Monitoring large-scale treatment wetlands is costly and time-consuming, but required by regulators. Some analytical results are available only after 5 days or even longer. Thus, adaptive neuro-fuzzy inference system (ANFIS) models were developed to predict the effluent concentrations of 5-day biochemical oxygen demand (BOD_{5}) and NH_{4}-N from a full-scale integrated constructed wetland (ICW) treating domestic wastewater. The ANFIS models were developed and validated with a 4-year data set from the ICW system. Cost-effective, quicker and easier to measure variables were selected as the possible predictors based on their goodness of correlation with the outputs. A self-organizing neural network was applied to extract the most relevant input variables from all the possible input variables. Fuzzy subtractive clustering was used to identify the architecture of the ANFIS models and to optimize fuzzy rules, overall, improving the network performance. According to the findings, ANFIS could predict the effluent quality variation quite strongly. Effluent BOD_{5} and NH_{4}-N concentrations were predicted relatively accurately by other effluent water quality parameters, which can be measured within a few hours. The simulated effluent BOD_{5} and NH_{4}-N concentrations well fitted the measured concentrations, which was also supported by relatively low mean squared error. Thus, ANFIS can be useful for real-time monitoring and control of ICW systems.

## INTRODUCTION

The growing interest in the use of constructed wetlands (CWs) for wastewater treatment, along with stringent water quality standards, increasingly stresses the need to develop better process design and monitoring tools (Rousseau *et al*. 2004). More specifically, the biochemical oxygen demand (BOD) is an important parameter that characterizes the biodegradable constituent of organic matter in treatment plant and CW effluents. However, BOD is relatively time-consuming to measure and requires at least 5 days. For real-time water quality control purposes, CWs increasingly require the development of accurate inferential models for predicting the BOD and other parameters for process monitoring and control. Accordingly, multiple efforts have been dedicated to the modelling of CW processes, ranging from simple rules of thumb and regression equations to the well-known first-order k-C* models, Monod-type equations and more complex dynamic and process-based models (Rousseau *et al*. 2004; Kumar & Zhao 2011).

More recently, the use of artificial intelligence (AI) modelling techniques has increased with the recognition of its potential (Chen *et al*. 2008). AI mimics human perception, learning and reasoning to solve complex problems. Their ability to construct non-linear relationships that can explain complex relationships within a data set without the difficult task of dealing with deterministic non-linear mathematics (Hamed *et al*. 2004) makes AI models particularly suitable for modelling the processes within complex environmental systems. More significantly, AI models have the ability to generalize the input–output relationship to produce an output when presented with previously unseen inputs. Furthermore, AI models are data-driven and so there is no requirement to specify the mathematical form of the relationship being modelled.

Of the range of AI models (Chen *et al*. 2008), the commonly used techniques are artificial neural networks (ANNs) and fuzzy logic systems (FLS), both of which have played important roles in the development of models for complex environmental systems (Cinar 2005). The fundamental and complementary features of ANNs and FLS have been combined into integrated systems, termed fuzzy neural network (FNN). FNN combines the benefits of both ANN and FLS by bringing together the learning and the computation powers of ANNs and the high-level human-like thinking and reasoning ability of FLS. They are effective: fast, efficient and easily designed, implemented and understood. By combining them, learning in ANNs reduces the need to prime fuzzy systems. In addition, fuzzy systems attenuate ‘noise’, from which some ANNs suffer (Chen *et al*. 2008).

This paper employed a well-known and easily understood FNN technique, namely adaptive neuro-fuzzy inference system (ANFIS), to demonstrate its feasibility for modelling full-scale CW systems. The aim was to develop an ANFIS model for monitoring a full-scale integrated constructed wetland (ICW) treating domestic wastewater in Ireland. The specific objective was to develop a model for the rapid prediction of 5-day BOD (BOD_{5}) and NH_{4}-N, using other cost-effective, quicker and easier to measure water quality variables, to facilitate the use of these parameters for real-time monitoring and control of key water quality parameters within ICW systems.

## MATERIALS AND METHODS

### Study site description

The ICW treatment system at the centre of the study is located within the walls of the Castle Leslie Estate at Glaslough in County Monaghan, Ireland (06 °53′37.94″W, 54 °19′6.01″N). Dimensions of the wetland cells are presented in Table 1. The ICW system (Figure 1) was commissioned in October 2007, to treat sewage from Glaslough. The design capacity of the ICW system is 1750 population equivalent. The functional water area of the ICW cells is 3.25 ha within a curtilage area of 6.74 ha.

ICW section . | Area (m^{2})
. | Depth (m) . | Total volume (m^{3})
. | Effective volume (m^{3})
. |
---|---|---|---|---|

Sedimentation pond 1 | 285 | 0.45 | 128.3 | 85.5 |

Sedimentation pond 2 | 365 | 0.45 | 164.3 | 109.5 |

Cell 1 | 4664 | 0.42 | 1958.9 | 1399.2 |

Cell 2 | 4500 | 0.38 | 1710.0 | 1350 |

Cell 3 | 12660 | 0.32 | 4051.2 | 3798 |

Cell 4 | 9170 | 0.36 | 3301.2 | 2751 |

Cell 5 | 1460 | 0.29 | 423.4 | 423.4 |

Total wetland system | 33104 | – | 11737.3 | 9916.6 |

ICW section . | Area (m^{2})
. | Depth (m) . | Total volume (m^{3})
. | Effective volume (m^{3})
. |
---|---|---|---|---|

Sedimentation pond 1 | 285 | 0.45 | 128.3 | 85.5 |

Sedimentation pond 2 | 365 | 0.45 | 164.3 | 109.5 |

Cell 1 | 4664 | 0.42 | 1958.9 | 1399.2 |

Cell 2 | 4500 | 0.38 | 1710.0 | 1350 |

Cell 3 | 12660 | 0.32 | 4051.2 | 3798 |

Cell 4 | 9170 | 0.36 | 3301.2 | 2751 |

Cell 5 | 1460 | 0.29 | 423.4 | 423.4 |

Total wetland system | 33104 | – | 11737.3 | 9916.6 |

Influent primary domestic wastewater from the village is pumped directly into a receiving sedimentation pond. From there, the wastewater subsequently flows by gravity sequentially through the five earthen-lined cells. The effluent of the last cell discharges directly into the adjacent Mountain Water River.

The wetland cells were planted in a club pattern, and the main plants were *Carex riparia* Curtis, *Phragmites australis* (Cav.) Trin. ex Steud., *Typha latifolia* L., *Iris pseudacorus* L., and *Glyceria maxima* (Hartm.) Holmb. Other plants were *Glyceria fluitans* (L.) R.Br., *Juncus effusus* L., *Sparganium erectum* L. emend Rchb, *Elisma natans* (L.) Raf., and *Scirpus pendulus* Muhl.

### Adaptive neuro-fuzzy inference system

ANFIS is a Takagi–Sugeno type (Takagi & Sugeno 1985; Jang 1993) fuzzy inference system implemented within the framework of adaptive neural networks. Based on a multilayer feed-forward network, ANFIS uses neural network learning algorithms and fuzzy reasoning to map a set of inputs to the output. In the network structure, part or all of the nodes are adaptive, which means that the output of each node depends on the parameter(s) pertaining to it. The parameter(s) should be changed to minimize a prescribed error measure according to the network's learning algorithm. Each node performs a particular function (node function) on incoming signals as well as providing a set of parameters pertaining to this node. The nature of node functions may vary from one node to the other, and the choice of each node function depends on the overall input–output function that the adaptive network is required to carry out (Jang 1993). To reflect different adaptive capabilities, an ANFIS uses both circle and square nodes, whereby a square (adaptive) node has parameters while a circle (fixed) node has none. The architecture of a typical ANFIS with two inputs, two fuzzy *if-then* rules and one output for the first-order Takagi and Sugeno type fuzzy model (Takagi & Sugeno 1985), where each input is assumed to have two associated membership functions (MFs), is shown in Figure 2.

*if-then*rules can be expressed as (Jang 1993; Wang & Elhag 2008)where and are the MFs for the inputs

*x*and respectively; and are consequent parameters.

The architecture of a typical ANFIS consists of five layers (Figure 2), and every node in a given layer performs particular functions in the ANFIS such as *input*, *fuzzification*, *rule inference*, *normalization* and *defuzzification*. A detailed description is provided in Jang (1993).

### Model development

#### Data variables selection

The general idea for the model development was to predict water quality parameters, which are time-consuming to measure, using other parameters, which are more cost-effective, quicker and easier to measure. Based on this consideration, five variables which can be measured within a few hours, namely water temperature (*T*), pH, dissolved oxygen (DO), oxidation–reduction potential (ORP) and electrical conductivity (EC), were selected. The corresponding expensive and time-consuming to measure variables were the 5-days at 20 °C *N*-allylthiourea BOD_{5} and ammonia-nitrogen (NH_{4}-N). Although NH_{4}-N may not always be expensive or time-consuming to measure in developed countries, there are potential cost, labour and time savings, if the analysis of many samples is required. Moreover, a predictive model can be particularly useful in situations where qualified technicians are unavailable to perform the analyses. Weekly data records for BOD_{5} and NH_{4}-N, with no missing values, collected over the period of February 2008 to April 2012 from the ICW at the centre of this study were selected for modelling. These data records were, however, incomplete, as there were missing values for the other five parameters, which occurred completely at random within the data array. Details of the water quality sampling and analyses are presented in Dong *et al*. (2011) and Dzakpasu *et al*. (2011). In summary, *N*-allylthiourea BOD_{5} was measured according to Method 5210 B published by APHA (1998). A respirometric (manometric) BOD OxiTop system (WTW GmbH, Weilheim, Germany) was used. NH_{4}-N was measured using test kits supplied by Hach Lange (Hach Method 8038, Hach Company, Loveland, CO, USA).

#### Data pre-treatment

For any modelling strategy, the quality of the outputs strongly depends on the quality of the selected input variables. Therefore, data pre-treatment provides essential techniques on how measured data sets can be validated, including how the quality of the data can be improved. This is necessary to obtain reliable analysis results. Pre-processing techniques to deal with the noise in data sets by replacing the missing values and omitting the outliers to improve the data quality and the performance of ANFIS is an option.

In the present study, all measurements were examined with respect to missing data, and missing values were replaced by values representing averages of adjacent data points. Furthermore, possible outliers and erroneous values were manually labelled. When identified, all outliers and erroneous values were subsequently removed from the data set and treated as missing values.

#### Selection of model input variables

In many previous models involving ANN and FLS, methods for input variable selection required generating different models while searching for the optimal combination of variables, which can be time-consuming and computationally expensive. In this study, a simple and effective method for selecting significant input variables on the basis of a class of sub-clusters created by a self-organizing network was used (Linkens & Chen 1999). Herein, a self-organizing map (SOM) network (Kohonen 1995) was applied to elucidate relationships and extract the most important input variables (i.e., *T*, pH, ORP, DO and EC), which independently and significantly influenced the effluent BOD_{5} and NH_{4}-N. The SOM is an unsupervised competitive learning neural network model and algorithm that implements a characteristic non-linear projection method from the high-dimensional space of sensory or other input signals onto a low-dimensional regular lattice of neurons. The SOM can be visualized with the help of the unified distance matrix (*U*-matrix) and the component planes. The *U*-matrix visualizes distances between neighbouring map units, and thus shows the cluster structure of the map. High values of the *U*-matrix point towards a cluster border. A uniform area of low values indicates a cluster. Each component plane indicates the values of one variable in each map unit (Vesanto *et al*. 1999).

#### Training and validation data sets

The selected pre-processed data records were divided into three subsets: a training set, a checking set to insure that models do not overfit the training data, and a validation set. During this step, care was taken to maintain the temporal coherence between data points.

#### Clustering of input and output variable values

Subtractive clustering is a fast and robust method for estimating the number and location of cluster centres present in a collection of data points. Initial fuzzy rules with rough estimates of MFs are obtained from the cluster centres; the MFs and other rule parameters are then optimized with respect to some output error criterion (Chiu 1997).

*ANFIS(BOD*and

_{5})*ANFIS(NH*models, respectively. Thus, each cluster represented a rule; the rules corresponding to Equation (3) may be stated aswhere is the rule , is the crisp input of rule

_{4}-N)*r*, is the correspondent crisp output of rule

*r*, is the antecedent clause of rule

*r*(fuzzy sets usually corresponding to linguistic labels), and is the consequent clause of rule

*r*. The cluster centres represent the initial value of the premise parameter in the function.

#### Development of the ANFIS models

The ANFIS models were built by the *anfisedit* function in MATLAB^{®}, where the data sets were initially analysed by fuzzy subtractive clustering to determine the cluster centres. The cluster centres represent the initial values of the premise parameters and, therefore, the initializing parameters were determined from here.

The types and number of MFs in each ANFIS, including *Gaussian curve, generalized bell curve, triangular* and *trapezoidal-*shaped functions, and the parameters were tested during clustering to determine an appropriate ANFIS model. The parameters for clustering were the following: squash factor, 1.25; aspect ratio, 0.5; rejection ratio, 0.15; range of influence, 0.5; error tolerance, 0. Table 2 presents the final architectures of the ANFIS models after clustering. With different input variables, the ANFIS models for BOD_{5} and NH_{4}-N had *Gaussian curve* and *generalized bell curve* MFs, respectively, for each input variable giving the best result.

Basic structure . | BOD . | NH_{4}-N
. |
---|---|---|

Number of nodes | 77 | 46 |

Number of linear parameters | 35 | 20 |

Number of non-linear parameters | 56 | 45 |

Number of inputs | 3 | 3 |

Number of input MFs | 7 | 5 |

Shape of input MFs | Gassmf | Gbellmf |

Number of training data pairs | 72 | 74 |

Number of fuzzy rules | 7 | 5 |

Basic structure . | BOD . | NH_{4}-N
. |
---|---|---|

Number of nodes | 77 | 46 |

Number of linear parameters | 35 | 20 |

Number of non-linear parameters | 56 | 45 |

Number of inputs | 3 | 3 |

Number of input MFs | 7 | 5 |

Shape of input MFs | Gassmf | Gbellmf |

Number of training data pairs | 72 | 74 |

Number of fuzzy rules | 7 | 5 |

When the initial values of premise parameters and the architecture of the predictive models were defined, the hybrid-learning algorithm trained the networks. Subsequently, the premise and consequent parameters of the network were pruned, and MFs of the variables were optimized. The models were then used for predicting BOD_{5} and NH_{4}-N.

#### Model performance evaluation criteria

*x*is the vector of the true values. An MSE of zero indicates that the estimator predicts observations of the parameter

*x*with perfect accuracy.

## RESULTS AND DISCUSSION

### Relations between input and output variables

Table 3 summarizes the selected ICW effluent water quality variables between February 2008 and April 2012. Up to 200 measurements per variable were taken. The mean treatment efficiencies for NH_{4}-N and BOD_{5} were 95 and 98%, respectively. According to the mean and median values, the ICW system achieved high treatment performance over the monitoring period.

. | T
. | pH . | ORP . | DO . | EC . | NH_{4}-N
. | BOD_{5}
. |
---|---|---|---|---|---|---|---|

Mean | 11.5 | 7.11 | –13 | 2.37 | 456 | 1.27 | 8 |

Standard error | 0.22 | 0.02 | 0.79 | 0.12 | 4.77 | 0.16 | 0.40 |

Median | 12.6 | 7.09 | –11 | 1.50 | 452 | 0.31 | 6 |

Mode | 13.0 | 6.99 | –12 | 0.4 | 400 | 0.15 | 4 |

Standard deviation | 4.1 | 0.31 | 14.82 | 2.28 | 89.06 | 2.36 | 7.44 |

Range | 18.5 | 1.47 | 111 | 11.37 | 747 | 12.75 | 46 |

Minimum | 2.8 | 6.45 | –60 | 0.12 | 128 | 0.05 | 4 |

Maximum | 21.3 | 7.92 | 51 | 11.49 | 875 | 12.80 | 50 |

. | T
. | pH . | ORP . | DO . | EC . | NH_{4}-N
. | BOD_{5}
. |
---|---|---|---|---|---|---|---|

Mean | 11.5 | 7.11 | –13 | 2.37 | 456 | 1.27 | 8 |

Standard error | 0.22 | 0.02 | 0.79 | 0.12 | 4.77 | 0.16 | 0.40 |

Median | 12.6 | 7.09 | –11 | 1.50 | 452 | 0.31 | 6 |

Mode | 13.0 | 6.99 | –12 | 0.4 | 400 | 0.15 | 4 |

Standard deviation | 4.1 | 0.31 | 14.82 | 2.28 | 89.06 | 2.36 | 7.44 |

Range | 18.5 | 1.47 | 111 | 11.37 | 747 | 12.75 | 46 |

Minimum | 2.8 | 6.45 | –60 | 0.12 | 128 | 0.05 | 4 |

Maximum | 21.3 | 7.92 | 51 | 11.49 | 875 | 12.80 | 50 |

SOM was applied to identify the relationships between the selected input data set. The *U*-matrix representation of the SOM visualizes the distances between the map nodes (Vesanto *et al*. 1999; Lee & Scholz 2006). The distances between the neighbouring map nodes were calculated and visualized by plotting different shades of grey between them. The component plane shows the value of the variable in each map unit (Lee & Scholz 2006), such that the lighter grey shades are associated with the high relative component value of the corresponding weight vector. This helps to identify and illustratively show clusters in the input data.

Figure 3 illustrates the SOM component planes visualization of the impact of the selected input variables on the concentrations of BOD_{5} and NH_{4}-N in the ICW effluent. According to the SOM, high and values were replaced the average of adjacent data points effluent BOD_{5} concentrations (>20 mg L^{−1}) were associated with relatively lower pH (<7), high *T* (>10 °C), and lower DO (<0.5 mg L^{−1}). The association of BOD_{5} to EC and ORP was weak (Figure 3(a)), although EC appeared to exhibit a negative effect. This indicated that BOD_{5} removal was probably influenced negatively by temperature and positively by DO and pH*.* Therefore, *T,* pH and DO, which showed stronger associations with BOD_{5}, were selected as the most important input variables, which independently and significantly influenced the effluent BOD_{5}. On the other hand, high effluent NH_{4}-N concentrations (>10 mg L^{−1}) appeared to be associated with relatively lower *T* (<5 °C), lower DO (<1.0 mg L^{−1}) and higher EC (>600 μS cm^{−1}) (Figure 3(b)). Thus, NH_{4}-N removal in the ICW was probably influenced negatively by temperature and DO, but positively by EC. There was no obvious association of pH and ORP to NH_{4}-N, and therefore, *T,* DO and EC were selected as the most important input variables, which independently and significantly influenced the effluent NH_{4}-N.

The relationships revealed by the SOM were found to conform well to the observed correlations reported by other previous studies. For example, it has been shown that organic matter and nutrient treatment efficiency were reduced by high salinity (measured as EC), which consequently, led to high effluent concentrations in CWs (Wu *et al*. 2008). Chapanova *et al*. (2007) demonstrated that a high salinity markedly reduced NH_{4}-N degradation and caused significant reductions in both nitrification and denitrification, resulting in higher effluent concentrations. Additionally, aerobic degradation of organic substances is noted to occur under high DO conditions, whereas most microbial processes occur under circum neutral pH conditions (Kadlec & Wallace 2009). Under high pH conditions, nevertheless, significant losses of N may occur in open water areas via ammonia gas volatilization, leading to lower NH_{4}-N effluent concentrations. Although the pH value measured in the ICW dropped to 6.45, there was no observed effect on NH_{4}-N removal, because the pH value remained within the circum neutral pH range between 6 and 8, which is near optimal for nitrification and denitrification processes to occur (Tchobanoglous *et al*. 2003; Kadlec & Wallace 2009). Moreover, water temperature modifies the rates of several key biological processes. For instance, microbial N processing is strongly influenced by water temperature, with doubling of rates over a temperature range of about 10 °C (Kadlec & Reddy 2001). The microbial activities related to denitrification can decrease considerably at water temperatures below 15 °C (Kuschk *et al*. 2003).

### Simulation of effluent BOD_{5} concentrations

Figure 4(a) depicts the prediction results of BOD_{5} concentrations in the ICW effluent using ANFIS. The performance of the model during validation, when presented with previously unseen data, namely the checking and validation data (after training the model), is shown. At the training step, MSE between the predicted and observed concentrations of BOD_{5} in the ICW effluent was 0.211, which was achieved after training over 60 epochs. A corresponding MSE of 0.876 was recorded for the checking data. During the validation, MSE recorded between the predicted and observed concentrations of BOD_{5} in the ICW effluent was 0.914.

Overall, the ANFIS model performed very well in predicting the BOD concentrations in the ICW effluent with relatively high accuracy. The recorded MSE was found to be lower than other AI models applied for modelling BOD_{5} concentrations in ICW effluents. For example, Zhang *et al*. (2009) recorded MSE of 6.351 for an ANN-based SOM model. Similarly, Dong *et al*. (2012) obtained MSE of 1.34 for predicting chemical oxygen demand using SOM. In addition, Tomenko *et al*. (2007) developed models with two different ANNs to predict the effluent BOD in a CW, in India, and recorded MSE of 8.34 and 15.80. In another study involving the use of ANN and partial least squares regression to predict the BOD, Basant *et al*. (2010) obtained MSE of 1.41 and 1.45, respectively.

### Simulation of effluent NH_{4}-N concentrations

Figure 4(b) depicts the prediction results of NH_{4}-N concentrations in the ICW effluent using ANFIS. The performance of the model during validation, when presented with previously unseen data, namely the checking and validation data (after training the model), is shown. At the training step, MSE between the predicted and observed concentrations of NH_{4}-N in the ICW effluent reached a final value of 0.0916, which was achieved after training over 60 epochs. A corresponding MSE of 0.301 was recorded for the checking data. During the validation, MSE recorded between the predicted and observed concentrations of NH_{4}-N in the ICW effluent was 0.0570.

Overall, the ANFIS model performed very well in predicting the NH_{4}-N concentrations in the ICW effluent with relatively high accuracy. The recorded MSE was found to be similar to Zhang *et al*. (2009), who recorded MSE of 0.042 for an ANN-based SOM model employed for modelling NH_{4}-N concentrations in ICW effluents, but lower than Dong *et al*. (2012), who obtained MSE of 1.03 using the SOM model.

## CONCLUSIONS

Findings indicate that ANFIS could predict the effluent quality variation quite strongly. Effluent concentrations of BOD_{5} and NH_{4}-N, which are time-consuming and expensive to measure, were predicted relatively accurately by other effluent water quality parameters, which can be measured quickly within a few hours and cost effectively. The simulated effluent BOD_{5} and NH_{4}-N concentrations well fitted the measured concentrations, which was also supported by relatively low MSE. Thus, by using ANFIS, it is possible to estimate the key effluent water quality parameters rapidly, which can assist the system operator to manage the ICW process operation and reduce the risk of failing regulatory requirements, while reducing man-hours, travel expenses and analytical costs.

## ACKNOWLEDGEMENTS

The authors would like to thank Monaghan County Council for funding this research. Technical support and advice from Mark Johnston (Monaghan County Council), Rory Harrington and Susan Cook (Waterford County Council) and Aila Carty (VESI Environmental Ltd), all in Ireland, were also greatly appreciated.