Predicting effluent from the wastewater treatment plant of industrial park based on fuzzy network and influent quality

(1)

Predicting effluent from the wastewater treatment plant of industrial

park based on fuzzy network and influent quality

T.Y. Pai

a,b,⇑

_{, P.Y. Yang}

a,c

_{, S.C. Wang}

a,c

_{, M.H. Lo}

a

_{, C.F. Chiang}

d

_{, J.L. Kuo}

a

_{, H.H. Chu}

a

_{, H.C. Su}

a

_,

L.F. Yu

a

, H.C. Hu

a

, Y.H. Chang

a

a_{Department of Environmental Engineering and Management, Chaoyang University of Technology, Wufeng, Taichung 41349, Taiwan, ROC}

b_{Department of Science Application and Dissemination, National Taichung University of Education Taichung 40306, Taiwan, ROC}

c_{Graduate Institute of Biochemical Science and Technology, Chaoyang University of Technology, Wufeng, Taichung 41349, Taiwan, ROC}

d_{Department of Public Health and Institute of Environmental Health, China Medical University, Taichung 40402, Taiwan, ROC}

a r t i c l e i n f o

Article history: Received 22 April 2009

Received in revised form 17 December 2010 Accepted 11 January 2011

Available online 22 January 2011 Keywords:

Adaptive neuro fuzzy inference system Artificial neural network

Biological wastewater treatment plant Conventional activated sludge process Industrial park

a b s t r a c t

In this study, three types of adaptive neuro fuzzy inference system (ANFIS) were employed

to predict effluent suspended solids (SSeff), chemical oxygen demand (CODeff), and pHeff

from a wastewater treatment plant in industrial park. For comparison, artificial neural net-work (ANN) was also used. The results indicated that ANFIS statistically outperformed ANN in terms of effluent prediction. The minimum mean absolute percentage errors of 2.67%,

2.80%, and 0.42% for SSeff, CODeff, and pHeffcould be achieved using ANFIS. The maximum

values of correlation coefficient for SSeff, CODeff, and pHeffwere 0.96, 0.93, and 0.95,

respec-tively. The minimum mean square errors of 0.19, 2.25, and 0.00, and the minimum root

mean square errors of 0.43, 1.48, and 0.04 for SSeff, CODeff, and pHeffcould also be achieved.

ANFIS’s architecture can overcome the limitations of traditional neural network. It also revealed that the influent indices could be applied to the prediction of effluent quality.

1. Introduction

Wastewater treatment becomes more important in Taiwan due to the amount of wastewater from industries is steadily increasing every year with the development of industries. If the industry locates in the industrial park, the effluent from one industry will be collected into the wastewater treatment plant (WWTP) of industrial park for regulation. The activated sludge process (ASP) is broadly used in the WWTP of Taiwan’s industrial parks. Since the untreated industrial wastewater contains several thousand types of chemicals, some problems will be encountered when adopting ASP in the WWTP of industrial park. Literatures have shown that many water-quality indices have been investigated to implement detailed study or to valid mechanistic models. So the more the items for wastewater characterization are, the better the reactions in ASP can be understood. In our previous work, different mechanistic models including Activated Sludge Model (ASM) and Taiwan Extension Activated Sludge Model No. 1 (TWEA1) were employed to describe the reactions in ASP[1–9].

In Taiwan, if the effluent comes from the designated sewers of industrial park, only four effluent characteristics, i.e., sus-pended solids (SS), biochemical oxygen demand (BOD), chemical oxygen demand (COD) and true color, are regulated accord-ing to effluent standard. Meanwhile, in order to save cost, effluent quality investigation from WWTP is only carried out to meet regulation standard, so their investigation data are few and incomplete compared with general study cases. Under this situation, the effluent quality cannot be predicted appropriately using some numerical models, especially mechanism

⇑ Corresponding author at: Department of Environmental Engineering and Management, Chaoyang University of Technology, Wufeng, Taichung 41349,

Taiwan, ROC. Tel.: +886 4 23323000 4465, fax: +886 4 23742365.

E-mail address:[email protected](T.Y. Pai).

Contents lists available atScienceDirect

Applied Mathematical Modelling

(2)

Author's personal copy

models. Some soft computation techniques, such as artificial neural network (ANN), in which the mechanism reactions can be ignored are available presently and applied in biological wastewater treatment process[10–15]. Although ANN can predict the effluent from WWTPs successfully, traditional neural network schemes still have several limitations which are resulted from the possibility of getting trapped in local minimum, and the choice of model architecture. If the predicting performance can be further promoted, better operation strategy can be formed. To overcome these limitations of traditional ANNs, and to increase their reliability, many new training algorithms have been proposed such as adaptive neuro fuzzy inference system (ANFIS) (Jang, 1993). ANFIS’s architecture consists of both ANN and fuzzy logic including linguistic express of membership functions (MFs) and if-then rules. ANFIS has been successfully applied in many fields of wastewater treatment[16–23]. However, no study has been applied in the prediction of effluent quality from industrial WWTP using ANFIS and influent quality.

The objectives of this study are listed as follows: (1) determine the correlation coefficients between effluent and influent quality of a WWTP. (2) Use ANFIS with different conditions to establish the relationship between effluent and influent qual-ity, then to predict the effluent quality. (3) For comparison, ANN was also employed to predict the effluent in this study. 2. Materials and methods

2.1. Treatment process

The WWTP in the industrial park locating in middle part of Taiwan was selected for study. The total number of industries in this park is 225 including manufacturers of fabricated metal products (25%), manufacturers of basic metal (11%), manu-facturers of machinery equipment and repairing (7%), manumanu-facturers of plastic products (7%), manumanu-facturers of non-metallic mining (6%) and others (44%). In this WWTP, the treatment processes were comprised of bar rack, aerated grit chamber, equalization tank, primary settling tank, aeration tank of conventional ASP, secondary settling tank. The flow rate was 7500 cubic meters per day (CMD). The influent and effluent quality data from 3 January 2005 to 6 October 2005 were inves-tigated. They were sampled and investigated every 2–3 days and their total number was 160. Among the total number of data, the numbers for training and testing (predicting) were 130 and 30, respectively. The input parameters included influent pH (pHinf), influent temperature (Tempinf), influent SS (SSinf), and influent COD (CODinf). The output parameters included effluent SS (SSeff), effluent COD (CODeff) and effluent pH (pHeff). All analytical methods used in this study were according to the Standard Method[24].

2.2. Brief description on ANFIS

Both ANN and fuzzy logic are adopted in ANFIS’s architecture in which if-then rules with appropriate MFs and the spec-ified input–output pairs are used. The learning algorithms of neural network are used for ANFIS training. Two methods are employed for updating MF parameters in ANFIS learning: (1) backpropagation for all parameters (steepest descent method), and (2) backpropagation for the parameters associated with the input MFs and least squares estimation for the parameters associated with the output MFs. Subsequently, the training errors decrease, at least locally, during the learning procedure. The more the initial MFs resemble the optimal ones, the more quickly the training parameters converge.

The fuzzy inference system with three inputs (I1, I2and I3) and one output (Of) is taken for example to explain the ANFIS architecture in this study. Considering a first order Sugeno type of fuzzy model, the if-then rule base can be expressed as

Rule 1 : If I1is A1and I2is B1and I3is C1;

Then f1;1;1¼

a

1;1;1 I1þ b1;1;1 I2þ

c

1;1;1 I3þ

g

1;1;1:

Then f1;1;2¼

a

1;1;2 I1þ b1;1;2 I2þ

c

1;1;2 I3þ

g

1;1;2:

Then f1;1;3¼

a

1;1;3 I1þ b1;1;3 I2þ

c

1;1;3 I3þ

g

1;1;3

.. .

Then f3;3;3¼

a

3;3;3 I1þ b3;3;3 I2þ

c

3;3;3 I3þ

g

3;3;3;

ð1Þ

where Ai, Bj, and Ck(i = 1 to 3) are the linguistic labels associated with this node function, respectively, i.e., the MFs for inputs Ii.

a

i,j,k, bi,j,k),

c

i,j,kand

g

i,j,k(i, j, k = 1 to 3) denote the consequent parameters[25]. As shown inFig. 1, the ANFIS’s architecture is formed by using five layer and 27 if-then rules as follows:.

2.2.1. Layer 1

Each ‘‘i’’ node in this layer is a square node with a node function as

O1_1;i¼

l

AiðI1Þ; for i ¼ 1;2;3;

O1

2;j¼

l

BjðI2Þ; for j ¼ 1;2;3;

O1_3;k¼

l

CkðI3Þ; for k ¼ 1;2;3;

ð2Þ

(3)

where I1, I2and I3are inputs to node i, and O11;i, O 1 2;jand O

1

3;kare the MFs of Ai, Bj, and Ck, respectively. The fuzzy MFs of

l

AiðI1Þ,

l

AiðI1Þ, and

l

AiðI1Þ can be described in many types. In this study, four types of common MFs including Gaussian, generalized bell shaped, triangular, and trapezoidal shaped functions with maximum value of 1 and minimum value of 0 were tested to find out the appropriate one and described as follows:

Gaussian

l

ðIÞ ¼ eÿðI-c2rÞ22

; ð3aÞ

Bell shape

l

ðIÞ ¼ ÿ 1

1 þ Iÿc

a

ÿ 2b; ð3bÞ

Triangular shape

l

ðIÞ ¼ max min I ÿ a

b ÿ a; c ÿ I c ÿ b ;0 ; ð3cÞ

Trapezoidal shape

l

ðIÞ ¼ max min I-a

b ÿ a;1; c ÿ I c ÿ b ;0 ; ð3dÞ 2th _Highest R 3th _Highest R Highest R

C

3

C

2

C

1

A

2

B

3

B

2

A

3

B

1

A

1 1 , 1 , 1

w

2 , 1 , 1

w

3 , 1 , 1

w

1 , 2 , 1

w

2 , 3 , 3

w

1 , 3 , 3

w

3 , 3 , 1

w

2 , 3 , 1

w

1 , 3 , 1

w

3 , 2 , 1

w

2 , 2 , 1

w

3 , 3 , 3

w

Layer-1 Layer-2 Layer-3 Layer-4

O

f 1

w

I1 I2 I3 I1 I3 I2

-

--Input Layer Layer-5 Output Layer

w3,3,3 f3,3,3

w1,1,1 f1,1,1

(4)

Author's personal copy

where a, b, c and

r

are the parameter set which are referred as premise parameters. 2.2.2. Layer 2

In Layer 2, each circle node labeled G multiplies the incoming signals and sends the product out. For instance,

O2_i;j;k¼ wi;j;k¼

l

AiðI1Þ

l

BjðI2Þ

l

CkðI3Þ; i;j;k ¼ 1;2;3: ð4Þ

2.2.3. Layer 3

In Layer 3, each circle node is labeled by N. The ith node calculates the ratio of the ith rule’s firing strength to the sum of all rule’s firing strengths, i.e., the normalized firing strength.

O3i;j;k¼ wi;j;k¼ wi;j;k P3 i;j;k¼1wi;j;k ; i;j;k ¼ 1;2;3: ð5Þ 2.2.4. Layer 4

Each square node i in this layer is a linear node function described as,

O4i;j;k¼ wi;j;k fi;j;k¼ wi;j;k ð

a

i;j;kI1þ bi;j;kI2þ

c

i;j;kI3þ

g

i;j;kÞ i;j;k ¼ 1;2;3: ð6Þ

2.2.5. Layer 5

The single circle node in this layer is depicted byRand computes the overall output as the summation of all incoming signals:

O5;i¼ Overall output ¼X

i wifi¼ P iwifi P iwi : ð7Þ

When adopting ANFIS, two parameters with higher correlation coefficients (ANFIS2-1), three parameters with higher corre-lation coefficients (ANFIS3-1) and all four parameters (ANFIS4-1) were taken as the input layer variables, respectively. Mean-while, each effluent quality, i.e., SSeff, CODeffand pHeff, was the single output layer variable.

2.3. Brief description on ANN

The ANN modeling approach in which the important operation features of human nervous system is simulated attempts to solve problems by using information gained from past experience to new problems. In order to operate analogous to a human brain, many simple computational elements called artificial neurons that are connected by variable weights are used in the ANN. With the hierarchical structure of a network of interconnected neurons, an ANN is capable of performing com-plex computations, although each neuron, alone, can only perform simple work. The multi-layer perceptron structure is commonly used for prediction among the many different types of structures. A typical neural network model consists of three independent layers: input, hidden, and output layers. Each layer is comprised of several operating neurons. Input neu-rons receive the values of input parameters that are fed to the network and store the scaled input values, while the calculated results in output layer are assigned by the output neurons. The hidden layer performs an interface to fully interconnect input and output layers. The pattern of hidden layer to be applied in the hierarchical network can be either multiple layers or a single layer. Each neuron is connected to every neuron in adjacent layers before being introduced as input to the neuron

0 50 100 150 200 250 300 350 400 0 1 /0 3 /0 5 0 1 /1 0 /0 5 0 1 /1 7 /0 5 0 1 /2 4 /0 5 0 1 /3 1 /0 5 0 2 /0 7 /0 5 0 2 /1 4 /0 5 0 2 /2 1 /0 5 0 2 /2 8 /0 5 0 3 /0 7 /0 5 0 3 /1 4 /0 5 0 3 /2 1 /0 5 0 3 /2 8 /0 5 0 4 /0 4 /0 5 0 4 /1 1 /0 5 0 4 /1 8 /0 5 0 4 /2 5 /0 5 0 5 /0 2 /0 5 0 5 /0 9 /0 5 0 5 /1 6 /0 5 0 5 /2 3 /0 5 0 5 /3 0 /0 5 0 6 /0 6 /0 5 0 6 /1 3 /0 5 0 6 /2 0 /0 5 0 6 /2 7 /0 5 0 7 /0 4 /0 5 0 7 /1 1 /0 5 0 7 /1 8 /0 5 0 7 /2 5 /0 5 0 8 /0 1 /0 5 0 8 /0 8 /0 5 0 8 /1 5 /0 5 0 8 /2 2 /0 5 0 8 /2 9 /0 5 0 9 /0 5 /0 5 0 9 /1 2 /0 5 0 9 /1 9 /0 5 0 9 /2 6 /0 5 1 0 /0 3 /0 5 Time (date) 0 10 20 30 40 50 60 70 80 90 100

pHinf SSinf CODinf Tempinf

SSeff CODeff pHeff

SS inf and COD inf (mg L -1 ), T emp inf ( o C), pH inf SS ef f and COD ef f (m g L -1 ), p H ef f

Fig. 2.Effluent variation.

(5)

in the next layer by a connection weight, which determines the strength of the relationship between two connected neurons. Each neuron sums all of the inputs that it receives and the sum is converted to an output value based on a predefined activation, or transfer, function. For prediction problems, a supervised learning algorithm is often adopted for training the network how to relate input data to output data. In recent years, the backpropagation algorithm is widely used for teaching multi-layer neural networks. Traditionally, the algorithm uses a gradient search technique (the steepest gradient descent method) to minimize a function equal to the mean square difference between the desired and the actual network outputs. To compare with ANFIS, two parameters with higher R (ANN2-1), three parameters with higher R (ANN3-1) and all four parameters (ANN4-1) were taken as the input layer variables, respectively. Meanwhile, each effluent quality, i.e. SSeff, CODeff and pHeff, was the single output layer variable. The calculation of both ANFIS and ANN was carried out using MATLAB.

Table 1

The correlation coefficients between the effluent quality and influent quality.

pHinf SSinf CODinf Tempinf

SSeff 0.0023 ÿ0.0402 0.0421 ÿ0.2057

CODeff 0.0576 0.1075 0.0065 ÿ0.1592

pHeff 0.1176 ÿ0.1099 ÿ0.1129 ÿ0.1164

Table 2

The selected input variables in ANFIS and ANN.

ANFIS ANN

Structure Input variables Structure Input variables

SSeff

ANFIS2-1 CODinf, pHinf ANN2-1 CODinf, pHinf

ANFIS3-1 CODinf, pHinf, Tempinf ANN3-1 CODinf, pHinf, Tempinf

ANFIS4-1 CODinf, pHinf, Tempinf, SSinf ANN4-1 CODinf, pHinf, Tempinf, SSinf

CODeff

ANFIS2-1 SSinf, pHinf ANN2-1 SSinf, pHinf

ANFIS3-1 SSinf, pHinf, CODinf ANN3-1 SSinf, pHinf, CODinf

ANFIS4-1 SSinf, pHinf, CODinf, Tempinf ANN4-1 SSinf, pHinf, CODinf, Tempinf

pHeff

ANFIS2-1 pHinf, SSinf ANN2-1 pHinf, SSinf

ANFIS3-1 pHinf, SSinf, CODinf ANN3-1 pHinf, SSinf, CODinf

ANFIS4-1 pHinf, SSinf, CODinf, Tempinf ANN4-1 pHinf, SSinf, CODinf, Tempinf

Table 3

Determination of the appropriate ANFIS and ANN models.

ANFIS ANN

Items 4-1 3-1 2-1 Items 4-1 3-1 2-1

Basic structure Basic structure

No. of total layers 7 7 7 No. of total layers 3 3 3

No. of layers excepting input and output layer 5 5 5 No. of hidden layer 1 1 1

No. of nodes in input layers 4 3 2 No. of neurons in input layers 4 3 2

No. of nodes in output layers 1 1 1 No. of neuron in output layers 1 1 1

SSeff SS

Shape of MFs Bell Bell Bell Speed of training 0.1 0.1 0.1

No. of MFs 4 4 4 No. of neurons in hidden layers 16 16 16

No. of training 100 110 130 No. of training 14,000 16,000 17,000

No. of fuzzy rules 44 ₄3 ₄2

CODeff COD

No. of fuzzy rules 44 ₄3 ₄2

pHeff pH

(6)

Author's personal copy

2.4. Evaluation of predicting performa nce In order to evaluate the predictin g performance of ANFIS and ANN, the mean absolute percentage error (MAPE), correla-tion coefficient (R ), mean square error (MSE), and root mean square error (RMSE) were employed and described as, 0 10 20 30 40 50 3-Jan 13-Jan 23-Jan 2-Feb 12-Feb 22-Feb 4-Mar 14-Mar 24-Mar 3-Apr 13-Apr 23-Apr 3-May 13-May 23-May 2-Jun 12-Jun 22-Jun 2-Jul 12-Jul 22-Jul 1-Aug 11-Aug 21-Aug 31-Aug 10-Sep 20-Sep 30-Sep T ime (date) Obs_SS Pred_SS Concentration (mg L-1₎ T ra n in g P re d ic ti n g 0 10 20 30 40 50 3-Jan 13-Jan 23-Jan 2-Feb 12-Feb 22-Feb 4-Mar 14-Mar 24-Mar 3-Apr 13-Apr 23-Apr 3-May 13-May 23-May 2-Jun 12-Jun 22-Jun 2-Jul 12-Jul 22-Jul 1-Aug 11-Aug 21-Aug 31-Aug 10-Sep 20-Sep 30-Sep T ime (date) Obs_SS Pred_SS Concentration (mg L-1₎ T ra n in g P re d ic ti n g 0 10 20 30 40 50 3-Jan 13-Jan 23-Jan 2-Feb 12-Feb 22-Feb 4-Mar 14-Mar 24-Mar 3-Apr 13-Apr 23-Apr 3-May 13-May 23-May 2-Jun 12-Jun 22-Jun 2-Jul 12-Jul 22-Jul 1-Aug 11-Aug 21-Aug 31-Aug 10-Sep 20-Sep 30-Sep T ime (date) Obs_SS Pred_SS Concentration (mg L-1₎ T ra n in g P re d ic ti n g 0 10 20 30 40 50 3-Jan 13-Jan 23-Jan 2-Feb 12-Feb 22-Feb 4-Mar 14-Mar 24-Mar 3-Apr 13-Apr 23-Apr 3-May 13-May 23-May 2-Jun 12-Jun 22-Jun 2-Jul 12-Jul 22-Jul 1-Aug 11-Aug 21-Aug 31-Aug 10-Sep 20-Sep 30-Sep T ime (date) Obs_SS Pred_SS Concentration (mg L-1₎ T ra n in g P re d ic ti n g 0 10 20 30 40 50 3-Jan 13-Jan 23-Jan 2-Feb 12-Feb 22-Feb 4-Mar 14-Mar 24-Mar 3-Apr 13-Apr 23-Apr 3-May 13-May 23-May 2-Jun 12-Jun 22-Jun 2-Jul 12-Jul 22-Jul 1-Aug 11-Aug 21-Aug 31-Aug 10-Sep 20-Sep 30-Sep T im e (d at e ) Obs_SS Pred_SS Concentration (mg L-1₎ T ra n in g P re d ic ti n g Concentration (mg L-1₎

a

b

c

d

e

f

0 10 20 30 40 50 3-Jan 13-Jan 23-Jan 2-Feb 12-Feb 22-Feb 4-Mar 14-Mar 24-Mar 3-Apr 13-Apr 23-Apr 3-May 13-May 23-May 2-Jun 12-Jun 22-Jun 2-Jul 12-Jul 22-Jul 1-Aug 11-Aug 21-Aug 31-Aug 10-Sep 20-Sep 30-Sep T ime (date) Obs_SS Pred_SS T raning P redicting Fig. 3. Prediction results of SS eff . (a) ANFIS2-1, (b) ANFIS3-1, (c) ANFIS4-1, (d) ANN2-1, (e) ANN3-1, and (f) ANN4-1. T.Y. Pai et al. /Applied Mathematical Modelling 35 (2011) 3674–3684 3679

(7)

MAPE ¼1 n X n i¼1 obsiÿ prei obsi 100%; ð8Þ R ¼ Pn

i¼1ðobsiÿ obsÞðpreiÿ preÞ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn

i¼1ðobsiÿ obsÞ

2Pn

i¼1ðpreiÿ preÞ

2 q ; ð9Þ MSE ¼1 n X n i¼1 ðobsiÿ preiÞ2; ð10Þ RMSE ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 n Xn

i¼1ðobsiÿ preiÞ

2 r

; ð11Þ

where obsiis the observed value, preiis the prediction value, obs and pre are the average values of observed values and pre-diction values, respectively.

3. Results and discussion 3.1. Variation trend of water quality

The number of data investigated from 3 January 2005 to 6 October 2005 was totally 160, as shown inFig. 2. Among the total numbers of data, the numbers for training and testing (predicting) were 130 and 30, respectively. In Taiwan, the efflu-ent regulation limits of SSeffand CODeffwere 30 and 100 mg Lÿ1, respectively. The effluent quality from this WWTP met the Effluent Standard of Taiwan..

3.2. Correlation coefficients between influent and effluent quality

The correlation coefficients (R) between the effluent quality (SSeff, CODeff, and pHeff) and four different influent wastewa-ter quality indices (pHinf, Tempinf, SSinf, and CODinf) were calculated as shown inTable 1. The R values of SSefwere in the following order: CODinf(0.0421) > pHinf(0.0023) > Tempinf(ÿ0.2057) > SSinf(ÿ0.0402). Those of CODeffwere in the following order: SSinf(0.1075) > pHinf(0.0576) > CODinf(0.0065) > Tempinf(ÿ0.1592). Those of pHeffwere in the following order: pHinf (0.1176) > SSinf (ÿ0.1099) > CODinf (ÿ0.1129) > Tempinf (ÿ0.1164). Based on the results of R values, the selected input Table 4

Predicting performance using different ANFIS and ANN.

ANFIS ANN

ANFIS4-1 ANFIS3-1 ANFIS2-1 ANN4-1 ANN3-1 ANN2-1

SSeff MAPE (%) Train 12.21 11.68 9.58 19.89 18.92 18.15 Predict 5.63 4.66 2.67 7.30 4.64 4.64 R Train 0.95 0.95 0.97 0.83 0.84 0.88 Predict 0.87 0.91 0.96 0.87 0.92 0.89 MSE Train 1.67 1.45 0.92 4.90 4.69 3.48 Predict 0.96 0.64 0.19 1.31 0.59 0.50 RMSE Train 1.29 1.20 0.96 2.21 2.17 1.87 Predict 0.98 0.80 0.43 1.15 0.77 0.71 CODeff MAPE (%) Train 9.95 8.75 7.66 11.57 10.86 9.91 Predict 4.54 3.66 2.80 5.87 4.89 4.77 R Train 0.80 0.84 0.88 0.70 0.74 0.79 Predict 0.80 0.88 0.93 0.82 0.85 0.83 MSE Train 14.77 12.59 9.04 19.85 17.57 14.68 Predict 4.40 2.81 2.25 5.37 4.57 6.11 RMSE Train 3.84 3.55 3.01 4.45 4.19 3.83 Predict 2.10 1.66 1.48 2.32 2.14 2.47 pHeff MAPE (%) Train 0.69 0.66 0.59 0.79 0.74 0.69 Predict 0.59 0.50 0.42 0.66 0.64 0.53 R Train 0.92 0.94 0.96 0.91 0.93 0.93 Predict 0.87 0.90 0.95 0.86 0.90 0.93 MSE Train 0.01 0.00 0.00 0.01 0.00 0.00 Predict 0.00 0.00 0.00 0.00 0.00 0.00 RMSE Train 0.07 0.07 0.06 0.07 0.07 0.07 Predict 0.06 0.05 0.04 0.06 0.06 0.05

(8)

Author's personal copy

variables in three types of ANFIS (ANFIS2-1, ANFIS3-1 and ANFIS4-1) and in three types of ANN (ANN2-1, ANN3-1 and ANN4-1) were shown in Table 2 . 3.3. Determinati on of an appropriate ANFIS and ANN model The types and numbers of MFs in Layer 2 including Gaussian ,generalized bell shaped, triangula r and trapezoidal shaped functions, and the paramete rs in Eqs. (1) and (3) were tested to determine an appropriate ANFIS model. After many trials in 0 20 40 60 80 100 3-Jan 13-Jan 23-Jan 2-Feb 12-Feb 22-Feb 4-Mar 14-Mar 24-Mar 3-Apr 13-Apr 23-Apr 3-May 13-May 23-May 2-Jun 12-Jun 22-Jun 2-Jul 12-Jul 22-Jul 1-Aug 11-Aug 21-Aug 31-Aug 10-Sep 20-Sep 30-Sep T ime (date) Obs_COD Pred_COD Concentration (mg L-1₎ T ra n in g P re di c tin g 0 20 40 60 80 100 3-Jan 13-Jan 23-Jan 2-Feb 12-Feb 22-Feb 4-Mar 14-Mar 24-Mar 3-Apr 13-Apr 23-Apr 3-May 13-May 23-May 2-Jun 12-Jun 22-Jun 2-Jul 12-Jul 22-Jul 1-Aug 11-Aug 21-Aug 31-Aug 10-Sep 20-Sep 30-Sep T ime (date) Obs_COD Pred_COD Concentration (mg L-1₎ T ra n in g P re d ic tin g 0 20 40 60 80 100 3-Jan 13-Jan 23-Jan 2-Feb 12-Feb 22-Feb 4-Mar 14-Mar 24-Mar 3-Apr 13-Apr 23-Apr 3-May 13-May 23-May 2-Jun 12-Jun 22-Jun 2-Jul 12-Jul 22-Jul 1-Aug 11-Aug 21-Aug 31-Aug 10-Sep 20-Sep 30-Sep T ime (date) Obs_COD Pred_COD Concentration (mg L-1₎ T ra n in g P re d ic tin g 0 20 40 60 80 100 3-Jan 13-Jan 23-Jan 2-Feb 12-Feb 22-Feb 4-Mar 14-Mar 24-Mar 3-Apr 13-Apr 23-Apr 3-May 13-May 23-May 2-Jun 12-Jun 22-Jun 2-Jul 12-Jul 22-Jul 1-Aug 11-Aug 21-Aug 31-Aug 10-Sep 20-Sep 30-Sep T ime (date) Obs_COD Pred_COD Concentration (mg L-1₎ T ra n in g P re d ic tin g 0 20 40 60 80 100 3-Jan 13-Jan 23-Jan 2-Feb 12-Feb 22-Feb 4-Mar 14-Mar 24-Mar 3-Apr 13-Apr 23-Apr 3-May 13-May 23-May 2-Jun 12-Jun 22-Jun 2-Jul 12-Jul 22-Jul 1-Aug 11-Aug 21-Aug 31-Aug 10-Sep 20-Sep 30-Sep T ime (date) Obs_COD Pred_COD Concentration (mg L-1₎ T ra n in g P re d ic tin g 0 20 40 60 80 1 0 0 3-Jan 13-Jan 23-Jan 2-Feb 12-Feb 22-Feb 4-Mar 14-Mar 24-Mar 3-Apr 13-Apr 23-Apr 3-May 13-May 23-May 2-Jun 12-Jun 22-Jun 2-Jul 12-Jul 22-Jul 1-Aug 11-Aug 21-Aug 31-Aug 10-Sep 20-Sep 30-Sep T ime (date) Obs_COD Pred_COD Concentration (mg L-1₎ T ra n in g P re d ic tin g

a

b

c

d

e

f

Fig. 4. Prediction results of COD eff . (a) ANFIS2-1, (b) ANFIS3-1, (c) ANFIS4-1, (d) ANN2-1, (e) ANN3-1, and (f) ANN4-1. T.Y. Pai et al. /Applied Mathematical Modelling 35 (2011) 3674–3684 3681

(9)

Author's personal copy

ation for the paramete rs were implemented , the final architectures of the ANFIS models are given in different input variables, all ANFIS models had generaliz ed bell shaped MFs and four MFs for each input the best result. Their numbers of training were between 100 and 130. The numbers of fuzzy rules in ANFIS showed the highest accuracy are also provided in Table 3 . with ANFIS, the appropriate ANN models were also shown in Table 3 .All ANN consisted of three independen t hidden, and output layers. The hidden layer was comprised of 16 operating neurons. The number of training 14,000 and 18,000. 0 5 10 15 20 3-Jan 13-Jan 23-Jan 2-Feb 12-Feb 22-Feb 4-Mar 14-Mar 24-Mar 3-Apr 13-Apr 23-Apr 3-May 13-May 23-May 2-Jun 12-Jun 22-Jun 2-Jul 12-Jul 22-Jul 1-Aug 11-Aug 21-Aug 31-Aug 10-Sep 20-Sep 30-Sep T ime (date) Obs_pH P re d _ p H T ra n in g P re d ic ti n g 0 5 10 15 20 3-Jan 13-Jan 23-Jan 2-Feb 12-Feb 22-Feb 4-Mar 14-Mar 24-Mar 3-Apr 13-Apr 23-Apr 3-May 13-May 23-May 2-Jun 12-Jun 22-Jun 2-Jul 12-Jul 22-Jul 1-Aug 11-Aug 21-Aug 31-Aug 10-Sep 20-Sep 30-Sep T ime (date) Obs_pH Pred_pH T ra n in g P re di ct in g 0 5 10 15 20 3-Jan 13-Jan 23-Jan 2-Feb 12-Feb 22-Feb 4-Mar 14-Mar 24-Mar 3-Apr 13-Apr 23-Apr 3-May 13-May 23-May 2-Jun 12-Jun 22-Jun 2-Jul 12-Jul 22-Jul 1-Aug 11-Aug 21-Aug 31-Aug 10-Sep 20-Sep 30-Sep T ime (date) Obs_pH Pred_pH T ra n in g P re di ct in g 0 5 10 15 20 3-Jan 13-Jan 23-Jan 2-Feb 12-Feb 22-Feb 4-Mar 14-Mar 24-Mar 3-Apr 13-Apr 23-Apr 3-May 13-May 23-May 2-Jun 12-Jun 22-Jun 2-Jul 12-Jul 22-Jul 1-Aug 11-Aug 21-Aug 31-Aug 10-Sep 20-Sep 30-Sep T ime (date) Obs_pH Pred_pH T ra n in g P re di ct in g 0 5 10 15 20 3-Jan 13-Jan 23-Jan 2-Feb 12-Feb 22-Feb 4-Mar 14-Mar 24-Mar 3-Apr 13-Apr 23-Apr 3-May 13-May 23-May 2-Jun 12-Jun 22-Jun 2-Jul 12-Jul 22-Jul 1-Aug 11-Aug 21-Aug 31-Aug 10-Sep 20-Sep 30-Sep T ime (date) Obs_pH Pred_pH T ra n in g P re di ct in g 0 5 10 15 20 3-Jan 13-Jan 23-Jan 2-Feb 12-Feb 22-Feb 4-Mar 14-Mar 24-Mar 3-Apr 13-Apr 23-Apr 3-May 13-May 23-May 2-Jun 12-Jun 22-Jun 2-Jul 12-Jul 22-Jul 1-Aug 11-Aug 21-Aug 31-Aug 10-Sep 20-Sep 30-Sep T ime (date) Obs_pH Pred_pH

Concentration (mg L-1₎ _{Concentration (mg L}-1₎ _{Concentration (mg L}-1₎ _{Concentration (mg L}-1₎ _{Concentration (mg L}-1₎ _{Concentration (mg L}-1₎

T ra n in g P re di ct in g

a

b

c

d

e

f

Fig. 5. Prediction results of pH eff . (a) ANFIS2-1, (b) ANFIS3-1, (c) ANFIS4-1, (d) ANN2-1, (e) ANN3-1, and (f) ANN4-1. T.Y. Pai et al. /Applied Mathematical Modelling 35 (2011) 3674–3684

(10)

Author's personal copy

3.4. Simulation of SSeff

Figs. 3(a)–(f)depict the prediction results of SSeffusing ANFIS2-1, ANFIS3-1, ANFIS4-1, ANN2-1, ANN3-1, and ANN4-1, respectively. All MAPE, R, MSE, and RMSE values are shown inTable 4The 1st to 130th values were used for model training, 131st to 160th values were used to evaluate the fitness. As shown inTable 4, when training, MAPEs between the predicted and observed values of SSeffwere between 9.58% and 12.21% using ANFIS, but they were 18.15–19.89% using ANN. When predicting, the MAPEs lay between 2.67% and 5.63% adopting ANFIS, but they were between 4.64% and 7.30% when using ANN. When training, R values increased from 0.83–0.88 to 0.95–0.97 using ANFIS. When predicting, R values also increased from 0.87–0.92 to 0.87–0.96. MSE and RMSE values also showed that the predicting performance of ANFIS prevailed. The MSE values of 0.92–1.67 using ANFIS were lower than those of 3.48–4.90 using ANN when model training. When predicting, the MSE values of 0.19–0.92 using ANFIS were also lower than those of 0.50–1.31 using ANN. When training, the RMSE val-ues of 0.96–1.29 using ANFIS were lower than those of 1.87–2.21 using ANN. The RMSE valval-ues of 0.43–0.98 using ANFIS were also lower than those of 0.71–1.15 using ANN when predicting.

3.5. Simulation of CODeff

Figs. 4(a)–(f)shows the prediction results of CODeff. When training, the MAPE values of 7.66–9.95% using ANFIS were lower than those of 9.91–11.57% using ANN. The MAPE values of 2.80–4.54% using ANFIS were also lower than those of 4.77–5.87% using ANN when predicting. When training, the R values of 0.80–0.88 using ANFIS were higher than those of 0.70–0.79 using ANN. The R values of 0.88–0.93 using ANFIS were also higher than those of 0.83–0.85 using ANN when predicting, excepting those of ANFIS4-1 vs. ANN4-1. When training, the MSEs of CODeffwere between 9.04 and 14.77 using ANFIS, but they were 14.68–19.85 using ANN. When predicting, the MSEs lay between 2.25 and 4.40 adopting ANFIS, but they were between 4.57 and 6.11 when using ANN. The RMSE values of 3.01–3.84 using ANFIS were lower than those of 3.83–4.45 using ANN when model training. When predicting, the RMSE values of 1.48–2.10 using ANFIS were also lower than those of 2.14–2.47 using ANN. 3.6. Simulation of pHeff

The prediction results of pHeffare shown inFigs. 5(a)–(f)When training, the MAPE values of 0.59–0.69% using ANFIS were lower than those of 0.69–0.79% using ANN. The MAPE values of 0.42–0.59% using ANFIS were also lower than those of 0.53– 0.66% using ANN when predicting. When training, the R values of 0.92–0.96 using ANFIS were higher than those of 0.91–0.93 using ANN. The R values of 0.87–0.95 using ANFIS were also higher than those of 0.86–0.93 using ANN when predicting. When training and predicting, the MSEs using both ANFIS and ANN were analogous, lying between 0.00 and 0.01, respec-tively. The RMSE values of 0.06–0.07 using ANFIS were lower than those of 0.7 using ANN when model training. When pre-dicting, the RMSE values of 0.04–0.06 using ANFIS were also lower than those of 0.05–0.06 using ANN.

Comparable observations were similarly made by Lee et al.[15]. Lee et al.[15]developed a real-time remote monitoring system for WWTP to give local operators a guideline that allowed them to arrive at the optimum operational strategy in the early stage of a process disturbance. They found that the RMSE values of the training and testing datasets were 0.787 and 1.287, respectively. Civelekoglu et al.[21]employed ANFIS to develop models for the prediction of carbon and nitrogen re-moval in the aerobic biological treatment stage of a full-scale WWTP in the sugar production industry. For the COD model; RMSE, average percentage error (APE) and R values were 9.4 mg/L, 8.37% and 0.978%, respectively. Such values for the nitro-gen model were 4.3 mg/L, 23.65% and 0.992%. Güçlü and Dursun[14]combined the mechanistic model and ANN in parallel configuration to predict effluent COD concentrations and compare the results for the purpose of evaluation of treatment per-formance. The results indicated that the best values of R, RMSE, and MAPE were 0.88%, 2.56%, and 4.25%, respectively when training. These values were 0.91%, 2.64%, and 4.08%, respectively when testing.

In this study, the minimum MAPEs of 2.67%, 2.80%, and 0.42% for SSeff, CODeffand pHeffcould be achieved using ANFIS. The maximum R values for SSeff, CODeff, and pHeffwere 0.96, 0.93, and 0.95, respectively. The minimum MSEs of 0.19, 2.25 and 0.00, and the minimum RMSEs of 0.43, 1.48 and 0.04 for SSeff, CODeffand pHeffcould also be achieved. ANFIS’s architecture consists of both ANN and fuzzy logic including linguistic express of MFs and if-then rules, so it can overcome the limitations of traditional neural network including possibility of getting trapped in local minimum and the choice of model architecture, and to increase the predicting performance. It also indicated that the influent indices could be applied on the prediction of effluent quality. 4. Conclusions

Three types of ANFIS were used to predict SSeff, pHeffand CODefffrom a WWTP of industrial park in Taiwan. The ANN was also adopted for comparison. The simulation results can be drawn as follows:

According to the results, ANFIS could predict the variation of industrial effluent. The minimum MAPEs of 2.67%, 2.80%, and 0.42% for SSeff, CODeffand pHeffcould be achieved using ANFIS. The maximum R values for SSeff, CODeff, and pHeffwere 0.96, 0.93, and 0.95, respectively. The minimum MSEs of 0.19, 2.25, and 0.00, and the minimum RMSEs of 0.43, 1.48, and 0.04 for SSeff, CODeff, and pHeffcould also be achieved.

(11)

It also revealed that the influent indices could be applied to the prediction of effluent quality.

After prediction, it is suggested that the ANFIS can be used as the objective function or constrains in optimization for best design or operation in the future study.

Acknowledgments

The authors are grateful to the National Science Council of Taiwan, ROC for financial support under the Grant No. NSC 97-2221-E-324-048.

References

[1] T.Y. Pai, C.F. Ouyang, J.L. Su, H.G. Leu, Modelling the steady-state effluent characteristics of the TNCU process under different return mixed liquid, Appl. Math. Model. 25 (12) (2001) 1025–1038.

[2] T.Y. Pai, Y.P. Tsai, Y.J. Chou, H.Y. Chang, H.G. Leu, C.F. Ouyang, Microbial kinetic analysis of three different types of EBNR process, Chemosphere 55 (1) (2004) 109–118.

[3] T.Y. Pai, S.H. Chuang, Y.P. Tsai, C.F. Ouyang, Modelling a combined A2_{O and RBC process under DO variation by using an activated sludge – biofilm}

hybrid model, J. Environ. Eng. ASCE 130 (12) (2004) 1433–1441.

[4] T.Y. Pai, Modeling nitrite and nitrate variations in A2_{O process under different return oxic mixed liquid using an extended model, Process Biochem. 42}

(6) (2007) 978–987.

[5] T.Y. Pai, S.C. Wang, H.M. Lo, C.F. Chiang, M.H. Liu, R.J. Chiou, W.Y. Chen, P.S. Hung, W.C. Liao, H.G. Leu, Novel modeling concept for evaluating the effects of cadmium and copper on heterotrophic growth and lysis rates in activated sludge process, J. Hazard. Mater. 166 (1) (2009) 200–206.

[6] T.Y. Pai, H.Y. Chang, T.J. Wan, S.H. Chuang, Y.P. Tsai, Using an extended activated sludge model to simulate nitrite and nitrate variations in TNCU2 process, Appl. Math. Model. 33 (11) (2009) 4259–4268.

[7] T.Y. Pai, S.C. Wang, C.Y. Lin, W.C. Liao, H.H. Chu, T.S. Lin, C.C. Liu, S.W. Lin, Two types of organophosphate pesticides and their combined effects on heterotrophic growth rates in activated sludge process, J. Chem. Technol. Biotechnol. 84 (12) (2009) 1773–1779.

[8] T.Y. Pai, T.J. Wan, Y.P. Tsai, C.J. Tzeng, H.H. Chu, Y.S. Tsai, C.Y. Lin, Effect of sludge retention time on biomass and kinetic parameter of two nitrifying species in anaerobic/oxic process, CLEAN – Soil, Air, Water 38 (2) (2010) 167–172.

[9] T.Y. Pai, R.J. Chiou, C.J. Tzeng, T.S. Lin, S.C. Yeh, P.J. Sung, C.H. Tseng, C.H. Tsai, Y.S. Tsai, W.J. Hsu, Y.L. Wei, Variation of biomass and kinetic parameter for nitrifying species in TNCU3 process at different aerobic hydraulic retention time, World J. Microbiol. Biotechnol. 26 (4) (2010) 589–597.

[10] T.Y. Pai, Y.P. Tsai, H.M. Lo, C.H. Tsai, C.Y. Lin, Grey and neural network prediction of suspended solids and chemical oxygen demand in hospital wastewater treatment plant effluent, Comput. Chem. Eng. 31 (10) (2007) 1272–1281.

[11] T.Y. Pai, Grey and neural network prediction of effluent from the wastewater treatment plant of industrial park using influent quality, Environ. Eng. Sci. 25 (5) (2008) 757–766.

[12] T.Y. Pai, S.H. Chuang, H.H. Ho, L.F. Yu, H.C. Su, H.C. Hu, Predicting performance of grey and neural network in industrial effluent using online monitoring parameters, Process Biochem. 43 (2) (2008) 199–205.

[13] T.Y. Pai, S.H. Chuang, T.J. Wan, H.M. Lo, Y.P. Tsai, H.C. Su, L.F. Yu, H.C. Hu, P.J. Sung, Comparisons of grey and neural network prediction of industrial park wastewater effluent using influent quality and online monitoring parameters, Environ. Monit. Assess. 146 (1–3) (2008) 51–66.

[14] D. Güçlü, S. Dursun, Amelioration of carbon removal prediction for an activated sludge process using an artificial neural network (ANN), CLEAN – Soil Air Water 36 (9) (2008) 781–787.

[15] M.W. Lee, S.H. Hong, H. Choi, J.H. Kim, D.S. Lee, J.M. Park, Real-time remote monitoring of small-scaled biological wastewater treatment plants by a multivariate statistical process control and neural network-based software sensors, Process Biochem. 43 (10) (2008) 1107–1113.

[16] J.P. Steyer, D. Rolland, J.C. Bouvier, R. Moletta, Hybrid fuzzy neural network for diagnosis – application to the anaerobic treatment of wine distillery wastewater in a fluidized bed reactor, Water Sci. Technol. 36 (6–7) (1997) 209–217.

[17] J.H. Tay, X. Zhang, Neural fuzzy modeling of anaerobic biological wastewater treatment systems, J. Environ. Eng. ASCE 125 (12) (1999) 1149–1159. [18] A. Perendeci, S. Arslan, A. Tanyolaç, S. Çelebi, Evaluation of input variables in adaptive-network-based fuzzy inference system modeling for an

anaerobic wastewater treatment plant under unsteady state, J. Environ. Eng. ASCE 133 (7) (2007) 765–771.

[19] A. Perendeci, S. Arslan, S.S. Çelebi, A. Tanyolaç, Prediction of effluent quality of an anaerobic treatment plant under unsteady state through ANFIS modeling with on-line input variables, Chem. Eng. J. 145 (1) (2008) 78–85.

[20] M. Cakmakci, Adaptive neuro-fuzzy modelling of anaerobic digestion of primary sedimentation sludge, Bioprocess Biosyst. Eng. 30 (5) (2007) 349–357. [21] G. Civelekoglu, A. Perendeci, N.O. Yigit, M. Kitis, Modeling carbon and nitrogen removal in an industrial wastewater treatment plant using an adaptive

network-based fuzzy inference system, CLEAN – Soil, Air, Water 35 (6) (2007) 617–625.

[22] T.Y. Pai, T.J. Wan, S.T. Hsu, T.C. Chang, Y.P. Tsai, C.Y. Lin, H.C. Su, L.F. Yu, Using fuzzy inference system to improve neural network for predicting hospital wastewater treatment plant effluent, Comput. Chem. Eng. 33 (7) (2009) 1272–1278.

[23] T.Y. Pai, S.C. Wang, C.F. Chiang, H.C. Su, L.F. Yu, P.J. Sung, C.Y. Lin, H.C. Hu, Improving neural network prediction of effluent from biological wastewater treatment plant of industrial park using fuzzy learning approach, Bioprocess Biosyst. Eng. 32 (6) (2009) 781–790.

[24] APHA, AWWA, WEF, Standard Methods for the Examination of Water and Wastewater, 19th ed., American Public Health Association/American Water Works Association/Water Environment Federation, Washington, DC, 1995.