et al., 2001). In contrast, local search (LS) approaches, such as the Nelder–Mead Simplex (NMS) and the Hooke–Jeeves pattern search method, focus mainly on locating locally better solutions by using a deterministic strategy, even though these methods are somewhat sensitive to the initial starting points. Hart (1994) and Land (1998) discuss the advantages of such LS procedures for determining the optima in a quick and computationally efficient manner when the search is focused on a local region. In this study, nongradient-based LS algorithms are examined as the heuristic search method due to the computational efficiency. Considering that the quality of LS solutions depends on the quality of the starting solution to these iterative search procedures, it is desirable that the smaller set of candidate nodes identified by the LR approach will serve as a set of good starting solutions for the subsequent LS procedure. Thus, the overall procedure investigated in this paper consists of: (1) a LR analysis-based prescreening and (2) a LS technique-based optimization. These components are described in the following subsections.