Holger R. Maier

NEURAL NETWORKS FOR THE PREDICTION AND FORECASTING OF WATER RESOURCES VARIABLES: A REVIEW OF MODELLING ISSUES AND APPLICATIONS

Abstract Artificial Neural Networks (ANNs) are being used increasingly to predict and forecast water resources variables. In this paper, the steps that should be followed in the development of such models are outlined. These include the choice of performance criteria, the division and pre-processing of the available data, the determination of appropriate model inputs and network architecture, optimisation of the connection weights (training) and model validation. The options available to modellers at each of these steps are discussed and the issues that should be considered are highlighted. A review of 43 papers dealing with the use of neural network models for the prediction and forecasting of water resources variables is undertaken in terms of the modelling process adopted. In all but two of the papers reviewed, feedforward networks are used. The vast majority of these networks are trained using the backpropagation algorithm. Issues in relation to the optimal division of the available data, data pre-processing and the choice of appropriate model inputs are seldom considered. In addition, the process of choosing appropriate stopping criteria and optimising network geometry and internal network parameters is generally described poorly or carried out inadequately. All of the above factors can result in non-optimal model performance and an inability to draw meaningful comparisons between different models. Future research efforts should be directed towards the development of guidelines which assist with the development of ANN models and the choice of when ANNs should be used in preference to alternative approaches, the assessment of methods for extracting the knowledge that is contained in the connection weights of trained ANNs and the incorporation of uncertainty into ANN models.

The Use of Artificial Neural Networks for the Prediction of Water Quality Parameters

This paper presents the use of artificial neural networks (ANNs) as a viable means of forecasting water quality parameters. A review of ANNs is given, and a case study is presented in which ANN methods are used to forecast salinity in the River Murray at Murray Bridge (South Australia) 14 days in advance. It is estimated that high salinity levels in the Murray cause

Review: Methods used for the development of neural networks for the prediction of water resource variables in river systems: Current status and future directions

US 22 million damage per year to water users in Adelaide. Previous studies have shown that the average salinity of the water supplied to Adelaide could be reduced by about 10% if pumping from the Murray were to be scheduled in an optimal manner. This requires forecasts of salinity several weeks in advance. The results obtained were most promising. The average absolute percentage errors of the independent 14-day forecasts for four different years of data varied from 5.3% to 7.0%. The average absolute percentage error obtained as part of a real-time forecasting simulation for 1991 was 6.5%.

Selecting among five common modelling approaches for integrated environmental assessment and management

Over the past 15 years, artificial neural networks (ANNs) have been used increasingly for prediction and forecasting in water resources and environmental engineering. However, despite this high level of research activity, methods for developing ANN models are not yet well established. In this paper, the steps in the development of ANN models are outlined and taxonomies of approaches are introduced for each of these steps. In order to obtain a snapshot of current practice, ANN development methods are assessed based on these taxonomies for 210 journal papers that were published from 1999 to 2007 and focus on the prediction of water resource variables in river systems. The results obtained indicate that the vast majority of studies focus on flow prediction, with very few applications to water quality. Methods used for determining model inputs, appropriate data subsets and the best model structure are generally obtained in an ad-hoc fashion and require further attention. Although multilayer perceptrons are still the most popular model architecture, other model architectures are also used extensively. In relation to model calibration, gradient based methods are used almost exclusively. In conclusion, despite a significant amount of research activity on the use of ANNs for prediction and forecasting of water resources variables in river systems, little of this is focused on methodological issues. Consequently, there is still a need for the development of robust ANN model development approaches.

The effect of internal parameters and geometry on the performance of back-propagation neural networks: an empirical study

The design and implementation of effective environmental policies need to be informed by a holistic understanding of the system processes (biophysical, social and economic), their complex interactions, and how they respond to various changes. Models, integrating different system processes into a unified framework, are seen as useful tools to help analyse alternatives with stakeholders, assess their outcomes, and communicate results in a transparent way. This paper reviews five common approaches or model types that have the capacity to integrate knowledge by developing models that can accommodate multiple issues, values, scales and uncertainty considerations, as well as facilitate stakeholder engagement. The approaches considered are: systems dynamics, Bayesian networks, coupled component models, agent-based models and knowledge-based models (also referred to as expert systems). We start by discussing several considerations in model development, such as the purpose of model building, the availability of qualitative versus quantitative data for model specification, the level of spatio-temporal detail required, and treatment of uncertainty. These considerations and a review of applications are then used to develop a framework that aims to assist modellers and model users in the choice of an appropriate modelling approach for their integrated assessment applications and that enables more effective learning in interdisciplinary settings. We review five common integrated modelling approaches.Model choice considers purpose, data type, scale and uncertainty treatment.We present a guiding framework for selecting the most appropriate approach.

Non-linear variable selection for artificial neural networks using partial mutual information

Abstract Artificial neural networks of the back-propagation type are being used increasingly for modelling environmental systems. One of the most difficult, and least understood, tasks in the design of back-propagation networks is the choice of adequate internal network parameters and appropriate network geometries. Although some guidance is available for the choice of these values, they are generally determined using a trial and error approach. This paper describes the effect of geometry and internal parameters on network performance for a particular case study. Although the information obtained from the tests carried out in this research is specific to the problem considered, it provides users of back-propagation networks with a valuable guide on the behaviour of networks under a wide range of operating conditions. The results obtained indicate that learning rate, momentum, the gain of the transfer function, epoch size and network geometry have a significant impact on training speed, but not on generalisation ability. The type of transfer and error function used was found to have a significant impact on learning speed as well as generalisation ability.

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

Artificial neural networks (ANNs) have been widely used to model environmental processes. The ability of ANN models to accurately represent the complex, non-linear behaviour of relatively poorly understood processes makes them highly suited to this task. However, the selection of an appropriate set of input variables during ANN development is important for obtaining high-quality models. This can be a difficult task when considering that many input variable selection (IVS) techniques fail to perform adequately due to an underlying assumption of linearity, or due to redundancy within the available data. This paper focuses on a recently proposed IVS algorithm, based on estimation of partial mutual information (PMI), which can overcome both of these issues and is considered highly suited to the development of ANN models. In particular, this paper addresses the computational efficiency and accuracy of the algorithm via the formulation and evaluation of alternative techniques for determining the significance of PMI values estimated during selection. Furthermore, this paper presents a rigorous assessment of the PMI-based algorithm and clearly demonstrates the superior performance of this non-linear IVS technique in comparison to linear correlation-based techniques.

Use of artificial neural networks for predicting optimal alum doses and treated water quality parameters

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.

Use of artificial neural networks for modelling cyanobacteria Anabaena spp. in the River Murray, South Australia

Abstract Coagulation is an important component of water treatment. Determination of optimal coagulant doses is vital, as insufficient dosing will result in undesirable treated water quality. On the other hand, doses that are too high can result in high cost and health problems related to high levels of residual aluminium (if alum is used as the coagulant). Traditionally, jar tests are used to determine the optimum coagulant dose. However, this is expensive and time-consuming and does not enable responses to changes in raw water quality in real time. Modelling can be used to overcome these limitations. In this paper, artificial neural network models are used to model alum dosing of southern Australian surface waters. The performance of the models is found to be very good, with correlation ( R 2 ) values ranging from 0.90 to 0.98 for the process models predicting treated water turbidity, colour and ultraviolet absorbance at a wavelength of 254 nm (UVA-254). An R 2 value of 0.94 is obtained for the process inverse model used to predict optimum alum doses. Two simulation tools, Sim TTP and Sim WT, are developed to enable operators to obtain optimum alum doses easily. In addition, the simulation tools enable alum dosing rates to be controlled automatically in real time.

Neural network based modelling of environmental variables: A systematic approach

The use of artificial neural networks (ANNs) for modelling the incidence of cyanobacteria in rivers was investigated by forecasting the occurrence of a species group of Anabaena in the River Murray at Morgan, Australia. The networks of backpropagation type were trained on 7 years of weekly data for eight variables, and their ability to provide a 4-week forecast was evaluated for a 28-week period. They were relatively successful in providing a good forecast of both the incidence and magnitude of a growth peak of the cyanobacteria within the limits required for water quality monitoring. The use of lagged versus unlagged inputs was evaluated in the implementation and performance of the networks. Lagged inputs proved far superior in providing a fit to the actual data. Sensitivity analysis of input variables was performed to evaluate their relative significance in determining the forecast values. The analysis indicated that for this data set for the River Murray, flow and temperature were the predominant variables in determining the onset and duration of cyanobacterial growth. Water colour was the next most important variable in determining the magnitude of the population growth peak. Plant nutrients nitrogen, phosphorus and iron, and turbidity were less important for this time period.