Using treated wastewater could be a realistic solution for the scarcity of fresh water in Iran; therefore, effluent quality evaluation is an essential task. In the present study, the effluent quality index (EQI) for south of Tehran municipal wastewater treatment plant was found considering eight quality parameters and sub-index formulae method. Further, with the help of an artificial neural network (ANN), design and applicability of feed-forward, three-layer perceptron neural network model for computing the EQI has been assessed. In this study, ANN modeling is done by ANN toolbox in MATLAB 2013. The modeling efforts showed that the optimal network architecture was 8–7–1 and that the best EQI predictions were associated with the Levenberg–Marquardt back propagation training algorithm and Tansig transfer function. The EQI predictions of this model had significant and very high correlation (R = 0.96, MSE = 0.1) with the measured EQI values. The ANN approach which is used in this article suggested powerful tool to EQI computation and prediction, since it reduced lengthy computations and using various sub-index formula for each value.

INTRODUCTION

Water quality management has become an important issue throughout the world (Najufpoor et al. 2007). Most countries have planned water quality monitoring and assessment of surface water in terms of their physical, chemical, biological and nutrient constituents (Sapkal & Valunjkar 2013).

Water quality index (WQI) is a description of biological, chemical, and physical characteristics of water in connection with intended use(s) and a set of standards (Liou et al. 2004; Boyacioglu 2007; Khalil et al. 2011; Gazzaz et al. 2012). Since no individual parameter can express water quality sufficiently, water quality indices have been developed to integrate measurements of a set of parameters into a single index (Zandbergen & Hall 1998).

Due to the scarcity of fresh water resources in the Middle East regions, wastewater reuse could be a realistic option to compensate the lack of fresh water and until now, the largest and most popular wastewater reuse has been in the agricultural irrigation field (Palese et al. 2009; Alfarra et al. 2011).

Wastewater treatment plant (WWTP) effluents must respect all the quality standards and cannot be described by purely theoretical models (Verlicchi et al. 2011).

Effluent quality index (EQI), which is able to rapidly evaluate whether an effluent is appropriate for agricultural, recreational, industrial or disposal purposes, could be of great help to managers and decision makers in water resources planning. Moreover, this index is a useful tool for comparing different wastewater treatment processes.

The index is an appropriate tool for:

  • (a) quick comparison of water quality;

  • (b) rapid evaluation of treatment options;

  • (c) rapid evaluation of the improvement in effluent quality.

Although constructing an EQI has many advantages, the calculations are complicated and unintentional errors make it difficult and inaccurate. Thus, an alternative direct and quick means of computing and forecasting EQI values based on artificial neural network (ANN) modeling is suggested. This model has the potential to reduce computation time and errors. Therefore, this study illustrates the design of a neural network model as an alternative to EQI computation methods.

The ANNs are popular tools for modeling highly complicated relationships, processes, and phenomena. They have been widely used in environmental modeling and predicting such as river flow forecasting (e.g. Shamseldin et al. 2002; Teschl & Randeu 2006); rainfall-runoff modeling (e.g. Riad et al. 2004; Wu & Chau 2011); water demand forecasting (Behboudian et al. 2013); solid waste forecasting (Abdoli et al. 2011) and WQ forecasting (e.g. Palani et al. 2008; Singh et al. 2009; Khalil et al. 2011). However, the specific use of ANNs to develop predictive models for EQI has not been yet investigated by researchers. Therefore, the main objectives of this study were to: (1) construct the EQI with traditional methods; (2) demonstrate the potential of the ANN for producing models capable of efficient forecasting of the EQI; (3) illustrate the general framework for ANN model design (e.g. selection of network type; determination of appropriate input variables and number of hidden neurons; and specification of the optimum settings of the network training parameters).

Among black-box models, ANN is a prevalent modeling method with growing applications (Banerjee et al. 2011). The most common application of ANN is to map a set of input vectors to the specified output ones. In the case of EQI modeling, the input vectors are quality parameters such as biochemical oxygen demand (BOD), total dissolved solids (TDS), fecal coliform (FC), etc. and the output vector is the EQI. Thus, in order to model EQI two steps must be followed: (1) EQI construction for a set of observed data; and (2) ANN modeling in order to predict EQI.

MATERIALS AND METHODS

Developing a new index for Iran's effluent of municipal wastewater treatment plants includes the following two sections.

EQI formula

Determining the significant parameters is the first step in developing the EQI. Initially, 15 parameters were selected including BOD, chemical oxygen demand (COD), total suspended solids (TSS), TDS, pH, total P, total N, NO3, NH3, NO2, T, dissolved oxygen (DO), fecal coliform, total coliform, and PO4. Based on the Delphi method 100 experts filled the questionnaires and the average weight of each parameter is calculated. Finally, the following parameters were selected: BOD, COD, TSS, PO4, NH4, fecal coliform, pH, TDS.

In the next step, a weight is assigned to each selected parameter based on the result of the Fuzzy Topsis method. The parameter which has adverse effects on human health has complicated and expensive treatment process and more aesthetically unpleasant is assigned higher weight in questionnaires so that it increases EQI. Afterward, the parameter weights are defined using the Fuzzy Topsis decision making method. The related formula and description about this method can be found in Hwang & Yoon (1981) and Wu & Chen (2007).

The third step involved determination of quality function (curve), i.e. sub-index for each selected parameter. Sub-indices are calculated by converting the value of each selected variable into a non-dimensional, scaled value through a sub-index rating curve where each variable has its own rating curve on a scale of deteriorating EQI, mostly from 0 to 100 (Liou et al. 2004; Kaurish & Younos 2007). Basically, these rating curves were developed in this study from statistical data analysis of raw data acquired by long-term treated wastewater analysis with the assistance of wastewater quality expert opinions. The final step is the aggregation and calculation of the EQI which is the most important step in calculating EQI. In order to minimize ambiguity and eclipsing, it is necessary to identify an appropriate function for aggregation (Obaid & Al-Shujairi 2013). In this study, the multiplicative product method of aggregation is used. Overall effluent quality index is determined by the formula given in Equation (1): 
formula
1
where In is the sub-index relating to the parameters COD, BOD, TSS, NH4, PO4, Fc and Wn is the corresponding weight for each parameter.

Developing artificial neural networks

ANNs are non-linear processing systems operating in parallel (Sarkar et al. 2009). The concept of ANNs was developed based on the real biological human brain. Analogous to the brain, ANNs are composed of nodes and connections. The nodes are called neurons, which are the simplest and the major computational units and the connections are network weights, which are responsible for establishing several types of ANN proposed so far. However, two kinds of networks, i.e. back-propagation neural network (BPNN) and radial basis function (RBF), are the most common network structures used for engineering purposes.

The feed forward back propagated MLP is the default network type for most MLPs. It has multiple layers of neurons with nonlinear transfer functions that allow the network to learn nonlinear and linear relationships between input and output vectors. Different training algorithms can be used in the training stage: gradient descent, gradient descent with momentum, gradient descent which has a variable learning rate, gradient descent with momentum, which has a variable learning rate, and RP are the most famous training functions. Conjugate gradient (CG) algorithms are the other algorithms for the training procedure. The standard back propagation algorithm adjusts the weights in the steepest descent direction (negative of the gradient), where the performance function is decreasing most rapidly. For faster convergence than steepest descent directions in the CG algorithms, a search is performed along conjugate directions. The Levenberg–Marquardt algorithm is also a training algorithm designed to approach second order training speed without having to compute the Hessian matrix.

Feed forward back-propagation neural network

BPNN is the most popular network, especially in the case of non-linear approximation (Kashaninejad et al. 2009). Each BPNN consists of an input layer, an output layer and one or more hidden layers. Back-propagation is used as the learning algorithm, and it involves working backward from the output layer to adjust the weights accordingly, and reducing the average error across all layers. This process is repeated until the weights reach their optimal values and the error between the output of the network and the actually desired output is minimized (Aydiner et al. 2005).

The sum of the weighted inputs forms the input to the transfer function. Neurons can use any differentiable transfer function to generate their output. In BPNN, a global function, like the tangent function or the logistic function, is often used as an activation function. The main task in designing a BPNN network is to find the appropriate number of layers and also the number of neurons in each layer in the way that the overall network error minimizes.

Model performance

To evaluate the performance of the ANN model, two indices are assessed: mean square error (MSE) and correlation coefficient (R). The accuracy of the model is determined according to these criteria (Abdoli et al. 2011). The MSE can be defined as follows: 
formula
2
where is the output of the process, is the ith output of the network corresponding to the and N is the total number of data points.

In order to reduce error impacts, it is necessary to standardize the data, that is, to convert the data into a non-dimensional form of uniform range of variability (Dawson & Wilby 2001; Özesmi et al. 2006). The variables input to the neural network (eight EQVs and the EQI) were standardized to the range of, namely, (0,1).

In order to ensure that the different EQVs would have equal weights in the analysis, the raw EQVs were standardized through z-scale transformation to a mean of 0.0 and variance of 1.0 by using the equation (Güler et al. 2002; Kowalkowski et al. 2006): 
formula
3
where Zij is the standard score of the jth value of the measured variable i; xij is the jth observation of variable i; and li and ri are the mean and standard deviation values, respectively, of the population of variable i.

Case study

South of Tehran, the WTP is located in the southeastern region of the city. It currently covers 525,000 inhabitants for each module and it contains eight modules. The average inlet flow rate of this WWTP is about 2,600 LPS and it is expected to provide about 3,700 LPS in future. Activated sludge is the biological wastewater treatment processes of this WWTP and it includes different units of screen bar unit, primary settling tank, selector, aerated tank, secondary settling tank, and UV units.

Data

In this study a data set from the south of Tehran wastewater treatment plant has been used. Daily measurements for 15 parameters including BOD, COD, TSS, TDS, pH, total P, total N, NO3, NH3, NO2, T, DO, fecal coliform, total coliform, PO4 over a range of 6 months was conducted. However, not all of them were used in ANN modeling and the most significant variables are defined through the Delfi method. Finally, eight variables were defined and involved in the simulation. Values of some descriptive statistics for these variables are shown in Table 1.

Table 1

Data for effluent of south of Tehran WTP

Variable BOD (mg/L) COD (mg/L) TSS (mg/L) Fecal coliform (CFU/100) NH4 (mg/L) PO4 (mg/L) pH TDS (mg/L) 
Minimum 1.00 5.60 1.00 100.00 0.04 0.50 5.50 120.00 
Maximum 120.00 210.00 100.00 5,320.00 55.30 18.00 9.50 1,600.00 
Average 17.80 33.57 18.49 638.51 4.80 5.68 7.31 588.60 
STD 24.70 43.42 23.29 686.99 10.46 3.70 0.64 283.66 
Variable BOD (mg/L) COD (mg/L) TSS (mg/L) Fecal coliform (CFU/100) NH4 (mg/L) PO4 (mg/L) pH TDS (mg/L) 
Minimum 1.00 5.60 1.00 100.00 0.04 0.50 5.50 120.00 
Maximum 120.00 210.00 100.00 5,320.00 55.30 18.00 9.50 1,600.00 
Average 17.80 33.57 18.49 638.51 4.80 5.68 7.31 588.60 
STD 24.70 43.42 23.29 686.99 10.46 3.70 0.64 283.66 

RESULTS AND DISCUSSION

The aim of developing an effluent quality index is to improve water quality by reducing the concentrations of the main pollutant parameters to the levels required for its final destination (Verlicchi et al. 2011).

As mentioned above, the most significant parameters for discharging the domestic effluent to the surface bodies and for reusing in irrigation and agriculture, industrial uses or recreational activities based on the Delphi method are as follows: BOD5, COD, TSS, PO4, NH4, fecal coliform, TDS, pH.

The Fuzzy Topsis method is utilized to estimate the rate of importance for each parameter based on the fulfilled questionnaires regarding the effect of each parameter on health, aesthetic effect, and treatment cost process. The related formula and extra descriptions about this method can be found in the literature (Hwang & Yoon 1981; Wu & Chen 2007).

A panel of experts of about 100 people was selected: wastewater treatment operators, university professors, wastewater consultant companies, wastewater managers. Decision makers completed the questionnaires and assigned a weight 1 to 5 for each parameter considering the adverse effect based on the criteria. In addition, each criterion itself is assigned a weight based on its significance by decision makers. Also, it is supposed that all the decision maker groups have similar weights.

Table 2 shows the results achieved by the Fuzzy Topsis method. In step 2 the sub-indices should be determined. The associated best-fit formulas to each parameter rating curve were used to calculate aggregated index. Each of eight parameter sub-indexes (SI) used to calculate the overall effluent quality index are listed in Table 3.

Table 2

Assigned weight to the parameters according to the Fuzzy Topsis method

Parameter Weight 
BOD 0.076 
COD 0.076 
TSS 0.088 
FC (fecal coliform) 0.17 
NH4 0.167 
PO4 0.157 
pH 0.134 
TDS 0.135 
Parameter Weight 
BOD 0.076 
COD 0.076 
TSS 0.088 
FC (fecal coliform) 0.17 
NH4 0.167 
PO4 0.157 
pH 0.134 
TDS 0.135 
Table 3

Sub-indices formula achieved from rating curves

Parameter   Sub-index 
BOD If 0 ≤ BOD ≤ 12 IBOD = −0.3299x2 + 11.731x − 22.184 
R² = 0.9975 
If 12 < BOD ≤ 107 IBOD = −12.991ln(x) + 38.244 
R² = 0.9935 
COD If COD ≤ 11 ICOD = 0 
If 11 < COD ≤ 53 ICOD = −0.0759x2 + 6.9783x − 67.439 
R² = 0.9957 
If 53 < COD ≤ 165 ICOD = 8.3501ln(x) + 57.746 
R² = 0.9465 
If 165 < COD ICOD = 100 
TSS If TSS ≤ 1 ITSS = 0 
If 1 < TSS ≤ 98 ITSS = 22.908ln(x) − 0.7474 
R² = 0.9841 
If 98 < TSS ITSS = 100 
Fecal coliform If FC ≤ 130 IFC = 0 
If 130 < FC ≤ 580 IFC = 0.1617x − 19.801 
R² = 0.9863 
If 580 < FC ≤ 3,700 IFC = =9E-09x3 − 6E-05x2 + 0.132x + 6.6894 
R² = 0.9892 
If 3,700 < Fc IFC = 100 
NH4 If NH4 ≤ 0.1 INH4 = 0 
If 0.1 < NH4 ≤ 53 INH4 = 16.259ln(x) + 40.013 
R² = 0.9775 
If 53 < NH4 INH4 = 100 
PO4 If PO4 ≤ 2.6 IPO4 = 0 
If 2.6 < PO4 ≤ 5 IPO4 = −12.083x3 + 136.29x2 − 465.36x + 501.72 
R² = 0.9938 
If 5 < PO4 ≤ 17 IPO42 = 6,069x + 57.506 
R² = 0.9815 
If 16 < PO4 IPO4 = 100 
TDS If TDS ≤ 296 ITDS = 0 
If 296 < TDS ≤ 1,600 ITDS = 1E-07x3 − 0.0004x2 + 0.4839x − 110.99 
R² = 0.9783 
If 1,600 < TDS ITDS = 100 
pH If pH ≤ 6 IpH=100 
If 6 < pH ≤ 9.2 IpH = 36.394x2 − 553.95x + 2,100.5 
R² = 0.9814 
If 9.2 < pH IpH = 100 
Parameter   Sub-index 
BOD If 0 ≤ BOD ≤ 12 IBOD = −0.3299x2 + 11.731x − 22.184 
R² = 0.9975 
If 12 < BOD ≤ 107 IBOD = −12.991ln(x) + 38.244 
R² = 0.9935 
COD If COD ≤ 11 ICOD = 0 
If 11 < COD ≤ 53 ICOD = −0.0759x2 + 6.9783x − 67.439 
R² = 0.9957 
If 53 < COD ≤ 165 ICOD = 8.3501ln(x) + 57.746 
R² = 0.9465 
If 165 < COD ICOD = 100 
TSS If TSS ≤ 1 ITSS = 0 
If 1 < TSS ≤ 98 ITSS = 22.908ln(x) − 0.7474 
R² = 0.9841 
If 98 < TSS ITSS = 100 
Fecal coliform If FC ≤ 130 IFC = 0 
If 130 < FC ≤ 580 IFC = 0.1617x − 19.801 
R² = 0.9863 
If 580 < FC ≤ 3,700 IFC = =9E-09x3 − 6E-05x2 + 0.132x + 6.6894 
R² = 0.9892 
If 3,700 < Fc IFC = 100 
NH4 If NH4 ≤ 0.1 INH4 = 0 
If 0.1 < NH4 ≤ 53 INH4 = 16.259ln(x) + 40.013 
R² = 0.9775 
If 53 < NH4 INH4 = 100 
PO4 If PO4 ≤ 2.6 IPO4 = 0 
If 2.6 < PO4 ≤ 5 IPO4 = −12.083x3 + 136.29x2 − 465.36x + 501.72 
R² = 0.9938 
If 5 < PO4 ≤ 17 IPO42 = 6,069x + 57.506 
R² = 0.9815 
If 16 < PO4 IPO4 = 100 
TDS If TDS ≤ 296 ITDS = 0 
If 296 < TDS ≤ 1,600 ITDS = 1E-07x3 − 0.0004x2 + 0.4839x − 110.99 
R² = 0.9783 
If 1,600 < TDS ITDS = 100 
pH If pH ≤ 6 IpH=100 
If 6 < pH ≤ 9.2 IpH = 36.394x2 − 553.95x + 2,100.5 
R² = 0.9814 
If 9.2 < pH IpH = 100 

Thus, by substituting the value of sub-indices, the EQI formula is calculated by the following relationship: 
formula
where I is the normalized sub-indices of the parameters. Treated wastewater can be reused for agricultural, industrial, or recreational purposes if their quality meets specific legal requirements. In Iran, the limitations set by the Iranian environmental agency focused on agricultural purposes, since other purposes are not widely used in Iran. Therefore, in the case where the Iran Environmental standard is incomplete, EPA and Jordanian limitations have been used (WHO 2005; EPA 1992). Major problems usually arise due to high concentrations of the parameters selected to develop the EQI. Their legal limitations for wastewater reuse and disposal are reported in Table 4.
Table 4

Reuse and disposal limitations of treated effluent

  BOD (mg/L) COD (mg/L) TSS (mg/L) Fecal coliform NH4 (mg/L) PO4 (mg/L) pH TDS (mg/L) EQI 
Recreational limitations 10 30 400 0.02 6–9 750 26 
Industrial reuse 30 75 30 200 6–9 1,000 48 
Surface water disposal 30 60 40 400 2.5 6.5–8.5 1,500 56 
Ground water disposal 30 60 40 400 5–9 1,500 53 
Agriculture limitations 100 200 100 400 50 15 5–9 1,500 75 
  BOD (mg/L) COD (mg/L) TSS (mg/L) Fecal coliform NH4 (mg/L) PO4 (mg/L) pH TDS (mg/L) EQI 
Recreational limitations 10 30 400 0.02 6–9 750 26 
Industrial reuse 30 75 30 200 6–9 1,000 48 
Surface water disposal 30 60 40 400 2.5 6.5–8.5 1,500 56 
Ground water disposal 30 60 40 400 5–9 1,500 53 
Agriculture limitations 100 200 100 400 50 15 5–9 1,500 75 

As can be seen in Table 4, the thresholds for different reuse purposes are calculated through the EQI formula and it can be concluded that the EQI formula can suggest the best reuse option for each effluent sample.

Step 2: developing ANN model

The ANNs represent an innovative and attractive solution to the problem of relating output to input variables in complex systems (Dawson & Wilby 2001) and prediction is a common reason for employment of the neural network technology. The major steps for the development of ANN models include defining the suitable model inputs, specifying network type, pre-processing and partitioning of the available data; determining network architecture; defining model performance criteria; training (optimization of connection weights); and validating the model (Govindaraju 2000; Maier & Dandy 2000; Dawson & Wilby 2001). These steps are outlined below with some detail.

In this study, ANN modeling is done by ANN toolbox in MATLAB 2013. The first step aimed at determining the numbers of input, hidden, and output neurons; and the optimal data splitting plan while the second phase involved specifying the training algorithm, learning rate, number of iterations, and training stopping criteria. Thereupon, this study employed a neural network with one input layer, one hidden layer, and the EQI as the output layer, thus producing a three-layer perceptron (TLP) network.

The hidden layers provide the network with its ability to generalize. In theory, a network with a hidden layer and adequate number of hidden neurons can simulate any continuous function and represents a rich and flexible class of universal approximates (Dawson & Wilby 2001; Fischer 2006; Palani et al. 2008).

Determining the number of hidden neurons is the significant part and is usually achieved through a trial and error task in ANN modeling (Özesmi et al. 2006; Palani et al. 2008; Singh et al. 2009). The Alyud Research Company (2003) suggested that the N should fall in I/2 to 4I where the I is the number of inputs. In this study, a different number of neurons from 4 to 15 with different train algorithms has been assessed.

Eventually, this search process depicted that the optimal network architecture was 8–7–1 and that the optimum associated partitioning scheme was 70–15–15% (i.e. the proportions of the samples allocated to the training, cross-validation, and testing sets were 70%, 15%, and 15%, respectively). This network had a testing error (RMSE) of 0.32 and the EQI predictions it produced had a significant, very high, positive correlation with the measured EQI values (R = 0.96).

The Levenberg–Marquardt (LM) training algorithm and tansig activated function achieved the best performance among the various training algorithms. Figure 1 illustrates the performance of different training algorithms. If the validation error was increased six times sequentially, the training would stop. Training was restarted using network weights, which had been obtained from the previous run until acceptable results on the testing block were reached.
Figure 1

The performance parameters of training algorithms.

Figure 1

The performance parameters of training algorithms.

Figure 2 illustrates the validation of ANN model by comparing with target EQI values. We used scatterplot to illustrate the relationship between the output EQI and target EQI and to see if the model fits the data (Figure 3). This line is a graphical representation of the mathematical regression equation. It is plotted using the least squares method which minimizes the sum of the squared distances between the points and the fitted line.
Figure 2

A graphical representation of the results of ANN model validation. This figure compares between the ANN-output EQI and the target EQI values for each individual observation.

Figure 2

A graphical representation of the results of ANN model validation. This figure compares between the ANN-output EQI and the target EQI values for each individual observation.

Figure 3

Scatter plot of the output and target EQI.

Figure 3

Scatter plot of the output and target EQI.

Sensitivity analysis

A sensitivity analysis was carried out to evaluate the relative importance of each of the eight variables in prediction of the EQI. Sensitivity analysis refers to assessment of the importance of predictors in the fitted models. This analysis ranks the predictor variables according to the deterioration in model performance that occurs if a variable is removed from the model. Ultimately, it identifies the variables that can be ignored safely in subsequent analyses as well as the essential variables which must be retained (Olszewski et al. 2008; Gazzaz et al. 2012). In this research each input parameter has been removed separately and the simulation has been conducted without that parameter. The ratio is obtained from the network error after individual variables were removed to the network error from using all variables in the network, i.e. the error of the reduced model against that of the full model. If the ratio is below 1, the parameter can be removed from the model since it is not so important in ANN modeling (Olszewski et al. 2008). Table 5 demonstrates the ratio of each parameter. As can be concluded from Table 5, pH and COD ratio was below 1 and can be omitted from modeling.

Table 5

Sensitivity analysis result

Parameter Ratio Rank 
Fecal coliform 1.26 
NH4 1.19 
TDS 1.18 
TSS 1.17 
PO4 1.13 
BOD 
PH 0.95 
COD 0.94 
Parameter Ratio Rank 
Fecal coliform 1.26 
NH4 1.19 
TDS 1.18 
TSS 1.17 
PO4 1.13 
BOD 
PH 0.95 
COD 0.94 

The ANN method for EQI calculation and forecasting offers some advantages over the traditional method. The traditional method uses manual calculations whereby the raw data of eight quality variables (BOD, COD, TSS, NH3-N, fecal coliform, PO4, TDS and pH) have to be converted into sub-indices (Table 2) before the EQI can be calculated. Since the calculations are not performed on the parameters and their sub-indices which consist of a set of equations should be used for calculations, EQI estimation becomes a time consuming task. On the contrary, the ANN approach utilized archived data to establish a model that can be used for direct calculation of the EQI from raw data without the need for sub-indexing. Of course, ANN approach is a more direct, rapid, and convenient means of calculation of the EQI than the traditional method.

Moreover, there is a chance by using ANNs to assess more than eight quality variables, which the EQI formula does not cover, since ANNs can be trained and calibrates the weights in order to reach satisfactory results.

The EQI obtained from the traditional method were considered as reference values for the ANN method. Gazzaz et al. (2012) used both the traditional method and the ANN approach to estimate EQI.

The performance of the ANN model can be evaluated by comparing its EQI outputs with those of the traditional method through regression analyses. The results demonstrate that a reasonable approximation was made by the ANN model across the calculated EQI values. The overall agreement between the calculated and simulated EQI value was very satisfactory (r = 0.96, P < 0.01; R2 = 92%; Mse = 0.12)

CONCLUSIONS

In this research two different nonlinear methods have been used in order to estimate effluent quality index for treated municipal wastewater samples. In the first part, a nonlinear formula was developed using Fuzzy Topsis weights and sub-indicing based on the observed data. In the second part, the applicability of feed-forward back propagation neural networks effluent quality index prediction was assessed. The EQI for 200 samples of treated wastewater is calculated through the statistical formula and sub-indicing was carried out. The network parameters to be tuned in designing the feed forward back propagation network were the number of hidden neurons and the connection weights. It could be concluded from the obtained results that a BPNN network with LM training algorithm, Tansig activation function and the architecture of 8:7:1 was the best for EQI prediction. The observed determination coefficient (R2) for the BPNN was 0.92, and the mean square error was 0.1.

Findings from this study emphasize that the ANN enables easy modeling of the EQI and allows for identification of the comparative importance and contribution of input parameters to the model predictions.

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