Development of experimental design approach and

Bioresource Technology 148 (2013) 550–559

Contents lists available at ScienceDirect

Bioresource Technology journal homepage: www.elsevier.com/locate/biortech

Development of experimental design approach and ANN-based models for determination of Cr(VI) ions uptake rate from aqueous solution onto the solid biodiesel waste residue M. Shanmugaprakash a, V. Sivakumar b,⇑ a b

Downstream Processing Laboratory, Department of Biotechnology, Kumaraguru College of Technology, Coimbatore 641 049, India Department of Food Technology, Kongu Engineering College, Perundurai, Erode 638 052, India

h i g h l i g h t s  This paper investigates the Cr(VI) uptake rate on DPOC in batch and continues mode.  RSM and ANN models were used for removal of Cr(VI) ion in batch and continuous mode.  ANN had better prediction capability than RSM for Cr(VI) uptake rate on DPOC.  pH and temperature are significant factors for removal of Cr(VI) ions in batch mode.  Metal ions concentration and bed height are significant factors in continuous mode.

a r t i c l e

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Article history: Received 26 June 2013 Received in revised form 21 August 2013 Accepted 25 August 2013 Available online 3 September 2013 Keywords: Artificial neural networks Biosorption Cr(VI) ions DPOC Response surface methodology

a b s t r a c t In the present work, the evaluation capacities of two optimization methodologies such as RSM and ANN were employed and compared for predication of Cr(VI) uptake rate using defatted pongamia oil cake (DPOC) in both batch and column mode. The influence of operating parameters was investigated through a central composite design (CCD) of RSM using Design Expert 8.0.7.1 software. The same data was fed as input in ANN to obtain a trained the multilayer feed-forward networks back-propagation algorithm using MATLAB. The performance of the developed ANN models were compared with RSM mathematical models for Cr(VI) uptake rate in terms of the coefficient of determination (R2), root mean square error (RMSE) and absolute average deviation (AAD). The estimated values confirm that ANN predominates RSM representing the superiority of a trained ANN models over RSM models in order to capture the non-linear behavior of the given system. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction An increase in the rate of industrialization and extensive use of machines in all sectors has contributed a great percentage to the heavy metal pollution, by releasing heavy metals in the effluents thus causing health hazards to the biological systems. The presence of heavy toxic metals in aqueous waste streams and lands, from the discharge of many industrial sources, such as metal plating, picking baths, electroplating, mine water, tanneries, plastic manufacturing, fertilizers, pigments and metallurgical processes, has received wide spread attention throughout the world in recent years (Nadaroglu et al., 2010). Due to its toxicological consequences in the ecosystem, agricultural and health systems, it is essential to make effluents free of heavy metals, before releasing them into the environment (Bishnoi et al., 2007). ⇑ Corresponding author. Tel.: +91 04294 226606; fax: +91 04294 220087. E-mail address: [email protected] (V. Sivakumar). 0960-8524/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.biortech.2013.08.149

Among the heavy metals present in the above effluents, chromium is a highly toxic pollutant generated from the industries. Chromium exists in aqueous solutions mainly in two states: trivalent Cr (III) (Cr3+, Cr (OH)2+ or Cr ((OH)2+) and hexavalent Cr(VI) 2 2 (HCrO 4 ; CrO4 ; CrO7 ). Hexavalent chromium is more toxic than the trivalent form, i.e., 100-times more toxic and this is due to its high oxidation potential, and the ease with which it penetrates easily into the biological membrane (Gomez and Callao, 2006). Moreover, Cr(VI) is known to be carcinogenic, mutagenic and it induces dermatitis (Gibb et al., 2000). The US EPA has set the maximum contaminant level for the exit Cr(VI) ions concentration in the effluent as 0.05 mg/L, and the United Nations Food and Agricultural organization recommends the maximal level of irrigational water as 0.1 mg/L (Apha, 2005). In order to decrease the high concentration of Cr(VI) ions present in the effluents to permissible levels, various physico-chemical treatment methods are available for the removal of chromium ions, such as activated carbon reverse osmosis, chemical precipitation,

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evaporation, and ion exchange (Owlad et al., 2009). However, the treatment cost, operational complexity of the technology, the skill required to operate, and problems in handling the generation of secondary waste, are major factors that should be considered before selecting the methods for the large scale treatment of waste water (Kundu and Gupta, 2005; Choong et al., 2007; Kumari et al., 2006; Mohan and Pittman, 2007). Moreover, these methods are not effective at metal concentrations ranging from 1.0 to 100 mg/L in the effluent (Gupta and Rastogi, 2008). The disadvantages of these traditional and chemical methods have induced the urge to find a new economical and environmentally safe method. In this regard, the biosorption of heavy metals has been suggested as an excellent alternative to the existing physicochemical technologies for the removal of metal ions from waste water streams. Because they are available in large quantities, certain waste products generated from the agricultural sector or industries may act as potential, cost effective, eco-friendly biosorbents for waste water treatment (Malkoc et al., 2006). Most of the previous research on waste water treatment using biosorbents, usually involves one-variable at a time (OVAT), on the experimental output, while other parameters are maintained constant; this is not only time consuming, but expensive as well, in the consumption of reagents and materials (Ravikumar et al., 2005). Also, this method does not give any information about the effect of various interactions between the independent and dependent variables. But, in the effluent treatment method, the output response depends on many variables involved in that particular system. The conventional method does not predict the complete interaction effects between the given variables. In order to eliminate these limitations of the traditional method, and to consider the interactive effects, a statistical experimental design, namely, Response surface methodology (RSM) has been applied for the last two decades (Box and Hunter, 1957). Suitable mathematical models, developed for the given system, based on the RSM data, were found to be convenient with minimum process knowledge, thereby saving time and experimental cost. However, RSM based models are exact for only a limited range of input process parameters, and thus impose a limitation on the use of RSM models, which are highly non-linear processes such as biosorption (Prakash et al., 2008). These constraints have led to the use of an artificial neural network (ANN) for developing the empirical model for a non-linear system (Desai et al., 2008; Haykin, 1998). Because of its applicability to the prediction of a non-linear multivariate system, it has been considered as a promising tool used in the optimization and modeling of various non-linear systems (Ranjan et al., 2011; Raj et al., 2012; Bingol et al., 2012; Celekli et al., 2012). The ability of an ANN to learn and generalize the behavior of any complex and non-linear process, makes it a powerful modeling tool (Geyikci et al., 2012). However, both ANN and RSM based models have different superiorities in the predictive and optimization capacities of a given system, which make researchers to compare the results of the different approaches, and also to understand better the processes under investigation (Geyikci et al., 2012). Recently, both ANN and RSM have been applied jointly for the modeling of the biosorption of lead using black cumin (Bingol et al., 2012). Therefore, in the present study, 2n levels full factorial design CCD and ANN based models have been developed, to predict the relationship between the input and output variables. Subsequently, the results predicted by the ANN and RSM techniques were compared for their predictive and generalization capabilities on the biosorption of Cr(VI) onto the DPOC, in both the batch and continuous modes. Furthermore, the efficiency of both the models was statistically compared by the coefficient of determination (R2), root mean square error (RMSE) and absolute average deviation

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(AAD) based on the validation data set. To our knowledge, this is the first report available for the Cr(VI) uptake onto the DPOC, by using the RSM and ANN in both the batch and continuous modes. 2. Methods 2.1. Preparation of the biosorbent and synthetic wastewater Pongamia oil cake was obtained from the local pongamia processing industry. The cake was crushed into fine particles using a mortar and pestle. The resulting biosorbent was then de-fatted with hexane, in a soxhlet extractor (Model No: 212, Sigma Instruments Ltd., Chennai, India), in order to remove the residual oil present in the oil cake. The de-fatted pongamia oil cake biosorbent (DPOC) was then stored in air-tight containers for further use in the experiments. A synthetic aqueous solution was prepared, by dissolving K2Cr2O7H2O (AR grade) crystals in distilled water. A stock solution of 1000 mg/L was prepared, and from this the working standards were diluted accordingly. The pH of the solution was adjusted with 0.1 M HCl and 0.1 M NaOH, using the pH meter (Li 120 Elico Ltd., Hyderabad, India), calibrated with buffers of pH 4.0, 7.0 and 9.2 in order to maintain constant pH throughout the experiment. All the chemicals involved in the experiments were of analytical grade. 2.2. Batch biosorption experiments Batch experiments were carried out in duplicate, by adding the required amount of DPOC in 75 ml of chromium solution, based on the experimental design. The four independent variables of pH (2.0–7.0), initial Cr(VI) ion concentration (75–500 mg/L), temperature (30–50 °C), and adsorbent doses (1–5 g/L) were taken to obtained the response as the Cr(VI) uptake rate onto the DPOC, by maintaining a stirring speed of 150 rpm (Scigenics, India). Samples were withdrawn at specified time intervals and centrifuged in a refrigerated centrifuge (Kubota 3700, Japan) at 10,000 rpm for 10 min. The supernatant was collected, and the residual Cr(VI) ions were determined, using the DPC method (1,5-diphenyl carbazide). The biosorption capacities of the adsorbent for each concentration of metal ions under equilibrium condition was calculated as

qe ðmg=gÞ ¼

Co  Ce xV M

ð1Þ

where, Co and Ce are the initial and equilibrium chromium concentrations in the solution (mg/L), M is the mass of the adsorbent (g) used, and V is the volume of the solution (L) (Muthusamy et al., 2013). 2.3. Continuous fixed-bed column biosorption experiment Continuous flow biosorption experiments were conducted in a glass column (2 cm internal diameter and 45 cm height) packed with an appropriate quantity of DPOC. A known concentration of the metal ions solution was pumped into the column at the desired flow rate, using a peristaltic pump (Miclins PP 20 Ex, india). The residual concentration of Cr(VI) at the outlet of the column was collected, and its concentrations were determined at regular time intervals. The adsorption capacity qe (mg/g) can be determined in the column studies from the Eq. (1), but with slight modifications. The equation is given as follows

qe ¼

ðC o  C b Þ  V ef M

ð2Þ

where, M is the mass of the biosorbent (g), Cb is the breakthrough concentration (mg/L) and Vef is the volume of the effluent that is

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Table 1 Experimental factors and levels. Batch mode

Low level Center level High level

Coded Uncoded Coded Uncoded Coded Uncoded

Continuous mode

pH

Initial Cr(VI) ion concentration (mg/L)

Temperature (°C)

Dosage (g/L)

Flow rate (ml/min)

Initial Cr(VI) ion concentration (mg/L)

Bed height (cm)

1 2 0 4.5 +1 7

1 75.00 0 287.50 +1 500.00

1 30 0 40 +1 50

1 1 0 3 +1 5

1 5 0 7.5 1 10

1 75.00 0 287.50 1 500.00

1 4 0 8 1 12

required to attain the exhaustion of the column (ml). Vef was calculated using the following equation

V ef ¼ Q  t total

ð3Þ

where ttotal is the total time (min), and Q is the flow rate at which the solution circulates through the column (mL/min) (Shanmugaprakash et al., 2013). 2.4. Experimental design 2.4.1. Response surface methodology In the study, the effects of the operating parameters (viz., pH, initial Cr(VI) ion concentration, temperature and dosage in the case of the batch mode, and the bed height, flow rate, and initial Cr(VI) concentration in the case of the continuous mode) were evaluated using response surface methodology (RSM). Response surface methodology (RSM) is an experimental technique, which consists of mathematical and statistical methods for designing experiments, building models, and evaluating the effects of the variables used to measure the optimal response within the specified range (Decarlo, 2007). The two most common designs generally applied

in the RSM are the central composite design (CCD) and the BoxBehnken design (BBD). In this study, the CCD was employed for the RSM in the experimental design, which is well suited for fitting the second order quadratic equations, and usually works well for the various process optimizations (Box and Wilson, 1951). Also, the CCD is an effective design that is an ideal candidate for sequential experimentation, and allows a reasonable amount of information for testing the lack of fit, while not involving an unusually large number of design points (Montgomery and Myers, 2002). Therefore, the face centered CCD with four factors in the case of the batch mode, and three factors in the case of the continuous mode with the limits of the different factors are shown in Table 1. The CCD gives coefficients for each term present in the model, and these values are used to represent the relationship between the dependent and independent variables used in the experiments. The response variable, adsorption capacity (mg/g) can be expressed as a function of the independent variables, according to the following equation:

qe ðmg=gÞ ¼ bo þ

k k k X X X 2 b i xi þ bi ixi þ bij xi xj þ e i¼1

i¼1

ð4Þ

16i6j

Table 2 Central composite design matrix of four independent variables along with experimental and predicted response for Cr(VI) uptake rate (mg/g) onto the DPOC in batch mode. Run order

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

pH

4.5 4.5 2 7 4.5 4.5 7 4.5 7 2 4.5 7 2 7 4.5 4.5 7 2 4.5 2 4.5 7 4.5 7 4.5 2 4.5 2 7 2 2

Initial Cr(VI) ion concentration

75 287.5 500 287.5 287.5 287.5 75 500 500 500 287.5 500 75 75 287.5 287.5 75 75 287.5 287.5 287.5 75 287.5 500 287.5 75 287.5 500 500 75 500

Temperature (°C)

40 40 50 40 40 40 30 40 30 50 30 50 50 30 40 40 50 50 40 40 40 50 40 50 50 30 40 30 30 30 30

Dosage (g/L)

3 3 1 3 1 3 5 3 1 5 3 5 5 1 3 5 5 1 3 3 3 1 3 1 3 1 3 5 5 5 1

Cr(VI) uptake rate (mg/g) Experimental

RSM

ANN

97.63 84.26 86.45 48.56 84.26 112.23 43.6 130.58 75.96 112.36 134.29 102.36 65.23 28.52 78.23 99.42 32.2 45 108.22 113.61 104.23 23.74 106.58 52.96 112.43 76.2 107.48 162.58 93.51 100.09 135.62

84.78 104.35 86.48 54.23 75.72 104.65 40.30 133.69 72.26 118.90 130.58 89.28 65.66 27.68 104.35 98.23 39.49 46.29 104.35 98.20 104.35 21.74 104.35 58.49 106.40 86.01 104.35 161.31 97.92 100.24 134.03

97.63 85.23 86.45 48.56 84.26 108.26 43.60 130.58 73.68 112.36 134.29 102.36 65.23 28.52 80.12 99.56 32.20 45.13 104.11 112.78 104.11 28.60 104.11 48.57 108.44 84.29 104.11 164.29 92.06 104.29 132.83

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where bo is the constant coefficient, bi , bii and bij are the coefficients for the linear, quadratic and interaction effects, respectively, xi and xj are the independent variables and e is the error. In this study, the statistical and graphical software package, Design Expert 8.0.7.1 (Stat-Ease, USA) was used for the regression analysis, graphical analysis and analysis of variance (ANOVA). 2.5. Artificial neural network Artificial neural networks are computer models, based on a simplified modeling of the brain’s biological functions, viz., having the ability to learn, think, remember reasons and solve problems. Conceptually, neural network models are composed of neurons and weights, and are based on the principle that a highly interconnected system of simple processing elements can learn complex interrelationships between independent and dependent variables (Haykin, 1998). Artificial neural networks (ANN) were introduced recently into the field of environmental studies, as a tool for the modeling and optimization of systematic parameter studies involved in that particular process. Developing an artificial neural network is not simple, but involves many critical steps; viz., (1) select a data generator, (2) data generation, (3) data processing, (4) neural network structure selection, (5) training algorithm selection, (6) neural network training, (7) testing of the trained artificial neural networks, and (8) using the trained ANN for simulation and validation (Rafiq et al., 2001). ANNs having a highly interconnected structure, consist of a large number of simple processing elements called neurons, which are arranged in different layers in the networks; an input layer(s), an output layer(s) and all other intermediate units, called hidden layers. Each of these layers consists of a number of inter-connected processing units, called neurons. These neurons interrelate one another by passing the signals by adjusted weighted connections. The input layer received signals from external sources, and weighted individually, sends this information for processing to the hidden layers (Ozdemir et al., 2011). The hidden layer then does all the pre-processing and gives the output based on the sum of the weighted values from the input layer, modified by a sigmoid transfer function (transig) at the hidden layer and a linear transfer function (purelin) as output were used. The most popular ANN multilayer perception (MLP) is supervised learning technique that compares the responses of the output units to the desired responses, and adjusts the weights in the

network, so that the next time when the same input data is presented to the network, the network’ s response will be very much closer to the desired response. The most important feature is that the learning process of the neural network and the information obtained are used to store across the network weights. The network is trained to make proper associations between the inputs and the respective outputs (Limpon, 1987; Nielsen, 1998; Fausett, 1994; Ranjan et al., 2011). The performance of the ANN process can be expressed in terms of the root mean square error (RMSE) and correlation coefficients (R2), and is given by

RMSE ¼

rffiffiffi 1X ðX im  X ip Þ2 n i¼1

ð5Þ

where n is the number of data points, and Xim and Xip are the measured and predicted values of the processes, respectively. The final network was selected, based on the lowest error in the train, and on the test data. The input and output data to the individual ANN nodes were normalized within a range of 1 to 1, in order to achieve fast convergence to obtain the minimal RMSE values. The output values obtained from the ANN are also in the range of 1 to 1, and converted to their original data based on the reverse method of normalization. The normalized values of each input and output are obtained according to the following formula

Normalized ¼

  2  ðX Ac  X min Þ 1 ðX max  X min Þ

ð6Þ

where X min , X max and X Ac are the minimum, maximum and actual data, respectively. For this purpose, the Neural network Toolbox of MATLAB mathematical software (MATLAB 7.5.0.0.342 (R2007 b), (The Mathworks Inc., MA, USA) was applied throughout the study. 3. Results and discussion 3.1. Modeling and optimization of biosorption using RSM From the view of our recent communication (Shanmugaprakash et al., 2013), it was found that the Cr(VI) uptake rate was influenced by the initial pH, the initial Cr(VI) ion concentration, temperature and biosorbent dosage in the case of the batch mode, and the

Table 3 Central composite design matrix of three independent variables along with experimental and predicted response (mg/g) for Cr(VI) uptake rate onto the DPOC in continuous mode. Run order

Flow rate (ml/min)

Initial Cr(VI) ions concentration (mg/L)

Bed height (cm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

7.5 7.5 5 7.5 7.5 5 7.5 5 10 10 10 10 7.5 7.5 5 5 10 7.5 7.5 7.5

287.5 500 500 287.5 287.5 500 287.5 75 75 287.5 500 75 287.5 287.5 75 287.5 500 75 287.5 287.5

8 8 12 8 8 4 8 4 12 8 4 4 4 8 12 8 12 8 8 12

Cr(VI) uptake rate (mg/g) Experimental

ANN predicted

RSM predicted

110.52 78.65 132.56 115.23 119.46 70.12 120.36 28.52 95.13 99.52 34.23 46.32 94.56 119.45 79.85 104.2 113.66 53.25 113.85 152.6

112.80 81.29 132.57 115.80 115.80 70.11 115.80 28.57 95.17 100.13 34.23 45.33 91.57 116.80 79.85 104.24 113.58 53.33 115.80 152.49

114.06 82.19 133.79 114.06 114.06 66.96 114.06 30.2 96.46 102.84 36.10 43.27 97.2 114.06 76.16 108.12 110.16 56.9 114.06 157.21

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effect of the flow rate, the initial Cr(VI) ions concentration, and the bed height in the case of the continuous mode. Experiments were performed in duplicate based on the CCD matrix and used for the modeling of biosorption in the batch mode as well as the continuous mode, and the average values were taken for the data analysis, and are presented in Tables 2 and 3 for the batch and continuous modes, respectively. The regression equation coefficients and constants were fitted to a second order polynomial equation, and the regression analysis was performed to fit the response to the experimental data. The significance of the regression coefficients of each parameter is measured by the standard error of the coefficient (SE coefficient), F-test and probability P values (Badkar et al., 2013). The greater the magnitude of the F-values, and the lesser the value of P, the more significant are the subsequent terms. Furthermore, a positive sign of the regression coefficient represents a synergistic effect, while a negative sign indicates an antagonistic effect of the factor on the selected response (Ranjan et al., 2011). The regression analysis obtained along with the constants and coefficients are given in Table S1, for the biosorption of the Cr(VI) ions onto the DPOC for the batch mode. It was found that the values of the constants was 104.35, which represents the average uptake rate of the Cr(VI) ions onto the DPOC, during the batch mode which did not depend on any variable, and the interaction of the variables was found to be significant, because they had a high F-value and low P-values. From Table S1, it is seen that the linear term of the pH of the Cr(VI) removal was significant (p < 0.05) with the F value = 63.42. However, the quadratic term of pH was also found to be significant (p < 0.05) with the F value = 14.96. The quadratic term has less F-values than the linear term of pH, and therefore, they had high values (63.43) of co-efficient. This reveals that the Cr(VI) uptake rate decreases with an increase in the pH of the solution. High values of the coefficient in the quadratic term represent the importance of pH in this process. The linear term of the initial Cr(VI) concentration is found to be significant (p < 0.05) and affects synergistically, which indicates that the Cr(VI) uptake rate increases with an increase in the initial metal ion concentration in the solution. The linear term of temperature was also found to be significant (p < 0.05) having a negative coefficient (12.09), which meant the uptake rate of Cr(VI) ion decreases with an increase in the temperature. The linear term of dosage concentration was also found to be significant (p < 0.05) and synergistically affects, which implies that an increase in the dosage concentration, increases the Cr(VI) uptake rate. All interaction terms were found to be insignificant (p > 0.05), except the interaction of the pH and temperature. The second order polynomial model in terms of the coded variables, which relate the Cr(VI) uptake rate, are given as follows

significant having a high F-value and low p value (p > 0.05). This indicates that the average uptake of the Cr(VI) ions onto the DPOC was found to be 114.06 (mg/g) in the continuous mode. The linear term of the initial metal concentration was found to be statistically significant, and synergistically affects the uptake rate of the Cr(VI) ions, indicating that the uptake rate increases with an increase in the initial Cr(VI) ion concentration in an aqueous solution. However, the uptake rate was antagonistically affected by the linear term of the flow rate, showing that the uptake rate decreases with an increase in the Cr(VI) ions concentration. Also, the linear term of the bed height was found to synergistically affect the Cr(VI) ions uptake rate, showing that the uptake rate increases with an increase in the Cr(VI) ions concentration. A high value of the coefficient for the linear terms of the initial metal ions concentration and bed height were found to be 12.81 and 30.00 respectively, indicating the importance of these variables in the column mode. On the basis of the results of the regression analysis, the second order polynomial was proposed and given as follows:

qe ðmg=gÞ ¼ 114:06  2:64A þ 12:61B þ 30:00C  10:98AB þ1:81AC þ 5:22BC  8:58A2 þ 44:4B2 þ 13:14C 2

qe ðmg=gÞ ¼ 104:34  21:95A þ 24:45B  12:09C þ 11:25D 0:86AB þ 8:44AC  0:40624AD  1:95BC þ 3:26BD þ1:28CD  28:12A2 þ 4:89B2 þ 14:14C 2  17:37D2 ð7Þ where qe is the Cr(VI) ions uptake rate in the batch mode (mg/g), A, B, C and D are the coded values of the given variables. The correlation coefficients (R2) were used to check the goodness of fit for the given model. For the Cr(VI) uptake rate, R2 was found to be 0.9364 which revealed that only 6.36% of the total variation was not explained by the model. A coefficient of variance (CV) of 13.18 suggests better precision and reliability of the data, obtained by performing the experiments, while a non-significant lack of fit value (greater than 0.05) indicates the validity of the quadratic model for the batch mode (Hamsaveni et al., 2001). The estimated regression analysis for biosorption of the Cr(VI) ions onto the DPOC, using the continuous mode (Table S2), showed that the value of the constant was 114.06, which was found to be

Fig. 1. Typical architectures of the ANN for (a) batch mode and (b) continuous mode.

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where qe is the Cr(VI) ion uptake rate in the continuous mode (mg/g), A, B, C and D are the coded values of the given variables. The value of R2 was found to be 0.98%, which indicates that the total variation explained by the residuals, is only 1.20% for the Cr(VI) uptake rate in the continuous mode. A coefficient of variance (CV) of 5.29 suggests better precision and reliability of the data, obtained by performing the experiments, while a non-significant lack of fit value (greater than 0.05) indicates the validity of the quadratic model for the continuous mode. Analysis of variance (ANOVA) was performed to measure the statistical significance of the F-value. Tables S1 and S2 showed that the F-value is 16.83 for the batch mode and 94.86 for the continuous mode, respectively, which were greater than the tabulated F14,16 value (2.38) and F9,10 value (3.02). Greater F values indicate that the second order polynomial models presented in Eqs. (7) and (8) for both the batch and continues mode were highly significant, and adequate to represent the actual relationship between the experimental and predicated values. The values of ‘‘Probability (p) > F’’ for both models are less than 0.05, which indicates that both the models are significant. 3.2. Modeling with neural network In the last two decades, ANN has proved to be a more powerful tool in modeling and simulation in various engineering fields, to predict the behavior of a non-linear multivariate system (Desai et al., 2008). ANN would require many more experiments than the RSM, to construct a suitable model. But in actual fact, ANN can also work well even with reasonably small data, if the data in the input and output domains were statistically significant, which is the case with the DOE. Therefore, the experimental data

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obtained through RSM, could be adequate to build effective ANN models (Desai et al., 2008). In this work, ANN based models were developed for the Cr(VI) uptake rate from an aqueous solution onto the DPOC in both the batch and the continuous modes. For ANN, there were 2 different experiments, out of which, the first experiment was with 31 data points for batch studies, each with 5 components (pH (X1); the initial Cr(VI) ions concentration (X2), temperature (X3) and dosage level (X4) were employed as the input and the Cr(VI) uptake rate (Y1) as the output; and for the second experiment, 20 data points for column studies with 4 components, flow rate (X1), initial Cr(VI) ions concentration (X2) and bed height (X3) were employed as the input and Cr(VI) uptake rate (Y1) as the output. The original experimental data sets were categorized into three subsets comprising of training (60% of the original experimental data sets), testing (20% of the original experimental data sets) and validation (20% of the original experimental data sets). The purpose of splitting the experimental data was to measure the performance of the neural network for the prediction of unseen data, that were not used for training and to assess the generalization capability of the ANNs. One of the most important tasks in constructing the ANNs is the choice of the number of hidden layers and numbers of neurons (Badkar et al., 2013). In this study, different training algorithms were tested by varying the number of hidden layers and neurons by training the different feed-forward networks of various topologies, in order to select the optimal architecture based on the minimization of the performance function –the Mean square error (MSE). Table S3 shows the best combination of the ANN parameters that were able to predict the output parameter. The learning rate and the error goal were selected, based on trial and error, in order to keep the minimum distance between the

Fig. 2. Neural network model with training, validation, test and all prediction set.

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experimental and predicted values. The optimum ANN architecture is taken as 4–10–1 (four neurons in the input layer, 10 in the hidden layer and 1 in the output layer) for the batch mode and 3–7–1 (three neurons in the input layer, 7 in the hidden layer and 1 in the output layer) for the continuous mode, by trial and error, when the mean square error (MSE) decreased gradually, and became constant. Typical architectures of the ANN for both the batch and continuous modes are shown in Fig. 1. The values of MSE obtained from the ANNs for both the batch and continuous modes were 2.25  106 and 0.0013329 respectively, which are close to the acceptance limit for the MSE set to zero. The closeness of the training and testing errors validates the accuracy of the model. The coefficient of determination R-squared (R2) indicates the goodness of fit between the experimental and predicated responses given by the ANN model. In this case, the values of R2 for the batch and continuous modes were found to be 0.991 and 0.997 respectively. Since the R2 values for all the models are nearly equal to 1, it indicates the significance of the model (Fig. 2). Thus, good, sufficient, higher values of coefficient (R2) of the ANN predicted and experimental responses for both the batch and continuous modes suggests, that the newly

constructed ANN has the ability to predict the adsorption capacities of Cr(VI) ions onto the DPOC. Another advantage of the newly constructed ANN model is its accuracy to determine the adsorption capacities of Cr(VI) ions for any range of given pH, Cr(VI) ion concentration, temperature and adsorbent dosage in the batch mode and any range of the bed height, flow rate and Cr(VI) ions concentration in the continuous mode, within the experimental range and outside its range as well. Figs. 3 and 4 (a) show the experimental and predicted values for each experimental run for the Cr(VI) uptake rate in the batch and continuous modes, respectively. From the above figures, it is evident that the trained neural network has efficient approximated experimental values. The distribution of the residual values for the batch and continuous modes is shown in the Figs. 3(b) and 4(b) respectively, and it is observed that the deviations of the residual values are relatively small and regular for the ANN compared with those of the RSM models. 3.3. Comparison between ANN and RSM models In order to test the predictive capability of both the ANN and RSM models, they are applied for modeling and optimization of

Fig. 3. Comparison of experimental with predicted value obtained by the ANN and RSM models for the prediction of Cr(VI) uptake rate in batch mode (a) for each experimental run (b) distribution of residual values.

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Fig. 4. Comparison of experimental with predicted value obtained by the ANN and RSM models for the prediction of Cr(VI) uptake rate in continuous mode (a) for each experimental run (b) distribution of residual values.

Table 4a Validation data set for batch mode. Run order

1 2 3 4 5 6

pH

4.5 4.5 2 2 7 7

Initial Cr(VI) ion concentration (mg/L)

75 300 500 100 400 100

Temperature (°C)

50 40 30 50 30 30

Dosage (g/L)

3 2 3 1 3 3

Response (mg/g) Experimental

ANN

RSM

85.23 104.45 184.29 50.41 106.36 65.48

95.60 108.4 180.02 55.64 97.50 57.59

32.09 85.23 134.27 45.98 109.88 108.26

Table 4b Validation data set for continuous mode. Run order

Flow rate (ml/min)

Initial Cr(VI)

Bed height (cm)

ion concentration (mg/L) 1 2 3 4 5

7 5 10 4 6

200 90 450 300 260

8 12 12 8 4

Response (mg/g) Experimental

RSM

ANN

90.25 75.42 120.25 104.1 40.85

32.10 85.23 134.28 45.98 109.88

89.60 64.84 116.57 104.24 36.45

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Table 5 Comparison of predictive abilities of RSM and ANN model. Parameters

RMSE R2 AAD (%)

Batch mode

Column mode

RSM

ANN

RSM

ANN

5.84 0.93 7.74

1.67 0.99 2.33

3.16 0.98 3.77

1.16 0.99 1.16

the removal of Cr(VI) ions from aqueous solution onto the DPOC. A completely new set of experiments was conducted (6 runs for the batch mode and 5 runs for the continuous mode) which does not belong to the training data sets. The experimental and predicted values of the responses along with their residual values for both the ANN and RSM models are given in Table 4.

The prediction abilities of the newly constructed ANN and RSM models were statistically measured, in terms of the root mean square error (RMSE), co-efficient of determination (R2) and absolute average deviation (AAD), as follows (Geyikci et al., 2012):

RMSE ¼

 X  2 2 n  1 T  T CrðVIÞ; exp CrðVIÞ;pred i¼1 n

 Pn    2 T CrðVIÞ;exp  T CrðVIÞ;exp T CrðVIÞ;pred  T CrðVIÞ;pred R2 ¼ P i¼1 2  2 n  T CrðVIÞ;pred  T CrðVIÞ;pred i¼1 T CrðVIÞ; exp  T CrðVIÞ; exp AAD ¼

! n  T CrðVIÞ;pred  T CrðVIÞ;exp 1X  100 n i¼1 T CrðVIÞ;exp

ð8Þ

ð9Þ

ð10Þ

where n is the number of data points, T CrðVIÞ;pred is the predicted value, T CrðVIÞ;exp is the actual value, and the ‘-’ is the average of the

Fig. 5. Comparison of experimental data with predicted value obtained by the RSM and ANN models for the prediction of Cr(VI) uptake rate in (a) batch mode and (b) continuous mode.

M. Shanmugaprakash, V. Sivakumar / Bioresource Technology 148 (2013) 550–559

experimental values. Table 5 represents the statistical comparison of the RSM and ANN models. The predictive values obtained from the RSM and ANN models onto the DPOC in both the batch and continuous modes were found to be as significant, as those obtained using experiments according to the DOE. Also, the predicted optimum values of the independent variables for the maximum uptake of the Cr(VI) ions in both the batch and column modes were found to be very compatible with those obtained in our earlier studies (Shanmugaprakash et al., 2013), where the conventional one variable at a time was applied, to optimize the independent variables in order to obtain the maximum removal of Cr(VI) ions in both the batch and column studies. This proves the applicability of the ANN and RSM in the prediction and optimization of the biosorption process, with the minimum experimental set-up, which minimizes the consumption of reagents, which in turn, reduces the effluent treatment cost. From Table 5, it is confirmed that the ANN model predicts more accurately than the RSM model, both data fitting and estimation capabilities. This higher predictive accuracy of ANN can be attributed to its universal ability to approximate the non-linearity of the given system, whereas the RSM is only restricted to a second order polynomial equation. Another advantage of the ANN is that, it does not require a standard experimental design to build the model (Geyikci et al., 2012). Also from Fig. 5, it is evident that all the data predicted by the ANN model for both the batch and continuous modes are close to the straight line, signifying that the ANN predicts better, compared to the RSM. Thus, the ANN based model is more flexible, and allows to add new experimental data to build a new trustworthy model. The performance of the network for predicting the biosorption efficiency of DPOC for Cr(VI) ions in both the batch and continuous modes is found to be very impressive. 4. Conclusion In this study, the performance of the RSM and ANN models with their modeling, predictive and generalization capabilities were compared for Cr(VI) uptake. The CCD based and a feed-forward multilayered perceptron (MLP) ANN trained models were developed to predict the Cr(VI) uptake rate onto the DPOC. The performance of two models were statistically determined which confirms that the ANN model was the best model for estimation of the target values in comparison to RSM model. To conclude, the model developed by ANN has superior ability than the RSM model, and can give deeper knowledge of the non-linear system. Acknowledgements The author (Shanmugaprakash M) is thankful to the management of Kumaraguru College of Technology, Coimbatore, India, for the providing the research facilities. References Apha, A., 2005. WPCF. 1989. Standard Methods for the Examination of Water and Wastewater, 17th ed. American Public Health Association, Washington DC. Badkar, D.S., Pandey, K.S., Buvanashekaran, G., 2013. Development of RSM and ANNbased models to predict and analyze the effects of process parameters of laserhardened commercially pure titanium on heat input and tensile strength. Int. J. Adv. Manuf. Technol., 1–20. Bingol, D., Hercan, M., Elevli, S., Kilic, E., 2012. Comparison of the results of response surface methodology and artificial neural network for the biosorption of lead using black cumin. Bioresour. Technol. 112, 111–115. Bishnoi, N.R., Kumar, R., Kumar, S., Rani, S., 2007. Biosorption of Cr (III) from aqueous solution using algal biomass Spirogyra spp. J. Hazard. Mater. 145, 142– 147.

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