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Artificial neural network modeling of mass transfer during osmotic dehydration of kaffir lime peel
Journal of Food Engineering 98 (2010) 214–223
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Artificial neural network modeling of mass transfer during osmotic dehydration of kaffir lime peel S. Lertworasirikul *, S. Saetan Department of Product Development, Faculty of Agro-Industry, Kasetsart University, 50 Phaholyothin Rd., Chatuchak, Bangkok 10900, Thailand
a r t i c l e
i n f o
Article history: Received 8 October 2009 Received in revised form 22 December 2009 Accepted 30 December 2009 Available online 6 January 2010 Keywords: Kaffir lime Osmotic dehydration Mathematical model Artificial neural network Mass transfer
a b s t r a c t Mass transfer of kaffir lime peel during osmotic dehydration was investigated in this paper. Processing factors were solute concentrations, process temperatures, and immersion time. The results showed that increasing solute concentration and process temperature resulted in a higher reduction in moisture contents of kaffir lime peel and increase in water loss and solid gain rates. Analysis of variance showed significant effects (P < 0.05) of all processing factors except process temperatures for water loss. Multilayer feedforward neural network (MFNN) was proposed to predict percentages of water loss and solid gain of kaffir lime peel during osmotic dehydration based on three processing factors as inputs. The best network with the lowest average mean squared error (MSE) of 0.0066 and the highest average regression coefficient (r2) of 0.9725 from normalized training and validating data sets was composed of one hidden layer with five hidden neurons and used Levenberg–Marquardt algorithm as a training algorithm. A simulation test showed good generalization of the successfully trained MFNN model with the average MSE of 6.5813 and 5.9340, and average r2 of 0.9745 and 0.9632, respectively, for water loss and solid gain. Compared with multiple linear regression models, MFNN was found to be more suitable for predicting water loss and solid gain during the OD process of kaffir lime peel. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Kaffir lime fruit (Citrus hystrix DC.) is a native lime fruit grown in Southeast Asia, commonly used in flavor, food, beverage, and fragrance industry. Juice of kaffir lime is principally used as a cleaner for clothing and hair, refreshing perfumes and natural deodorizers. After the juice is extracted from the fruit, there remain residues comprising of peel (flavedo and albedo), pulp (juice sac residue), rag (membranes and cores), and seeds. The outer green peel (flavedo) of kaffir lime is commonly used in curry pastes and traditional medicines, while the inner white peel (albedo), which is rich in pectin and dietary fiber, is usually discarded or becomes a feed for animals (Sinclair, 1984). The inner peel of kaffir lime, as a major waste, has become a substantial burden to the environment. Hence it is necessary to find a feasible way to dispose of the kaffir lime peel in order to have a positive environmental impact or to turn them into useful products. To add value to kaffir residue, the production of osmotic dehydrated kaffir lime peel is an interesting application. Osmotic dehydration (OD) is a pre-processing step prior to drying and freezing of food products. An OD process of food generally * Corresponding author. Tel.: +662 562 5012; fax: +662 562 5005. E-mail addresses: [email protected], [email protected] (S. Lertworasirikul). 0260-8774/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2009.12.030
involves significant removal of water from food by soaking it in a hypertonic solution, so that water and little amounts of natural solutes are transferred from the food to the solution and solutes migrate from the solution into food. A mass transfer rate during the OD process depends on several factors such as concentration and temperature of an OD solution, immersion time, size, and shape of products, an osmotic solution to fruit ratio, and a type of osmotic agents (Lerici et al., 1985; Raoult-Wack, 1994; Rastogi et al., 1997). Much work has been done in developing models to predict the mass transfer kinetics of an OD process at an atmospheric pressure. Nevertheless, it is not an easy task to develop a mathematical model incorporating all of the factors involved in an OD process (Ochoa-Martínez and Ayala-Aponte, 2007). From a strict sense, mathematical models for an OD process can be classified into theoretical models (or knowledge-driven models) and empirical models (data-driven models). Theoretical models are developed from assumptions about phenomena and are validated with experimental data. Theoretical models, which describe process mechanisms, are sometimes called mechanistic models. They provide detailed information about all process variables, but their determinations of unknown physical parameters are computationally intensive and time-consuming. For an OD process, the models are usually based on the mechanisms of heat and mass transfer. The most widely used theoretical OD model has been a diffusion model, which can be derived from the Fick’s law of diffusion in unsteady
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Nomenclature xi x zl z m0 mt M0 Mt tlk tm tlm
input variable i vector of input xi predicted output l vector of output initial weight of solids (dry matter) of sample (g) weight of solids (dry matter) of sample after osmotic dehydration for time t (g) initial weight of sample (g) weight of sample after osmotic dehydration for time t (g) experimental output l of the observation k average value of all experimental outputs average value of experimental output l
state (Beristian et al., 1990; Salvatori et al., 1999). Some other authors have proposed an approach based on a cellular structure (Toupin et al., 1989; Yao and Le Maguer, 1996). On the other hand, empirical models are developed from experimental data. Their uses are limited because they are only capable of representing data at conditions similar to those on which such models were developed (Trelea et al., 1997). However, recent work has shown that the empirical models give a reasonable fit to experimental data and can successfully predict mass transfer mechanism (Ochoa-Martínez and Ayala-Aponte, 2007). Also, the main advantage of an empirical modeling approach is that it has a capability to learn from experimental data. Many authors have used a simplified version of the non-steady state form of Fick’s law to model OD mechanism. The empirical models, which these authors proposed, considered proportionality relationships between a concentration parameter and the square root of time (Conway et al., 1983; Hawkes and Flink, 1978; Magee et al., 1983). In these models, simultaneous water and solute transfer is resolved to a simple transfer of water or solute, which is inefficient as far as the technological control of both dewatering and impregnation effects are concerned (Raoult-Wack, 1994). In case of food processes, nonlinear models are more suitable due to variability and nonlinear behavior of natural products. In addition, many production processes involve with fluctuation in process conditions, and rely to a great extent on the skill and experience of operators. Therefore, artificial neural network (ANN) models recently have gained momentum for process modeling and control. ANN models are recognized as a good tool for dynamics modeling because it does not require parameters of physical models, has an ability to learn the solution of problems from a set of experimental data, and is capable to handle complex systems with nonlinearities and interactions between decision variables. ANN models were constructed by interconnecting many nonlinear computational elements, known as neurons or nodes, operating in parallel, and arranging in patterns similar to biological networks (Smith, 1996). ANN models can be classified into two classes: supervised networks and unsupervised networks. Supervised networks require a training algorithm and a training data set to adjust the connection weights, while unsupervised networks can adjust weights by themselves to achieve the required results without using any training algorithm. Supervised networks are mostly used for classification, prediction, and function approximation. Unsupervised networks are used for clustering and content addressable memory. For prediction and control of food processing operations, supervised networks are suitable (Jindal and Chauhan, 2001; Smith, 1996). Applications of ANN models include extrusion processes, filtration, drying processes, etc. (Bardot et al., 1994; Dornier et al., 1995; Jindal and Chauhan, 2001). Due to the complexity of the osmotic
zlk i l k m 0 t L K MSE r2 WL SG
predicted output l of the observation k index of input variables index of output variables index of observations average value starting time (time 0) sampling time (hour) number of outputs total number of observations mean squared error regression coefficient water loss (%) solid gain (%)
dehydration process, several authors have recommended the use of ANN for modeling mass transfer kinetics during the OD process (Baruch et al., 2004; Ochoa-Martínez and Ayala-Aponte, 2007; Shi and Le Maguer, 2002). Nevertheless, few works have been done on the application of ANN to model OD process. Also, there was no study on the effect of OD conditions on water loss and solid gain of kaffir lime peel. The purpose of this work was to investigate the effect of process parameters (solute concentrations, process temperatures and immersion time) on mass transfer in the OD process of kaffir lime peel. ANN models were developed to predict water loss (WL) and solid gain (SG) for the OD process of the kaffir lime peel. The performance of ANN was then compared with the performance of multiple linear regression (MLR) models. 2. Materials and methods 2.1. Experimental procedures 2.1.1. Sample preparation Kaffir limes (Citrus hystrix DC.) were purchased from a local market in Bangkok, Thailand. The kaffir limes were sorted visually for the same size. The samples were washed and the exterior green peels were removed from the albedo. Then, the samples were cut into halves perpendicular to the apex-base direction, handsqueezed, and the seeds and pulp were removed before dehydration. The kaffir lime peels were composed of albedo and rag as shown in Fig. 1. The initial weight of each sample was 6 g. The average initial moisture content of the sample was 91.05% in wet basis. 2.1.2. Osmotic solution Sucrose (food grade) dissolved in distilled water was used as the osmotic agent. The solute contents varied from 50% to 70% (w/w). The weight ratio of the sample to the solution was 1:5 (w/w) in order not to dilute the osmotic solution by water removal from the sample during the experiments and in concerns with economics and transfer of water loss and solid gain (Lenart and Flink, 1984; Kaymak-Ertekin and Sultanoglu, 2000; Zenoozian and Devahastin, 2009). 2.1.3. Osmotic dehydration The experiment was conducted using a 5 5 13 factorial completely randomized design (CRD) with three main factors (concentrations, temperature levels, and osmotic time). The OD process was performed in a beaker containing the osmotic solutions with the concentrations of 50%, 55%, 60%, 65%, and 70% w/w and
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are performed using five different partitions (five cross-validation experiments). Mean squared errors (MSE) and regression coefficients (r2) between the predicted values from the MLR models and the experimental values were calculated by using Eqs. (8) and (9). Then average MSE and average r2 from five cross-validation experiments were used as performance criteria for MLR modeling. 2.3. Artificial neural network modeling In this study, a supervised network was used to model the OD process of the kaffir lime peel. A widely used ANN model for prediction and control of food processing operations is a multilayer feedforward neural network (MFNN), which has more than one layer as shown in Fig. 2. An MFNN model can learn nonlinear and complex relationships by using a training algorithm with a set of input–output pairs (Lertworasirikul, 2008). An MFNN model was developed to predict the percentages of water loss (z1) and solid gain (z2) of osmotic dehydrated kaffir lime peel simultaneously based on three input variables; solute concentration (x1), process temperature (x2), and immersion time (x3) as follows.
2
Fig. 1. Kaffir lime peel before osmotic dehydration.
x1
3
6 7 x ¼ 4 x2 5; solution temperature levels of 30, 35, 40, 45, 50 °C. A mechanical stirrer (JEIOTECH HP-3000, Korea) with a diameter of 100 mm provided agitation of the osmotic solutions and the rotation speed was monitored at 100 rpm. For each temperature and concentration, the kaffir lime peels were weighed and placed into a beaker to dehydrate for 12 h. After every 1 h time interval, the samples were removed from the solute solution, rinsed with deionised water and blotted with absorbent paper to remove excess surface solution. Three pieces of the samples were drawn to weigh and determine the average moisture content (%, wb) using a vacuum oven (model VD53, Binder, Germany) for drying to constant weight at 70 °C under a reduced pressure of 10 kPa (adaptation of method 934.06 AOAC, 2000). Then, the percentages of water loss (%WL) and solid gain (%SG) of the samples were calculated from Eqs. (1) and (2), respectively, and used as outputs for MLR and ANN modeling.
%WL ¼
%SG ¼
ðM 0 m0 Þ ðM t mt Þ 100 M0
mt m0 100 M0
ð1Þ
ð2Þ
2.2. Analysis of variance and multiple linear regression modeling The development of MLR models and the analysis of variance were done by using a regression tool in Microsoft Excel. MLR models were developed to predict the percentages of water loss (z1) and solid gain (z2) of osmotic dehydrated kaffir lime peel based on three input variables; x1 was solute concentration (50%, 55%, 60%, 65%, 70% w/w), x2 was process temperature (30, 40, 45, 50 °C), and x3 was immersion time (0–12 h). The significant effect of the input variables over the outputs was checked by conducting analysis of variance from the whole set of data at 95% confidence level. To develop a MLR model for each output, available data were randomized and partitioned into two subsets for cross validation. The first subset (85%) was used for developing the model. The second subset was the test set (15%), which was used to examine the network generalization capability. These data subsets were also used for ANN modeling but the first subset here was divided into a training set and a validation set in ANN modeling to prevent over-fitting. To reduce variability, five rounds of cross validation
z¼
x3
z1
ð3Þ
z2
Available data were randomized and divided into three subsets for cross validation. The first subset was the training set (70%), which was used for computing the gradient and updating the network weights and biases. The second subset was the cross validation set (15%), which was used to prevent over-fitting. The last subset is the test set (15%), which was not used during the training but was used to examine the network generalization capability (Smith, 1996). Due to the different ranges of each input and each output, the inputs and outputs were normalized into the interval [1, 1] before feeding into the network. The MFNN model was designed using neural network toolbox in MATLAB version 6.5. Levenberg–Marquardt algorithm (Trainlm) was used as a training algorithm in this study. Trainlm is a network training function that updates weight and bias states according to Levenberg–Marquardt optimization. A transfer function was a logarithmic sigmoid transfer function (logsig) in the first layer of the network, and a linear transfer function (purelin) was used in the second layer.
logsigðxÞ ¼
1 ; ð1 þ ex Þ
ð4Þ
purelinðxÞ ¼ x
ð5Þ
Fig. 2. Structure of MFNN.
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Fig. 3. Effects of process temperatures and immersion time on average moisture content (%, wb) at the concentrations of 50%, 55%, 60%, 65%, and 70%.
Fig. 4. Effects of solute concentrations and immersion time on average water loss (%) at process temperature of 30, 35, 40, 45, and 50 °C.
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There is no fixed rule for determining the required hidden layers and nodes. In general, one hidden layer has been found to be adequate, and only in some cases, a slight advantage may be gained by using two hidden layers (Hecht-Nielsen, 1989). Therefore, the number of hidden layers was fixed at one, while the number of neurons in the hidden layer was investigated. In this study, the networks with 1, 3, 5, 7, and 9 hidden neurons were compared. The performance of the networks was measured by mean squared error (MSE) and regression coefficient (r2) between the predicted values of the network and the target or experimental values as follows.
PK PL MSE ¼
k¼1
l¼1 ðzlk
tlk Þ2
;
ð6Þ
PK PL 2 l¼1 ðzlk t lk Þ r 2 ¼ 1 Pk¼1 K PL 2 k¼1 l¼1 ðt lk t m Þ
ð7Þ
KL
The MSEl and r 2l of each output l could also be calculated by using the following equations.
PK MSEl ¼
k¼1 ðzlk
t lk Þ2
;
ð8Þ
PK ðzlk t lk Þ2 r2l ¼ 1 PKk¼1 2 k¼1 ðt lk t lm Þ
ð9Þ
K
During the learning process, training and validating data sets were simultaneously used to avoid over-fitting. This was done by 5-fold-cross-validation and in each cross validation, initial weights were randomly selected three times for training. The learning stopped after 1000 iterations, MSE became zero, or the performance on the validation vectors failed to improve or remains the same for five epochs in a row. After the termination of the learning process, weights and biases of the network were obtained. For each cross validation, the network with minimum MSE and maximum r2 from using three initial weights was selected. Then average MSE and average r2 from five cross validations were calculated to find the best network. The best network model was the network having the minimum MSE and maximum r2 using the normalized
Fig. 5. Effects of solute concentrations and immersion time on average solid gain (%) at process temperature of 30, 35, 40, 45, and 50 °C.
Fig. 6. Effects of process temperatures and solute concentrations on average water loss (%) at equilibrium.
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3. Results and discussion 3.1. Effect of process parameters on osmotic dehydration of kaffir lime peel From the OD process of kaffir lime peel, the average moisture content (%, wb), the percentages of water loss and solid gain were measured at every 1 h time interval for each process parameter. 3.1.1. Moisture content The effects of process parameters on the average moisture contents of osmotic dehydrated kaffir lime peel were shown in Fig. 3. At each solution concentration and process temperature, average moisture content of the samples decrease significantly during the first period of OD process (the first 2 h) and then decrease slowly until the system reached the equilibrium. An increase in solute concentration resulted in a higher reduction in moisture content.
Fig. 7. Effects of process temperatures and solute concentrations on average solid gain (%) at equilibrium.
predicted and target data, and this network was not over-fitting the data. The best network was then used to predict outputs using the testing data set to further check if the network achieved good generalization.
3.1.2. Water loss and solid gain The average values of water loss and solid gain during the OD process of kaffir lime peel were shown in Figs. 4 and 5, respectively.
Table 1 Analysis of variance and coefficients of input variables from multiple linear regression modeling using the whole set of data. Variable
Water loss
Concentration (% w/w) Temperature (°C) Time (h)
Solid gain
P value
Coefficient
P value
Coefficient
1.17 107 0.3131 7.51 1051
0.47558 0.08868 3.0547
3.26 1018 0.0200 1.1 1046
0.66467 0.16805 2.3524
Table 2 MSE and r2 of water loss from the development and testing processes of multiple linear regression models. Regression model
Cross-validation experiment
MSE of water loss
r2 of water loss
Regression model for water loss
Development process
1 2 3 4 5 Average SD
121.7118 123.4582 125.3109 106.7957 130.4860 121.5525 8.8791
0.5296 0.5381 0.5343 0.5211 0.5314 0.5309 0.0064
z1 = 0.5996 + 0.4561x1 + 0.0931x2 + 3.0452x3 z1 = 1.9382 + 0.5149x1 + 0.0630x2 + 3.0811x3 z1 = 1.2287 + 0.4945x1 + 0.0777x2 + 3.0681x3 z1 = 2.8013 + 0.4767x1 + 0.0552x2 + 2.7824x3 z1 = 0.7251 + 0.4369x1 + 0.1064x2 + 3.1165x3
Testing process
1 2 3 4 5 Average SD
126.7564 117.5176 106.3982 219.0499 77.9198 129.5284 53.3022
0.5427 0.4817 0.5128 0.6099 0.5210 0.5336 0.0479
Table 3 MSE and r2 of solid gain from the development and testing processes of multiple linear regression models. Regression model
Cross-validation experiment
Development process
1 2 3 4 5 Average SD
Testing process
1 2 3 4 5 Average SD
r2 of solid gain
Regression model for solid gain
82.7157 82.8077 82.1708 73.3755 86.8484 81.5836 4.9552
0.5436 0.5584 0.5596 0.5364 0.5474 0.5491 0.0099
z2 = 21.8748 + 0.6574x1 + 0.1723x2 + 2.3436x3 z2 = 24.0919 + 0.7148x1 + 0.1374x2 + 2.3847x3 z2 = 22.2317 + 0.6773x1 + 0.1431x2 + 2.3893x3 z2 = 20.3798 + 0.6647x1 + 0.1624x2 + 2.1309x3 z2 = 21.4906 + 0.6469x1 + 0.1664x2 + 2.3952x3
78.4212 79.1853 81.8526 136.4691 55.3594 86.2575 30.0280
0.5676 0.4767 0.4640 0.6136 0.5336 0.5311 0.0625
MSE of solid gain
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The rapid changes in water loss and solid gain took place in the first 2 h of the OD process. The most significant changes in water loss and solid gain took place in the beginning period were apparently due to the significant difference in the osmotic pressure of the kaffir lime peel and that of the osmotic solution. During the osmotic treatment, increased solute concentrations resulted in increased water loss and solid gain rates. It was also observed that increasing process temperatures resulted in slightly increased average water loss and increased average solid gain as shown in Figs. 6 and 7, respectively. Fig. 6 and 7 showed the average water loss and average solid gain with their standard errors. These results were presumably due to changes in physical properties of the samples and viscosity of the osmotic solution. Higher temperatures cause the
increase in membrane permeability, which promotes swelling and plasticization of the cell membranes. In addition, increasing temperatures causes a reduction in solution viscosity, reducing external resistance to mass transfer and making water and solute transport easier. These results were in agreement with previous works by _ Agarry et al. (2008), Hawkes and Flink (1978), Ispir and Tog˘rul (2009), Lenart and Flink (1984). 3.2. Analysis of variance and multiple linear regression modeling Analysis of variance for water loss and solid gain was shown in Table 1, which showed a significant effect (P < 0.05) of all variables except temperature for water loss. Since the MFNN model was
Table 4 MSE and r2 from the learning process and testing process of MFNN. Number of hidden nodes
Cross-validation experiment
MSE from learning process
r2 from learning process
MSE from testing process
r2 from testing process
1
1 2 3 4 5 Average SD
0.0366 0.0340 0.0365 0.0360 0.0339 0.0354 0.0013
0.8477 0.8641 0.8569 0.8252 0.8653 0.8518 0.0165
0.0250 0.0349 0.0365 0.0316 0.0360 0.0328 0.0048
0.9018 0.8283 0.8223 0.9209 0.7608 0.8468 0.0649
3
1 2 3 4 5 Average SD
0.0093 0.0081 0.0084 0.0080 0.0082 0.0084 0.0005
0.9614 0.9677 0.9669 0.9611 0.9673 0.9649 0.0033
0.0052 0.0079 0.0093 0.0098 0.0074 0.0079 0.0018
0.9796 0.9605 0.9532 0.9761 0.9508 0.9640 0.0132
5
1 2 3 4 5 Average SD
0.0080 0.0064 0.0067 0.0060 0.0058 0.0066 0.0009
0.9668 0.9744 0.9738 0.9708 0.9769 0.9725 0.0039
0.0057 0.0055 0.0079 0.0077 0.0072 0.0068 0.0011
0.9768 0.9724 0.9602 0.9816 0.9522 0.9686 0.0121
7
1 2 3 4 5 Average SD
0.0075 0.0062 0.0065 0.0062 0.0076 0.0068 0.0007
0.9688 0.9753 0.9747 0.9700 0.9698 0.9717 0.0030
0.0043 0.0055 0.0089 0.0077 0.0062 0.0065 0.0018
0.9828 0.9724 0.9553 0.9808 0.9593 0.9701 0.0124
9
1 2 3 4 5 Average SD
0.0072 0.0064 0.0067 0.0065 0.0071 0.0068 0.0004
0.9702 0.9743 0.9738 0.9686 0.9718 0.9717 0.0024
0.0047 0.0076 0.0086 0.0074 0.0058 0.0068 0.0016
0.9810 0.9625 0.9571 0.9818 0.9620 0.9620 0.0116
Table 5 MSE and r2 from the learning and testing processes of the successfully trained MFNN with 5-hidden-nodes using unnormalized input and output data. MFNN Process
Cross-validation experiment
Learning
1 2 3 4 5 Average SD
Testing
1 2 3 4 5 Average SD
r2 of water loss
MSE of solid gain
r2 of solid gain
6.5808 6.3633 6.3279 6.2606 5.9589 6.2983 0.2245
0.9751 0.9770 0.9783 0.9722 0.9785 0.9762 0.0026
7.7093 5.4580 6.0121 4.9333 4.8419 5.7909 1.1701
0.9582 0.9715 0.9691 0.9687 0.9749 0.9685 0.0063
6.4601 5.1786 4.6601 10.3120 6.2958 6.5813 2.2177
0.9780 0.9778 0.9789 0.9777 0.9602 0.9745 0.0080
4.3288 4.9243 8.9531 4.7541 6.7095 5.9340 1.9173
0.9762 0.9682 0.9407 0.9858 0.9449 0.9632 0.0197
MSE of water loss
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Fig. 8. The predicted and experimental water loss (%) and solid gain (%) from the learning and testing processes of the 5-hidden-nodes neural network for pilot experiments (1)-(5).
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developed to predict both water loss and solid gain simultaneously, all variables should be used for the MFNN modeling. MSE, r2 and MLR equations from the development and testing processes of the MLR modeling for water loss and solid gain were shown in Tables 2 and 3, respectively. It was seen that average MSE was high and average r2 was low; therefore, the MLR models were not a good model for prediction of water loss and solid gain from the OD process of kaffir lime peel. 3.3. Artificial neural network modeling MSE and r2 from the learning and testing processes using normalized data were shown in Table 4. The third and fourth columns of Table 4 displayed MSE and r2 from the learning process of the networks, while the fifth and sixth columns displayed MSE and r2 from the testing process of the networks. The results from Table 4 showed that the average MSE tended to decrease and the average r2 tended to increase as the number of hidden nodes was increased until it reached 5-hidden-nodes. After that there was no significant improvement in average MSE and average r2 for both learning and testing processes. This agrees with what other works (Ochoa-Martínez and Ayala-Aponte, 2007; Lertworasirikul, 2008; Singh et al., 2009) had also reported about network performance due to the number of hidden nodes. Increasing more hidden nodes would increase more complexities and take more computational time. Therefore, the MFNN model with 5-hidden-nodes was chosen as the best network in this study. Low standard deviations (SD) of MSE and r2 from five pilot experiments also showed that the network was reliable and any MFNN models from these five experiments could be used for the prediction of water loss and solid gain of osmotic dehydrated kaffir lime peel. Table 5 showed MSE and r2 for water loss and solid gain of the successfully trained networks with 5-hidden-nodes using unnormalized input and output data. The average MSE of water loss and solid gain from the five pilot experiments of learning and testing processes were reasonably low and the average r2 for the water loss and solid gain were high. Fig. 8 showed the comparison between the predicted and experimental water loss and solid gain from cross-validation experiments (1)–(5) of the network with 5-hidden-nodes. The results in this figure showed that the plots between the predicted and experimental water loss and solid gain were almost straight line for both learning and testing processes. These results showed good agreements between the predicted and experimental values in all experiments. Therefore, the developed MFNN model had a good generalization in predicting water loss and solid gain of osmotic dehydrated kaffir lime peel. Compared with the MLR models, the MFNN models performed better due to the high nonlinearity and complex relationships of the system. These results were in agreement with previous works by other authors (Chen et al., 2001; Ochoa-Martínez and Ayala-Aponte, 2007). 4. Conclusions This paper studied the OD process of kaffir lime peel. The study on the effects of process parameters on moisture content, water loss, and solid gain showed that increasing solute concentration and process temperature resulted in a higher reduction in average moisture content of kaffir lime peel and increase in average water loss and average solid gain rates. Significant changes in moisture contents, water loss, and solid gain took place in the first period (the first 2 h) of the OD process following with slightly changes until the system reached the equilibrium. The analysis of variance showed a significant effect (P < 0.05) of all process parameters on
water loss and solid gain except process temperature for water loss. In this study, MLR and MFNN models were developed for the prediction of water loss and solid gain of osmotic dehydrated kaffir lime peel. The developed MLR and MFNN models used solute concentrations, osmotic temperatures and immersion time as inputs to predict network outputs, which were water loss and solid gain. The results showed that MFNN model with 5-hidden-nodes using Levenberg–Marquardt algorithm was suitable for predicting the water loss and solid gain of kaffir lime peel during the OD process. From both learning and testing processes of MFNN, the average MSE between predicted and experimental values of water loss and solid gain were reasonably low and the average r2 between predicted and experimental values of water loss and solid gain were high. Compared with MLR models, the MFNN models performed better due to the complexity and nonlinearity of the OD system. Therefore, the developed MFNN model was suitable for predicting water loss and solid gain of kaffir lime peel during the OD process.
Acknowledgment This work was funded by Kasetsart University Research and Development Institute, 2008.
References Agarry, S.E., Yusuf, R.O., Owabor, C.N., 2008. Mass transfer in osmotic dehydration of potato: a mathematical model approach. Journal of Engineering and Applied Sciences 3 (2), 190–198. AOAC, 2000. Official methods of analysis, 17th ed. Association of Official Analytical Chemists, Washington, DC. Bardot, I., Martin, N., Trystram, G., Hossenlopp, J., Rogeaux, M., Bochereau, L., 1994. A new approach for the formulation of beverages. Part II: interactive automatic method. Lebensmittel-Wissenschaft und-Technologie 27 (6), 513–521. Baruch, I., Genina-Soto, P., Nenkova, B., Barrera-Cortés, J., (2004). Neural model of osmotic dehydration kinetics of fruits cubes. In: Bussler, C., Fensel, D. (Eds.), Artificial Intelligence: Methodology, Systems, and Applications: 11th International Conference, AIMSA 2004, Varna, Bulgaria, September 2–4 2004, Proceedings, Springer-Verlag, Berlin, pp. 312–320. Beristian, C.I., Azuara, E., Cortes, R., Garcia, H.S., 1990. Mass transfer during osmotic dehydration of pineapple rings. International Journal of Food Science and Technology 25 (5), 576–582. Chen, C.R., Ramaswamy, H.S., Alli, I., 2001. Prediction of quality changes during osmo-convective drying of blueberries using neural network models for process optimization. Drying Technology 19 (3–4), 507–523. Conway, J., Castaigne, F., Picard, G., Voxan, X., 1983. Mass transfer considerations in the osmotic dehydration of apples. Canadian Institute of Food Science and Technology 16 (1), 25–29. Dornier, M., Decloux, M., Trystram, G., Lebert, A., 1995. Dynamic modeling of crossflow microfiltration using neural networks. Journal of Membrane Science 98 (3), 263–273. Hawkes, J., Flink, J.M., 1978. Osmotic dehydration of fruit slices prior to freeze dehydration. Journal of Food Processing and Preservation 2 (4), 265–284. Hecht-Nielsen, R. (1989). Theory of the backpropagation neural network. In Proceedings of International Joint Conference on Neural Networks, Washington, DC, pp. 593–605. _ _ Ispir, A., Tog˘rul, I.T., 2009. Osmotic dehydration of apricot: kinetics and the effect of process parameters. Chemical Engineering Research and Design 87 (2), 166– 180. Jindal, V.K., Chauhan, V., 2001. Neural networks approach to modeling food processing operations. In: Irudayaraj, J. (Ed.), Food Processing Operations Modeling: Design and Analysis. Marcel Dekker, New York, pp. 305–342. Kaymak-Ertekin, F., Sultanoglu, M., 2000. Modelling of mass transfer during osmotic dehydration of apples. Journal of Food Engineering 46 (4), 243–250. Lenart, A., Flink, J.M., 1984. Osmotic concentration of potato: I. criteria for the end point of the osmosis process. International Journal of Food Science and Technology 19 (1), 45–63. Lerici, C.R., Pinnavaia, G., Dalla Rosa, M., Bartolucci, L., 1985. Osmotic dehydration of fruit: influence of osmotic agents on drying behaviour and product quality. Journal of Food Science 50 (5), 1217–1219. Lertworasirikul, S., 2008. Drying kinetics of semi-finished cassava crackers: a comparative study. Lebensmittel-Wissenschaft und-Technologie 41 (8), 1360– 1371.
S. Lertworasirikul, S. Saetan / Journal of Food Engineering 98 (2010) 214–223 Magee, T.R.A., Hassaballah, A.A., Murphy, W.R., 1983. Internal mass transfer during osmotic dehydration of apple slices in sugar solution. Irish Journal of Food Science and. Technology 7, 147–155. Ochoa-Martínez, C.I., Ayala-Aponte, A.A., 2007. Prediction of mass transfer kinetics during osmotic dehydration of apples using neural networks. LebensmittelWissenschaft und-Technologie 40 (4), 638–645. Raoult-Wack, A.L., 1994. Recent advances in the osmotic dehydration of foods. Trends in Food Science and Technology 5 (8), 255–260. Rastogi, N.K., Raghavarao, K.S.M.S., Niranjan, K., 1997. Mass transfer during osmotic dehydration of banana: Fickian diffusion in cylindrical configuration. Journal of Food Engineering 31 (4), 423–432. Salvatori, D., Andr´es, A., Chiralt, A., Fito, P., 1999. Osmotic dehydration progression in apple tissue I: spatial distribution of solutes and moisture content. Journal of Food Engineering 42 (3), 125–132. Shi, J., Le Maguer, M., 2002. Osmotic dehydration of foods: mass transfer and modeling aspects. Food Reviews International 18 (4), 305–335. Sinclair, W.B. (1984). The biochemistry and physiology of the lemon and other citrus fruits. Division of Agriculture and National Resources, University of California, Oakland, CA, USA.
223
Singh, R.R.B., Ruhil, A.P., Jain, D.K., Patel, A.A., Patil, G.R., 2009. Prediction of sensory quality of UHT milk – a comparison of kinetic and neural network approaches. Journal of Food Engineering 92 (2), 146–151. Smith, M. (1996). Neural Networks for Statistical Modeling, first ed. Itp New Media. Toupin, C.J., Marcotte, M., Le Maguer, M., 1989. Osmotically induced mass transfer in plant storage tissues, part I: a mathematical model. Journal of Food Engineering 10 (1), 13–38. Trelea, I.C., Raoult-Wack, A.L., Trystram, G., 1997. Note: application of neural network modeling for the control of dewatering and impregnation soaking process (osmotic dehydration). Food Science and Technology International 3 (6), 459–465. Yao, Z., Le Maguer, M., 1996. Mathematical modelling and simulation of mass transfer in osmotic dehydration processes, part I: conceptual and mathematical models. Journal of Food Engineering 29 (3&4), 349–360. Zenoozian, M.S., Devahastin, S., 2009. Application of wavelet transform coupled with artificial neural network for predicting physicochemical properties of osmotically dehydrated pumpkin. Journal of Food Engineering 90 (2), 219–227.
Contents lists available at ScienceDirect
Journal of Food Engineering journal homepage: www.elsevier.com/locate/jfoodeng
Artificial neural network modeling of mass transfer during osmotic dehydration of kaffir lime peel S. Lertworasirikul *, S. Saetan Department of Product Development, Faculty of Agro-Industry, Kasetsart University, 50 Phaholyothin Rd., Chatuchak, Bangkok 10900, Thailand
a r t i c l e
i n f o
Article history: Received 8 October 2009 Received in revised form 22 December 2009 Accepted 30 December 2009 Available online 6 January 2010 Keywords: Kaffir lime Osmotic dehydration Mathematical model Artificial neural network Mass transfer
a b s t r a c t Mass transfer of kaffir lime peel during osmotic dehydration was investigated in this paper. Processing factors were solute concentrations, process temperatures, and immersion time. The results showed that increasing solute concentration and process temperature resulted in a higher reduction in moisture contents of kaffir lime peel and increase in water loss and solid gain rates. Analysis of variance showed significant effects (P < 0.05) of all processing factors except process temperatures for water loss. Multilayer feedforward neural network (MFNN) was proposed to predict percentages of water loss and solid gain of kaffir lime peel during osmotic dehydration based on three processing factors as inputs. The best network with the lowest average mean squared error (MSE) of 0.0066 and the highest average regression coefficient (r2) of 0.9725 from normalized training and validating data sets was composed of one hidden layer with five hidden neurons and used Levenberg–Marquardt algorithm as a training algorithm. A simulation test showed good generalization of the successfully trained MFNN model with the average MSE of 6.5813 and 5.9340, and average r2 of 0.9745 and 0.9632, respectively, for water loss and solid gain. Compared with multiple linear regression models, MFNN was found to be more suitable for predicting water loss and solid gain during the OD process of kaffir lime peel. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Kaffir lime fruit (Citrus hystrix DC.) is a native lime fruit grown in Southeast Asia, commonly used in flavor, food, beverage, and fragrance industry. Juice of kaffir lime is principally used as a cleaner for clothing and hair, refreshing perfumes and natural deodorizers. After the juice is extracted from the fruit, there remain residues comprising of peel (flavedo and albedo), pulp (juice sac residue), rag (membranes and cores), and seeds. The outer green peel (flavedo) of kaffir lime is commonly used in curry pastes and traditional medicines, while the inner white peel (albedo), which is rich in pectin and dietary fiber, is usually discarded or becomes a feed for animals (Sinclair, 1984). The inner peel of kaffir lime, as a major waste, has become a substantial burden to the environment. Hence it is necessary to find a feasible way to dispose of the kaffir lime peel in order to have a positive environmental impact or to turn them into useful products. To add value to kaffir residue, the production of osmotic dehydrated kaffir lime peel is an interesting application. Osmotic dehydration (OD) is a pre-processing step prior to drying and freezing of food products. An OD process of food generally * Corresponding author. Tel.: +662 562 5012; fax: +662 562 5005. E-mail addresses: [email protected], [email protected] (S. Lertworasirikul). 0260-8774/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2009.12.030
involves significant removal of water from food by soaking it in a hypertonic solution, so that water and little amounts of natural solutes are transferred from the food to the solution and solutes migrate from the solution into food. A mass transfer rate during the OD process depends on several factors such as concentration and temperature of an OD solution, immersion time, size, and shape of products, an osmotic solution to fruit ratio, and a type of osmotic agents (Lerici et al., 1985; Raoult-Wack, 1994; Rastogi et al., 1997). Much work has been done in developing models to predict the mass transfer kinetics of an OD process at an atmospheric pressure. Nevertheless, it is not an easy task to develop a mathematical model incorporating all of the factors involved in an OD process (Ochoa-Martínez and Ayala-Aponte, 2007). From a strict sense, mathematical models for an OD process can be classified into theoretical models (or knowledge-driven models) and empirical models (data-driven models). Theoretical models are developed from assumptions about phenomena and are validated with experimental data. Theoretical models, which describe process mechanisms, are sometimes called mechanistic models. They provide detailed information about all process variables, but their determinations of unknown physical parameters are computationally intensive and time-consuming. For an OD process, the models are usually based on the mechanisms of heat and mass transfer. The most widely used theoretical OD model has been a diffusion model, which can be derived from the Fick’s law of diffusion in unsteady
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215
Nomenclature xi x zl z m0 mt M0 Mt tlk tm tlm
input variable i vector of input xi predicted output l vector of output initial weight of solids (dry matter) of sample (g) weight of solids (dry matter) of sample after osmotic dehydration for time t (g) initial weight of sample (g) weight of sample after osmotic dehydration for time t (g) experimental output l of the observation k average value of all experimental outputs average value of experimental output l
state (Beristian et al., 1990; Salvatori et al., 1999). Some other authors have proposed an approach based on a cellular structure (Toupin et al., 1989; Yao and Le Maguer, 1996). On the other hand, empirical models are developed from experimental data. Their uses are limited because they are only capable of representing data at conditions similar to those on which such models were developed (Trelea et al., 1997). However, recent work has shown that the empirical models give a reasonable fit to experimental data and can successfully predict mass transfer mechanism (Ochoa-Martínez and Ayala-Aponte, 2007). Also, the main advantage of an empirical modeling approach is that it has a capability to learn from experimental data. Many authors have used a simplified version of the non-steady state form of Fick’s law to model OD mechanism. The empirical models, which these authors proposed, considered proportionality relationships between a concentration parameter and the square root of time (Conway et al., 1983; Hawkes and Flink, 1978; Magee et al., 1983). In these models, simultaneous water and solute transfer is resolved to a simple transfer of water or solute, which is inefficient as far as the technological control of both dewatering and impregnation effects are concerned (Raoult-Wack, 1994). In case of food processes, nonlinear models are more suitable due to variability and nonlinear behavior of natural products. In addition, many production processes involve with fluctuation in process conditions, and rely to a great extent on the skill and experience of operators. Therefore, artificial neural network (ANN) models recently have gained momentum for process modeling and control. ANN models are recognized as a good tool for dynamics modeling because it does not require parameters of physical models, has an ability to learn the solution of problems from a set of experimental data, and is capable to handle complex systems with nonlinearities and interactions between decision variables. ANN models were constructed by interconnecting many nonlinear computational elements, known as neurons or nodes, operating in parallel, and arranging in patterns similar to biological networks (Smith, 1996). ANN models can be classified into two classes: supervised networks and unsupervised networks. Supervised networks require a training algorithm and a training data set to adjust the connection weights, while unsupervised networks can adjust weights by themselves to achieve the required results without using any training algorithm. Supervised networks are mostly used for classification, prediction, and function approximation. Unsupervised networks are used for clustering and content addressable memory. For prediction and control of food processing operations, supervised networks are suitable (Jindal and Chauhan, 2001; Smith, 1996). Applications of ANN models include extrusion processes, filtration, drying processes, etc. (Bardot et al., 1994; Dornier et al., 1995; Jindal and Chauhan, 2001). Due to the complexity of the osmotic
zlk i l k m 0 t L K MSE r2 WL SG
predicted output l of the observation k index of input variables index of output variables index of observations average value starting time (time 0) sampling time (hour) number of outputs total number of observations mean squared error regression coefficient water loss (%) solid gain (%)
dehydration process, several authors have recommended the use of ANN for modeling mass transfer kinetics during the OD process (Baruch et al., 2004; Ochoa-Martínez and Ayala-Aponte, 2007; Shi and Le Maguer, 2002). Nevertheless, few works have been done on the application of ANN to model OD process. Also, there was no study on the effect of OD conditions on water loss and solid gain of kaffir lime peel. The purpose of this work was to investigate the effect of process parameters (solute concentrations, process temperatures and immersion time) on mass transfer in the OD process of kaffir lime peel. ANN models were developed to predict water loss (WL) and solid gain (SG) for the OD process of the kaffir lime peel. The performance of ANN was then compared with the performance of multiple linear regression (MLR) models. 2. Materials and methods 2.1. Experimental procedures 2.1.1. Sample preparation Kaffir limes (Citrus hystrix DC.) were purchased from a local market in Bangkok, Thailand. The kaffir limes were sorted visually for the same size. The samples were washed and the exterior green peels were removed from the albedo. Then, the samples were cut into halves perpendicular to the apex-base direction, handsqueezed, and the seeds and pulp were removed before dehydration. The kaffir lime peels were composed of albedo and rag as shown in Fig. 1. The initial weight of each sample was 6 g. The average initial moisture content of the sample was 91.05% in wet basis. 2.1.2. Osmotic solution Sucrose (food grade) dissolved in distilled water was used as the osmotic agent. The solute contents varied from 50% to 70% (w/w). The weight ratio of the sample to the solution was 1:5 (w/w) in order not to dilute the osmotic solution by water removal from the sample during the experiments and in concerns with economics and transfer of water loss and solid gain (Lenart and Flink, 1984; Kaymak-Ertekin and Sultanoglu, 2000; Zenoozian and Devahastin, 2009). 2.1.3. Osmotic dehydration The experiment was conducted using a 5 5 13 factorial completely randomized design (CRD) with three main factors (concentrations, temperature levels, and osmotic time). The OD process was performed in a beaker containing the osmotic solutions with the concentrations of 50%, 55%, 60%, 65%, and 70% w/w and
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are performed using five different partitions (five cross-validation experiments). Mean squared errors (MSE) and regression coefficients (r2) between the predicted values from the MLR models and the experimental values were calculated by using Eqs. (8) and (9). Then average MSE and average r2 from five cross-validation experiments were used as performance criteria for MLR modeling. 2.3. Artificial neural network modeling In this study, a supervised network was used to model the OD process of the kaffir lime peel. A widely used ANN model for prediction and control of food processing operations is a multilayer feedforward neural network (MFNN), which has more than one layer as shown in Fig. 2. An MFNN model can learn nonlinear and complex relationships by using a training algorithm with a set of input–output pairs (Lertworasirikul, 2008). An MFNN model was developed to predict the percentages of water loss (z1) and solid gain (z2) of osmotic dehydrated kaffir lime peel simultaneously based on three input variables; solute concentration (x1), process temperature (x2), and immersion time (x3) as follows.
2
Fig. 1. Kaffir lime peel before osmotic dehydration.
x1
3
6 7 x ¼ 4 x2 5; solution temperature levels of 30, 35, 40, 45, 50 °C. A mechanical stirrer (JEIOTECH HP-3000, Korea) with a diameter of 100 mm provided agitation of the osmotic solutions and the rotation speed was monitored at 100 rpm. For each temperature and concentration, the kaffir lime peels were weighed and placed into a beaker to dehydrate for 12 h. After every 1 h time interval, the samples were removed from the solute solution, rinsed with deionised water and blotted with absorbent paper to remove excess surface solution. Three pieces of the samples were drawn to weigh and determine the average moisture content (%, wb) using a vacuum oven (model VD53, Binder, Germany) for drying to constant weight at 70 °C under a reduced pressure of 10 kPa (adaptation of method 934.06 AOAC, 2000). Then, the percentages of water loss (%WL) and solid gain (%SG) of the samples were calculated from Eqs. (1) and (2), respectively, and used as outputs for MLR and ANN modeling.
%WL ¼
%SG ¼
ðM 0 m0 Þ ðM t mt Þ 100 M0
mt m0 100 M0
ð1Þ
ð2Þ
2.2. Analysis of variance and multiple linear regression modeling The development of MLR models and the analysis of variance were done by using a regression tool in Microsoft Excel. MLR models were developed to predict the percentages of water loss (z1) and solid gain (z2) of osmotic dehydrated kaffir lime peel based on three input variables; x1 was solute concentration (50%, 55%, 60%, 65%, 70% w/w), x2 was process temperature (30, 40, 45, 50 °C), and x3 was immersion time (0–12 h). The significant effect of the input variables over the outputs was checked by conducting analysis of variance from the whole set of data at 95% confidence level. To develop a MLR model for each output, available data were randomized and partitioned into two subsets for cross validation. The first subset (85%) was used for developing the model. The second subset was the test set (15%), which was used to examine the network generalization capability. These data subsets were also used for ANN modeling but the first subset here was divided into a training set and a validation set in ANN modeling to prevent over-fitting. To reduce variability, five rounds of cross validation
z¼
x3
z1
ð3Þ
z2
Available data were randomized and divided into three subsets for cross validation. The first subset was the training set (70%), which was used for computing the gradient and updating the network weights and biases. The second subset was the cross validation set (15%), which was used to prevent over-fitting. The last subset is the test set (15%), which was not used during the training but was used to examine the network generalization capability (Smith, 1996). Due to the different ranges of each input and each output, the inputs and outputs were normalized into the interval [1, 1] before feeding into the network. The MFNN model was designed using neural network toolbox in MATLAB version 6.5. Levenberg–Marquardt algorithm (Trainlm) was used as a training algorithm in this study. Trainlm is a network training function that updates weight and bias states according to Levenberg–Marquardt optimization. A transfer function was a logarithmic sigmoid transfer function (logsig) in the first layer of the network, and a linear transfer function (purelin) was used in the second layer.
logsigðxÞ ¼
1 ; ð1 þ ex Þ
ð4Þ
purelinðxÞ ¼ x
ð5Þ
Fig. 2. Structure of MFNN.
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Fig. 3. Effects of process temperatures and immersion time on average moisture content (%, wb) at the concentrations of 50%, 55%, 60%, 65%, and 70%.
Fig. 4. Effects of solute concentrations and immersion time on average water loss (%) at process temperature of 30, 35, 40, 45, and 50 °C.
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There is no fixed rule for determining the required hidden layers and nodes. In general, one hidden layer has been found to be adequate, and only in some cases, a slight advantage may be gained by using two hidden layers (Hecht-Nielsen, 1989). Therefore, the number of hidden layers was fixed at one, while the number of neurons in the hidden layer was investigated. In this study, the networks with 1, 3, 5, 7, and 9 hidden neurons were compared. The performance of the networks was measured by mean squared error (MSE) and regression coefficient (r2) between the predicted values of the network and the target or experimental values as follows.
PK PL MSE ¼
k¼1
l¼1 ðzlk
tlk Þ2
;
ð6Þ
PK PL 2 l¼1 ðzlk t lk Þ r 2 ¼ 1 Pk¼1 K PL 2 k¼1 l¼1 ðt lk t m Þ
ð7Þ
KL
The MSEl and r 2l of each output l could also be calculated by using the following equations.
PK MSEl ¼
k¼1 ðzlk
t lk Þ2
;
ð8Þ
PK ðzlk t lk Þ2 r2l ¼ 1 PKk¼1 2 k¼1 ðt lk t lm Þ
ð9Þ
K
During the learning process, training and validating data sets were simultaneously used to avoid over-fitting. This was done by 5-fold-cross-validation and in each cross validation, initial weights were randomly selected three times for training. The learning stopped after 1000 iterations, MSE became zero, or the performance on the validation vectors failed to improve or remains the same for five epochs in a row. After the termination of the learning process, weights and biases of the network were obtained. For each cross validation, the network with minimum MSE and maximum r2 from using three initial weights was selected. Then average MSE and average r2 from five cross validations were calculated to find the best network. The best network model was the network having the minimum MSE and maximum r2 using the normalized
Fig. 5. Effects of solute concentrations and immersion time on average solid gain (%) at process temperature of 30, 35, 40, 45, and 50 °C.
Fig. 6. Effects of process temperatures and solute concentrations on average water loss (%) at equilibrium.
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3. Results and discussion 3.1. Effect of process parameters on osmotic dehydration of kaffir lime peel From the OD process of kaffir lime peel, the average moisture content (%, wb), the percentages of water loss and solid gain were measured at every 1 h time interval for each process parameter. 3.1.1. Moisture content The effects of process parameters on the average moisture contents of osmotic dehydrated kaffir lime peel were shown in Fig. 3. At each solution concentration and process temperature, average moisture content of the samples decrease significantly during the first period of OD process (the first 2 h) and then decrease slowly until the system reached the equilibrium. An increase in solute concentration resulted in a higher reduction in moisture content.
Fig. 7. Effects of process temperatures and solute concentrations on average solid gain (%) at equilibrium.
predicted and target data, and this network was not over-fitting the data. The best network was then used to predict outputs using the testing data set to further check if the network achieved good generalization.
3.1.2. Water loss and solid gain The average values of water loss and solid gain during the OD process of kaffir lime peel were shown in Figs. 4 and 5, respectively.
Table 1 Analysis of variance and coefficients of input variables from multiple linear regression modeling using the whole set of data. Variable
Water loss
Concentration (% w/w) Temperature (°C) Time (h)
Solid gain
P value
Coefficient
P value
Coefficient
1.17 107 0.3131 7.51 1051
0.47558 0.08868 3.0547
3.26 1018 0.0200 1.1 1046
0.66467 0.16805 2.3524
Table 2 MSE and r2 of water loss from the development and testing processes of multiple linear regression models. Regression model
Cross-validation experiment
MSE of water loss
r2 of water loss
Regression model for water loss
Development process
1 2 3 4 5 Average SD
121.7118 123.4582 125.3109 106.7957 130.4860 121.5525 8.8791
0.5296 0.5381 0.5343 0.5211 0.5314 0.5309 0.0064
z1 = 0.5996 + 0.4561x1 + 0.0931x2 + 3.0452x3 z1 = 1.9382 + 0.5149x1 + 0.0630x2 + 3.0811x3 z1 = 1.2287 + 0.4945x1 + 0.0777x2 + 3.0681x3 z1 = 2.8013 + 0.4767x1 + 0.0552x2 + 2.7824x3 z1 = 0.7251 + 0.4369x1 + 0.1064x2 + 3.1165x3
Testing process
1 2 3 4 5 Average SD
126.7564 117.5176 106.3982 219.0499 77.9198 129.5284 53.3022
0.5427 0.4817 0.5128 0.6099 0.5210 0.5336 0.0479
Table 3 MSE and r2 of solid gain from the development and testing processes of multiple linear regression models. Regression model
Cross-validation experiment
Development process
1 2 3 4 5 Average SD
Testing process
1 2 3 4 5 Average SD
r2 of solid gain
Regression model for solid gain
82.7157 82.8077 82.1708 73.3755 86.8484 81.5836 4.9552
0.5436 0.5584 0.5596 0.5364 0.5474 0.5491 0.0099
z2 = 21.8748 + 0.6574x1 + 0.1723x2 + 2.3436x3 z2 = 24.0919 + 0.7148x1 + 0.1374x2 + 2.3847x3 z2 = 22.2317 + 0.6773x1 + 0.1431x2 + 2.3893x3 z2 = 20.3798 + 0.6647x1 + 0.1624x2 + 2.1309x3 z2 = 21.4906 + 0.6469x1 + 0.1664x2 + 2.3952x3
78.4212 79.1853 81.8526 136.4691 55.3594 86.2575 30.0280
0.5676 0.4767 0.4640 0.6136 0.5336 0.5311 0.0625
MSE of solid gain
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The rapid changes in water loss and solid gain took place in the first 2 h of the OD process. The most significant changes in water loss and solid gain took place in the beginning period were apparently due to the significant difference in the osmotic pressure of the kaffir lime peel and that of the osmotic solution. During the osmotic treatment, increased solute concentrations resulted in increased water loss and solid gain rates. It was also observed that increasing process temperatures resulted in slightly increased average water loss and increased average solid gain as shown in Figs. 6 and 7, respectively. Fig. 6 and 7 showed the average water loss and average solid gain with their standard errors. These results were presumably due to changes in physical properties of the samples and viscosity of the osmotic solution. Higher temperatures cause the
increase in membrane permeability, which promotes swelling and plasticization of the cell membranes. In addition, increasing temperatures causes a reduction in solution viscosity, reducing external resistance to mass transfer and making water and solute transport easier. These results were in agreement with previous works by _ Agarry et al. (2008), Hawkes and Flink (1978), Ispir and Tog˘rul (2009), Lenart and Flink (1984). 3.2. Analysis of variance and multiple linear regression modeling Analysis of variance for water loss and solid gain was shown in Table 1, which showed a significant effect (P < 0.05) of all variables except temperature for water loss. Since the MFNN model was
Table 4 MSE and r2 from the learning process and testing process of MFNN. Number of hidden nodes
Cross-validation experiment
MSE from learning process
r2 from learning process
MSE from testing process
r2 from testing process
1
1 2 3 4 5 Average SD
0.0366 0.0340 0.0365 0.0360 0.0339 0.0354 0.0013
0.8477 0.8641 0.8569 0.8252 0.8653 0.8518 0.0165
0.0250 0.0349 0.0365 0.0316 0.0360 0.0328 0.0048
0.9018 0.8283 0.8223 0.9209 0.7608 0.8468 0.0649
3
1 2 3 4 5 Average SD
0.0093 0.0081 0.0084 0.0080 0.0082 0.0084 0.0005
0.9614 0.9677 0.9669 0.9611 0.9673 0.9649 0.0033
0.0052 0.0079 0.0093 0.0098 0.0074 0.0079 0.0018
0.9796 0.9605 0.9532 0.9761 0.9508 0.9640 0.0132
5
1 2 3 4 5 Average SD
0.0080 0.0064 0.0067 0.0060 0.0058 0.0066 0.0009
0.9668 0.9744 0.9738 0.9708 0.9769 0.9725 0.0039
0.0057 0.0055 0.0079 0.0077 0.0072 0.0068 0.0011
0.9768 0.9724 0.9602 0.9816 0.9522 0.9686 0.0121
7
1 2 3 4 5 Average SD
0.0075 0.0062 0.0065 0.0062 0.0076 0.0068 0.0007
0.9688 0.9753 0.9747 0.9700 0.9698 0.9717 0.0030
0.0043 0.0055 0.0089 0.0077 0.0062 0.0065 0.0018
0.9828 0.9724 0.9553 0.9808 0.9593 0.9701 0.0124
9
1 2 3 4 5 Average SD
0.0072 0.0064 0.0067 0.0065 0.0071 0.0068 0.0004
0.9702 0.9743 0.9738 0.9686 0.9718 0.9717 0.0024
0.0047 0.0076 0.0086 0.0074 0.0058 0.0068 0.0016
0.9810 0.9625 0.9571 0.9818 0.9620 0.9620 0.0116
Table 5 MSE and r2 from the learning and testing processes of the successfully trained MFNN with 5-hidden-nodes using unnormalized input and output data. MFNN Process
Cross-validation experiment
Learning
1 2 3 4 5 Average SD
Testing
1 2 3 4 5 Average SD
r2 of water loss
MSE of solid gain
r2 of solid gain
6.5808 6.3633 6.3279 6.2606 5.9589 6.2983 0.2245
0.9751 0.9770 0.9783 0.9722 0.9785 0.9762 0.0026
7.7093 5.4580 6.0121 4.9333 4.8419 5.7909 1.1701
0.9582 0.9715 0.9691 0.9687 0.9749 0.9685 0.0063
6.4601 5.1786 4.6601 10.3120 6.2958 6.5813 2.2177
0.9780 0.9778 0.9789 0.9777 0.9602 0.9745 0.0080
4.3288 4.9243 8.9531 4.7541 6.7095 5.9340 1.9173
0.9762 0.9682 0.9407 0.9858 0.9449 0.9632 0.0197
MSE of water loss
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Fig. 8. The predicted and experimental water loss (%) and solid gain (%) from the learning and testing processes of the 5-hidden-nodes neural network for pilot experiments (1)-(5).
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developed to predict both water loss and solid gain simultaneously, all variables should be used for the MFNN modeling. MSE, r2 and MLR equations from the development and testing processes of the MLR modeling for water loss and solid gain were shown in Tables 2 and 3, respectively. It was seen that average MSE was high and average r2 was low; therefore, the MLR models were not a good model for prediction of water loss and solid gain from the OD process of kaffir lime peel. 3.3. Artificial neural network modeling MSE and r2 from the learning and testing processes using normalized data were shown in Table 4. The third and fourth columns of Table 4 displayed MSE and r2 from the learning process of the networks, while the fifth and sixth columns displayed MSE and r2 from the testing process of the networks. The results from Table 4 showed that the average MSE tended to decrease and the average r2 tended to increase as the number of hidden nodes was increased until it reached 5-hidden-nodes. After that there was no significant improvement in average MSE and average r2 for both learning and testing processes. This agrees with what other works (Ochoa-Martínez and Ayala-Aponte, 2007; Lertworasirikul, 2008; Singh et al., 2009) had also reported about network performance due to the number of hidden nodes. Increasing more hidden nodes would increase more complexities and take more computational time. Therefore, the MFNN model with 5-hidden-nodes was chosen as the best network in this study. Low standard deviations (SD) of MSE and r2 from five pilot experiments also showed that the network was reliable and any MFNN models from these five experiments could be used for the prediction of water loss and solid gain of osmotic dehydrated kaffir lime peel. Table 5 showed MSE and r2 for water loss and solid gain of the successfully trained networks with 5-hidden-nodes using unnormalized input and output data. The average MSE of water loss and solid gain from the five pilot experiments of learning and testing processes were reasonably low and the average r2 for the water loss and solid gain were high. Fig. 8 showed the comparison between the predicted and experimental water loss and solid gain from cross-validation experiments (1)–(5) of the network with 5-hidden-nodes. The results in this figure showed that the plots between the predicted and experimental water loss and solid gain were almost straight line for both learning and testing processes. These results showed good agreements between the predicted and experimental values in all experiments. Therefore, the developed MFNN model had a good generalization in predicting water loss and solid gain of osmotic dehydrated kaffir lime peel. Compared with the MLR models, the MFNN models performed better due to the high nonlinearity and complex relationships of the system. These results were in agreement with previous works by other authors (Chen et al., 2001; Ochoa-Martínez and Ayala-Aponte, 2007). 4. Conclusions This paper studied the OD process of kaffir lime peel. The study on the effects of process parameters on moisture content, water loss, and solid gain showed that increasing solute concentration and process temperature resulted in a higher reduction in average moisture content of kaffir lime peel and increase in average water loss and average solid gain rates. Significant changes in moisture contents, water loss, and solid gain took place in the first period (the first 2 h) of the OD process following with slightly changes until the system reached the equilibrium. The analysis of variance showed a significant effect (P < 0.05) of all process parameters on
water loss and solid gain except process temperature for water loss. In this study, MLR and MFNN models were developed for the prediction of water loss and solid gain of osmotic dehydrated kaffir lime peel. The developed MLR and MFNN models used solute concentrations, osmotic temperatures and immersion time as inputs to predict network outputs, which were water loss and solid gain. The results showed that MFNN model with 5-hidden-nodes using Levenberg–Marquardt algorithm was suitable for predicting the water loss and solid gain of kaffir lime peel during the OD process. From both learning and testing processes of MFNN, the average MSE between predicted and experimental values of water loss and solid gain were reasonably low and the average r2 between predicted and experimental values of water loss and solid gain were high. Compared with MLR models, the MFNN models performed better due to the complexity and nonlinearity of the OD system. Therefore, the developed MFNN model was suitable for predicting water loss and solid gain of kaffir lime peel during the OD process.
Acknowledgment This work was funded by Kasetsart University Research and Development Institute, 2008.
References Agarry, S.E., Yusuf, R.O., Owabor, C.N., 2008. Mass transfer in osmotic dehydration of potato: a mathematical model approach. Journal of Engineering and Applied Sciences 3 (2), 190–198. AOAC, 2000. Official methods of analysis, 17th ed. Association of Official Analytical Chemists, Washington, DC. Bardot, I., Martin, N., Trystram, G., Hossenlopp, J., Rogeaux, M., Bochereau, L., 1994. A new approach for the formulation of beverages. Part II: interactive automatic method. Lebensmittel-Wissenschaft und-Technologie 27 (6), 513–521. Baruch, I., Genina-Soto, P., Nenkova, B., Barrera-Cortés, J., (2004). Neural model of osmotic dehydration kinetics of fruits cubes. In: Bussler, C., Fensel, D. (Eds.), Artificial Intelligence: Methodology, Systems, and Applications: 11th International Conference, AIMSA 2004, Varna, Bulgaria, September 2–4 2004, Proceedings, Springer-Verlag, Berlin, pp. 312–320. Beristian, C.I., Azuara, E., Cortes, R., Garcia, H.S., 1990. Mass transfer during osmotic dehydration of pineapple rings. International Journal of Food Science and Technology 25 (5), 576–582. Chen, C.R., Ramaswamy, H.S., Alli, I., 2001. Prediction of quality changes during osmo-convective drying of blueberries using neural network models for process optimization. Drying Technology 19 (3–4), 507–523. Conway, J., Castaigne, F., Picard, G., Voxan, X., 1983. Mass transfer considerations in the osmotic dehydration of apples. Canadian Institute of Food Science and Technology 16 (1), 25–29. Dornier, M., Decloux, M., Trystram, G., Lebert, A., 1995. Dynamic modeling of crossflow microfiltration using neural networks. Journal of Membrane Science 98 (3), 263–273. Hawkes, J., Flink, J.M., 1978. Osmotic dehydration of fruit slices prior to freeze dehydration. Journal of Food Processing and Preservation 2 (4), 265–284. Hecht-Nielsen, R. (1989). Theory of the backpropagation neural network. In Proceedings of International Joint Conference on Neural Networks, Washington, DC, pp. 593–605. _ _ Ispir, A., Tog˘rul, I.T., 2009. Osmotic dehydration of apricot: kinetics and the effect of process parameters. Chemical Engineering Research and Design 87 (2), 166– 180. Jindal, V.K., Chauhan, V., 2001. Neural networks approach to modeling food processing operations. In: Irudayaraj, J. (Ed.), Food Processing Operations Modeling: Design and Analysis. Marcel Dekker, New York, pp. 305–342. Kaymak-Ertekin, F., Sultanoglu, M., 2000. Modelling of mass transfer during osmotic dehydration of apples. Journal of Food Engineering 46 (4), 243–250. Lenart, A., Flink, J.M., 1984. Osmotic concentration of potato: I. criteria for the end point of the osmosis process. International Journal of Food Science and Technology 19 (1), 45–63. Lerici, C.R., Pinnavaia, G., Dalla Rosa, M., Bartolucci, L., 1985. Osmotic dehydration of fruit: influence of osmotic agents on drying behaviour and product quality. Journal of Food Science 50 (5), 1217–1219. Lertworasirikul, S., 2008. Drying kinetics of semi-finished cassava crackers: a comparative study. Lebensmittel-Wissenschaft und-Technologie 41 (8), 1360– 1371.
S. Lertworasirikul, S. Saetan / Journal of Food Engineering 98 (2010) 214–223 Magee, T.R.A., Hassaballah, A.A., Murphy, W.R., 1983. Internal mass transfer during osmotic dehydration of apple slices in sugar solution. Irish Journal of Food Science and. Technology 7, 147–155. Ochoa-Martínez, C.I., Ayala-Aponte, A.A., 2007. Prediction of mass transfer kinetics during osmotic dehydration of apples using neural networks. LebensmittelWissenschaft und-Technologie 40 (4), 638–645. Raoult-Wack, A.L., 1994. Recent advances in the osmotic dehydration of foods. Trends in Food Science and Technology 5 (8), 255–260. Rastogi, N.K., Raghavarao, K.S.M.S., Niranjan, K., 1997. Mass transfer during osmotic dehydration of banana: Fickian diffusion in cylindrical configuration. Journal of Food Engineering 31 (4), 423–432. Salvatori, D., Andr´es, A., Chiralt, A., Fito, P., 1999. Osmotic dehydration progression in apple tissue I: spatial distribution of solutes and moisture content. Journal of Food Engineering 42 (3), 125–132. Shi, J., Le Maguer, M., 2002. Osmotic dehydration of foods: mass transfer and modeling aspects. Food Reviews International 18 (4), 305–335. Sinclair, W.B. (1984). The biochemistry and physiology of the lemon and other citrus fruits. Division of Agriculture and National Resources, University of California, Oakland, CA, USA.
223
Singh, R.R.B., Ruhil, A.P., Jain, D.K., Patel, A.A., Patil, G.R., 2009. Prediction of sensory quality of UHT milk – a comparison of kinetic and neural network approaches. Journal of Food Engineering 92 (2), 146–151. Smith, M. (1996). Neural Networks for Statistical Modeling, first ed. Itp New Media. Toupin, C.J., Marcotte, M., Le Maguer, M., 1989. Osmotically induced mass transfer in plant storage tissues, part I: a mathematical model. Journal of Food Engineering 10 (1), 13–38. Trelea, I.C., Raoult-Wack, A.L., Trystram, G., 1997. Note: application of neural network modeling for the control of dewatering and impregnation soaking process (osmotic dehydration). Food Science and Technology International 3 (6), 459–465. Yao, Z., Le Maguer, M., 1996. Mathematical modelling and simulation of mass transfer in osmotic dehydration processes, part I: conceptual and mathematical models. Journal of Food Engineering 29 (3&4), 349–360. Zenoozian, M.S., Devahastin, S., 2009. Application of wavelet transform coupled with artificial neural network for predicting physicochemical properties of osmotically dehydrated pumpkin. Journal of Food Engineering 90 (2), 219–227.