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Biosorption of copper(II) ions by ﬂax meal: Empirical modeling and process optimization by response surface methodology (RSM) and artiﬁcial neural network (ANN) simulation Daria Podstawczyka,* , Anna Witek-Krowiaka , Anna Dawieca , Amit Bhatnagarb a b

Division of Chemical Engineering, Department of Chemistry, Wrocław University of Technology, Norwida 4/6, 50-373 Wrocław, Poland Department of Environmental Science, University of Eastern Finland, FI-70211 Kuopio, Finland

A R T I C L E I N F O

A B S T R A C T

Article history: Received 13 January 2015 Received in revised form 16 June 2015 Accepted 4 July 2015 Available online xxx

In the present study, application of waste ﬂax meal was investigated for the removal of copper(II) ions from aqueous solution. The effect of operating parameters such as metal ions concentration (20– 200 ppm), biosorbent dosage (1–10 g/L) and solution pH (2–5) was modeled by both response surface methodology (RSM) and artiﬁcial neural network (ANN). This study compares central composite design (CCD), Box–Behnken design (BBD) and full factorial design (FFD) utility for modeling and optimization by response surface methodology. The best statistical predictability and accuracy resulted from CCD (R2 = 0.997, MSE = 0.34). Maximum biosorption efﬁciency expressed as the sorption capacity, which was found to be 34.4 mg/g, at initial Cu2+ concentration of 200 ppm, biosorbent dosage of 1 g/L and initial solution pH of 5. The precision of the equation obtained by RSM was conﬁrmed by the analysis of variance and calculation of correlation coefﬁcient relating the predicted and the experimental values of biosorption efﬁciency. A feed-forward neural network with a topology optimized by response surface methodology was applied successfully for prediction of biosorption performance for the removal of Cu2+ ions by waste ﬂax meal. The number of hidden neurons, the number of epochs, the adaptive value and the training goal were chosen for optimization. The multilayer perceptron with three neurons in one input layer, twenty two neurons in one hidden layer and one neuron in one output layer were required to build the model. The neural network turned out to be more accurate than RSM model in the prediction of Cu2+ biosorption by ﬂax meal. The novelty of this paper is application of response surface methodology in order to optimize artiﬁcial neural network topology. The research on modeling biosorption by RSM and ANN has been highly developed and new waste material ﬂax meal as potential biosorbent has been proposed. ã 2015 Elsevier B.V. All rights reserved.

Keywords: Biosorption Flax meal Response surface methodology Optimization Empirical modeling Artiﬁcial neural network

1. Introduction

Abbreviations: ANN, artiﬁcial neural network; ANOVA, analysis of variance; BBD, Box–Behnken design; BET, Brunauer, Emmett and Teller method; CCC, circumscribed central composite; CCD, central composite design; CCF, face-centered composite; CCI, inscribed central composite; Dfe, degree of freedom; DoE, design of experiments; FFD, full factorial design; FM, ﬂax meal; FT-IR, fourier transform infrared spectroscopy; ICP-OES, inductively coupled plasma-optical emission spectrometry; LM, Levenberg–Marquardt; MLP, multilayer percepton; MS, mean squares; MSE, mean squared error; OVAT, one variable in time; PBD, Plackett– Burman design; RE, relative error; RSM, response surface methodology; SEM-EDX, scanning electron microscopy with energy dispersive X-ray; SS, sum of squares; TP, training performance; TSP, testing performance; VP, validation performance. * Corresponding author. E-mail address: [email protected] (D. Podstawczyk). http://dx.doi.org/10.1016/j.ecoleng.2015.07.004 0925-8574/ ã 2015 Elsevier B.V. All rights reserved.

Biosorption is the process of binding contaminants (metal ions, dyes etc.) on the surface of biological material due to the presence of characteristic functional groups (e.g., carboxylic, hydroxyl, amino, carbonyl, phosphate, sulfonic etc.). Biosorption has become an effective and promising alternative for currently used methods in either the removal of heavy metal ions from wastewater or production of novel fertilizers and animal feed (Michalak et al., 2013; Bhatnagar and Sillanpää, 2010). Biosorption as a very complex process, is strongly dependent on many environmental factors such as solution pH, sorbent dosage or concentration, initial sorbate concentration, time of the process, temperature (WitekKrowiak et al., 2014) or, in case of biosorption carried out in the column mode, bed height, liquid velocity or particles diameter, etc. (Tovar-Gómez et al., 2013; Oguz and Ersoy, 2010; Cavas et al., 2011).

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In application of biosorption process on an industrial scale, it is crucial to improve process efﬁciency, reduce operational cost and time to minimum and take into account the most important factors, what can be achieved by applying the optimization techniques such as response surface methodology (RSM) and artiﬁcial neural network (ANN). Determining the effect of a single factor on the efﬁciency of the process is relatively simple (OVAT— one variable in time). It is deﬁnitely more of a challenge to assess the effect of several parameters at once. Response surface methodology based on experimental data makes easier to plan the entire modeling process by reducing the number of experiments to the necessary minimum, and allows a mathematical equation to ﬁt the experimental results, which is required for the process optimization (Witek-Krowiak et al., 2014). In general, RSM is a mathematical technique applied in the progression of an appropriate functional relationship between the response and the related input variables. The structure of this relationship is unknown, but can be approximated by low-order polynomials (the most common are ﬁrst and second-degree polynomial models) (Khuri and Mukhopadhyay, 2010). This methodology helps to determine the most important parameters and its main, quadratic effect or interactions which inﬂuence the response. RSM has been extensively used as an optimization, prediction and interpretation technique for factorial designs (Montgomery and Runger, 2003; Das et al., 2014; Zolgharnein et al., 2013). Artiﬁcial neural network (ANN) is an useful tool for the modeling and analysis of systems in which response of interest depends on several factors and the relationship between independent and dependent variables in a system is unknown. ANN modeling has been successfully applied for biosorption in the past few years (Ahmad et al., 2014; Bingol et al., 2012; Shojaeimehr et al., 2014; Mandal et al., 2015; Roy et al., 2014) The present study investigates the application of response surface methodology and artiﬁcial neural network approaches to predict biosorption capacity of waste ﬂax meal for the removal of copper(II) ions from aqueous solution. Polish industry is largely based on the processing of copper, thus methods of removal as well as recovery of this metal are widely investigated by Polish scientists. The application of ﬂax meal, which is a polish agricultural waste, as a biosorbent for the removal of Cu2+ is an innovative approach. The effect of operating parameters such as solution pH, initial Cu2+ concentration and biosorbent dosage were examined and modeled by both techniques. The RSM and the ANN with structure optimized by RSM models were compared in terms of predictability and accuracy of ﬁt, taking into account their implementations and limitations. Optimization of artiﬁcial neural network by response surface method is completely novel approach of ANN approximation application in chemical processes.

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2. Materials and methods 2.1. Materials NaOH, HCl, CuSO4 were purchased from POCh (Poland). All the chemicals were of analytical reagent grade and were used without further puriﬁcation. Aqueous stock solution of CuSO4 (1000 ppm) was prepared through the dissolution of solid reagent in double distilled water. Required dilutions were made from the stock solution. The initial pH of each solution was adjusted to the required value with 0.1 M HCl and 0.1 M NaOH. 2.2. Biosorbent preparation Flax meal was obtained from local suppliers as a byproduct from oil extraction with supercritical CO2. Sorbent had varied granularity, and thus the material was sieved and fraction 0.4 mm was selected for experiments. The biomaterial was rinsed three times with double distilled water followed by drying at 50 C for 24 h in the oven. The prepared material was further used in biosorption experiments. 2.3. Biosorbent characterization Sorbent surface morphology was analyzed using scanning electron microscope (SEM/HITACHI S-3400N/2007) instrument equipped with energy dispersive X-ray (EDX) adapter. SEM-EDX technique was used to quantify the chemical composition of the surface. Fourier transform infrared spectroscopy (PerkinElmer, 2000 FT-IR) studies were carried out to identify the functional groups present on the biosorbent in 4000–400 cm1 range. The speciﬁc surface area was measured by BET method. 2.4. Analytical measurements The concentration of Cu2+ and alkali and alkaline earth metals (K+, Na+, Ca2+ and Mg2+) ions was measured using ICP-OES (Inductively Coupled Plasma-Optical Emission Spectrometry, Varian Vista MPX, Australia at laboratory certiﬁed by Polish Center for Accreditation and ICAC-MRA according to PN-EN ISO 17025) method. 2.5. Batch biosorption experiments The biosorption of Cu2+ on the ﬂax meal (FM) was investigated in batch mode. Batch biosorption experiments were conducted in 250 mL Erlenmeyer ﬂasks containing 100 mL of known Cu2+ concentration in solution and known amount of added biosorbent. The ﬂasks were agitated (200 rpm) on an orbital shaker (water bath

Table 1 Plackett–Burman design matrix for evaluating variables inﬂuencing biosorption of copper(II) by ﬂax meal with predicted responses. No.

1 2 3 4 5 6 7 8 9 10 11 12

Coded values (uncoded values)

Y [mg/g]

X1 [ppm]

X2 [g/L]

X3

X4 [ C]

X5 [rpm]

Experimental values

Predicted responses

1 (200) 1 (20) 1 (20) 1 (20) 1 (20) 1 (20) 1 (200) 1 (200) 1 (20) 1 (200) 1 (200) 1 (200)

1 (10) 1 (10) 1 (1) 1 (1) 1 (10) 1 (1) 1 (1) 1 (1) 1 (10) 1 (10) 1 (10) 1 (1)

1 (5) 1 (2) 1 (2) 1 (2) 1 (5) 1 (5) 1 (5) 1 (2) 1 (5) 1 (2) 1 (2) 1 (5)

1 (20) 1 (20) 1 (40) 1 (20) 1 (40) 1 (40) 1 (40) 1 (20) 1 (20) 1 (40) 1 (40) 1 (20)

1 (300) 1 (200) 1 (300) 1 (200) 1 (200) 1 (300) 1 (200) 1 (300) 1 (300) 1 (300) 1 (200) 1 (200)

11.12 0.77 0.11 0 1.11 6.03 34.23 5.02 0.56 4.56 4.99 33.89

12.97 0.00 0.00 4.15 6.65 8.08 30.21 10.42 0.00 1.00 8.94 30.27

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shaker type 357, Elpin) at constant temperature of 20 C until equilibrium was reached. Subsequently, samples were centrifuged and the Cu2+ ion concentration remaining in supernatant was analyzed. All experiments were conducted in duplicate. 2.6. Selection of the signiﬁcant parameters The most signiﬁcant process variables were identiﬁed by Plackett–Burman (PB) experimental design. The advantage of this design is its ability to investigate of a large number of factors in a relatively low number of experimental runs. In this study 12 run PB design with 5 factors, including Cu2+ concentration (X1), biosorbent dosage (X2), pH (X3), temperature (X4) and agitation speed (X5), was considered. Each independent variable was tested at two levels, high and low, which were 1 and 1, respectively. All experiments were conducted in duplicate and the average values of biosorption capacity were taken as a response (Y). The matrix design is shown in Table 1. On the basis of PBD three the most signiﬁcant parameters were chosen for further investigation (modeling and optimization by RSM and ANN). 2.7. The range of the parameters In PBD experiments, temperature and agitation speed were investigated at two levels, 20 and 40 C and 200 and 300 rpm, respectively, while in RSM and ANN experiments, they were kept constant at their lowest values. RSM and ANN experiments were performed for different initial solution pH (from 2 to 5), initial Cu2+ concentration (from 20 to 200 ppm) and biosorbent dose (from 1 to 10 g/L). The parameters were chosen as three of the most inﬂuencing the removal of Cu2+ via biosorption process. The form of copper ions existing in an aqueous solution is strongly dependent on solution pH. At pH higher than 5, different hydroxyl low-soluble species can be formed such as Cu(OH)+, Cu (OH)22+ as well as Cu2OH3+ and Cu3(OH)42+ (Witek-Krowiak and Reddy, 2013). Therefore, pH experiments were limited up to pH 5 in order to be sure that only the biosorption mechanism is responsible for the removal of Cu2+ ions. The range of the sorbate in model aqueous solutions (20– 200 ppm) corresponds to the actual content of Cu2+ in industrial wastewater (Markovi c et al., 2011). The dosage of a biosorbent strongly inﬂuences the extent of biosorption. Predominantly, the lower the amount of biosorbent, the higher the uptakes and lower the percentage removal efﬁciencies. The amount of adsorbate usually increases with the increase of biosorbent dosage, due to the increased surface area of the biosorbent and in turn higher the number of available binding sites for ions. Consequently, the biosorbent dosage has to be sufﬁcient to remove metal ions effectively. Thus, in this study, the biosorbent concentration varies from 1 to 10 g/L. 2.8. Response surface methodology Response surface methodology is an experimental technique used for predicting and modeling complicated relation between independent factors and one or more responses (Box and Wilson, 1951). In this study, response surface methodology was applied to optimize the biosorption of copper(II) ions by FM. Experiments were performed using face-centered composite design (CCFD), Box– Behnken design (BBD), full factorial design (FFD). The second-order polynomial equation extended with additional cubic effects was employed as an objective function. The second order model is usually sufﬁcient for the modeling and optimization on the basis of designs, however third order and higher effects are sometimes important,

especially in order to achieve better ﬁt and insigniﬁcant lack-of-ﬁt. For instance, Box–Behnken design was created to estimate the second-order model, however there may be situations in which nonrandom portion of this model provides an inadequate representation of the true mean response, an indication of lack-of-ﬁt of the secondorder model (Arshad et al., 2012). Thus, in this study some third order model terms were added to the second order polynomial equation. Accuracy of model ﬁtting was evaluated by means of ANOVA. All calculations were performed in Matlab 7.14. 2.8.1. Central composite design In this study, the CCF (Supplementary Fig. 1A) design methodology was used to predict impacts of respective parameters on the biosorption process. Among many factors affecting the biosorption process, three were selected (initial Cu2+ concentration (X1), biosorbent dosage (X2) solution pH (X3)) whose simultaneous effects on process efﬁciency (Y) was deﬁned and modeled. Example of face-centered composite plan for standardized input variables is shown in Supplementary Fig. 1A. CCD contains set of 24 experiment runs whose values of each factor is coded to standard values (1, 0, 1) in the appropriate range of parameters (Table 2). Subsequently experimental data was ﬁtted to the second order polynomial equation extended with additional cubic interaction effects (Eq. (1)) using the least square procedure. Y ¼ b0 þ b1 X 1 þ b2 X 2 þ b3 X 3 þ b12 X 1 X 2 þ b13 X 1 X 3 þ b23 X 2 X 3 þb11 X 21 þ b22 X 22 þ b33 X 23 þ b123 X 1 X 2 X 3 þ b112 X 21 X 2 þ b113 X 21 X 3 þ b122 X 1 X 22

(1) The coefﬁcients in the equation represent: the intercept (b0), the main (b1,b2, b3), quadratic (b11, b22, b33) and interactions (b12, b23, b13, b123, b112, b113, b122) effects, respectively. Validation of the model ﬁt and signiﬁcance analysis of variables were performed using analysis of variance (ANOVA). 2.8.2. Box–Behnken design The Box–Behnken design (Supplementary Fig. 1B) consists of 15 experimental points. The experimental conditions, and the Table 2 Central composite design with coded and uncoded values of the independent variables and experimental and predicted values of the response. No. Coded values (uncoded values)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Y [mg/g]

X1 [ppm]

X2 [g/L]

X3

Experimental values Predicted responses

1 (20) 1 (20) 1 (20) 1 (20) 1 (200) 1 (200) 1 (200) 1 (200) 1 (20) 1 (200) 0 (110) 0 (110) 0 (110) 0 (110) 0 (110) 0 (110) 0 (110) 0 (110) 0 (110) 0 (110) 0 (110) 0 (110) 0 (110) 0 (110)

1 (1) 1 (1) 1 (10) 1 (10) 1 (1) 1 (1) 1 (10) 1 (10) 0 (5.5) 0 (5.5) 1 (1) 1 (10) 0 (5.5) 0 (5.5) 0 (5.5) 0 (5.5) 0 (5.5) 0 (5.5) 0 (5.5) 0 (5.5) 0 (5.5) 0 (5.5) 0 (5.5) 0 (5.5)

1 (2) 1 (5) 1 (2) 1 (5) 1 (2) 1 (5) 1 (2) 1 (5) 0 (3.5) 0 (3.5) 0 (3.5) 0 (3.5) 1 (2) 1 (5) 0 (3.5) 0 (3.5) 0 (3.5) 0 (3.5) 0 (3.5) 0 (3.5) 0 (3.5) 0 (3.5) 0 (3.5) 0 (3.5)

0 5.96 0.57 0.78 2.17 34.37 4.56 10.23 0.53 17.39 12.47 4.24 3.07 9.30 8.91 7.90 7.23 8.02 8.32 7.67 7.61 6.96 8.42 7.59

0.04 6.00 0.60 0.80 2.20 34.4 4.60 10.24 0.42 17.28 12.37 4.13 2.97 9.19 7.91 7.91 7.91 7.91 7.91 7.91 7.91 7.91 7.91 7.91

D. Podstawczyk et al. / Ecological Engineering 83 (2015) 364–379 Table 3 Box–Behnken design with coded and uncoded values of the independent variables and experimental and predicted values of the response. No. Coded values (uncoded values)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Y [mg/g]

X1 [ppm]

X2 [g/L]

X3

Experimental values Predicted responses

1 (20) 1 (20) 1 (200) 1 (200) 1 (20) 1 (20) 1 (200) 1 (200) 0 (110) 0 (110) 0 (110) 0 (110) 0 (110) 0 (110) 0 (110)

1 (1) 1 (10) 1 (1) 1 (10) 0 (5.5) 0 (5.5) 0 (5.5) 0 (5.5) 1 (1) 1 (1) 1 (10) 1 (10) 0 (5.5) 0 (5.5) 0 (5.5)

0 (3.5) 0 (3.5) 0 (3.5) 0 (3.5) 1 (2) 1 (5) 1 (2) 1 (5) 1 (2) 1 (5) 1 (2) 1 (5) 0 (3.5) 0 (3.5) 0 (3.5)

7.70 0.88 40.11 10.71 0.69 0.99 6.46 14.82 11.27 27.32 4.57 4.51 7.57 8.30 6.84

6.86 1.72 39.27 11.55 0.69 0.98 6.45 14.82 12.11 28.16 3.73 3.67 7.57 7.57 7.57

biosorption capacity obtained for each point set by the Box– Behnken design are shown in Table 3 (1–11), together with the three central point repetitions (12–15). The relationship between responses and processed variables was examined for the response approximation function (Y) using Eq. (1), following by the statistical analysis of the model obtained. 2.8.3. Full factorial design A three factor, three-level full factorial statistical experimental design (Supplementary Fig. 1C) with 27 experimental points (Table 4) was used to predict biosorption capacity of the ﬂax meal. The behavior of the system was explained by the polynomial equation (Eq. (1)).

Table 4 Full factorial design with coded and uncoded values of the independent variables and experimental and predicted values of the response. Lp. Coded values (uncoded values)

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

Y [mg/g]

X1 [ppm]

X2 [g/L]

X3

Experimental values Predicted responses

1 (20) 0 (110) 1 (200) 1 (20) 0 (110) 1 (200) 1 (20) 0 (110) 1 (200) 1 (20) 0 (110) 1 (200) 1 (20) 0 (110) 1 (200) 1 (20) 0 (110) 1 (200) 1 (20) 0 (110) 1 (200) 1 (20) 0 (110) 1 (200) 1 (20) 0 (110) 1 (200)

1 (1) 1 (1) 1 (1) 0 (5.5) 0 (5.5) 0 (5.5) 1 (10) 1 (10) 1 (10) 1 (1) 1 (1) 1 (1) 0 (5.5) 0 (5.5) 0 (5.5) 1 (10) 1 (10) 1 (10) 1 (1) 1 (1) 1 (1) 0 (5.5) 0 (5.5) 0 (5.5) 1 (10) 1 (10) 1 (10)

1 (2) 1 (2) 1 (2) 1 (2) 1 (2) 1 (2) 1 (2) 1 (2) 0 (3.5) 0 (3.5) 0 (3.5) 0 (3.5) 0 (3.5) 0 (3.5) 0 (3.5) 0 (3.5) 0 (3.5) 0 (3.5) 1 (5) 1 (5) 1 (5) 1 (5) 1 (5) 1 (5) 1 (5) 1 (5) 1 (5)

0 11.27 2.17 0.69 3.07 6.43 0.57 4.57 4.56 7.70 12.47 40.11 0.53 8.30 17.39 0.88 4.24 10.71 5.96 27.32 34.37 0.99 9.30 14.82 0.78 4.51 10.23

1.26 7.96 10.31 0 2.71 4.20 0.20 3.68 5.95 6.60 18.70 27.60 2.42 9.30 14.56 2.79 6.12 9.40 6.17 23.67 39.11 0.61 10.12 19.15 0 2.79 7.07

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2.8.4. Analysis of variance (ANOVA) ANOVA expounds every variation in the statistically obtained model and importance of each model parameters. The signiﬁcance of the model was evaluated by F-test for a conﬁdence level of 95% as well as lack-of-ﬁt test. In general, the greater the F-value and the smaller the p-value, the more signiﬁcant is a model. Moreover, effects and their importance in the model were investigated adapting t-test and p-value. Usually, the larger the t-value and lower probability p-value (p < 95%), the model parameter is considered as signiﬁcant (Sudamalla et al., 2012). The sum of squares, degree of freedom and mean squares were also determined for the model and error. 2.9. Artiﬁcial neural network ANN is a parallel network made up of signal processing elements called neurons. Neurons are interconnected by means of weighted linkages which are synaptic connections, shortly called synapses, holding information. By adjustment of the weights under the learning algorithm, ANN has the ability to learn from observed data (Falamarzi et al., 2014). General structure of neuron symbol is shown in Fig. 1. The mathematical expression of the network is as follows: ! n X wi xi þ b ¼ f ðnetÞ (2) y ¼ f ðw0 x þ bÞ ¼ f i¼1

w ¼ ðw1 ; w2 ; ; wn Þ

(3)

x ¼ ðx1 ; x2 ; ; xn Þ

(4)

where f (w0 x + b) is an activation function deﬁned as a scalar product of weights (w) and inputs (x) vectors plus a bias (b). The activation function commonly preferred in the literature and used in this study is hyperbolic tangent sigmoid function (Eq. (5)). f ðnetÞ ¼

2 1 1 þ expð2netÞ

(5)

The most popular algorithm, which is backpropagation is efﬁcient in simulation of uncomplicated issues, however algorithms such as Levenberg–Marquardt (LM) are more successive in prediction of performance for complex relationships between input variables. The LM algorithm is a trust-region model based method consisting three main steps: (1) data enters at the inputs and passes layer by layer through the network; (2) the mean squared error (MSE) (Eq. (6)) of the output computed by the net is propagated and minimized to the training goal; (3) the connection weights are adjusted and updated.

Fig. 1. General neuron symbol.

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MSE ¼

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1 Xn n

i¼1

ðti yi Þ2

(6)

where yi is the network output, ti is desired target and n is the number of inputs. The LM algorithm was used in this investigation. Each cycle of error propagation during the network training is an epoch. The number of epochs decides how long the ANN simulation lasts. The simulation can be stopped either by the end of number of epochs or by achieving the learning goal, which is the minimal value of error, satisfying the user. Both criteria were investigated in present study. 2.9.1. Selection of input variables The ranges of appropriate variables were the same as in RSM modeling. The data set of 528 experimental points was no randomly divided into three groups: training, testing and validation, according to indices provided (using Matlab division function divideind). The number of neurons in the input and output layers are, respectively, equal to the number of inputs and outputs, while the number of neurons in the hidden layer are usually determined by either a trial-and-error procedure or by RSM, like it was performed in this study. 2.9.2. Optimization of neural network topology by RSM In order to optimize the artiﬁcial neural network structure and verify the predictability of ANN model, response surface methodology on the basis of Box–Behnken design was carried out with four variables at three levels (low, medium and high, being coded as 1, 0 and 1) and a total number of runs of 27 (Table 5). The number of neurons in hidden layer (X1A), the number of epochs (X2A), the training goal (X3A) and the initial adaptive value m (X4A) for updating LM algorithm, were selected to be optimized, while mean squared error (MSE) was employed as a response (YA). A second-order polynomial equation (Eq. (7)) was ﬁtted to the experimental data. The results were analyzed by analysis of

variance (ANOVA) and a calculation correlation coefﬁcient (R2) between predicted and experimental points. Subsequently, the quadratic expression obtained from RSM modeling was minimized using fmincon function with constraints (fval greater than zero) and optimal values of variables were found for minimum value of MSE. Y A ¼ b0A þ b1A X 1A þ b2A X 2A þ b3A X 3A þ b4A X 4A þ b12A X 1A X 2A þb13A X 1A X 3A þ b23A X 2A X 3A þ b14A X 1A X 4A þ b24A X 2A X 4A þb34A X 3A X 4A þ b11A X 1A 2 þ b22A X 2A 2 þb33A X 3A 2 þb44A X 4A 2 (7) A feed-forward multilayer perceptron with three layers (input, hidden and output) and hyperbolic tangent sigmoid at hidden layer and pure linear at output layer, was trained by the Levenberg– Marquardt (LM) using Matlab trainlm function. Preliminary investigation showed that one hidden layer is sufﬁcient for good data approximation. The number of neurons in hidden layer, the number of epochs, the training goal and the adaptive value were optimized by response surface methodology on the basis of Box– Behnken design, while m decrease and increase factors were 0.1 and 10, respectively. 3. Results and discussion 3.1. Biosorbent characterization and biosorption mechanism Speciﬁc surface area measured by BET method for ﬂax meal is 78.57 m2/g. Fig. 2(A,B) presents SEM micrographs of FM structure before (A) and after (B) the biosorption. SEM micrographs reveal that the surface of the biosorbent is not homogenous and contains small brighter pellets like structure, located on the surface and in the matrix interior. These places have the most remarkable contribution in ion binding, conﬁrmed by EDX analysis before (Fig. 3A) and after (Fig. 3B) the biosorption process. The major

Table 5 Box–Behnken design for optimization of the neural network topology. No.

Coded values (uncoded values) X1A (no. of neurons)

X2A (no. of epochs)

X3A (adaptive value)

X4A (training goal)

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

1 (4) 1 (4) 1 (26) 1 (26) 0 (15) 0 (15) 0 (15) 0 (15) 1 (4) 1 (4) 1 (26) 1 (26) 0 (15) 0 (15) 0 (15) 0 (15) 1 (4) 1 (4) 1 (26) 1 (26) 0 (15) 0 (15) 0 (15) 0 (15) 0 (15) 0 (15) 0 (15)

1 (50) 1 (450) 1 (50) 1 (450) 0 (250) 0 (250) 0 (250) 0 (250) 0 (250) 0 (250) 0 (250) 0 (250) 1 (50) (50) 1 (450) 1 (450) 0 (250) 0 (250) 0 (250) 0 (250) 1 (50) 1 (50) 1 (450) 1 (450) 0 (250) 0 (250) 0 (250)

0 (6) 0 (6) 0 (6) 0 (6) 1 (0.5) 1 (0.5) 1 (11.5) 1 (11.5) 0 (6) 0 (6) 0 (6) 0 (6) 1 (0.5) 1 (11.5) 1 (0.5) 1 (11.5) 1 (0.5) 1 (11.5) 1 (0.5) 1 (11.5) 0 (6) 0 (6) 0 (6) 0 (6) 0 (6) 0 (6) 0 (6)

0 (0.00025) 0 (0.00025) 0 (0.00025) 0 (0.00025) 1 (0.000) 1 (0.0005) 1 (0.000) 1 (0.0005) 1 (0.000) 1 (0.0005) 1 (0.000) 1 (0.0005) 0 (0.00025) 0 (0.00025) 0 (0.00025) 0 (0.00025) 0 (0.00025) 0 (0.00025) 0 (0.00025) 0 (0.00025) 1 (0.000) 1 (0.0005) 1 (0.000) 1 (0.0005) 0 (0.00025) 0 (0.00025) 0 (0.00025)

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Fig. 2. Scanning electron micrograph of FM loaded with Cu2+ before (A) and after (B) the process of biosorption.

Fig. 3. EDX analysis of FM surface before (A) and after biosorption (B) of Cu(II).

chemical elements in the composition of the measured sample are Mg, K and P. Minor amounts of Ca and Al were also observed. The EDX pattern of FM (without Cu2+ biosorption) did not show the characteristic peak of Cu2+, however after the biosorption, three signals corresponding to copper appeared. The peak intensities for Mg, K and Ca decreased after the binding process, which indicates that these elements are involved in ion exchange with Cu (Table 6). The analysis of copper(II) solution before and after the biosorption revealed (Table 7) that the main cation exchangeable ions in ﬂax meal are K+, Na+, Ca2+ and Mg2+. Signiﬁcant amount of released alkali and alkaline earth metals (K+, Na+, Ca2+ and Mg2+) in solution could suggest ion exchange mechanism as predominant mechanism in the biosorption of Cu2+ by ﬂax meal, which was previously conﬁrmed by EDX analysis. The copper uptake by FM is associated to the presence of several functional groups on the surface of biosorbent.

The FT-IR spectra of ﬂax meal before and after the biosorption of copper(II) ions were compared in order to determine functional groups involved in the binding process (Fig. 4). Cellulose, Table 7 ICP-OES analysis of the solution before and after biosorption of Cu(II). Symbol

Before [mg]

After [mg]

Difference [mg]

Release Mg K Ca Na Uptake Cu

12 88 18 14

1.7

0.07 0.17 1.60 0.29

189

11.93 87.83 16.40 13.71

187.3

[mmole]

[meqv]

0.491 2.247 0.409 0.597

0.245 2.247 0.205 0.298

2.947

1.474

370

D. Podstawczyk et al. / Ecological Engineering 83 (2015) 364–379

Table 6 Elemental composition of the biosorbent surface before and after biosorption process on the basis of % weight determined by EDX analysis. %Weights Elements

C

N

O

Mg

Al

P

S

K

Ca

Fe

Cu

Sum

Before After

33.92 29.43

11.10

42.64 47.94

4.33 0.26

0.11 0.01

4,54 5.84

0.36 0.88

2.62 0.66

0.37 0.16

0.09

14.73

100 100

70

FLAX FLAX-Cu

60

T [%]

50

40

30

dosage and pH are signiﬁcant process variables (the highest tvalues at 95% conﬁdence interval and the highest percentage contribution), while temperature and agitation speed had very low standardized effect at 95% conﬁdence interval. The percentage contribution of each factor to the overall biosorption capacity was also determined. The ﬁrst factor (X1) had the highest percentage contribution of 40.82%, followed by X3 (28.73%) and X2 (17.72%), while the total % contribution of insigniﬁcant factors was 12.73%. Eq. (8) represents the linear relationship between independent parameters and the biosorption capacity (q [mg/g]), which is the result of proposed linear model: Y A ¼ 8:53 þ 7:10X 1 4:68X 2 þ 5:96X 3 0:03X 4 3:97X 5

20

10

0 4000

3500

3000

2500 2000 1500 Wave number [cm-1]

1000

500

Fig. 4. FT-IR spectra for biosorption of copper(II) ions by ﬂax meal.

hemicellulose, and lignin present in the cell wall of FM are the most important sorption sites. Fourier transform infrared (FTIR) spectra analysis on the basis of Silverstein et al. (1981) indicated the presence of hydroxyl, carboxylic, carbonyl, amino and nitro groups which are important sites for metal biosorption (Table 8). The shift of some functional groups bands observed in the FTIR spectra conﬁrmed changes in the biosorbent surface due to Cu2+ biosorption, suggesting that these groups are responsible for metal ions binding. The broad band positioned around 3396 cm1 was assigned the stretching vibration of hydroxyl functional groups from alcohols and carboxylic acids, indicating exchange of counter cations bonded to the functional group. The absorption bands located at 1656 and 1658 cm1 correspond to the C¼O bonds in protein amide group. Most changes (+21) occurring on the biosorbent after the biosorption of copper are reﬂected in the broad band present at 1538 cm1 and 1517 cm1 indicating that nitro groups from organic compounds are highly involved in the adsorption process. The changes observed between 1316 and 1318 cm1 and between 1240 and 1237 cm1 indicate stretching vibrations of C O bonds due to carboxyl groups and may be responsible for electrostatic interactions between positive copper ions and negatively charged carboxylic groups. The shift between 1061 and 1068 cm1 is indicative of stretching vibration of C O bonds from alcohols and carboxylic acids and C N bonds from amines. All these observations indicated the involvement of the functional groups present in ﬂax meal surface in the biosorption process and conﬁrmed ion exchange has the largest contribution in metal binding. 3.2. Screening of signiﬁcant parameters by Plackett–Burman design Table 1 presented the experimental and predicted by PBD values of the response, whereas Table 9 showed the statistical analysis of PBD results. The analysis of variance (ANOVA) as shown in Table 9 revealed that copper(II) ions concentration, biosorbent

(8)

The signs “+” and “” represent either a positive or a negative effect on the response. Thus, factors X1 and X3 had positive effects on the biosorption capacity, whereas X4 and X5 had negative effects. Insigniﬁcant factors were not included in the modeling and optimization steps by RSM and ANN methods and they were kept constant at the lowest level due to their negative coefﬁcients. The optimum levels of three variables, (Cu2+ concentration, biosorbent dosage and pH) were further determined by RSM. 3.3. Modeling by RSM 3.3.1. Comparison of CCD, BBD and FFD Comparison of central composite, Box–Behnken and fullfactorial designs was based on the statistical analysis, the prediction precision and the efﬁciency. The experimental values obtained for the response variables were ﬁtted to Eq. (1) by multiple regression analysis. The ﬁt of the model was evaluated by means of ANOVA revealing the effects of the model that were statistically signiﬁcant for a conﬁdence level of 95% (p-value <0.05), and those that were not statistically signiﬁcant. The best obtained model was further modiﬁed by eliminating insigniﬁcant terms. The results of the ﬁt of the models to the experimental data by multiple regression analysis together with the values of coefﬁcients and the model summary statistics for central composite, Box–Behnken and full-factorial designs are shown in Tables 10–12 , respectively. It can be observed that the ﬁnal models obtained were statistically signiﬁcant for a conﬁdence level of 95% (p-value <0.05) and exhibit insigniﬁcant lack-of-ﬁt. The analysis of the statistical results revealed that the best model is that attained on the basis of CCD. The model with the lower value for the sum of squares and mean square will ﬁt the data better. CCD based model was characterized by (a) the lowest value of the total sum of squares (1123.4), (b) the lowest value of the regression (83.4) and residual (0.31) mean squares, as well as (c) the highest F-value (276.0) with p-value lower than 0.000, conﬁrming high accuracy of ﬁtting and the statistical signiﬁcance of the model. Moreover, ANOVA for the lack of ﬁt test for the model was insigniﬁcant (Fvalue of 0.29 with p-value of 0.603) indicating that the model adequately ﬁtted the experimental data. The values of R2, which were 0.997, 0.996 and 0.85 for CCD, BBD and FFD, respectively, conﬁrmed that the correlation between predicted and actual values of responses is the best for CCD based model and more than

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Table 8 The FTIR spectral characteristics of ﬂax meal before and after biosorption of Cu2+ [26]. No.

Wavelength range [cm

Flax meal

1

]

3600–3200 3100–2800 1690–1640/1860–1620 1560–1515 1480–1350 1320–1210 1320–1210/1360–1080 1360–1080/1050–1150

1 2 3 4 5 6 7 8

Before sorption

After sorption

Differences

3396 2932 1656 1538 1399 1316 1240 1061

3405 2931 1658 1517 1415 1318 1237 1068

9 +1 2 +21 16 2 +3 7

Bond

Functional group

OH-stretching H-bonded CH stretching C¼O stretching/C¼C stretching NO stretching CH bending CO stretching CO stretching CO stretching/CN stretching

Alcohols Alkanes Amides/alkenes Nitro Alkanes Carboxyl acids Carboxyl acids Alcohols/amines

Table 9 Statistical analysis of Plackett–Burman design showing calculated regression coefﬁcient, t-value and p-value of each variable on biosorption process. Source

Sum of squares (SS)

Mean squares (MS)

Degrees of freedom (Dfe)

F-value

p (>95%)

Regression Residual Total

1482 197 1679

296 33

5 6 11

9.05

0.009

Factor

bPBD

t

p (>95%)

% Contribution

Signiﬁcance

Constant X1 X2 X3 X4 X5

8.53 7.10 4.68 5.96 0.028 3.97

5.16 4.30 2.83 3.60 0.02 2.40

0.0021 0.0051 0.0299 0.0113 0.9873 0.0534

40.822 17.730 28.720 0.001 12.727

Signiﬁcant Signiﬁcant Signiﬁcant Signiﬁcant – –

99.7% of the variance in the response can be explained by the empirical model obtained on the basis of central composite design of experiments. p-value and t-statistic were utilized in order to examine the importance of the model effects. The p-values estimated for factors X1, X2, X3, X12, X32, X1 X2 X3, X12 X3, X1 X22 were less than 0.05, indicating that these effects were signiﬁcant in the prediction process. p-value of X22 and X12 X2 was greater than 0.05, thus these model terms were not important in the biosorption process. Negative and positive values of the coefﬁcients represent, respectively, antagonistic and synergistic effect of each model term on the response of the system. The positive sign causes an increase in the response, while the negative sign a decrease of the response. Copper(II) concentration, pH, interaction

between them, quadratic effect of copper(II) concentration, quadratic effect of pH, interaction between Cu2+ concentration, biosorbent dosage and pH, interaction between quadratic effect of Cu2+ concentration and pH and interaction between quadratic effect of Cu2+ concentration and biosorbent dosage had positive effect and others had negative impact on the biosorption capacity. Furthermore, the terms, that were not statistically signiﬁcant, were eliminated from the model. The F-value increased from 276.0 for the ﬁrst model to 298.3 the ﬁnal model obtained, conﬁrming statistical signiﬁcance of the model for a conﬁdence level of 95% (pvalue <0.05). The coded coefﬁcient values for the model were further decoded in order to obtain the polynomial models for the response variables as a function of the actual independent

Table 10 Analysis of variance of the regression model obtained on the basis of CCD and t-test and probability values of the effects. Source

Sum of squares (SS)

Mean squares (MS)

Degrees of freedom (Dfe)

F-value

p (>95%)

Regression Residual Lack-of-ﬁt Pure error Total

1123.4 3.1 0.1 3.0 1126

86.4 0.31 0.01 0.30

13 10 1 9 23

276.0

0.000

0.29

0.603

Factor

bCCD

t

p (>95%)

Signiﬁcance

Constant X1 X2 X3 X1 X2 X1 X3 X2 X3 X12 X22 X32 X1 X2 X3 X12 X2 X12 X3 X1 X22

7.91 8.43 4.12 3.11 2.14 3.96 4.04 0.94 0.34 1.83 2.60 0.82 2.39 2.93

49.44 21.08 10.30 7.78 10.70 19.80 20.20 2.85 1.03 5.55 13.00 1.86 5.43 6.62

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.009 0.314 0.000 0.000 0.076 0.000 0.000

Signiﬁcant Signiﬁcant Signiﬁcant Signiﬁcant Signiﬁcant Signiﬁcant Signiﬁcant Signiﬁcant – Signiﬁcant Signiﬁcant – Signiﬁcant Signiﬁcant

372

D. Podstawczyk et al. / Ecological Engineering 83 (2015) 364–379 Table 11 Analysis of variance of the regression model obtained on the basis of BBD and t-test and probability values of the effects. Source

Sum of squares (SS)

Mean squares (MS)

Degrees of freedom (Dfe)

F-value

p (>95%)

Regression Residual Lack-of-ﬁt Pure error Total

1572.0 6.7 5.6 1.1 1126

142.91 2.23 5.63 0.53

11 3 1 2 23

64.25

0.003

10.56

0.083

Factor

bBBD

t

p (>95%)

Signiﬁcance

Constant X1 X2 X3 X1 X2 X1 X3 X2 X3 X12 X22 X32 X12 X3 X1 X22

7.57 4.90 8.22 4.00 5.64 2.01 4.03 0.55 6.73 2.38 1.83 5.66

8.78 6.56 15.56 5.35 7.56 2.70 5.39 0.71 8.66 3.06 1.73 5.36

0.000 0.000 0.000 0.000 0.000 0.017 0.000 0.489 0.000 0.009 0.106 0.000

Signiﬁcant Signiﬁcant Signiﬁcant Signiﬁcant Signiﬁcant Signiﬁcant Signiﬁcant – Signiﬁcant Signiﬁcant – Signiﬁcant

respectively, thus the extrapolation is possible, however without empirical conﬁrmation each computed by the model value of the capacity is precarious.

variables (Eq. (9)). Y CCD ¼ 11:43 þ 0:04X 1 1:76X 2 þ 7:59X 3 þ 0:02X 1 X 2 þ 0:01X 1 X 3 0:13X 2 X 3 0:0007X 21 þ 0:19X 22 0:81X 23 0:004X 1 X 2 X 3 þ 0:00002X 21 X 2 þ 0:0002X 21 X 3 þ 0:001X 1 X 22

(9)

As it can be seen from Eq. (10), the coefﬁcients attained after the uncoding process do not have the same or even similar the order of magnitude, while the uncoding process can be performed only if all parameters have the same or similar scale in order to provide fair comparison between them. Thus, even though the model showed in Eq. (10) is calculated properly, it is better to use the model with coefﬁcients obtained for normalized values of independent variables. The insigniﬁcant coefﬁcients were eliminated after examining the coefﬁcients and the model was ﬁnally reﬁned as follows (Eq. (10)). Y CCD ¼ 7:94 þ 8:43X 1 3:46X 2 þ 3:11X 3 2:14X 1 X 2 þ 3:96X 1 X 3 4:04X 2 X 3 1:08X 21 1:70X 23 2:60X 1 X 2 X 3 þ 2:39X 21 X3 2:93X 1 X 22

(10)

3.3.2. Veriﬁcation of the models In contrast to response surface methodology, in artiﬁcial neural network simulation, experimental data is divided into training testing and validating sets prior to a simulation, thus the accuracy of the model obtained is veriﬁed instantly. The adequacy of ﬁnal RSM models should be additionally validated afterwards by the comparison of experimental data points randomly preformed and the values predicted by a model. In this study, additional ﬁve experiments were conducted in order to check accuracy of the BBD, CCD and FFD based models. Table 13 presents the comparison of ﬁve experimental points and the values of the biosorption capacity predicted by the models. As can be seen for CCD based model, which was chosen as the best predictor, there are minor differences (expressed by the relative errors (RE)) between the actual and the calculated values of the response, indicating high accuracy of the model ﬁtting. The fourth and the ﬁfth experimental points corresponds to the values outside the given range to examine the feasibility of extrapolation in close proximity of the range. The experimental value is very close to the actual one with relative errors of 0.01 and 0.00 for the fourth and the ﬁfth point,

3.3.3. Determination of optimal conditions The second order polynomial models extended with additional cubic interaction effects obtained in the study were applied to acquire speciﬁed optimum biosorption conditions in terms of the metal ions concentration, FM dosage and solution pH. For all of the models, optimum values of the variables were exactly the same, conﬁrming the correctness of the optimization. The optimal conditions were as follows: Cu2+ concentration of 200 ppm, the biosorbent dosage of 1 g/L, and solution pH of 5. The maximum predicted efﬁciency expressed as the biosorption capacity was 45.10 mg/g, 34.40 mg/g, and 39.11 mg/g for the BBD, CCD and FFD based models, respectively. The relative error value between the actual and predicted value for the biosorption capacity is 0.00 indicating that the value of the capacity predicted by the CCD model is close to the average value of the actual capacity (34.37 mg/g). Results of optimization study showed that at the optimum point, process parameters can be used to remove copper(II) ions effectively from an aqueous solution. Thus, optimization is an essential step for designing and modeling processes such as biosorption in order to maximize the efﬁciency of the removal. The optimal parameters were also conﬁrmed by the analysis of 3D response surface plots for the models. The relationship between independent and dependent variables was graphically represented by 3D response surface plots and 2D contour plots generated by the models (Figs. 5–7 ). Analysis of the 3D response surface plots for all the models revealed that the relationship between independent variables is the same for BBD, CCD as well as FFD based models. In the present investigation, each ﬁgure represented the effect of two test variables on the response, while the third variable was ﬁxed at the zero level. Although there is no elliptical nature of the contour plots and global maximum wasn't being achieved, the relationship between the independent variables and the response as well as surface trend are explicitly evident. Figs. 5–7A shows the effect of copper (II) concentration (X1) and biosorbent dosage (X2) on the efﬁciency of the metal ions removal. It can be observed that the higher the value of the sorbate concentration and the lower the value of the biosorbent dosage, the higher the biosorption capacity. As it can be seen in Fig. 5A an increase of Cu2+ concentration from 20 to 200 ppm and a decrease of biosorption capacity from 10 to 1 g/L

D. Podstawczyk et al. / Ecological Engineering 83 (2015) 364–379

B Sorption capacity [mg/g]

Sorption capacity [mg/g]

A

40

20

1

0 1

15 10 5 0 1

0

0.5 0

-0.5 -1

Biosorbent dosage [g/L]

373

-1

0

Copper ion concentration [ppm]

-1

pH

-0.5

-1

1

0.5

0

Copper ion concentration [ppm]

Sorption capacity [mg/g]

C 30 20 10 0 1 0 -1

pH

-1

-0.5

1

0.5

0

Biosorbent dosage [g/L]

Fig. 5. 3D surface plots of interactive effects on sorption capacity obtained on the basis of BB Design. The inﬂuence of two independent variables: (A) biosorbent dosage [g/L] and copper ion concentration [ppm], (B) pH and copper ion concentration, (C) pH and biosorbent dosage [g/L].

B

30

Sorption capacity [mg/g]

Sorption capacity [mg/g]

A

20

10

0 1 0

Biosorbent dosage [g/L]

0.5

0 -1

-1

30

20

10

0 1

1 0

0

-0.5

-1

pH

Copper ion concentration [ppm]

-1

0.5

1

-0.5

Copper ion concentration [ppm]

Sorption capacity [mg/g]

C

20 15 10 5 0 1 0

pH

0 -1

-1

0.5

1

-0.5

Biosorbent dosage [g/L]

Fig. 6. 3D surface plots of interactive effects on sorption capacity obtained on the basis of CC Design. The inﬂuence of two independent variables: (A) biosorbent dosage [g/L] and copper ion concentration [ppm], (B) pH and copper ion concentration, (C) pH and biosorbent dosage [g/L].

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D. Podstawczyk et al. / Ecological Engineering 83 (2015) 364–379

B

30

Sorption capacity [mg/g]

Sorption capacity [mg/g]

A

20

10

0 1

20 10 0 -10 -20 1 1

1 0

0

Biosorbent dosage [g/L]

0

0 -1

-1

-1

pH

Copper ion concentration [ppm]

-1

0.5

-0.5

Copper ion concentration [ppm]

Sorption capacity [mg/g]

C

25 20 15 10 5 0 1 1 0.5

0

pH

0 -0.5

-1

-1

Biosorbent dosage [g/L]

Fig. 7. 3D surface plots of interactive effects on sorption capacity obtained on the basis of FF Design. The inﬂuence of two independent variables: (A) biosorbent dosage [g/L] and copper ion concentration [ppm], (B) pH and copper ion concentration, (C) pH and biosorbent dosage [g/L].

promoted and increase of biosorption capacity from 0.0 mg/g to the value of about 20.0 mg/g. It can be explained by the fact that the initial concentration of metal ions plays an important role in biosorption process due to the fact that less active sites on a biosorbent surface are available for a large amount of ions, while at a given metal concentration, the lower the biosorbent dosage, the

higher the metal amount bound by a sorbent unit. Quite different situation is observed for the simultaneous effect of Cu2+ concentration and pH (Figs. 5–7B). A rise of both parameters causes an increase of the response, achieving eventually maximum value of the biosorption capacity in the range of the concentration from 150 to 200 ppm and pH from 4 to 5. pH is one of the most

Table 12 Analysis of variance of the regression model obtained on the basis of FFD and t-test and probability values of the effects. Source

Sum of squares (SS)

Mean squares (MS)

Degrees of freedom (Dfe)

F-value

p (>95%)

Regression Residual Lack-of-ﬁt Pure error Total

2344.4 401.1 382.2 18.9 2745.5

180.3 30.9 31.9 18.9

13 13 12 1 26

5.84

0.002

1.68

0.544

Factor

bCCD

t

p (>95%)

Signiﬁcance

Constant X1 X2 X3 X1 X2 X1 X3 X2 X3 X12 X22 X32 X1 X2 X3 X12 X2 X12 X3 X1 X22

9.30 6.07 6.29 3.70 3.60 3.20 4.15 0.81 3.11 2.89 2.77 0.79 0.57 0.83

3.18 2.68 2.77 1.63 2.14 1.79 2.32 0.36 1.36 1.24 1.21 0.28 0.20 0.29

0.004 0.013 0.010 0.115 0.042 0.085 0.029 0.722 0.186 0.226 0.237 0.782 0.843 0.774

Signiﬁcant Signiﬁcant Signiﬁcant – Signiﬁcant – Signiﬁcant – – – – – – –

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375

Table 13 Veriﬁcation of the models ﬁtness. No. Uncoded values of random experimental points

1 2 3 4 5 6

Experimental values of the biosorption capacity [mg/g]

Predicted values [mg/g]

Cu2+ concentration [ppm]

Biosorbent dosage [g/ pH L]

BBD

88 178 178 268 200 65

6.6 8.9 2.1 10 2.1 7.8

5.60 8.40 31.35 16.75 35.83 2.68

4.2 5.22 3.5 10.01 4.6 23.93 3.1 12.99 5.8 37.42 2.8 2.98

important parameter in biosorption process since it can inﬂuence a charge on a biosorbent surface. The lower pH, the more H+ competes with Cu2+ to active sites on the biosorbent surface. Figs. 5–7C present the interaction between solution pH and the biosorbent dosage and their effect on the biosorption efﬁciency. Although an increase of solution pH from 2 to 5 improves the response, an increase in the biosorption capacity is inhibited by the increase of biosorbent dosage from 1 to 10 g/L. The analysis of the plots allowed for determination of optimal conditions and comparison of them with calculated by the model. The optimal values of parameters obtained by maximization of the polynomial equation were in agreement with the optimum points read from the graphs and were equal to Cu2+ concentration of 200 ppm, the biosorbent dosage of 1 g/L, and pH 5, respectively. 3.4. Simulation by ANN 3.4.1. Optimum ANN topology On the basis of the experimental results, empirical regression model was determined (Eq. (11)), by ﬁtting approximation function (second order polynomial equation) to the coded values of four parameters (number of hidden neurons, number of epochs, adaptive value and training goal) and the response of the system, the mean squared error (MSE). Y A ¼ 0:0002 0:0118X 1A 0:0005X 2A 0:0020X 3A þ 0:0002X 4A þ0:0001X 1A X 2A þ 0:0062X 1A X 3A þ 0:0001X 1A X 4A 0:0000X 2A X 3A þ 0:0001X 2A X 4A þ 0:0000X 3A X 4A þ 0:0116X 1A 2 0:0005X 2A 2 þ 0:0020X 3A 2 0:0008X 4A 2

dBBD

CCD (CCF)

dCCD

[] 0.07 0.16 0.31 0.29 0.04 0.11

5.30 9.77 25.57 13.09 37.45 2.32

0.01 0.02 0.07 0.01 0.00 0.22

FFD

dFFD []

6.90 9.09 28.66 8.96 36.10 3.55

0.32 0.09 0.20 0.14 0.03 0.19

[]

standpoint. It was observed that X1A (the number of neurons) was a key factor inﬂuencing the topology of neural networks, due to its high t-value (6.97) among the all parameters. Optimal values of the parameters and corresponding the predicted minimum value of the MSE were determined by optimization of the approximation function. The optimization problem was constrained by the condition for the response greater than zero. Thus, the minimum of the MSE was found to be 1.11 1014 for the optimal values of the factors presented in Table 15. 3.4.2. Simulation of the artiﬁcial neural network with optimum topology Subsequently, the optimum conditions obtained by means of response surface methodology were veriﬁed by the ANN training. The training (TP), the validation (VP) and the test performance (TSP) progresses during the simulation versus the number of epochs were plotted in Fig. 8. The mean squared error values drop gradually epoch by epoch, until the performances achieved the minimum value. The best performance (MSE) was reached after 450 of the epochs as values of 6.1 106 (TP), 7.8 104 (VP), 1.3 104 (TSP). For the training state showed in Fig. 9, the values of gradient, adaptive value (m), and validation check at epoch 450, were 2.84 105, 0.0345 and 0 respectively. The gradient adopted a low value, as the training achieves a minimum of the performance. The adaptive value is responsible for adjusting of weights during a network training. In the case of this study, the initial m value was one of the parameter optimized by response surface methodology,

(11)

Negative and positive values of the coefﬁcients represent, respectively, antagonistic and synergistic effect of each independent variable on the response of the system. The values of the coefﬁcients are relatively low, due to the low values of the MSEs employed as the responses of the system. The correlation coefﬁcient between the experimental values and responses predicted by the model was 0.96, implying that more than 96% of the variance in the response can be explained by the empirical model. The analysis of variance (ANOVA) for the quadratic model and the effects is presented in Table 14. The analysis was carried out for a signiﬁcance level of a = 0.05 (probability of 95%). The calculated F-value (8.90), with the signiﬁcance level less than 0.05 (pvalue = 0.0003), turned out to be higher than the tabulated F-value (2.64), which means that the model is signiﬁcant statistically and can be used as a predictor of the experimental data. The analysis of the student t-test for terms of quadratic models and the corresponding p-values showed that four coefﬁcients, which are (1) the linear term of the number of neurons, (2) the interaction effect of the ﬁrst and the third parameters, (3) the squared effect of the number of neurons, are valid from a statistical

Fig. 8. The training, validation and test performance.

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D. Podstawczyk et al. / Ecological Engineering 83 (2015) 364–379

Fig. 9. The progress of the training statistics (the training state): gradient, validation fails and adaptive value during the simulation.

Fig. 10. The error histogram of the network.

thus its value at epoch 450 was 0.0345 which is a multiproduct of the initial adaptive value and the decrease factor. Presentation of errors in the form of histogram is the best visualization of the differences between the true values and the network outputs. Fig. 10 shows the error distribution of the training data set, the testing data and the validation data set. The high center peaks indicate that in most instances, the errors between the outputs and targeted values are very small (close to 0), while in only few instances the MSE was higher than 0.01. The error

histogram as an additional veriﬁcation network performance conﬁrmed that the ﬁnal optimized ANN model is satisﬁed and validated. Another option to verify network performance is a regression analysis between the network response and the corresponding targets for an independent data set. The value of the correlation coefﬁcient (R2) computed on the basis of the regression plot (thick continuous line) shown in Fig. 11 was 0.96, indicating almost perfect correlation between the predicted responses and the

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in prediction of response without any further analysis after a simulation. On the other hand, RSM can be used only within speciﬁc ranges of parameters, which are selected before the modeling. Thus, the selection of appropriate method for simulating speciﬁc issues such as complex biosorption process is not easy, and all advantages and disadvantages of both methods should be considered before modeling. In this study the comparison of RSM and ANN for predictive capability was made on the basis of various factors such as the correlation coefﬁcients, the mean squared errors, and the requirements of both approaches. The coefﬁcient of determination (R2) and the mean square error (MSE) values were respectively equal to 0.99 and 6.10 104 for the ANN training set, 0.98 and 1.30 104 for the ANN testing set, and 0.97 and 5.78 for the RSM set. Although both models exhibited high predictability in determining of the biosorption efﬁcacy in the case of the removal of copper(II) ions from aqueous solution (the overall value of R2 for the ANN is even smaller (0.96) than for the RSM model (0.997)), the ANN showed a clear advantage over the RSM for the data ﬁtting as well as for the estimation capabilities. 3.6. Limitations of ANN and RSM applications in modeling of the biosorption process Fig. 11. The linear regression of targets relative to outputs.

targets. After the network was trained, the obtained model can be used to predict the biosorption capacity for new values of parameters (solution pH, biosorbent dosage and initial Cu2+ concentration). 3.5. Comparison of ANN and RSM predictabilities The main advantage of RSM in nonlinear modeling is the ability to determine the contribution of each factor in predicted response due to the accurate statistical analysis. Thus, insigniﬁcant parameters can be identiﬁed and excluded from the model, leading to reduce complexity of the issue. It has been proved in this study that ANN better ﬁts experimental data to a model than RSM, however, although for an ANN model development a few experiments are sufﬁcient, a more accurate ﬁt is obtained for a large number of experimental points. Moreover, there is no information about a contribution of ANN parameters such as weights and biases

Despite many advantages such as modeling of complex nonlinear issues, both ANN and RSM methods have limitations of applications. Artiﬁcial neural network simulation has for example, a disadvantage of the necessity of large amounts of training data, while response surface methodology cannot be used for solving highly nonlinear relationships. Moreover, both RSM and ANN models cannot be extrapolated outside the range of the collected data, especially in the case of biosorption, where the effect of each parameter is unpredictable without experimental conﬁrmation due to the biological nature of sorbents. In the case of RSM, extrapolation issue can be overcome by removing insigniﬁcant effects from approximating equation, improving model ﬁtting and thus correlation coefﬁcient is closer to unity. In this study, insigniﬁcant effects were eliminated from the equation obtained on the basis of central composite design and F-value increased from 276.0 to 298.3 for p-value lower than 0.05, making the model more accurate. The improvement in model ﬁtting does not mean that there is no risk in predicting responses beyond the observable values and extrapolation should be considered.

Table 14 Analysis of variance (ANOVA) of the quadratic equation obtained using response surface methodology. Source

Sum of square (SS)

Mean square (MS)

Degrees of freedom (Dfe)

F-value

p (>95%)

Between groups Within groups Total

0.0028 0.0003 0.0031

0.0002 0.0000

14 12 26

8.8969

0.0003

Factor

b

t

p (>95%)

Signiﬁcance

Constant X1A X2A X3A X4A X1A X2A X1A X3A X1A X4A X2A X3A X2A X4A X3A X4A X1A2 X2A2 X3A2 X4A2

0.0002 0.0118 0.0005 0.0020 0.0002 0.0001 0.0062 0.0001 0.0000 0.0001 0.0000 0.0116 0.0005 0.0020 0.0008

5.25 6.97 0.06 2.21 0.22 0.03 2.61 0.05 0.02 0.05 0.00 0.24 0.97 0.39 0.657

0.000 0.000 0.955 0.048 0.826 0.978 0.023 0.964 0.984 0.962 0.999 0.000 0.815 0.353 0.706

Signiﬁcant Signiﬁcant – Signiﬁcant – – Signiﬁcant – – – – Signiﬁcant – – –

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Table 15 Optimal neural network topology in terms of the optimum (1) the number of neurons, (2) the number of epochs, (3) the adaptive value and (4) the training goal. Factor

Coded value

Uncoded value

1 2 3 4

0.63 1.00 0.46 1.00

22 450 3.45 0.00

Moreover, RSM is unsuitable for the description of systems where responses vary discretely. Although biosorption process is hardly predictable, response of a system can easily be modeled by continuous nonlinear function, as for example, in this study. One of the problems of neural networks training is overﬁtting. In this work, overtraining of neural network was prevented by early stopping of training, which was conducted by dividing a large set of input data into three subsets: training, validation and test. If the training is done correctly, the validation error decreases until it achieves its minimum value and then ANN learning is stopped and the weights and biases at the minimum of the validation error are returned. Two criteria were used to stop network training, which were (1) maximum number of training epochs (early stopping of training) and (2) minimum performance goal (data not shown). The training can be stopped only by one of them, not two at once. The value of the former (450 epochs) was determined by optimization by RSM method. An increase in the number of epochs caused an extension of learning time and in turn an occurrence of the model overﬁtting (a rise of MSE) and its failure to train the data set properly. The value of the latter was set to 0.00 determined by optimization by RSM method. For this value the training algorithm ran too long and overtraining occurred. Although it seems that the lower value of the error is the best for proper learning of the network, it can cause invalid training of the network. The other drawback of ANN is high data requirements, however batch biosorption experiments are not highly timeconsuming and their duration is not very long, thus any experimental point can be used to train the network until it Table 16 Connection weights approach for estimating the ranked importance of the parameters. Neuron number

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 P Sum of product ( input output) Importance Percent importance [%]

Connection weights Input 1

Input 2

Input 3

Output

1.88 2.56 0.71 3.09 1.76 0.63 1.68 0.05 3.35 2.93 0.80 0.31 1.15 0.41 3.11 2.49 0.78 1.56 0.98 2.36 0.04 1.34 0.96 1 42.86

2.16 2.52 0.49 1.84 2.44 0.13 1.18 3.22 1.22 2.03 0.82 0.26 0.81 2.44 1.71 2.20 2.40 1.38 0.21 1.54 0.32 1.66 0.57 3 25.45

1.77 0.85 0.51 0.56 3.07 0.07 1.26 1.92 1.88 0.39 1.20 0.27 0.84 1.94 0.95 1.91 2.04 1.71 0.06 1.65 0.36 1.73 0.71 2 31.69

0.0014 0.0026 1.0095 0.0027 0.0018 0.5852 0.0361 0.0007 0.0003 0.0009 0.0080 0.6275 0.1145 0.0017 0.0010 0.0001 0.0047 0.0074 0.1970 0.0409 0.9466 0.0488 –

can be standardized and refers to appropriate range. In this study, set of 528 experimental points with different values of the biosorption affecting parameters after standardization was utilized to train network properly. In artiﬁcial neural modeling, the standardized coefﬁcients corresponding to each variable cannot be easily computed as in nonlinear regression. The connections between neurons, and therefore the links between inputs and outputs are represented by weights, which are very difﬁcult to interpret and express using a mathematical formula. The inﬂuence of particular independent variable on the prediction of output depend mostly on the value and the sign of the connection weights. The greater the weight value, the higher the contribution of independent variable in response predicting process. The effect of negative weights on neurons is antagonistic, and therefore the value of the predicted output declines, while positive weights have synergistic impact on neurons and increase the value of the response. Connection Weights Approach (Olden et al., 2004) provides a method for quantifying variable importance in artiﬁcial neural network on the basis of input-hidden and hidden-output connection weights. In the approach the sum of the product of input-hidden and hiddenoutput weights is calculated. Table 16 shows weights values for the neural network modeling of the copper(II) biosorption investigated in this study. Application of connection weights approach allowed for estimating the ranked importance, the contribution and the inﬂuence (either negative or positive) of each independent variable in the prediction process on the basis of the calculated weights. The most important parameter was turned out to be the concentration of Cu2+ (42.86% of the importance), followed by solution pH (31.69%), while the least signiﬁcant is the biosorbent dosage (25.45%). 4. Economic beneﬁts of the models Although the models were developed and investigated on the basis of copper-containing wastewater synthetic solutions, the conditions were selected to best reﬂect the reality. The metal concentration and pH are the most important parameters in copper-containing wastewater treatment. They also inﬂuence biosorption, one of the several biological treatment processes. Moreover, the efﬁciency of the process depends strongly on the quality and the quantity of adsorbent. Taking into account economic aspects of industrial wastewater treatment, the biosorbent dosage is very important when the initial metal ion concentration in a solution is constant. The lower the amount of biosorbent sufﬁcient to achieve high removal efﬁciency, the lower the costs of the process. The actual selling price of ﬂax meal in the Polish market is very low (less than 0.5 s/kg), however excessive and unsustainable use can lead to an increase of waste disposal costs. The appropriate design, scale-up and optimization of industrial biosorption process depend on the description of inﬂuence of operating conditions on the process. The models proposed in this study predict the efﬁciency of biosorption in batch mode with high accuracy for varying operational conditions characteristic for industrial copper-containing wastewater, thus they have potential applicability in wastewater industry. Industrial implementation of the models can improve process monitoring and controlling and in turn save time and reduce costs. 5. Conclusion In this study, application of waste ﬂax meal for removal of copper ions via biosorption process was investigated. Characterization of the biosorbent by analysis of FT-IR spectra and SEM-EDX images of the FM surface revealed that the most probable mechanism responsible for the metal binding is the exchange of

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Cu2+ with counter ions bonded to the surface mostly by carboxyl, hydroxyl and nitro groups. CCD turned out to be the best design of experiments for modeling of the effect of the process conditions by the equation in terms of correlation coefﬁcient (R2 of 0.997) and analysis of variance (F-value of 276.0 with p-value lower than 0.000). Subsequently, the insigniﬁcant terms in the model obtained on the basis of CCD were eliminated in order to reduce the complexity of the problem. The model obtained was further used to determine optimal conditions in order to maximize the process efﬁciency expressed as the biosorption capacity. The maximum biosorption capacity 34.40 mg/g, was achieved at initial Cu2+ concentration of 200 ppm, biosorbent dosage of 1 g/L and solution pH of 5. Afterwards, the equation was validated experimentally with relative error value of 0.1%, conﬁrming high precision of the ﬁtting. However, the results of the CCD (MSE = 0.34) based model indicate that the model is less more accurate in estimating the values of dependent variables when compared with the ANN model due to its lower value of MSE (6.1 104). Summarizing, despite the complex relationship between operation parameters and their high impact on the biosorption efﬁciency, copper ions can be effectively removed from aqueous solution via biosorption process by waste ﬂax meal. Modeling of the effects of process variables by using either RSM or ANN tools can improve conducting a process and allow to scale up and in turn reduce the cost of the operation in wastewater treatment. Therefore, the reduction of cost by both (1) application of waste materials and (2) relatively easy evaluation of the effect of process conditions makes biosorption economically feasible. Acknowledgements This study is co-ﬁnanced by the European Union as part of the European Social Fund. The work was co-ﬁnanced by a statutory activity subsidy from the Polish Ministry of Science and Higher Education for the Faculty of Chemistry of Wroclaw University of Technology (S40579/Z0307) Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j. ecoleng.2015.07.004. References Ahmad, M.F., Haydar, S., Bhatti, A.A., Bari, A.J., 2014. Application of artiﬁcial neural network for the prediction of biosorption capacity of immobilized Bacillus

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