Prediction of the optimal dosage of coagulants in water treatment plants through developing models based on artificial neural network fuzzy inference system (ANFIS)

Abstract

Purpose

Coagulation and flocculation are the prominent processes and unit-operations in water treatment plants. One of the most challenging operations in water treatment process is determining of the coagulant dose.

Method

The Jar-test method is usually used to determine the coagulant dose. Considering that this traditional method is time consuming, associated with human error and highly affected by raw water quality fluctuations. In this study, artificial fuzzy neural network (ANFIS) according to subtractive clustering (SUB) method was applied in order to determine the optimal dose of coagulant in the water treatment plants.

Results

Adopting SUB method tend to moderate the number of rules and the interconnections besides enhancing the model responsibility and smart model recognition. The amount of pH, turbidity of raw water influent, alkalinity, temperature, and electrical conductivity were collected as input data.

Conclusions

The results of modeling by ANFIS with correlation coefficients of 0.85 and 0.84 and RMSE 1.32 and 1.83, respectively, for alum and polyaluminum chloride (PAC) coagulant dose, indicated that ANFIS is an effective method for determination of the optimal coagulation dose in the water treatment plant.

Introduction

Various unit operations such as aeration, coagulation and flocculation, sedimentation, and clarification are used in a water treatment processes. One of the major water treatment processes is coagulation and flocculation. Appropriate coagulation can aggregate particles to form larger sizes that can be easily separated from water [1]. Determining the coagulant dose is a challenging issue in water treatment facilities. Determining the coagulant dosage is a nonlinear, time consuming, and multfactor process, also is a complex chemical process. This complexity is not only regarding raw water turbidity, raw water flow rate, temperature, pH value, and organic content of water, but also can be affected by the rapid mixing, the hydraulic factors of coagulation tank, and surrounding environment condition [2, 3]. Normally, operators use jar-test apparatus to obtain the coagulation dose, but this technique is not suited for real-time control of a continuous process, especially when the raw water quality rapidly varies in time and discharge rate [4]. Establishing the conditions like those happen in a water treatment plant is of great importance in the jar-test method. Doing this requires knowledge of the hydraulic characteristics of the treatment steps including rapid mixing, flocculation, and clarification [5]. Poor regulation of the coagulation dose wastes large amounts of chemicals annually that is a significant economic, and environmental concern. Furthermore, inoculating underestimated amounts of the required coagulant dose causes inefficient removal of the contaminants from effluent water. Consequently, the release of high concentrations of metals in coagulants structure, including aluminum and ferrous salts, into drinking water can cause health hazards for the consumers. Using the improper doses of coagulants causes the production of sediment and sludge, which will lead to problems related to disposal.

In recent decades, data from jar tests, pilot-plant tests, and full-scale treatment systems have been evaluated by means of advanced mathematical tools in order to derive relationships between the input parameters and the optimal coagulant dosage as the output result [4, 6]. Currently, artificial intelligence models have been applied to determine the optimal coagulant dose in various water treatment systems. Artificial neuro-fuzzy inference system (ANFIS) is an efficient machine learning techniques, which has been successfully employed in wide variety of applications [7, 8]. With the ability to combine the linguistic basis of a fuzzy system with the crisp nature of a neural system adaptive network, ANFIS has been shown to be powerful in modeling numerous processes, such as motor fault detection and diagnosis [9]. One of the first ANFIS model developed by Jang in 1993. With respect to types of inference operations upon the ‘IF-THEN rules most fuzzy inference systems are classified into three types: Mamdani’s system (1975), Sugeno’s system (1985) and Tsukamoto’s system (1979)[10]. ANFIS is a kind of artificial intelligence of the Takazaki-Sugeno type that can learn to use the data of the input function and find the relationship between the input and the output variables [11]. By means of the three methods of time series, regression, and artificial neural network, Yu et al. predicted the optimal coagulation dose in the Taiwan water treatment plant, which results indicated that the artificial neural network model was successful in predicting the required dose [12]. Joo 2000 employed ANN to measure the dose of alum in the Quebec, Canada water treatment plant [13]. In 2004, Maier et al., made use of ANN to predict the dose of alum coagulant in the south Australian water treatment plant and simulated the results of model evaluation at the water treatment plant [14]. Lamrini et al. (2005) predicted the coagulation dose of Marrakech Morocco using online systems [15]. Zangooei et al. In 2016, used two types of artificial neural networks (MLP, RBF) and fuzzy regression, predicted turbidity after coagulation in the Northeast Tehran water treatment plant and the results indicated that MLP performed better in measurement of the coagulant dose [16]. In 2020, Yamamura et al. predicted the coagulation dose of alum and poly aluminum chloride (PAC) at the Tokyo water treatment plant by means of convolutional neural network (CNN) [17]. Kenndy et al. (2015) predicted the optimal coagulation dose in the water treatment plant by artificial neural network (Akron, Ohio, USA) [18]. Evans et al. (1998) utilized ANFIS to predict coagulation dose at Huntington, UK water treatment plant. Consequently, several regression models were compared to ANFIS model concluded in ANFIS modeling results being more reliable and accurate than regression models [19]. In 2008, Wu et al. utilized both models of artificial neural network and ANFIS to predict the dose of PAC coagulant in Taiwan water treatment plant, which resulted that the ANFIS model performs more preferable than the artificial neural network [20].

In this study, it was aimed to determine the optimal coagulation dose in Hamadan water treatment plant by applying an ANFIS model. In addition, the predicted coagulation doses obtained by ANFIS models were compared with the jar-test results. Furthermore, considering it one of the crucial factors in determining the optimal dose of coagulant, pH was modeled and studied simultaneously with the optimal dose of coagulant. Besides, the impact of variables such as temperature, turbidity of raw water intake and pH on the coagulant dose consumption was discussed.

Materials and methods

Case study area

This study was conducted in Hamadan, a city located in the western part of Iran, in a mountainous topography with an average altitude of 1800 m above the sea level. The drinking water demand of the city population, which is around 600,000, is supplied by three water treatment plants located in the southeastern areas of the city having an overall water discharge of 1.6 m³/s. Figure 1 illustrates the study area, Ekbatan water treatment plant, located in the vicinity of the Ekbatan dam reservoir and provides up to 0.3 m³/s treated water, approximately 30 % of Hamadan drinking water demand.

Fig. 1.

The study area; Ekbatan water treatment plant, Hamadan, Iran

As shown in Fig. 2, Ekbatan water treatment plant comprises a conventional process based on Accelator® solids contact clarifier; a well-known system relied on the sludge blanket suspension developed by a French company, Degremont®. Colloids in raw water are entrapped by the sludge blanket; a cloud of coagulants that are formed by metal hydroxides. Determining the precise dosage of coagulants is a vital factor, both in terms of cost-saving and to obtain maximum removal of contaminants.

Fig. 2.

Ekbatan WTP process showing Coagulation dosage

Data collection

The sampling was performed from the intake of the water treatment plant twice a week for a period of 9 months. Two 20 L sampling containers were used according to standard method 4101 sampling criteria [21]. Sampling period was performed continuously from January 2018 through September 2019. Electrical conductivity (EC), temperature, initial turbidity of raw water, alkalinity and pH of raw water were determined in the sampling location.

Jar test operation was performed applying doses 5, 10, 15, 20, 25, 30 mg/L of aluminum sulfate (Alum) and poly-aluminum chloride (PAC) coagulants, separately. Blending was adjusted at 120 rpm/15 min and 20 rpm/30 min for rapid and slow mixing operations, respectively. After determining the optimum doses of aluminum sulfate (Alum) and poly-aluminum chloride (PAC), the optimum pH of the abovementioned coagulants were also determined.

138 samples were examined in the study and the parameters of electrical conductivity, temperature, alkalinity, initial turbidity, and pH of raw water were applied as the input values for the ANFIS modeling. Accordingly, 70 and 20 % of the data were selected as model training and testing, respectively. Then the model output was compared with the results of Jar-test experiments.

ANFIS (Artificial Neuro–Fuzzy Inference System)

Artificial neuro-fuzzy inference system (ANFIS) is an efficient machine learning techniques, which has been successfully employed in wide variety of applications [7, 8]. With the ability to combine the linguistic basis of a fuzzy system with the crisp nature of a neural system adaptive network, ANFIS has been shown to be powerful in modeling numerous processes, such as motor fault detection and diagnosis [9]. One of the first ANFIS model developed by Jang in 1993. With respect to types of inference operations upon the ‘IF-THEN rules most fuzzy inference systems are classified into three types: Mamdani’s system (1975), Sugeno’s system (1985) and Tsukamoto’s system (1979)[10]. Fuzzy values are comprised between 0 and 1 [22, 23]. It is assumed that the fuzzy inference system has two inputs, x, y and one output [9]. Equations 1 and 2 reveals formal ‘IF-THEN rules examples.

$$\text{Rule}1:\text{If}\mathrm{x}\text{is}{A}_{1}and\mathrm{y}\text{is}{B}_1,then{f}_1=P_{1}x+q_{1}y+r_1$$ 1

$$\text{Rule}2:\text{If}\mathrm{x}\text{is}{A}_{2}and\mathrm{y}\text{is}{B}_2,then{f}_2=P_{2}x+q_{2}y+r_2$$ 2

Where, x and y are the inputs, $A_i$and $B_i$are membership functions of input values x and y and$q_i$, $p_i$and $r_i$are the parameters of the output function. The ANFIS architecture with two inputs (x and y) and one output shown in Fig. 3.

Fig. 3.

The architecture of ANFIS (see Haddam et al. 2012)

Subtractive clustering (SUB)

ANFIS approach follows two different identification methods: the grid partition (GRID) andthe subtractive clustering (SUB) methods [24]. In the Grid partition method, data isdivided into grid data. It can be said that grid partition is only suitable for cases with small number of input variables [25]. Each linguistic variable can be partitioned using its linguistic values indicated by fuzzy numbers via MFs [26]. The clustering method is one of the important methods fordata analysis and decision making that allows retrieval of the useful information by grouping or categorizing multidimensional data in clusters [27]. The four factors that determine the radius of the cluster are: Influential radius$R_c$, quash factor $C_{Quash}$, accept ratio $R_{Accept}$, reject ration $R_{Reject}$.

The penetration radius factor is between zero and one. Besides, squash, accept and reject factors are effective in the number of rolls. By increasing the squash and the reject factor, the number of fuzzy rules are increased. The density of each data point is calculated from Eq. 3.

$$d_1=\sum _{n=1}^{m}exp\left(\frac{{\parallel x_i-x_n\parallel }^2}{\left(\frac{r_c}{2}\right)}\right)$$ 3

Where, $r_c$ is influence radius, $x_i$ is center of cluster and $x_n$ is the remaining data set points. The new density for center cluster remainder data is calculated Eq. (4). The closest points to the first cluster center will have significantly reduced potential and have less chance to be selected as next cluster center [22].

$$d_{io}=d_i-d_v\times exp\left(\frac{{\parallel x_i-x_f\parallel }^2}{\left(\frac{r_e}{2}\right)}\right)$$ 4

Where, $x_f$is the location of the first cluster center, $d_v$ is potential value, $r_e$ is influence radius and it is equals to 1.25 $r_c$ [28].

Effects of noise data

Poor data quality increases operational cost because time and other resources are spent detecting and correcting errors [29]. Noise data leading to unreliable results. It is not unusual to have some extreme patterns which will decrease the model [25]. It can be said that clustering methods are sensitive to noise data and the presence of noise data has a significant effect on clustering results.

Model evaluation

Correlation coefficients, RMSE and MAE, were applied to evaluate the models and estimate the prediction accuracy. The relationship between input and output parameters and model prediction with the experimental value of the model can be calculated using the correlation coefficient.

The$R^2$ provides an indication of the accuracy of the model in terms of the percentage of variation that can be explained by the regression equation [11].

$$R^2=1-\frac{\sum _{i=1}^n{(a_i-b_i)}^2}{\sum _{i=1}^n{(a_i-\stackrel{-}{a})}^2}$$ 5

Where $b_i$ is the predicted value and $a_i$ is the observed value; $\stackrel{-}{a}$ is average values of the observed and predicted outputs, respectively and n is the number of samples. To calculate the amount of model prediction error in the ANFIS training and testing stages, the mean square error was used, which is obtained from Eq. 6.

$$RMSE=\frac{1}{n}\sqrt{\sum _{i=1}^n{\left(a-b\right)}^2}$$ 6

Where, n is the number of data; a is the predicted value and b is the real operating value.

The MAE is a measure of errors between observed value and model predictions.

$$\text{MAE}=\frac{1}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}\left|\mathrm{a}-\mathrm{b}\right|$$ 7

Models with lower RMSE values and$R^2$ higher values are good models performance. Models that perform well should have a high frequency of low error predictions [18].

Result and discussion

Table 1 presents the performances of ANFIS-SC models in different radii. ANFIS subtractive clustering (ANFIS-SC) model is a combination of combining ANFIS and subtractive clustering (SC) method [22]. In subtractive clustering, the range of a cluster in each dimension is controlled by radius parameter, and thus, finding optimal radius is important for subtractive clustering algorithm [24]. The number of clusters determines the number of rules [30]. If the radius of the cluster is set to be small, the size of the clusters also becomes small. Therefore, the number of clusters increases. By contrast, if the radius of the cluster is set to be large, the size of the cluster becomes large, so that the number of clusters decreases and the number of fuzzy rules also becomes small [31].

Table 1.

Performances of ANFIS-SC models in different radii

Type of model	Radii	Number of rules	Number of MF	Training		Testing		all
				RMSE	MAE	RMSE	MAE	RMSE	MAE
Optimal pH (Alum)	0.1	47	47	0.000098	0.000063	0.78	0.64	0.43	0.19
Optimal pH (PAC)	0.1	46	46	0.0001	0.000076	0.89	0.76	0.49	0.22
Optimal Alum dosage	0.35	43	43	0.00042	0.00027	2.44	1.61	1.32	0.47
Optimal PAC dosage	0.1	42	42	0.00027	0.0002	3.42	2.86	1.83	0.82

In this study, the radius of the cluster was obtained by trial and error, data was placed several times randomly in the training, and testing stages and the models that had the best statistical evaluation were selected as the appropriate models (Table 1). Increasing the radius of the cluster seems to reduce the number of fuzzy rules (Rule) and increase the amount of RMSE (Fig. 4). Stages related to training and testing are illustrated in Fig. 5. RMSE was at its lowest point during the model training stage, considering that ANFIS tries to use data as a template in this stage. As a result, the proper radius of the cluster is measured through the error caused by the testing step. Rules of ANFIS prediction dosage of coagulants in Fig. 6.

Fig. 4.

The cluster radius versus RMSE for training (a), testing (b), and total (c) stages

Fig. 5.

The optimal models of ANFIS; pH values of Alum (a), PH values of PAC(b), Alum dosage(c), PAC dosage (d)

Fig. 6.

Rules of ANFIS prediction dosage of coagulants; alum dosage (a), PAC dosage (b)

The ANFIS model is built to create the fuzzy inference system and then to estimate the coagulant dosage rate on given input–output patterns [30]. ANFIS model is developed using genfis2 command in Fuzzy Logic Toolbox of MATLAB, which generates fuzzy inference system structure from data using subtractive clustering algorithm [24]. The subtractive cluster is an algorithm which uses a great deal of to estimate the cluster number and its cluster location automatically [32]. Subtractive clustering assumes that each data point is a potential cluster center and calculates the potential for each data point based on the density of surrounding [25].

In this study, the optimal dose of Alum, with pH 8, was obtained 20 (mg/L) and the optimal dose of PAC (mg/L) was obtained 25. It was also observed that with increasing of the turbidity of raw water intake, especially on rainy days, the efficiency of coagulants decreased. The pH of water in the range of 5.7 to 6.5 was associated with an increase in the dose of alum coagulant dose up to 25 (mg/L) and decreased from 6.6 to 6.9 down to 20 (mg/L); also at pH 7.3 this amount reached 17 mg/L. It can be said that the best coagulation effect using Alum occurs in pH 6.9 and 7.7 and for PAC coagulant in pH 7.

In this study, the turbidity of the inlet raw water ranged from 2.88 to 77.8, which in the initial turbidity of less than 20 N. Turbidity in both Alum and PAC coagulants caused an increase in the coagulant dose. Accordingly, the dose of Alum coagulant was noticed to be increased in pH higher than 7.5. Besides, lowering the temperature to 4° C increases the dose of Alum coagulant while rising the temperature to 10 ° C leads to reduction in the consumption of Alum coagulant dose (Fig. 7(a-b)). In addition, in the case of PAC coagulant, at 8 ° C, the lowest coagulant consumption takes place. (Fig. 7(a-d)).

Fig. 7.

GraPHic surfaces of ANFIS outputs related to the input parameters

The output of laboratory results was summarized in four models of optimal pH of Alum, optimal pH of PAC, optimal Alum dose and optimal PAC dose. Electrical conductivity, temperature, initial turbidity, alkalinity and pH were selected as inputs. 70 % of the data were selected as model training and 30 % of the data were selected as model testing. Through trial and error, best cluster radius was obtained 0.35 for the optimal dose of Alum and 0.1 for the models of optimal pH of Alum, optimal pH of PAC, and dose of PAC (Table 1). The ANFIS acquired models were compared in the training stage and in the testing stage (Fig. 5(a-d)). Consequently, it was observed that the optimal dose of Alum had the highest correlation coefficient in the training stage while other models had a correlation coefficient higher than 0.9, which indicates that ANFIS performance in the learning and data patterning stages was satisfactory. The optimal pH of Alum model with the lowest RMSE (0.43) in the training and testing stage among the coagulation pH models and the optimal Alum dose model with RMSE 1.32 were observed to be the most satisfactory in evaluation of the models, in this section. The comparison between the experimental data obtained from the tests results along with the model prediction is illustrated in the point pH (Fig. 8). In this comparison, the optimal dose of Alum and PAC with a correlation coefficient of 0.87 and 0.85 had the best performance, respectively. Compared to similar studies conducted by Heddam & Bermad (2012), although the comparison of the two differential clustering algorithms and the grid method was done correctly, the effect of optimal coagulant pH, which is one of the crucial factors in determination of the dose of coagulants, was not examined. Equally, in the studies of Blue et al., The lack of comparison of the results of the models with the traditional methods used in the treatment plant (Jar-test) and the economic estimation of the usefulness of the model compared to the traditional methods were the limitations of the study; Also, model performance simulation tools were not used.

Fig. 8.

Comparing the experimental data obtained from the tests versus the model prediction results

Conclusions

This study aims in determination of the optimal coagulant dose by ANFIS differential clustering in Hamadan water treatment plant.

• Comparing the evaluations of the model, it was observed that the optimal dose of Alum and its PH had the lowest RMSE and the highest correlation coefficient among the models.

• The highest accuracy was noticed in the model training stage, for all models.

• Using model evaluation, it can be concluded that ANFIS can be a proper alternative to the traditional Jar-test method.

• It can also be a valuable tool for the use of water treatment plant operators.

• It is strongly hoped that the outputs obtained from the ANFIS model are used to achieve the goals of the water treatment industry in online dose-PH controlling devices, in the near future.

Authors’ contributions

All authors contributed to the study conception and design. Narges Shakeri and Mohammad Khazaei have participated in all stages of the study (design of the study, conducting the experiments, analyzing of data and manuscript preparation. Hassan Khotanlou participated in developing the conceptual aspects of ANFIS. Ghorban Asgari carried out technical analysis of data and preparing the manuscript draft. All authors read and approved the final manuscript.

Declarations

Conflicts of interest

All authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript.