John B. Nixon

Parametric study for an ant algorithm applied to water distribution system optimization

Much research has been carried out on the optimization of water distribution systems (WDSs). Within the last decade, the focus has shifted from the use of traditional optimization methods, such as linear and nonlinear programming, to the use of heuristics derived from nature (HDNs), namely, genetic algorithms, simulated annealing and more recently, ant colony optimization (ACO), an optimization algorithm based on the foraging behavior of ants. HDNs have been seen to perform better than more traditional optimization methods and amongst the HDNs applied to WDS optimization, a recent study found ACO to outperform other HDNs for two well-known case studies. One of the major problems that exists with the use of HDNs, particularly ACO, is that their searching behavior and, hence, performance, is governed by a set of user-selected parameters. Consequently, a large calibration phase is required for successful application to new problems. The aim of this paper is to provide a deeper understanding of ACO parameters and to develop parametric guidelines for the application of ACO to WDS optimization. For the adopted ACO algorithm, called AS/sub i-best/ (as it uses an iteration-best pheromone updating scheme), seven parameters are used: two decision policy control parameters /spl alpha/ and /spl beta/, initial pheromone value /spl tau//sub 0/, pheromone persistence factor /spl rho/, number of ants m, pheromone addition factor Q, and the penalty factor (PEN). Deterministic and semi-deterministic expressions for Q and PEN are developed. For the remaining parameters, a parametric study is performed, from which guidelines for appropriate parameter settings are developed. Based on the use of these heuristics, the performance of AS/sub i-best/ was assessed for two case studies from the literature (the New York Tunnels Problem, and the Hanoi Problem) and an additional larger case study (the Doubled New York Tunnels Problem). The results show that AS/sub i-best/ achieves the best performance presented in the literature, in terms of efficiency and solution quality, for the New York Tunnels Problem. Although AS/sub i-best/ does not perform as well as other algorithms from the literature for the Hanoi Problem (a notably difficult problem), it successfully finds the known least cost solution for the larger Doubled New York Tunnels Problem.

Application of partial mutual information variable selection to ANN forecasting of water quality in water distribution systems

Recent trends in the management of water supply have increased the need for modelling techniques that can provide reliable, efficient, and accurate representation of the complex, non-linear dynamics of water quality within water distribution systems. Statistical models based on artificial neural networks (ANNs) have been found to be highly suited to this application, and offer distinct advantages over more conventional modelling techniques. However, many practitioners utilise somewhat heuristic or ad hoc methods for input variable selection (IVS) during ANN development. This paper describes the application of a newly proposed non-linear IVS algorithm to the development of ANN models to forecast water quality within two water distribution systems. The intention is to reduce the need for arbitrary judgement and extensive trial-and-error during model development. The algorithm utilises the concept of partial mutual information (PMI) to select inputs based on the analysis of relationship strength between inputs and outputs, and between redundant inputs. In comparison with an existing approach, the ANN models developed using the IVS algorithm are found to provide optimal prediction with significantly greater parsimony. Furthermore, the results obtained from the IVS procedure are useful for developing additional insight into the important relationships that exist between water distribution system variables.

Forecasting chlorine residuals in a water distribution system using a general regression neural network

In a water distribution system (WDS), chlorine disinfection is important in preventing the spread of waterborne diseases. The ability to forecast chlorine residuals at strategic points in the WDS would be a significant aid to water quality managers in helping them to ensure the satisfaction and safety of their customers. In this research, general regression neural networks (GRNNs) are developed for forecasting chlorine residuals in the Myponga WDS, to the south of Adelaide, South Australia, up to 72 h in advance. A number of critical model issues are addressed including: the selection of an appropriate forecasting horizon; the division of the available data into subsets for modelling; and the determination of the inputs relevant to the chlorine forecasts. To determine if the GRNN is able to capture any nonlinear relationships that may be present in the data set, a comparison is made between the GRNN model and a multiple linear regression (MLR) model. Additional investigations are also performed to simulate the effects of a reduced sampling frequency, and to estimate model performance for longer lead-time forecasts. When tested on an independent validation set of data, the GRNN models are able to forecast chlorine levels to a high level of accuracy, up to 72 h in advance. The GRNN also significantly outperforms the MLR model, thereby providing evidence of the existence of nonlinear relationships in the data set.

Investigation into the relationship between chlorine decay and water distribution parameters using data driven methods

Drinking water contaminated by micro-organisms can be a major risk to public health. Disinfection is used to destroy micro-organisms that are potentially dangerous to humans. In order to prevent bacterial regrowth, it is also desirable to maintain a disinfectant residual throughout the water distribution system. The most commonly used disinfectant is chlorine. If the dosing rate of chlorine is too low, there may be insufficient residual at the end of the distribution system, resulting in bacterial regrowth. On the other hand, the addition of too much chlorine can lead to customer complaints about taste and odour, corrosion of the pipe network and the formation of potentially carcinogenic by-products. Consequently, in order to determine the optimal chlorine dosing rate, it is necessary to be able to predict chlorine decay in the network. In this paper three different data-driven techniques are used to predict chlorine concentrations at two key locations in the Hope Valley water distribution system, located to the north of Adelaide, South Australia. The data-driven methods applied include a linear regression model and two artificial neural networks: the Multi Layer Perceptron (MLP); and the General Regression Neural Network (GRNN). A 5-year data set containing routinely measured parameters is used for model development and validation. The results indicate that data-driven techniques are relatively successful in predicting chlorine concentrations in the distribution system. This is despite the fact that there is no hydraulic model of the system, and that only data that are collected on a routine basis were used for model development.

Field Tests for Leakage, Air Pocket, and Discrete Blockage Detection Using Inverse Transient Analysis in Water Distribution Pipes

Stephens, Mark Leslie; Lambert, Martin Francis; Simpson, Angus Ross; Vitkovsky, John; Nixon, John B. Field tests for leakage, air pocket, and discrete blockage detection using inverse transient analysis in water distribution pipes Critical transitions in water and environmental resources management [electronic resource] : proceedings of the World Water and Environmental Resources Congress : June 27-July 1, 2004, Salt Lake City, UT / sponsored by Environmental and Water Resources Institute (EWRI) of the American Society of Civil Engineers ; Gerald Sehlke, Donald F. Hayes, and David K. Stevens (eds.): pp. 1-10

Minimum Number of Generations Required for Convergence of Genetic Algorithms

Genetic Algorithms (GAs) have been applied to a wide range of optimization problems, however a great deal of time and effort is required to calibrate the GA parameters to ensure that the best possible solutions are located. It is proposed that there exists a minimum number of GA generations before the members of a population will converge to a solution for a given optimization problem. This property would be useful in the calibration of a GA, as if there is a constant number of generations to solve the problem, the best population size can be determined using the desired number of function evaluations divided by the minimum number of generations. The hypothesis is tested for two versions of a test function; a commonly used separable test function, and a version of the function with epistatic interactions introduced between decision variables. Different problem sizes and convergence criteria are also considered. Two different relationships are identified. For the case where epistatic interactions are introduced into the test function the hypothesis is validated, as a constant number of generations before convergence is identified, and this increases with the size of the problem. However, for the case with no interactions between decision variables, the smallest population size produced the best results, regardless of problem size or convergence criteria.

Improving Metamodel-based Optimization of Water Distribution Systems with Local Search

Metamodels can be used to aid in improving the efficiency of computationally expensive optimization algorithms in a variety of applications, including water distribution system (WDS) design and operation. Genetic Algorithm (GA)-based optimization of WDSs is very computationally expensive to optimize a system in a practical amount of time for real-sized problems. A metamodel, of which Artificial Neural Networks (ANNs) are an example, is a model of a complex simulation model. It can be used in place of the simulation model where repeated use is necessary, such as when carrying out GA optimization. To complement the ANN-GA, six local search algorithms have been developed or applied in this research, with the aim of improving the performance of metamodel-based optimization of WDSs. All algorithms performed well, however, using computational intensity as a criterion with which to evaluate results, the best local search algorithms were sequential downward mutation (SDM) and maximum savings downward mutation (MSDM).

Estimating Risk Measures for Water Distribution Systems using Metamodels

Recent developments in the field of optimization of Water Distribution Systems (WDS) have focused on incorporating uncertainty into the analysis, recognizing that variables such as demand should be considered as stochastic variables. As a result hydraulic reliability must be considered as a constraint, rather than pressure heads. The most common method of quantifying reliability is to use a Monte Carlo Simulation (MCS). However, this is a very computationally expensive process. In this research, a metamodeling approach was used to reduce this computational intensity. A metamodel is an approximation of an existing model, which takes less time to run, making it much more computationally efficient upon repeated use, such as in a MCS or during optimisation with a Genetic Algorithm. The specific type of metamodel used in this research was an Artificial Neural Network (ANN), as it is capable of approximating any function without specifying the form it will take. Two metamodeling scenarios are used in this research to approximate reliability. First, a metamodel was developed that approximated pressure heads and chlorine residuals for an adaptation of the New York Tunnels problem, from which reliability was calculated. Second, reliability was approximated directly with a metamodel, thus eliminating the need of a MCS completely. The results in this paper have shown that ANN metamodels can be used to accurately approximate common risk measures used to evaluate WDS performance, such as hydraulic and water quality reliability and vulnerability, while offering considerable savings in computational time. It was found that it was more computationally efficient to use ANNs to approximate pressure heads and chlorine residuals than to approximate reliability directly. This was due to the fact that it took a significant amount of time to generate training data for the latter case.

Selection of Genetic Algorithm Parameters for Water Distribution System Optimization

Abstract The ability of Genetic Algorithm (GA) methods, to find near optimal solutions to Water Distribution System (WDS) optimization problems has been widely demonstrated. However, one of the main concerns in applying these methods is identifying suitable values for the GA parameters. The values selected for these parameters have a significant impact on the algorithm’s behavior, and therefore greatly affect the quality of the final solution found, as well as the time taken to find that solution. A considerable amount of time and effort must be dedicated to the calibration of these parameters for the GA practitioner to have any confidence that the values used are producing the desired results. The impact of each parameter will be dependent on the values of the other parameters, and it is likely that there exists different combinations that will produce the same exploration/exploitation behavior. This offers the potential to reduce the number of parameters requiring calibration, thus making the task of applying these methods much simpler. This paper describes large-scale sensitivity analyses that have been used to calibrate a real coded GA with a distributed crossover operator, for a WDS optimization problem, the Cherry Hill–Brushy Plains network, ultimately leading to the identification of a new optimal solution. Through these analyses, groups of parameter values are identified that cause the algorithm to perform very well in terms of algorithm convergence and the quality of the final solutions obtained. These results demonstrate that by understanding the parameters controlling the GA, and the relationships between them, the effort required to calibrate a GA for a given application can be reduced significantly.

Using field measured transient responses in a water distribution system to assess valve status and network topology

1 ABSTRACT Uncertainty about the status of valves in a water distribution system, or the existence of total blockages, is not uncommon. This paper presents an approach for determining topological changes using transient response analysis. Precise information is not available regarding all the physical elements contributing to the transient response of a water distribution system. Thus a parameterised model is developed and calibrated to represent “real” transient responses from a field water distribution system. The robustness of this model, and the methodology for diagnosing topological changes, are confirmed when used to successfully identify closed valves in the field.