Evolutionary self-organising modelling of a municipal wastewater treatment plant
Introduction
Many different biological wastewater treatment processes exist, but the most widely used process system for municipal wastewater treatment is the activated-sludge process system.
Municipal activated-sludge wastewater treatment plant (WTP) has inherently dynamic characteristics that have high temporal variability of inflow as well as variable concentrations of components in the incoming wastewater to the plant. It has many complex and poorly known phenomena at work, such as interacting mechanisms among several different unit processes, hydrodynamic phenomena, the adaptive responses of living microorganisms due to changing environment conditions, and settling characteristic, etc. There is a strongly nonlinear relationship among the important process variables, and there are limitations in the ability to measure dynamic performance of the WTP directly.
In order to improve the monitoring, control, and performance of a WTP, building good predictive models is important both for understanding the dynamics of these complex systems and in the development of optimal control support and management schemes. The intelligent modelling approaches have recently attracted considerable attention in modelling of wastewater treatment processes [1], [2]. The purpose of this paper is to present a new approach, which is called genetic programming [8] as a self-organising modelling tool, to model dynamic performance of municipal activated-sludge WTP.
Genetic programming (GP), a branch of the well-known field of evolutionary computation, belong to the class of artificial intelligence (AI) computation algorithms. Genetic programming is exactly what the name implies: The technique to evolving computer models automatically by methods of natural selection (‘survival of the fittest’). There is a special form of genetic programming, called symbolic regression [3], where the induced models are restricted to mathematical functions. The purpose of symbolic regression is to develop mathematical models that fit the input–output data to satisfy the complex problem.
GP has the advantages that no a priori modelling assumption has to be made. Moreover, this technique can discriminate between relevant and irrelevant system inputs, yielding parsimonious model structures that accurately represent system characteristics [4] and provide us with a descriptive solution. Due to its advantages, GP has successfully been used for engineering problems such as process modelling and control [4], [5], [6], [7], [8], [9], robot control [10], environmental modelling [11], [12], [13], [14], medical applications [15], and applications for financial systems [16].
Firstly, this paper gives an extensive overview of genetic programming such as basic theory of GP, and its power as a new wastewater treatment process modelling tool. Secondly, the practical implementation technique of genetic programming for general modelling work is described in detail. Real data taken from municipal activated-sludge WTP is used to demonstrate how GP can automatically evolve to models with relatively simple, understandable structures. The resulting models evolved by GP are used to predict dynamic behaviour of the key process variables in the WTP. This shows the feasibility of using genetic programming as an intelligent self-organising modelling tool for the full-scale WTP system. Two different models, namely the nonlinear state–space model with neural network [17] and IAWQ ASM2 [18], are also applied to this WTP for comparison purposes.
Section snippets
Basics of genetic programming
Evolutionary algorithms (EA) are stochastic search methods that mimic the metaphor of natural biological evolution. A variety of evolutionary algorithms have been proposed. The major ones are: genetic algorithms [19], [20], evolutionary programming [21], evolutionary strategies [22], and genetic programming [3]. Each of these constitutes a different approach, however, they all are inspired in the same principles of natural evolution and share a common conceptual base of simulating the evolution
Paraparaumu municipal WTP
The Paraparaumu wastewater treatment is located on Paraparaumu city, the north of Wellington, the capital city of New Zealand and was originally built with the specification of the conventional activatedsludge process. The recipient, the Kapiti Coast, is considered to be an environmentally important area. This led to an upgrade of the plant in the 1990s, aiming at enhanced biological nutrient removal capability with a capacity of UV disinfection. For this paper, the data set before the plant
Designing the fitness criterion
A crucial fist step for evolving any model under the GP is to design a fitness function which determines how well an evolved model is able to solve the problem. In symbolic regression of genetic programming, the fitness is based on the error between the model inducted by genetic programming and the actual data. The performance of each model inducted is tested against a set of fitness cases.
In our case, the fitness is a numeric value assigned to each member of the population based on the error
Conclusions
In this paper, results have demonstrated the applicability of genetic programming to model the dynamic behaviour of the WTP. GP is not only capable of predicting the process behaviour accurately but provides insight into the dynamic behaviour of a partially known WTP system by allowing knowledge extraction of the evolved models. Our results show that GP can work most efficiently where the possible model is unknown or partially known and the understanding of the resulting model is important.
The
Acknowledgements
This work was funded by the Foundation for Research Science & Technology (FRST), New Zealand. Authors are grateful to Mr. Ian Basire of Kapiti District Council for providing the plant operation data used in this study.
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