Modeling biogas production from anaerobic wastewater treatment plants using radial basis function networks and differential evolution

Highlights

• A new method for modeling biogas production from wastewater treatment is introduced.

• A novel training algorithm for RBF neural networks is proposed to increase accuracy.

• Differential evolution is wrapped around the training procedure to boost efficiency.

• The method is evaluated successfully on a real-world wastewater treatment plant.

• The method outperforms other machine learning schemes regarding modeling performance.

Abstract

This study presents a new method for modeling biogas production obtained from anaerobic digestion treatment plants with increased accuracy. The method is based on artificial neural networks (ANNs) and more specifically on the efficient architecture of radial basis function (RBF) networks. A novel RBF training scheme is proposed, based on the non-symmetric fuzzy means (NSFM) algorithm, which has been shown to offer increased accuracy compared to other ANN methods, but cannot handle efficiently a large number of input variables. As this is the case in biogas production modeling, the algorithm is enhanced with an optimizer based on differential evolution (DE), which helps to properly tune the algorithm, ultimately boosting the accuracy of the produced models. The proposed approach is applied for modeling the biogas production on a real world, full-scale operational wastewater treatment plant. A comparison study shows the superiority of the proposed model, compared to different machine learning approaches.

Introduction

Industrial waste treatment is a multi-parametric task consisting of a number of processes, which - under certain assumptions centered around physicochemical characteristics of the waste, process and environmental conditions etc. - can be described by modeling techniques in order to predict its performance. Such processes exist in anaerobic digestion (AD) treatment plants, where organic biodegradable waste, such as agricultural, food, sludge and livestock wastes, are converted into a valuable energy source (Moustakas et al., 2020). Among the produced by-products, the main focus is given on biogas due to its high calorific value. It can therefore be burned and/or converted into electricity and heat via an appropriate electromechanical equipment (Achinas and Euverink, 2016; Bitton, 2005). Biogas can be compared to natural gas because of its ∼65% methane (CH₄) and ∼29% carbon dioxide (CO₂) content. Significant initiatives towards the development of biogas technology date back to the 19th century; since then, many improvements have been made worldwide, as more and more evidence testifies to the fact that biogas is a promising renewable source of energy, being able to reduce the need of fossil fuels and therefore greenhouse gas emissions (Deng et al., 2017; Sinsel et al., 2020).

Biogas fermentation is a complex biochemical process consisting of four (4) stages, known as hydrolysis, acidogenesis, acetogenesis and methanogenesis, each of which is controlled by the corresponding types of micro-organisms, bacteria and enzymes, which are highly sensitive to operational factors (Ghosh et al., 2020). The digestion process begins by microbial hydrolysis of organic material in order to dissolve insoluble organic polymers, such as carbohydrates. Next, acidogenic bacteria convert amino acids into carbon dioxide, hydrogen, ammonia and organic acids. In the last stage, the methanogenic bacteria convert the products of the process into carbon dioxide and methane.

The factors that affect the CH₄ production process during anaerobic treatment are numerous and include, among others, the characteristics of the incoming wastewater, temperature, pH, moisture content, the carbon to nitrogen to phosphorous ratio (C:N:P) known as nutrient elements, toxic substances, volatile fatty acid (VFA) content and hydraulic residence time (HRT) (Lohani and Havukainen, 2018). Chemical Oxygen Demand (COD) is often used as a measurement of wastewater quality, and thus provides a good indicator of wastewater plant efficiency. Temperature determines the digestion rate and defines a range which affects microbial development. Due to the sensitivity of anaerobic bacteria to the acid concentration there is an optimum pH range, whereas the pH value of a digester is affected by the alkalinity of the system and the concentration of VFA (Ward et al., 2008).

In order to achieve a smooth and optimal functioning of anaerobic digestion, it is necessary to supply the microorganisms with a variety of nutrients necessary for their growth and metabolism; there are specific levels of essential nutrient C and N (Abu Qdais et al., 2010). Thus, all feedstock should contain nutrients and essential trace elements for an efficient AD process. It is reported that C:N:P ratio of 100:3:1 is suitable for high methane yield (Lohani and Havukainen, 2018). Toxicity or inhibition of methanogenesis results in decreased methane production and increased VFA concentrations, which in turn affects pH values (Ward et al., 2008). HRT concerns the average time during which the substrate is retained in the digester and plays an important role in the process of anaerobic digestion; depending on the wastewater characteristics, different residence times are recommended for optimal processing conditions (Liu et al., 2018).

It is evident that AD is a biological process that depends not only on quantity and quality of microbial populations, but also on the design factors of the plant, as well as on physicochemical properties of the waste and therefore on the operating conditions of the anaerobic reactor. Simulation and control of the aforementioned factors is of primary importance when it comes to effective treatment; absence of due care on the values of these factors may result in the process being suspended, or completely blocked.

Therefore, modeling of the wastewater biodegradation process plays an important role, either as an effective performance analysis tool avoiding time consuming physicochemical analysis, or in terms of maximization of biogas production. However, several restrictions exist when it comes to the selection of modeling techniques, because such systems are characterized by nonlinearity and complex relations between the parameters affecting them. Furthermore, complex mechanisms often dominate in these elaborate systems, which make modeling with first-principle methods highly unfavorable. Hence, the interest is focused on sophisticated, yet simple modeling techniques.

Among the modeling techniques that have been developed to address such demanding tasks, many works focus on computational intelligence (CI) tools, e.g. artificial neural networks (ANNs); ANNs are inspired by biological neural networks (Haykin, 1999), and have been applied successfully to a wide range of complex nonlinear systems. Due to their advantageous characteristics, such as nonlinearity, generalization capabilities and robustness, to name but a few, ANNs are most capable of dealing with complex and highly nonlinear relations. Furthermore, due to their inherent ability to model any system based merely on input-output data pairs, no further knowledge about technical details of the system is required. Based on these properties, the role of CI tools in process system engineering is expected to grow further in the future (Pistikopoulos et al., 2021), while they seem to be able to offer an efficient tool for modeling and simulating wastewater biodegradation processes (Al et al., 2019; Fisher et al., 2020).

In literature, there are many works dealing with CI models for modeling wastewater treatment (WWT) processes. In Abu Qdais et al. (2010), an ANN combined with a genetic algorithm is used to simulate and optimize a biogas process using various digester operational parameters, such as temperature, total volatile solids and pH. The results of the study are promising, since the model is able to effectively estimate methane production and the optimal operational conditions are suggested. In Vyas et al. (2011), an ANN was applied to an effluent treatment plant in order to improve its operating performance by predicting the COD; using historical data, the developed ANN was able to provide operational guidance for plant operators. In Tümer and Edebali (2015), an ANN model is obtained for modeling a WWT plant of Konya, using daily data records over a four month period; several input variables are considered in this study, such as pH, temperature, COD, TSS and BOD. The aim of the work is to model the output values of TSS and according to the authors, the produced model can effectively predict the plant performance.

Additionally, in Vijayan and Mohan (2016), an ANN is developed for predicting effluent biochemical oxygen demand (BOD), COD, and total suspended solids (TSS), using historical plant data from an effluent treatment plant in dairy industry. The results indicate that the ANN model offers an efficient and robust tool for prediction and modeling purposes. In Hamada et al. (2018), both ANN and linear models have been used for the prediction of three major water quality parameters of a wastewater treatment plant in Gaza. Historic data records with many input variables concerning influent wastewater quality parameters, such as pH, temperature, BOD, COD and TSS are employed to predict BOD, COD and TSS values of the effluent. Experimental results showed that the ANN model outperforms a linear model, being able to predict the three important parameters more accurately. Moreover, results showed that the effluent BOD, COD and TSS are primarily affected by influent TSS and temperature input parameters. In Beltramo et al. (2019), an ANN was established to predict biogas production rate at an agricultural biogas plant in Germany using 15 input variables, including concentration of VFA, total solids, volatile solids to HRT and organic loading rate, among others. Ant colony optimization and genetic algorithms were implemented for feature reduction, yielding a reduced model dimension and improved prediction capabilities of the ANN model.

The aforementioned works center on a standard ANN architecture, i.e., multilayer perceptrons (MLPs), which consist of different number of hidden layers and neurons and employ standard algorithms for determining the parameter values of the network, while the neural network size is usually determined by trial-and-error. Even if the results of the above recently-published works testify to the fact that CI tools can be successfully used for modeling and simulation of wastewater plants, the implementation of novel, non-standard algorithms integrated with more robust ANN architectures can further improve modeling accuracy.

Radial basis function neural networks (RBFNNs) (Haykin, 1999) constitute a simple one-layered ANN architecture; RBFNNs provide several noteworthy advantages when it comes to accuracy and training times compared to other well-known architectures, for example MLP networks. RBFNNs exhibit numerous significant properties, such as universal approximation, robustness, good generalization and as a result, they represent a very competitive choice for modeling nonlinear processes. RBFNNs have been successfully applied for modeling WWT plants; for example, in Kowalczyk-Juśko et al. (2020) a simple RBFNN, amongst other ANN architectures including MLP networks, is developed in order to estimate the energy value of silage in shorter times without the necessity of expensive and long-term analysis. The results were in favor of RBF networks, as they were able to rival their competitors in terms of modeling accuracy. In Sakiewicz et al. (2020), several ANN architectures, including RBFNNs, are used in order to provide a tool for effective strategies of biogas production. The approach takes into account seven (7) controlled parameters, along with five (5) wastewater characteristics. The results showed that the produced models can be used as a predictive tool, pointing out the dominance of RBFNNs.

It should be noted however, that the accuracy of the RBFNN models depends heavily on the optimal selection of their parameters, and especially the number and location of RBF centers. When the RBFNN training procedure is viewed as an optimization task, it is plain to notice that the problem itself presents characteristics, such as non-linearity and non-differentiability, which are difficult to be addressed using conventional approaches. Therefore, more elaborate methods need to be incorporated, as for example evolutionary computation methods (Engelbrecht, 2007), derived from the family of nature-inspired algorithms. Evolutionary computation encapsulates numerous robust tools, such as differential evolution (DE), which have been applied successfully to a wide range of optimization problems (Bilal et al., 2020) and just like ANNs, these tools do not require prior knowledge of the studied system.

In this paper, the advantages of the RBF network architecture and the robust DE algorithm are incorporated in a novel and unified framework in order to develop a tool for modeling biogas production in an industrial AD treatment plant taking into account multiple inputs that affect biogas production. The network parameters are determined automatically through a novel training scheme based on the non-symmetric fuzzy means (NSFM) partitioning algorithm of the input space (Alexandridis et al., 2013). The NSFM algorithm presents a variant of the original symmetric fuzzy means that has been applied successfully in many applications, offering greater flexibility and thus yielding models with increased accuracy. However, due to the fact that tedious search procedures are required for parameter optimization in NSFM, its use becomes impractical in datasets with high dimensionality, as is the case when modeling biogas production. Thus, we introduce an algorithmic framework making use of an approach based on the concepts of DE to automatically search for the optimal configuration in the NSFM algorithm. The innovative integration of the DE and NSFM algorithms facilitates the learning procedure so as to determine the optimal network structure and parameters at an acceptable computational cost avoiding impractical exhaustive search procedures and eventually rendering the method suitable for producing highly accurate models for biogas production modeling.

The outline of this paper is as follows: in Section 2, a description of the AD treatment plant under study and the available data is provided. Section 3 gives an introduction to the RBF network architecture and the proposed training algorithm, whereas Section 4 presents the experimental part of the work, including dataset preparation, results, and relative discussion. Finally, Section 5 summarizes the conclusions of the current study, and provides plans for future work.