Prediction analysis of a wastewater treatment system using a Bayesian network
Introduction
Wastewater treatment is a complicated process which is affected by several microbial, chemical, and physical factors. Real-time prediction analysis of a wastewater treatment system is difficult because of the complex biological reactions that vary with time and environmental conditions.
A series of activated sludge models have been used to predict the performance of wastewater treatment systems (Gernaey et al., 2004; Gujer et al., 1999; Henze, 2007; Henze et al., 1999) and neural network-based modeling has been used to capture the relationships between variables in complex wastewater treatment systems (Cote et al., 1995; Lee et al., 2005). However, activated sludge models involve a large number of reactions and the parameters are often difficult to measure, while neural networks are black-box models that tend not to show dependencies between variables. Given the nonlinearity, uncertainty, and dynamic features of the wastewater treatment process, an alternative modeling platform is needed.
Bayesian networks also called the Bayesian belief networks, are a powerful knowledge representation tool that deals explicitly with uncertainty (Jensen, 1996; Jensen and Nielsen, 2007; Pearl, 1986, Pearl, 1995a). In the past few decades, Bayesian networks have been used in medical diagnoses (Berzuini et al., 1992; Shwe et al., 1991), military applications (Grois et al., 1998; Hautaniemi et al., 2000), ecological studies (Borsuk et al., 2006; Pollino et al., 2007; Stow et al., 2003; Young et al., 2011), environmental management (Borsuk et al., 2004; Bromley et al., 2005; Uusitalo, 2007; Varis and Keskinen, 2006), water resource management (Castelletti and Soncini-Sessa, 2007; Henriksen et al., 2007; Molina et al., 2010), environmental modeling (Aguilera et al., 2011; Chen and Pollino, 2012), and environmental change (Varis, 1995; Varis and Kuikka, 1997). Bayesian networks have a solid theoretical foundation, flexible inference capability, and convenient decision support mechanism. However, only a few articles have reported the application of Bayesian network in wastewater treatment plants. Chong and Walley (1996) described the use of a Bayesian network to analyze faults in an aerobic wastewater treatment plant and Sahely and Bagley (2001) developed a Bayesian network for diagnosing upsets in an anaerobic wastewater treatment system.
Modified Sequencing Batch Reactors (MSBR) is an advanced Sequencing Batch Reactor (SBR)-based wastewater treatment process. Despite the potential of the Bayesian network technique in the analysis of MSBR, its application for this purpose has not been reported to date. In this paper, we introduce the use of Bayesian networks for the analysis of MSBR. The objective of this work was to find a way to model and predict a wastewater treatment system based on MSBR via Bayesian networks. Our final objective was to set up an automatic real-time prediction and diagnosis system for a wastewater treatment system.
Section snippets
Brief introduction of the Bayesian network
Bayesian networks are directed acyclic graphs comprising of nodes and directed edges connecting the nodes (Jensen, 1996; Pearl, 1995a). Each node represents a random variable and its associated probability distribution or conditional probability distribution. The Bayesian network can be defined as N = (<V,E>,P), where V is a set of nodes expressed as V = {V1,V2,…,Vn}, E is a set of arcs, and P represents a set of conditional probability distributions. A probability distribution is a conditional
Description of MSBR
MSBR is an advanced wastewater treatment technology based on SBR (Yang, 2001). Over the years, MSBRs with four, five, six, seven, and nine pools have been developed in an effort to further improve the technology. In this work, a six-pool MSBR was employed. Fig. 2 shows the process flow of this MSBR.
The MSBR comprises of two functional areas, the anaerobic–anoxic–oxic and SBR functional areas. The sewage initially enters the anoxic zone, then enters the anaerobic zone before eventually entering
Framework of the prediction analysis
Mixed inference was used to analyze the network. Once the Bayesian network was constructed and entered into the BayesiaLab software, the probabilities of the query variables were updated by considering the states of the observed variables.
Fig. 5 shows the flowchart for the prediction analysis of MSBR. A key point of the predictive analysis of MSBR when using the proposed flowchart (Fig. 5) is to compare the probability of the previous Bayesian network state against that of the Bayesian network
Results
To consider the seasonal variation of some parameters (e.g., temperature), a one-year pilot study was conducted to verify the suggested Bayesian network-based model and the procedure for prediction analysis. During this period, we collected a set of data every day. The time of data collection was stochastic. Test data collected over a span of 335 days, except those collected during inclement weather, were selected as verification data.
Our prediction analysis can be divided into three typical
Conclusion
Bayesian network-based analysis is one of the best methods for addressing uncertainty in artificial intelligence applications (Jensen, 1996; Jensen and Nielsen, 2007; Pearl, 1995a). Owing to its flexible inferential capability and convenient decision support mechanism, it provides an effective approach for real-time prediction analysis of wastewater treatment systems. Therefore, this method has great potential in the analysis of MSBRs.
In this study, a Bayesian network-based approach was
Acknowledgments
The authors appreciate the helpful comments given by the editors and anonymous reviewers of this paper.
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