MODELING OF MILK LACTOSE REMOVAL BY COLUMN … No4_p369-382... · 2019-12-26 · printed polymers...

Chemical Industry & Chemical Engineering Quarterly

Available on line at Association of the Chemical Engineers of Serbia AChE www.ache.org.rs/CICEQ

Chem. Ind. Chem. Eng. Q. 25 (4) 369−382 (2019) CI&CEQ

369

MANUELA SOUZA LEITE

MATHEUS A. SANTOS EULINA M. F. COSTA

ACENINI BALIEIRO ÁLVARO S. LIMA

ODELSIA L. SANCHEZ CLEIDE M. F. SOARES

Tiradentes University, Institute of Technology Research, Farolândia,

Aracaju, Sergipe, Brazil

SCIENTIFIC PAPER

UDC 66.081.3:637.12.047:004.8

MODELING OF MILK LACTOSE REMOVAL BY COLUMN ADSORPTION USING ARTIFICIAL NEURAL NETWORKS: MLP AND RBF

Article Highlights • Mathematical models are proposed for the removal of lactose from milk • Multilayer perceptron and radial basis function neural networks are applied • Neural models (MLP and RBF) were developed to predict breakthrough curves • The operational parameters were evaluated for lactose adsorption capacity • The models effectively predicted the breakthrough curves under various conditions Abstract

Artificial neural network (ANN) techniques are effective in modeling nonlinear processes, are simple to implement and require low computational time. In this work, the lactose adsorption process for continuous flow in a fixed-bed column with a molecularly imprinted polymer (MIP) adsorbent was modeled using an ANN technique. The neural models allowed predicting the relative lactose con-centration (C/C0) from the interactions between the variables of contact time (min), temperature (°C), granulometry (mesh), bed height (cm) and flow rate (mL min-1). The ANN models were developed in MATLAB using multilayer perceptrons (MLP) and a radial basis function network (RBF). The MLP model was developed using a three-layer feed forward backpropagation network with 5, 8 and 4 neurons in the first, second and third layer, respectively. The function (RBF) network is also proposed and its performance is compared to a traditional network type. The best architecture configuration RBF model was developed using 5, 14 and 1 neurons in the first, second and third layer, res-pectively. The proposal of development of mathematical models applied to multi-component adsorption system for milk using these approaches is inno-vative. The resulting breakthrough curve models for lactose adsorption were in good agreement with the experimental results. Performance indices, such as R², MSE, RMSE, SSE, MAE and RME were used to evaluate the reliabilities and accuracies of the models. A comparison between the ANN models shows the ability to predict the breakthrough curves of lactose removal in the milk adsorption process. Though, the MLP network model shows more accurately a higher correlation coefficient (R2 = 0.9751) and lower values for the obtained error indices. The accuracy of the model is confirmed by the comparison between the predicted and experimental data. The results showed that both neural models efficiently described the non-linear process of lactose ads-orption in a fixed-bed column.

Keywords: ANN, MLP, RBF, fixed-bed column, lactose, breakthrough curves modeling.

Correspondence: M.S. Leite, Tiradentes University, Institute of Technology Research, Av. Murilo Dantas, 300, Farolândia, 49032-490 Aracaju, Sergipe, Brazil. E-mail: [email protected] Paper received: 6 June, 2018 Paper revised: 13 November, 2018 Paper accepted: 9 April, 2019

https://doi.org/10.2298/CICEQ180606015L

M.S. LEITE et al.: MODELING OF MILK LACTOSE REMOVAL… Chem. Ind. Chem. Eng. Q. 25 (4) 369−382 (2019)

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Lactose is the major carbohydrate in the milk of most species, in addition to other components such as moisture, protein(s), fat, mineral and lactic acid [1]. However, the consumption of milk as an energy source is limited by the relatively high percentage of people who are unable to digest lactose [2]. The possibilities of lactose removal techniques from milk are applied to offer the customers products with reduced lactose content. Among these, it is possible to highlight the process of milk lactose removal by adsorption. This versatile and widely used method has the ability to separate diverse types of chemical compounds using simple operating procedures [3,4]. Its practical application is generally performed in a fixed-bed column [5]. In this separation system, the adsorption rates are favored because the adsorbent is continuously in contact with the solution [6]. The adsorbent efficiency can be improved by using the molecular imprinting technique to obtain molecularly printed polymers (MIP). The main advantage that MIPs have over the conventional materials used in extraction in the solid phase, is their molecular speci-ficity [7]. Balieiro et al. [8] and Oliveira et al. [9] stu-died the adsorption process of molecularly imprinted silica in a fixed-bed column with continuous flow, for the extraction of lactose and cholesterol from milk, respectively.

Some studies have used phenomenological models to describe the adsorption mechanism [8-15]. In addition to the phenomenological models, the lite-rature abounds with studies that use empirical models developed using artificial neural network (ANN) tech-niques, to obtain a model that best describes various adsorption processes [9,11,16-22]. However, public-ations with mathematical modeling for milk adsorption systems are incipient.

The ANN has three layers including an input layer, one or more hidden layers, and an output layer. For each ANN, the input layers are composed of inde-pendent variables and the output layer by dependent variables. The input and output layers are intercon-nected by intermediate layers, with multiple neurons. Each neuron sums all the inputs it receives and con-verts the sum to an output value based on a pre-defined activation or the transfer function [23,24].

Neural networks have been successfully used in multivariate and nonlinear systems and ANNs are promising modeling techniques for multicomponent processes [25-32]. Thus, an ANN approach was emp-loyed by the authors to explore its potential applic-ation in a multi-component sample, such as milk, with specific emphasis on the adsorption of lactose. The modeling of the adsorption process can be performed

by various types of architectures, such as multilayer perceptron (MLP), as seen in the work of Oliveira et al. [9], Sargolzae et al. [28] and Razavi et al. [29]; and by networks with radial basis functions (RBF), such as in the work of Hassanzadeh et al. [18] and Solei-mani et al. [33]. Oliveira et al. [9] modeled the process of cholesterol removal from milk in a continuous flow adsorption column with a MIP adsorbent using ANN models. In that study, the Levenberg–Marquardt training algorithm for MLP was developed and a satis-factory prediction of the experimental data was obtained because it presented an efficient perform-ance. Also, in the work of Sargolzae et al. [28] the effectiveness of ultrafiltration milk modeling has been assessed using an MLP. The modeling results reveal that ANN modeling also has a high ability in simul-ating the dynamic behavior of permeate flux, total hydraulic resistance using temperature and time as the input parameters in the modeling of ultrafiltration processes. Razavi et al. [29] also investigated the neural network approach to predict complete perme-ate flux, total hydraulic resistance and solutes reject-ion during crossflow ultrafiltration of skim milk as a function of the transmembrane pressure and tempe-rature and to specify the role of these factors on the mechanisms of flux, fouling and retention. The authors concluded that the neural networks can be successfully used to predict the milk ultrafiltration per-formance.

However, there is no prior publication dealing with ANN or other models to predict the breakthrough curves of lactose for this system. In particular, the modeling of lactose is challenging due to the com-plexity of the physical interactions in a highly non-linear water-in-oil emulsion (milk). In this context, the present work aimed to investigate the capability of two neural model types (MLP and RBF) in predicting the breakthrough curves of milk lactose by a column adsorption process with continuous flow, from the effects of parameters including contact time (min), temperature (°C), granulometry (mesh), bed height (cm) and flow rate (ml min-1). Explanations of the simulated results, from the models and the predicted ANN results are presented.

MATERIALS AND METHODS

Milk and reagents

The bovine milk was packaged in plastic bags, conditioned under refrigeration in thermal boxes and transported to the Food Research Laboratory (LPA) of the Institute of Technology and Research (ITP), 112 km from the collection point, where they were frozen (-20 °C) until use.


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The reagents used in this study were tetra-ethyl ortho-silicate (98%), lactose (purity >99%), acetonit-rile (99.9%), hexane (65%), hydrogen peroxide (32%), sodium hydroxide (97%), hydrochloric acid (37%), ammonium hydroxide (30%), chloroform (99.8%) and ethanol (99.8%) and were all analytical grade.

Preparation of the adsorbent and analytical determination of lactose

The preparation of the adsorbent and the ana-lytical determination of the lactose were performed as described by Balieiro et al. [8]. The adsorbent was prepared using the sol-gel process and tetraethoxy-silane (TEOS) as raw material. For molecularly imp-rinted polymer (MIP-lac) adsorbent the TEOS and the target molecule (lactose) were dissolved in ethanol. The steps were as follows: pre-hydrolysis, hydrolysis, solid material synthesis through gelation for 18 h, ext-raction (washing) and drying at 277.2 K.

The calibration curve and measurement of lac-tose were performed by high performance liquid chro-matography (HPLC) using a liquid chromatography (Shimadzu), with refractive index detector (RID-10A) and software (LC-Solution) for the location of the data. The concentration of the standard solution of lactose ranged from 30 to 300 ppm. For processing the data, the analytical column used was a Luna NH2 (250 mm×4.6 mm) (Phenomenex). The mobile phase consisted of acetonitrile and ultrapure water (60:40) at a flow rate of 1.5 mL min-1, with an analysis time of 10 min. For the determination of lactose from milk samples: 30 µL samples were diluted in a 2 mL volu-metric flask in ultrapure water and then the samples were filtered through a 0.45 Millipore membrane and subsequently injected into the equipment [8].

Adsorption column experimental method

Balieiro et al. [8] studied the effect of operational variables on the adsorption of lactose in the packed column by a fractional factorial design (24-1) with four independent variables (flow rate, temperature, granu-lometry and bed height) and adsorption capacity as dependent variable. The experimental variables and its levels are shown in Table 1. The experiments (with four replicates) for the removal of lactose were per-

formed following the experimental design presented in Table 2.

Table 2. Experimental plan

Exp. test T G H Q

(°C) (mEsh) (cm) (mL min-1)

1 - + - -

2 + + - +

3 - - - +

4 + - - -

5 - + + +

6 + + + +

7 - - + -

8 + - + +

9 0 0 0 0

10 0 0 0 0

11 0 0 0 0

12 0 0 0 0

Initially, the column was filled with the MIP ads-orbent and then the adsorbent was hydrated for 30 min with deionized water. Next, the milk was fed downwards into the column by a peristaltic pump using the flow rates corresponding to the experimen-tal design. A thermostatic bath was used to maintain the column at a constant temperature by recirculating the water in the system. The milk flow scheme is schematically represented in Figure 1.

Figure 1. Schematic diagram of experimental unit for lactose

removal.

Throughout the experimental tests, samples were collected from the base of the column at random time intervals. These collections were performed until the system reached equilibrium. The samples were analyzed by HPLC to quantify the lactose concen-trations. From the relative lactose concentration (C/C0) data as a function of time, experimental break-through curves were constructed to analyze the influ-ence of the process variables. Then, to evaluate the

Table 1. Levels of experimental factors (codified and uncoded values)

Operating variable -1 0 +1

X1 (temperature, K) 307.1 320.1 333.1

X2 (particle size, mesh) 32 42 60

X3 (bed height, cm) 7.5 10.0 12.5

X4 (flow rate, mL.min-1) 3 6 9


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ideal operating conditions, the adsorption capacity (qo) for each test was calculated by Eq. (1) and the results expressed as milligrams of lactose per gram of adsorbent [8]:

2t00 0

0 00 0

d4C

mVC VC q CDt HC C

επ− = + (1)

where V is the flow rate (mL min-1), ε is the porosity of the bed, D is the particle diameter, H is the height of the particle. C0 is the initial concentration (mg mL-1), C is the concentration at the exit (mg mL-1) from the bed, and m is the mass of the adsorbent (g).

Artificial neural network (ANN)

Characteristics of ANN models ANN techniques have been used to develop

nonlinear models. The number of ideal neurons in the hidden layer is optimized through a learning proce-dure and its output layer provides the results of the processed information. The performance of the net-work is influenced by the selection of the appropriate number of hidden neurons and the transfer functions [24]. The connection between the neurons in separate layers is defined in terms of weights and bias, as shown in Figure 2. The activation of the neuron (Ωj) is given by Eq. (2):

( )ij j i ji

W x βΩ = + (2)

Figure 2. Schematic representation of a single neuron with “n”

inputs and of ANN structure in a feedforward network.

where Wij represents the weight binding of neuron i to

neuron j, xi is the input of neuron i, and βj is the deviation of neuron j.

In the MLP model, the following transfer func-tions can be used: pure linear activation function (purelin), hyperbolic tangent sigmoid (tansig) and logarithmic sigmoid (logsig). These are represented by the equations given in Table 3. The linear function is generally used in the output layer. Logsig is a non-linear and limited function between 0 and 1, and tansig is delimited between -1 and +1. These func-tions are often used in engineering applications in process description [24–26,33,34].

Table 3. Typical transfer functions of the MLP model and their respective equations

Transfer function Equation

Linear ( ) y x x=

Sigmoidal logarithm (Sig. log.) ( ) 1

1 xy xe −=

+

Hyperbolic tangential sigmoid (Hyp. tang. sig.)

2( ) 2 / (1 ) 1xy x e −= + −

The RBF model can also be applied to various tasks due to its high efficiency, speed, and simplicity. It is easy to learn because there are few parameters to be optimized, which include the constant spread of the radial basis function and the number of neurons in the hidden layer. Each layer of an RBF network can have any number of neurons, but more neurons may be required in the hidden layer than the MLP model [23,36]. Furthermore, unlike the MLP networks, which have sigmoid functions, the RBF networks have radial basis functions in the middle layer. The radial basis transfer function is presented in Eq. (3):

2( ) xy x e −= (3)

Development of ANN models The ANN models in this work were developed in

MATLAB software (R2015a) for MLP and RBF archi-tectures. This research was conducted according to the sequence of steps illustrated in Figure 2. The top-ology of the MLP model was evaluated to determine the ideal architecture, i.e., the number of neurons required in the hidden layer, the transfer functions and the training algorithm, which provide the best result. The number of epochs, the learning rate, and the objective error remained unchanged. The RBF model has no change in its transfer function. The constant spread (width of the radial basis functions) and the number of neurons were investigated to achieve the combination that provided the best response.


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The database was constructed from experimen-tal data and the contact time (min) temperature (°C) granulometry (mesh) bed height (cm) and flow rate (ml min-1) were defined as the input variables for the ANN model. The relative concentration (C/C0) was selected as the output parameter of the ANN model. The initial structure of the network is shown in Figure 3.

A total of 249 data were used, which were shuf-fled and divided into three groups: 70% for training, 15% for validation and 15% for testing. Table 4 shows the minimum and maximum values for each set, where the test and validation ranges are contained within the training range. The origin of the conver-gence problem lies in the use of denormalized experi-mental input data to the model [33] so, for the con-duction of the learning process, the database was normalized in a range of -1 to 1.

In order to find the ideal topology of the models, we compared some performance indices, which mea-

sure the efficiency of ANN prediction, such as the coefficient of determination (R2), mean square error (MSE), root of the mean square error (RMSE), sum of the squared error (SSE), mean absolute error (MAE) and relative mean error (RME), which are defined in Eqs. (4)–(9), respectively, where ti is the experimental value, pi is the predicted value, N is the data number, tm is the mean of the experimental values, and pm is the mean of the predicted values:

2

2 12

1

( )1

( )

Ni ii

Ni mi

ptR

t t

=

=

−= − −

(4)

2

1( )

Ni ii

ptMSE

N=

−= (5)

2

1( )

Ni ii

ptRMSE

N=

−= (6)

Figure 3. Structure of the constructed neural network (MLP and RBF).

Table 4. Experimental ranges of the input and output variables for training, validation, and testing

Variable Training Validation Test

Min. Max. Min. Max. Min. Max.

Input Time (min) 1.5 40 2 40 2 30

Temperature (°C) 34 60 34 60 34 60

Granulomety (mesh) 32 60 32 60 32 60

Bed height (cm) 7.5 12.5 7.5 12.5 7.5 12.5

Flow rate (ml min-1) 3 9 3 9 3 9

Output C/C0 0.0077 1.1951 0.0069 1.0855 0.0085 1.0951


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2

1( )

Ni mi

SSE pt=

−= (7)

1

1 Ni ii

MAE ptN == − (8)

1

100 N i i

ii

ptRMEN p=

−= (9)

The R² is a statistical measure of how well the regression line approximates the predicted points to the real data. An R² equal to 1, indicates that the regression line fits perfectly to the data [22]. The MSE measures the sum of the squared difference between the network output and the experimental value divided by the number of data. When the MSE approaches zero, it indicates that the model error is minimal. The RMSE is the square root of the MSE. The lower the value of RMSE, the better the model performance [23]. The SSE is the sum of the squared difference between the experimental data and the mean of the predicted data. The MAE is a quantity used to mea-sure how close predictions are to the eventual out-comes. The MAE describes the average magnitude of the errors, regardless of their signal. MAE values range from zero to ∞, where smaller values are better [23,36]. The RME values are the mean of the relative errors in percentage and are obtained by dividing the difference between the experimental data and that predicted by the model by the predicted value.

Relative importance of variables in lactose removal process

The relative importance of the process variables is the contribution of each of the variables in pre-dicting the dependent variable. In the quantification of the relative importance of the independent variables, used in the prediction of the output variable of the neural network, a method referred to as connection weights (CWs) was used. The CWs algorithm calcul-ates the sum of the products between the weights of the input layer for each intermediate and the final CWs of the hidden neurons to the output layer [36]. The relative importance of a given input variable can be defined by Eq. (10):

1

1 1

mxy yzy

x n mxy yzx y

w wRI

w w

=

= =

=

(10)

where RIx is the relative importance of the input neuron x,

1

mxy yzy w w= is the sum of the product

between the weights of input layers for hidden layers and the weights of hidden layers for output layers, y is the total number of hidden neurons, z is the number of output neurons, and

1 1

n mxy yzx y w w= = is the total

sum of the products among the weights. This approach is based on estimates of the net weights obtained by network generation [36]. It is observed that these estimates of the final weights can vary with the change in initial weights used to start the training process.

RESULTS AND DISCUSSION

Optimization of ANN structure

The MLP model was developed with feedfor-ward architecture. Initially, the number of neurons in the intermediate layer was determined and, as a cri-terion of choice, its validation MSE was analyzed. The Levenberg–Marquardt training algorithm, and tansig between the input layer and the intermediate layer, and purelin for the output layer were initially retained. A three-layer ANN, an input layer with 5 neurons (contact time, temperature, granulometry, bed height and flow rate), a hidden layer with 8 neurons and an output layer with 1 neuron (5-8-1), is established. Fig-ure 4a shows the relation between the number of neurons and MSE for the selected ANN model and confirms that the construction of the model containing eight hidden neurons permits the accurate, repeat-able and predictive behavior of lactose adsorption (minimum MSE of 0.0217).

When the number of neurons in the hidden layer is much greater than necessary, a problem called over-fitting may occur. This phenomenon refers to the reduction in generalization ability that can occur as networks are trained, and it must be avoided [23,28,29,36]. In contrast, an insufficient number of neurons in the hidden layer implies another problem called under-fitting, which is the incompetence of the neural network to solve the addressed process, namely, the model has a complexity inferior to the problem [9,18,19,21,38]. Thus, to avoid these prob-lems occurring in the performance of the production of relative concentration (C/C0), the cross-validation technique was used. Figure 4a shows the results obtained and verify that there was no over-fitting because the validation MSE did not increase relative to the training and test MSE. This decrease in the validation error also indicates an obtained model with generalization capacity of the network.

The effect of the transfer functions on the per-formance of the model was evaluated based on the comparison between the training R² results, validation and test, and the validation MSE. These results are presented in Table 5 for each combination of the transfer functions in the input and intermediate layers.


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Among the results, the ANN-5 model, with tansig between the two layers, provided the best values for R² and MSE, giving the better correlation between the model data and the experimental data. Different training algorithms were also analyzed based on MSE and R², in addition to considering the number of epochs and their interactions. Table 6 presents the results for the various types of model algorithms.

The Levenberg–Marquardt algorithm provided the best performance indices, with fewer times and interactions, as observed by Maghsoudi et al. [3] and Kundu et al. [34]. By finding the ideal parameters of the network architecture, the training was interrupted and the weights and bias used to generate the MLP model are presented in Table 7.

Figure 4. a) Effect of neuron number in the hidden layer and Performance of the MLP model (5-8-1) in the training phase

(MSE = 0.021677 after 14 epochs). b) Effect of neuron number in the hidden layer and training MSE results used to evaluate the ideal spread constant of the RBF model.

Table 5. Determination of the transfer functions for the MLP model with eight neurons in the hidden layer

Model Transfer function 1 Transfer function 2 Training R² Validation R² Test R² MSE of validation

ANN-1 Sig. log. Hyp. tang. sig. 0.9572 0.9624 0.9543 0.0223

ANN-2 Hyp. tang. sig. Linear 0.9514 0.9604 0.9462 0.0316

ANN-3 Sig. log. Linear 0.9583 0.9619 0.9513 0.0293

ANN-4 Hyp. tang. sig. Sig. log. 0.8801 0.9081 0.9551 0.4676

ANN-5 Hyp. tang. sig. Hyp. tang. sig. 0.9607 0.9711 0.9693 0.0217

ANN-6 Sig. log. Sig. log. 0.8419 0.8936 0.9268 0.4693

ANN-7 Linear Sig. log. 0.6542 0.6803 0.6949 0.4932

ANN-8 Linear Linear 0.8289 0.8219 0.8454 0.1215

ANN-9 Linear Hyp. tang. sig. 0.9062 0.9025 0.9551 0.0891


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The general formula of the MLP model for the calculation of the prediction is described in Eq. (11):

( )2

22 12

21

1

21

1

x

j ij ij jx

MLPe

b bw x we

−

−

= − × + × + − + +

(11)

The RBF model was constructed using the same database as the MLP model. Initially, the RBF model was trained with 30 neurons and its objective error was the smallest possible, so its constant spread was determined according to the evaluation of the smallest MSE generated.

Figure 4b shows the data of the constant spread determination step relative to the training MSE. It is observed that an adequate spread constant was 0.2. Figure 4b shows the behavior of the MSE decrease and the number of neurons during optimization of the RBF model. It was verified that the increase in the number of neurons directly influenced the perform-ance of the model and that after 14 neurons, the performance of the model did not change signific-

antly. After obtaining the ideal structure of the RBF network (5-14-1), the training step was completed. Thus, its weights and bias are shown in Table 8. Eq. (12) is a general formula of the RBF model:

( ) ( )2222 1

sj ij ij jsRBF e b e bw x w− −= + + (12)

In order to compare the quality of the production between the two models of ANNs, a test was per-formed with 30% of the database that is not included in the training stage. Figure 5 shows the regression plots for the MLP and RBF models, respectively.

The MLP model presented a R² higher than the RBF model, indicating a better approximation in its prediction.

Efficiency of lactose removal and influence of process variables

According to Table 9, the bed height in the studied range expressed the greatest significant influ-ence on the process, whereas the temperature was the variable of least influence.

Table 6. Optimization of training algorithms

Training algorithm Training R² (70%) Validation R² (15%) Test R² (15%) MSE of validation Epoch Iterations

Gradient descent backpropagation 0.5424 0.5203 0.3183 0.283 1000 1000

Gradient descent with momentum backpropagation

0.5221 0.6287 0.2754 0.2415 1000 1000

Levenberg-Marquardt backpropagation 0.9672 0.9711 0.9751 0.0105 14 20

BFGS quasi-Newton backpropagation 0.9205 0.9469 0.9001 0.0488 34 40

Gradient descent with adaptive learning rate backpropagation

0.8911 0.9023 0.8822 0.0739 429 435

One-step secant backpropagation 0.9092 0.9415 0.9026 0.0596 38 44

Random order incremental training with learning functions

0.7625 0.8091 0.4985 0.1596 29 35

Resilient backpropagation 0.8416 0.8471 0.7607 0.1136 14 20

Scaled conjugate gradient backpropagation

0.8871 0.9022 0.8925 0.0824 44 50

Table 7. Network weights and biases of the MLP model

Neurons Weights from input layers to hidden layers Bias to hidden

layers Weights from hidden

layers to output layers Bias to output layers Time Temperature Granulometry Bed height Flow rate

1 -1.6411 -1.0314 -0.2218 1.4326 1.0767 1.0627 2.4494 -2.2668

2 -1.8958 0.7684 2.5437 0.7062 0.2812 2.2404 1.4611

3 -1.9015 -0.7206 -2.3748 1.8732 1.4295 1.1361 -2.0602

4 4.0264 1.9543 -3.2454 -0.5353 1.3658 3.1884 1.6843

5 -2.1390 1.5682 -1.6511 0.5067 -2.6376 0.6011 -1.9889

6 2.4698 3.0636 -1.1665 -0.7547 -2.5089 2.6911 0.7432

7 -6.4296 1.8824 1.5393 -1.7996 1.7874 -6.2597 -2.5910

8 -1.0912 -0.3890 1.4388 0.1959 1.7282 2.3409 -1.9751


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Table 8. Network weights and biases of the RBF model

Neurons Weights from input layers to hidden layers Bias to hidden

layers Weights from hidden

layers to output layers Bias to output

layers Time Temperature Granulometry Bed height Flow rate

1 -0.9740 0.0000 -0.2857 0.0000 0.0000 4.1628 -1.4422 0.4692

2 -0.9688 1.0000 -1.0000 1.0000 1.0000 4.1628 -1.4518

3 -0.9740 -1.0000 1.0000 1.0000 1.0000 4.1628 -1.4655

4 -0.9584 -1.0000 1.0000 -1.0000 -1.0000 4.1628 -1.3966

5 -0.9688 -1.0000 -1.0000 -1.0000 1.0000 4.1628 -2.3817

6 -0.6104 0.0000 -0.2857 0.0000 0.0000 4.1628 0.1244

7 -0.6104 0.0000 -0.2857 0.0000 0.0000 4.1628 0.0000

8 -0.6987 -1.0000 -1.0000 1.0000 -1.0000 4.1628 -1.2770

9 -1.0000 1.0000 1.0000 -1.0000 1.0000 4.1628 -2.1296

10 -0.8182 -1.0000 -1.0000 -1.0000 1.0000 4.1628 1.1880

11 -0.8182 1.0000 1.0000 1.0000 -1.0000 4.1628 -1.4047

12 -0.8182 1.0000 1.0000 -1.0000 1.0000 4.1628 1.0385

13 0.2208 0.0000 -0.2857 0.0000 0.0000 4.1628 0.2160

14 -0.7662 1.0000 -1.0000 -1.0000 -1.0000 4.1628 -1.3967

15 0.4805 -1.0000 1.0000 1.0000 1.0000 4.1628 0.5903

16 1.0000 0.0000 -0.2857 0.0000 0.0000 4.1628 0.4656

Figure 5. Regression plot showing regression coefficient of MLP and RBF models in 30% of the test data.

Table 9. Quantification of the relative importance of input vari-ables

Variable Temperature Granulometry Bed height Flow rate

Relative imp-ortance (%)

19.3960 22.2805 30.5598 27.7637

The results of the adsorption capacity (q0) of each experimental condition studied, according to the experimental design (Table 1), are presented in Figure 6.

In relation to bed height, the increased lactose removal is associated with a greater amount of filling, the MIP adsorbent is more selective, so it absorbs more lactose, allowing a maximum mass transfer between particles through the bed. It is verified, in these cases, that the greater the height of the bed, for

the same flow, the greater the saturation of the bed, as expected [8,9]. It was observed that the best oper-ating conditions were associated with experimental test 5 (temperature = 34 °C, granulometry = 60 mesh, bed height = 12.5 cm, flow = 9 mL min-1), which provided an adsorption capacity equal to 63.31 mg g-1.

The maximum adsorption capacity of batch chol-esterol related in work of Oliveira et al. [9] was 74.2 mg g-1 cholesterol from molecular imprinting tech-nique for the removal of cholesterol in milk in a batch regime. Ji et al. [39] applied molecularly imprinted polymer for rapid determination of bisphenol A in environmental water and milk samples, and the ads-orption capacity of the adsorbent was found to be 390 and 270 mg g-1. The authors note that the adsorption capacity of the MIP is equivalent to the contribution from the specific binding sites on the adsorbent, and


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this contribution increases with the concentration of bisphenol A because more specific recognition sites are activated at higher BPA concentrations. Cheng et al. [40] studied the application of surface molecularly imprinted silica gel was adopted as the adsorbent of solid-phase extraction for detecting melamine from milk samples. Based on the Langmuir adsorption equation, the saturated adsorption capacity was 7.719 mg g-1. Soleimani et al. [41] used synthesis of molecularly imprinted polymer as a sorbent for solid phase extraction of bovine albumin from whey, milk, urine and serum. The adsorption capacity of the ads-orbent reported by the authors was 24 mg g-1. From the data reported in the literature, it can be seen that the adsorption capacity depends, in addition to the form of preparation of the adsorbent, especially on the molecule to be extracted.

In the process used as a case study in this paper, the best adsorption capacity was obtained in test 5 when the lowest temperature (34 °C), the maximum flow (9 mL min-1) and the maximum bed height (12.5) in the studied range were applied. In contrast, an unsatisfactory result was obtained when a higher temperature (60 °C) and the minimum flow rate (3 mL min-1) were applied (test 6), with the same granulometry and bed height as test 5. The tempera-ture influenced the process when combined with the flow rate. Normally, the increase in temperature is detrimental to the removal efficiency because at higher temperatures there is an increase in molecular agitation, which makes it difficult for the adsorbent to adsorb the lactose molecules.

An unsatisfactory result was also obtained in test 7, when the bed height was maximum (12.5 cm) and the flow rate was minimal (3 mL min-1). Main-taining the temperature and the flow rate, the influ-ence of the granulometry and bed height variables was observed in tests 3 and 5. An increase in the

granulometry and bed height increased the lactose removal because the contact surface area increased, increasing the number of sites available for adsorption.

Comparing model responses and experimental data

With the developed MLP and RBF models, their relative concentration predictions (C/C0) were com-pared graphically to the experimental tests, whose conditions are presented in the experimental design. These data were used to calculate the performance indices: mean values of R², MSE, RMSE, SSE, MAE and RME (Table 10).

Table 10. Mean values of performance indices for the MLP and RBF models in the prediction of tests 1-9

Performance index Model

MLP RBF

R² 0.9751 0.9505

MSE 0.0105 0.0178

RMSE 0.0888 0.1291

SSE 2.4551 2.4348

MAE 0.0646 0.0901

RME / % 34.5456 36.3801

When error indexes approach 0 it means that the error of our model decreases. It is a good mea-sure of accuracy. Smaller values of error indices mean a better performance of the model. These indi-ces (defined in Eqs. (4)-(9)) describe the average magnitude of the errors. It is a good measure of accuracy. Under these conditions, all indices of assay quality were acceptable for both ANN models [28,29,33,42], as shown in Table 10.

The best approximation predictions were related to the MLP and this behavior can be attributed to the fact that this model has a validation step in its learn-ing process [43,44] However, the RBF model was

Figure 6. Adsorption capacity data for the experimental tests.


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efficient in some experimental tests, but, like the MLP model, could not predict some points.

Figures 7–9 show the profiles of the break-through curves under various operating conditions (tests 1−9), with the predictions of the three different

models. These curves describe the adsorption pro-cess of milk lactose, where the final and initial lactose concentrations are equal when the relative concentra-tion reaches the breakpoint, namely when the ads-orbent is saturated [12,15,44].

Figure 7. Breakthrough curves of experimental tests (1, 2 and 3) and prediction of the ANN models.


0 5 10 15 20 25 30

Rel

ativ

e C

once

ntra

tion

(C/C

o)

0

0.5

1

Test data 7 Prediction MLP Prediction RBF

Time (min)

0 5 10 15 20 25 300

0.5

1


0 5 10 15 20 25 300

0.5

1


T: 34 (ºC) G: 32 (mesh) B: 12.5 (cm) F: 3 (mL/min)

T: 47 (ºC) G: 42 (mesh) B: 10 (cm) F: 6 (mL/min)

T: 60(ºC) G: 32 (mesh) B: 12.5 (cm) F: 9 (mL/min)



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Initially, it was noticed that the adsorbent MIP was able to efficiently adsorb the lactose. However, the lactose concentration increased as a function of time and the removal efficiency decreased because the number of active sites in the adsorbent available to adsorb lactose also decreased. At the end of the process, the final concentration was higher than the initial one and this can be explained by the desorption process, which occurs when the adsorbed lactose is released from the adsorbent after saturation. In test 5, a plateau is present, which indicates a period with constant lactose removal. This unusual behavior imp-lied a difficulty in the prediction of the RBF models. However, the dynamics were captured and predicted by the MLP neural model.

The breakthrough curves were atypical com-pared to the ones described in the literature because it surpassed the breakpoint. This behavior may be because milk is a multicomponent mixture [8,9]. For these fluids, the C/C0 ratio can extrapolate the bound-ary of the unit, considering the different adsorption affinities of the various solutes. Curves of this type reflect the phenomenon of sequential exchange, in which a more selective solute is able to remove, from the site, another previously exchanged solute, which is released into the liquid medium [45]. Similar results have been reported by another researcher who used an adsorption process in a multicomponent system [46].

As can be seen from the breakthrough curves (Figures 7 and 9), higher breakpoint time of the pro-cess was achieved at a lower flow rate. As the flow rate increases, breakthrough time was obtained earlier. This can be explained by the fact that the dif-fusion process that controls the adsorption becomes slow, and hence, the adsorbent needs more time to bind with the lactose efficiently. The decrease in the breakthrough time with an increase in the flow rate may be due to a fixed saturation capacity of the bed based on the same driving force giving rise to a shorter time for saturation at higher flow rates [45,47].

It was verified that the model MLP obtained the most satisfactory performance even for the profiles that presented the plateau, thus, demonstrating that the model is apt to predict nonlinear problems. In addition, this model was able to predict the experi-mental data, regardless of the conditions analyzed. Hence, the ANN modeling technique is promising to describe processes involving non-linear problems and can be used to optimize the operational conditions of lactose removal. The precision of data influences the applicability of the models.

CONCLUSION

In the present work, milk lactose adsorption in a fixed bed column with a MIP adsorbent was modeled using an empirical approach by neural networks. Neural models efficiently predicted the nonlinear behavior of relative lactose concentration (C/C0) in milk from interactions between the contact time (min), temperature (°C), granulometry (mesh), bed height (cm) and flow rate (ml min-1) parameters. The MLP model with Levenberg-Marquardt algorithm had a mean R² of 0.9751, MAE of 0.064 and RMSE of 0.0888 in the prediction of the experimental tests of this study. The RBF model also showed a satisfactory performance, which had an average R² of 0.9505, MAE of 0.090 and RMSE of 0.1291. Both models give highly accurate predictions, since the performance indices values are close. The high coefficient of deter-mination of both networks (for the whole data set) together with the important statistical parameters indi-cated that the neural networks have been well trained. These ANN models aimed to predict the breakthrough curve in lactose adsorption. The results showed that the ANN is a powerful technique to use when dealing with multicomponent fluid processes. Besides being simple to implement and requiring low computational time, the neural network models satis-factorily described the milk lactose adsorption and these models can provide an additional contribution to optimize and a better understanding of the dynamic of the process. Furthermore, this allowed a feasible way for on-line control of the process.

Nomenclature

Symbols b1j bias to hidden layers b2 bias to output layers C0 initial concentration (mg mL-1) C concentration at the exit (mg mL-1) from the bed D particle diameter (cm) H height of the particle (cm) m mass of the adsorbent (g) N data number pi predicted value pm mean of the predicted values. q0 adsorption capacity (mg g-1) ti experimental value tm mean of the experimental values V flow rate (mL min-1) xi input of neuron i xij input values Wij weight binding of neuron i to neuron j


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wij and wxy weights from input layers to hidden layers

w2j and wyz weights from hidden layers to output layers

Greek symbols ε porosity of the bed (mesh) βj deviation of neuron j

Acknowledgment

The authors are grateful to the Brazilian financial support of CAPES, CNPq and FAPITEC/SE.

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MANUELA SOUZA LEITE MATHEUS A. SANTOS

EULINA M. F. COSTA ACENINI BALIEIRO

ÁLVARO S. LIMA ODELSIA L. SANCHEZ CLEIDE M. F. SOARES

Tiradentes University, Institute of Technology Research, Farolândia,

Aracaju, Sergipe, Brazil

NAUČNI RAD

MODELOVANJE UKLANJANJA LAKTOZE IZ MLEKA ADSORPCIONOM KOLONOM KORIŠĆENJEM MLP I RBF VEŠTAČKIH NEURONSKIH MREŽA

Veštačke neuronske mreže (ANN) su efikasne u modelovanju nelinearnih procesa, jednostavne su za implementaciju i zahtevaju kratko vreme računanja. U ovom radu, kontinualni proces adsorpcije laktoze u koloni sa fiksnim slojem molekularno utisnutim polimernim (MIP) adsorbentom je modelovan korišćenjem ANN tehnike. Ovi neuralni modeli omogućili su predviđanje relativne koncentracije laktoze (C/C0) iz interakcija između procesnih promenljivih: vremena kontakta, temperature, veličine čestica, visine sloja i protoka. Modeli ANN razvijeni su u MATLAB-u uz pomoć višeslojnih perceptrona (MLP) i mreže radijalnih baznih funkcija (RBF). MLP model je razvijen korišćenjem tro-slojne povratne mreže sa 5, 8 i 4 neurona u prvom, drugom i trećem sloju. Predložena je i RBF mreža i njena performansa je upoređena sa tradicionalnim tipom mreže. Najbolji model arhitekture RBF je razvijen koristeći 5, 14 i 1 neuron u prvom, drugom i trećem sloju. Korišćenjem ovih pristupa, razvojeni su inovativni matematički modeli koji su pri-menjeni na višekomponentni adsorpcioni sistem za mleko. Dobijeni modeli krivih pro-boja za adsorpciju laktoze se dobro slažu sa eksperimentalnim podacima. Kriterijumi, kao što su R², MSE, RMSE, SSE, MAE i RME, korišćeni su za procenu pouzdanosti i tačnosti modela. Poređenjem ANN modela mogu se predvideti krive proboja za uklanja-nje laktoze iz mleka procesom adsorpcije. Ipak, MLP model je tačniji i sa većim koefici-jentom korelacije (R2 = 0,975) i manjim vrednostima greški. Tačnost modela je potvrđen poređenjem predviđenih i eksperimentalnih podataka. Rezultati su pokazali da oba modela efikasno opisuju nelinearni proces adsorpcije laktoze u koloni sa fiksnim slojem.

Ključne reči: ANN, MLP, RBF, kolona sa fiksnim slojem, laktoza, modelovanje krive proboja.

MODELING OF MILK LACTOSE REMOVAL BY COLUMN … No4_p369-382... · 2019-12-26 · printed polymers...

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