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Modeling of water sorption isotherm for corn starch
Journal of Food Engineering 80 (2007) 562–567 www.elsevier.com/locate/jfoodeng
Modeling of water sorption isotherm for corn starch Guilan Peng, Xiaoguang Chen, Wenfu Wu *, Xiujuan Jiang Department of Biological and Agriculture Engineering, Jilin University, Renmin Street 142, Changchun 130025, China Received 25 December 2005; received in revised form 30 March 2006; accepted 11 April 2006 Available online 5 September 2006
Abstract Adsorption and desorption isotherms for corn starch powders were determined at 30, 45 and 60 °C using a gravimetric technique. Samples were equilibrated in desiccators containing sulphuric acid solutions of known water activity (0.05–0.95), and placed in temperature-controlled cabinets for approximately 10 days. The data obtained were fitted to several Halsey, Oswin, Henderson, Modified-BET and Smith GAB, Ferro-Fontan, Peleg and a new sorption model of corn starch powder on BP neural network were established. Analysis showed within the temperature range investigated, GAB, Peleg and Henderson models better describes the experimental data for corn starch powder. BP neural network model not only accommodated temperature and water activity parameter, but also is better than other mathematical models. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Sorption isotherm; Corn starch; Modeling; BP neural network
1. Introduction The quality of most foods preserved by drying depends to a great extent upon their physical, chemical and microbiological stability. This stability is mainly a consequence of the relationship between the equilibrium moisture content (EMC) of the food material, and its correspondence water activity (aw), at a given temperature. These water sorption isotherms are unique for individual food materials, and can be used directly to solve food processing design problems, predict energy requirements, determine proper storage conditions (Myara, Taylor, & AL-Bulushi, 1996). Water sorption isotherm equations can be used to predict water sorption properties of foods. Many empirical and semi-empirical equations describing the sorption characteristics of foods have been proposed in the literature. Labuza (1975) attributed this to the fact that the water is associated with the food matrix by different mechanisms in different water activity regions.
*
Corresponding author. Tel./fax: +86 431 5691908. E-mail address: [email protected] (W. Wu).
0260-8774/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2006.04.063
Models available in the literature to describe moisture sorption isotherm can be divided into several categories; kinetic models based on a mono-layer (Mod-BET model), kinetic models based on a multi-layer and condensed film (GAB model), semi-empirical (Ferro-Fontan, Henderson and Halsey models) and empirical models (Smith and Oswin models). The BET model represents a fundamental milestone in the interpretation of multilayer sorption isotherms, particularly Types II and III (Timmermann, 1989). Many researchers modified the BET model and the modified equation gave a good fit up to water activity 0.9 (Aguerre, Suarez, & Viollaz, 1989). The GAB model is considered to be the most versatile sorption model available in the literature and has been adopted by a group of European food researchers COST 90 (Bizot, 1983; Van den Berg & Bruin, 1981). Chirife, Bouquet, Ferro-Fontan, and Iglesias (1983) proposed the Ferro-Fontan model. Iglesias and Chirife (1995) reported that the Ferro-Fontan equation accurately represented the sorption isotherm of 92 different food products. Peleg (1993) proposed a four parameter model and noted that the model can be used for both sigmoid and non-sigmoid isotherms, and that it fitted as well as, or better than, the GAB model. Smith
G. Peng et al. / Journal of Food Engineering 80 (2007) 562–567
model (1947) is useful in describing the sorption isotherm of biological materials such as starch and cellulose. Henderson (1952) proposed a semi-empirical model for the equilibrium moisture content of cereal grains. Chirife and Iglesias (1978) found that Halsey and Oswin models are also versatile. Chirife and Iglesias (1978) reviewed the 23 equations existing in the literature for fitting moisture sorption isotherms of foods and food products. Later, Boquet, Chirife, and Iglesias (1978) evaluated eight equations for 39 different foods. Van den Berg and Bruin (1981) collected and classified 77 such equations. In all these studies, the researchers reported which equations gave the best fit to food isotherms. Among the sorption models, the Guggenheim–Ander-son de Boer (GAB) equation has been applied successfully to various foods (Van den Berg, 1985) and it is recommended by the European project Cost 90 on physical properties of foods (Wolf et al., 1984). The three parameter GAB model for multilayer adsorption which is based on Brunauer–Emmett–Teller (BET) theory was reported to fit sorption data over a wider range of aw than the widely used BET equation. All this models include only one parameter. While incorporation of water activity and temperature data into a single model can be achieved when artificial neural networks (ANN) are used. ANN is an alternative for this application because modeling is carried out by using data recorded during normal productions. ANN is general non-linear model inspired on a simplified model of human brain function. More than other modeling strategies, they have the capability to internally self-adapt and relate complex non-linear relationships between input and output variables, without the need for rigid a priori models (Thibault & Grandjean, 1992). This makes them particularly useful when a phenomenological model of the process is not available or would be far too complex to derive. ANN concepts have been used in many food and agricultural applications such as psychrometry (Sreekanth, Ramaswamy, & Sablani, 1998), drying (Huang & Mujumdar, 1993), thermal processing (Sablani, Ramaswamy, & Prasher, 1995) rheology (Ruan, Almaer, & Zhang, 1995) and sensory science (Park, Chen, Whittaker, Miller, & Hale, 1994). The objective of this research was to develop a model of water sorption isotherms using an ANN as a tool. The model should be able to predict the equilibrium moisture content of the data variety given the aw, temperature. The performance of the ANN model was then compared to the empirical and semi-empirical equations. Furthermore, the influence of the independent factors on the dependent variable EMC was determined. 2. Materials and methods 2.1. Experimental procedure Corn starch (0.4% protein, 0.1% ash, 0.1% fat) used for the experiments were obtained from Jilin region of China.
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The equilibrium moisture contents of corn starch were determined by a gravimetric technique, in which the weight was monitored discontinuously within a standard static system of thermally stabilized desiccators. This method was recommended by the COST 90 project (Wolf, Spiess, & Jung, 1985). For adsorption a 1.5 ± 0.001 g sample of the bone dry powder was placed in a petri-dish (diameter is 40 mm) inside a desiccator (the distance from petri-dish to sulphuric acid solutions is 100 mm). Schematic diagram of the equipment for determination of equilibrium moisture content is presented in Fig. 1. For desorption a 2.5 ± 0.001 g sample of 0.75 kg/kg dry basis powder was used. Each experiment was carried out in triplicate. Sulphuric acid solutions were used to maintain the specified relative humidity inside the desiccators. The effect of temperature and acid concentration on the equilibrium relative humidity values of sulphuric acid solutions are presented in Table 1 (Ruegg, 1980). The prepared desiccators were then placed in temperature controlled cabinets maintained at 30, 45 and 60 ± 1 °C. The samples were weighed interval 24 h, the samples were allowed to equilibrate until there was no discernible weight change, as evidenced by constant weight values (±0.001 g). This involved a period of approximately 10 days for corn starch powder. The total time required for removal, weighing and replacing the samples in the desiccators was approximately 30 s. This minimized the degree of atmospheric moisture sorption during weighing. Each experiment was carried out in triplicate. The bone dry mass was determined gravimetrically by drying in a convectional oven at 105 °C for 8–10 h (AOAC, 1980).
Fig. 1. Schematic diagram of the equipment for determination of equilibrium moisture content. Table 1 Water activity of sulphuric acid solutions at selected concentrations and temperatures H2SO4 solution % (v/v) 5 20 30 40 50 60 70 80
Water activity (aw) 30 °C
45 °C
60 °C
0.9808 0.8814 0.7549 0.5711 0.3574 0.1677 0.0470 0.0059
0.9812 0.8839 0.7629 0.5866 0.3765 0.1834 0.0548 0.0077
0.9818 0.8882 0.7711 0.5989 0.3936 0.1988 0.0611 0.0103
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G. Peng et al. / Journal of Food Engineering 80 (2007) 562–567
2.2. Data analysis
3. Results and discussion
The isotherm models and artificial neural network used to fit the data. The adsorption and desorption experimental data for corn starch powder at 30, 45 and 60 °C are shown in Figs. 2 and 3. A non-linear least square regression analysis was used to evaluate the model parameters. To evaluate the goodness-of-fit of each model, the mean relative percentage deviation modulus (E) was used, which is defined by n mi mpi 1 X E¼ m 100% N
3.1. Traditional models
i¼1
i
Equilibrium Moisture Content(d.b.)
where mi is the experimental value, mpi is the predicted value, and N is the number of experimental data. The mean relative percentage deviation modulus (E) is widely adopted throughout the literature, with a modulus value below 10% indicative of a good fit for practical purposes (Lomauro, Bakshi, & Labuza, 1985).
0.3
3.2. Neural network predicted model 3.2.1. ANN configuration The experiment consisted of two inputs that were water activity and temperature and one output that was equilibrium moisture content. In order to find optimal configuration of neural networks, based on repeating tryout, two
0.2
0.1
0.0 0.0
0.2
0.4 0.6 Water Activity 30ºC
45ºC
0.8
1.0
60ºC
Fig. 2. Experimental adsorption isotherms for corn starch powder.
0.4
Equilibrium Moisture Content(d.b.)
The parameters for the sorption models for corn starch powder are shown in Tables 2 and 3, together with the mean relative percentage deviation module (E). Examination of the results in Tables 3 and 4 indicate that the GAB model best describes the experimental adsorption and desorption data for corn starch powder throughout the entire range of water activity. The GAB model gives E values ranging from 3.43% to 7.05%, with average values of 4.73% for adsorption and 6.28% for desorption. Van den Berg (1984), McMinn and Magee (1999) and Timmermann, Chirife, and Iglesias (2001) reported that the GAB model adequately represented the sorption isotherms of potato, wheat starch, potato and starchy materials. In the range of water activity 0.35 < aw < 0.9, Al-Muhtaseb, McMinn, and Magee (2004) reported GAB and model adequately represented the sorption isotherms of potato, highly amylopectin and highly amylose starch.
Table 2 Estimated values of coefficients and mean relative percentage deviation module obtained for sorption models applied to experimental adsorption data Model
Constants
30 °C
GAB
X0 C K E (%)
0.0446 14.1646 0.8536 3.4291
0.0411 9.3075 0.8591 6.1045
0.0373 5.5678 0.8682 4.665
Peleg
K1 K2 n1 n2 E (%)
0.1685 0.1344 9.7702 0.7774 6.409
0.1570 0.1331 10.8348 0.9241 5.9002
0.1433 0.1344 12.4142 1.1966 11.4637
Ferro-Fontan
c a r E (%)
0.0252 1.1271 1.3058 10.0964
0.0296 1.1396 1.1933 15.5580
0.0385 1.1591 1.0398 14.2398
Henderson
A B E (%)
23.9261 1.3726 8.8795
23.0711 1.2958 6.2403
21.1248 1.1884 5.1775
Oswin
A B E (%)
0.0787 0.3233 27.5716
0.0707 0.3363 31.2188
0.0616 0.3562 39.1051
Smith
A B E (%)
0.0259 0.1479 14.55
0.0195 0.1427 18.6828
0.0119 0.1383 13.6546
0.3
0.2
0.1
0.0 0.0
0.2
0.4
0.6
0.8
1.0
Water Activity 30ºC
45ºC
60ºC
Fig. 3. Experimental desorption isotherms for corn starch powder.
45 °C
60 °C
G. Peng et al. / Journal of Food Engineering 80 (2007) 562–567 Table 3 Estimated values of coefficients and mean relative percentage deviation module obtained for sorption models applied to experimental desorption data Model
Constants
30 °C
45 °C
60 °C
GAB
X0 C K E (%)
0.0556 19.6845 0.8264 5.1938
0.0480 19.3915 0.8453 6.6047
0.0450 19.7003 0.8506 7.0525
K1 K2 n1 n2 E (%)
0.1682 0.1563 9.7839 0.6722 4.8581
0.1697 0.1478 11.5091 0.7333 5.3209
0.1666 0.1419 11.7917 0.7504 6.6539
c a r E (%)
0.0232 1.1290 1.4625 10.5026
0.0165 1.0990 1.5153 11.7335
0.0146 1.0919 1.5313 10.954
Henderson
A B E (%)
27.8275 1.5728 7.9837
26.0649 1.4643 9.6351
26.3568 1.4349 9.2097
Oswin
A B E (%)
0.0960 0.2925 17.2208
0.0861 0.3072 16.8931
0.8206 0.3094 17.0344
A B E (%)
0.0397 0.1541 17.7311
0.0329 0.1484 14.7806
0.0309 0.1432 12.9687
Peleg
Ferro-Fontan
Smith
aw EMC T Input layer
3.2.2. Pretreatment of data In the process of network learning, it is necessary to pretreat the sample data to make training easy and to reflect better correlations among them. The general weight value of each network output is between [0, 1]. To make bigger inputs lie in the region of higher neural activation function gradient, it’s better to make the weight value of each net-
Hidden layers
Ouput layer
Fig. 4. Schematic of a multilayer ANN used in adsorption isotherm.
aw EMC
T Input layer
Hidden layers
Ouput layer
Fig. 5. Schematic of a multilayer ANN used in desorption isotherm.
work input at [0, 1] too. Therefore before training networks, input and output samples are normalized as follows: X 0i ¼
and three neurons were respectively assigned to two hidden layers in the adsorption models, and one and three neurons were respectively assigned to two hidden layers in the desorption models. Transfer functions among hidden layers and output layers were designed based on Elman network. That is, transfer function between hidden layers and output layers is sigmoid function of f ðxÞ ¼ 1þe1 x , and transfer function between hidden layers and output layers is a kind of linear function. BP network configuration of adsorption isotherm is shown in Fig. 4, and BP network configuration of desorption isotherm is shown in Fig. 5.
565
X i X i min X i max X i min
where Ximax and Ximin is, respectively, the maximum and minimum of weight value of each neural; Xi and X 0i is, respectively, the weight value before and after pretreatment of neutral i. 3.2.3. Network learning Choose the sorption data of 30 °C and 60 °C as training samples of sorption model. The square sum of error of sorption model attains to 2.06E29 after training the samples 2336 times. The square sum of error of desorption model attains to 1.52E5 after training the samples 10,000 times. 3.2.4. Fitting analysis As Table 4, Figs. 6 and 7 show predicted values by BP neural network model are compared with the measured sorption and desorption values at 45 °C. The average relative error of sorption BP network model is 2.96% and
Table 4 Predicted values by BP neural network model compared with equilibrium values Water activity
0.9812 0.8839 0.7629 0.5866 0.3765 0.1834 0.0548
Adsorption data
Desorption data
Experimental values
Predicted values
Relative error
Experimental values
Predicted values
Relative error
0.2591 0.1572 0.1184 0.0769 0.0533 0.0286 0.0119
0.2597 0.1598 0.1192 0.0777 0.0500 0.0281 0.0130
0.22 1.67 0.70 1.09 6.14 1.69 9.18
0.2828 0.1728 0.1367 0.0945 0.0714 0.0418 0.0219
0.2845 0.1713 0.1408 0.1033 0.0675 0.0413 0.0249
0.62 0.87 3.02 9.28 5.41 1.23 13.48
Equilibrium Moisture Content(d.b.)
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G. Peng et al. / Journal of Food Engineering 80 (2007) 562–567
0.3
0.2
0.1
0.0 0.0
0.2
0.4
0.6
0.8
1.0
Water Activity Experimental Values
A new sorption model of corn starch powder on BP neural network is established. Analysis showed that BP neural network model not only accommodated temperature and water activity parameter, but also is more accurate than other mathematical models. The average relative error of sorption BP network model is 2.96% and desorption BP network model is 4.84% at 45 °C. The GAB model is considered to be the most versatile sorption model available in the literature, however the average relative error of GAB model is 6.10% and 6.60% at 45 °C. So within the temperature range investigated, BP network model can be used to describe sorption isotherms of corn starch powder.
Predicted Values
References
Equilibrium Moisture Content (d.b.)
Fig. 6. Predicted values by BP neural network model compared with experimental values for adsorption data.
0.3
0.2
0.1
0.0 0.0
0.2
0.4 0.6 Water Activity
Experimental Values
0.8
1.0
Predicted Values
Fig. 7. Predicted values by BP neural network model compared with experimental values for desorption data.
determination coefficients (R2) value between the experimental value and predicted value is 0.9996. The average relative error of desorption BP network model is 4.84% and determination coefficients (R2) value between the experimental value and predicted value is 0.9979. BP neural network model includes two parameters of temperature and water activity with higher determination coefficient and lower average relative error, while the other models only include one parameter of water activity and therefore have to establish different models to adapt to different temperature parameter. Myhara, Sablani, Al-Alawi, and Taylor (1998) reported the ANN model was able to capture water sorption isotherm crossing due to temperature effects. Therefore, BP neural network can be used to effectively describe the isothermal sorption of corn starch powder within temperature range investigated. 4. Conclusion On the basis of this work the following conclusions can be drawn.
Al-Muhtaseb, A. H., McMinn, W. A. M., & Magee, T. R. A. (2004). Water sorption isotherms of starch powders Part 1: mathematical description of experimental data. Journal of Food Engineering, 61, 297–3071. Aguerre, R. J., Suarez, C., & Viollaz, P. E. (1989). New BET type multiplayer sorption isotherms. Part II: modelling water sorption in foods. Lebensmittel-Wissenchaft and Technology, 22, 192–195. AOAC (1980). Official methods of analysis. Washinghton, DC: Association of Official Analytical Chemists Inc.. Bizot, H. (1983). Using the GAB model to construct sorption isotherms. In R. Jowitt et al. (Eds.), Physical properties of foods (pp. 43–54). New York: Applied Science. Boquet, R., Chirife, J., & Iglesias, H. A. (1978). Equations for fitting water sorption isotherms of foods. II. Evaluation of various two parameter models. Journal of Food Technology, 13, 319–327. Chirife, J., & Iglesias, H. A. (1978). Equations for fitting water sorption isotherms of foods: part 1. A review. Journal of Food Technology, 13, 159–174. Chirife, J., Bouquet, R., Ferro-Fontan, C., & Iglesias, H. A. (1983). A new model for describing the water sorption isotherm of foods. Journal of Food Science, 48, 1382–1383. Henderson, S. M. (1952). A basic concept of equilibrium moisture. Agricultural Engineering, 33, 29–32. Huang, B., & Mujumdar, A. S. (1993). Use of neural network to predict industrial dryer performance. Drying Technology, 11, 525–541. Iglesias, H. A., & Chirife, J. (1995). An alternative to the Guggenheim, Anderson and de Boer model for the mathematical description of moisture sorption isotherms of foods. Food Research International, 28, 317–321. Labuza, T. P. (1975). Interpretation of sorption data in relation to the state of constituent water. In R. Duckworth (Ed.), Water relations in foods (pp. 155–172). New York: Academic Press. Lomauro, C. J., Bakshi, A. S., & Labuza, T. P. (1985). Evaluation of food moisture sorption isotherm equations. Part I. Fruit, vegetable and meat products. Lebensmittel-Wissenchaft und Technology, 18, 111–117. McMinn, W. A. M., & Magee, T. R. A. (1999). Studies on the effect of temperature on the moisture sorption characteristics of potatoes. Journal of Food Process Engineering, 22, 113–128. Myara, R., Taylor, M., & AL-Bulushi, I. (1996). Moisture sorption isotherms of Omani data. 10th international drying symposium. Kracow, Poland, July 29 August 3, 1996 (Vol. B, pp. 989–996). Lodz University Press. Park, B., Chen, Y. R., Whittaker, A. D., Miller, R. K., & Hale, D. S. (1994). Neural network modeling for beef sensory evaluation. Transactions of the American Society of Agricultural Engineers, 37, 1547–1553. Peleg, M. (1993). Assessment of a semi-empirical four parameter general model for sigmoid moisture sorption isotherms. Journal of Food Process Engineering, 16, 21–37.
G. Peng et al. / Journal of Food Engineering 80 (2007) 562–567 Ruan, R., Almaer, S., & Zhang, J. (1995). Prediction of dough rheological properties using neural networks. Cereal Chemistry, 72, 308–311. Ruegg, M. (1980). Calculation of the activity of water in sulphuric acid solutions at various temperature. Lebensmittel-Wissenchaft and Technology, 13, 22–24. Myhara, R. M., Sablani, S. S., Al-Alawi, S. M., & Taylor, M. S. (1998). Water sorption isotherms of dates: modeling using GAB equation and artificial neural network approaches. Lebensmittel-Wissenschaft undTechnologie, 31, 699–706. Sablani, S. S., Ramaswamy, H. S., & Prasher, S. O. A. (1995). network approach for thermal processing applications. Journal of Food Processing and Preservation, 19, 283–301. Smith, S. E. (1947). The sorption of water vapour by high polymers. Journal of the American Chemical Society, 69, 646. Sreekanth, S., Ramaswamy, H. S., & Sablani, S. S. (1998). Prediction of psychrometric parameters using neural networks. Drying Technology, 16, 825–837. Thibault, J., & Grandjean, B. P. A. (1992). Process control using feedforward neural networks. Journal of Systems Engineering, 2, 198–212. Timmermann, E. O. (1989). A BET-like three sorption stage isotherm. Journal of Chemical Society, Faraday Transaction, 85, 1631–1645.
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Timmermann, E. O., Chirife, J., & Iglesias, H. A. (2001). Water sorption isotherms of foods and foodstuffs: BET or GAB parameters? Journal of Food Engineering, 48, 19–31. Van den Berg, C. (1984). Description of water activity of foods for engineering purposes by means of the GAB model of sorption. In B. M. McKenna (Ed.). Engineering and food (Vol. 1, pp. 311–321). New York: Elsevier Applied Science. Van den Berg, C. (1985). Development of B.E.T. like models for sorption of water of foods; theory and relevance. In D. Simatos & J. L. Multon (Eds.), Properties of water in foods (pp. 119). Dordrecht: Martinus Nijhoft. Van den Berg, C., & Bruin, S. (1981). Water activity and its estimation in food systems: theoretical aspects. In L. B. Rockland & G. E. Stewart (Eds.), Water activity; influence on food quality (pp. 45). New York: Academic Press. Wolf, W., Spiess, W. E. L., Jung, G., Weisser, H., Bizot, H., & Duckworth, R. B. (1984). The water vapour sorption isotherms of microcrystalline cellulose (MCC) and of purifed potato starch: results of a collaborative study. Journal of Food Engineering, 3, 51–72. Wolf, W., Spiess, W. E. L., & Jung, G. (1985). Standarization of isotherm measurements. In D. Simatos & J. L. Multon (Eds.), Properties of water in foods (pp. 661–679). The Netherlands: Martinus Nijhoff.
Modeling of water sorption isotherm for corn starch Guilan Peng, Xiaoguang Chen, Wenfu Wu *, Xiujuan Jiang Department of Biological and Agriculture Engineering, Jilin University, Renmin Street 142, Changchun 130025, China Received 25 December 2005; received in revised form 30 March 2006; accepted 11 April 2006 Available online 5 September 2006
Abstract Adsorption and desorption isotherms for corn starch powders were determined at 30, 45 and 60 °C using a gravimetric technique. Samples were equilibrated in desiccators containing sulphuric acid solutions of known water activity (0.05–0.95), and placed in temperature-controlled cabinets for approximately 10 days. The data obtained were fitted to several Halsey, Oswin, Henderson, Modified-BET and Smith GAB, Ferro-Fontan, Peleg and a new sorption model of corn starch powder on BP neural network were established. Analysis showed within the temperature range investigated, GAB, Peleg and Henderson models better describes the experimental data for corn starch powder. BP neural network model not only accommodated temperature and water activity parameter, but also is better than other mathematical models. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Sorption isotherm; Corn starch; Modeling; BP neural network
1. Introduction The quality of most foods preserved by drying depends to a great extent upon their physical, chemical and microbiological stability. This stability is mainly a consequence of the relationship between the equilibrium moisture content (EMC) of the food material, and its correspondence water activity (aw), at a given temperature. These water sorption isotherms are unique for individual food materials, and can be used directly to solve food processing design problems, predict energy requirements, determine proper storage conditions (Myara, Taylor, & AL-Bulushi, 1996). Water sorption isotherm equations can be used to predict water sorption properties of foods. Many empirical and semi-empirical equations describing the sorption characteristics of foods have been proposed in the literature. Labuza (1975) attributed this to the fact that the water is associated with the food matrix by different mechanisms in different water activity regions.
*
Corresponding author. Tel./fax: +86 431 5691908. E-mail address: [email protected] (W. Wu).
0260-8774/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2006.04.063
Models available in the literature to describe moisture sorption isotherm can be divided into several categories; kinetic models based on a mono-layer (Mod-BET model), kinetic models based on a multi-layer and condensed film (GAB model), semi-empirical (Ferro-Fontan, Henderson and Halsey models) and empirical models (Smith and Oswin models). The BET model represents a fundamental milestone in the interpretation of multilayer sorption isotherms, particularly Types II and III (Timmermann, 1989). Many researchers modified the BET model and the modified equation gave a good fit up to water activity 0.9 (Aguerre, Suarez, & Viollaz, 1989). The GAB model is considered to be the most versatile sorption model available in the literature and has been adopted by a group of European food researchers COST 90 (Bizot, 1983; Van den Berg & Bruin, 1981). Chirife, Bouquet, Ferro-Fontan, and Iglesias (1983) proposed the Ferro-Fontan model. Iglesias and Chirife (1995) reported that the Ferro-Fontan equation accurately represented the sorption isotherm of 92 different food products. Peleg (1993) proposed a four parameter model and noted that the model can be used for both sigmoid and non-sigmoid isotherms, and that it fitted as well as, or better than, the GAB model. Smith
G. Peng et al. / Journal of Food Engineering 80 (2007) 562–567
model (1947) is useful in describing the sorption isotherm of biological materials such as starch and cellulose. Henderson (1952) proposed a semi-empirical model for the equilibrium moisture content of cereal grains. Chirife and Iglesias (1978) found that Halsey and Oswin models are also versatile. Chirife and Iglesias (1978) reviewed the 23 equations existing in the literature for fitting moisture sorption isotherms of foods and food products. Later, Boquet, Chirife, and Iglesias (1978) evaluated eight equations for 39 different foods. Van den Berg and Bruin (1981) collected and classified 77 such equations. In all these studies, the researchers reported which equations gave the best fit to food isotherms. Among the sorption models, the Guggenheim–Ander-son de Boer (GAB) equation has been applied successfully to various foods (Van den Berg, 1985) and it is recommended by the European project Cost 90 on physical properties of foods (Wolf et al., 1984). The three parameter GAB model for multilayer adsorption which is based on Brunauer–Emmett–Teller (BET) theory was reported to fit sorption data over a wider range of aw than the widely used BET equation. All this models include only one parameter. While incorporation of water activity and temperature data into a single model can be achieved when artificial neural networks (ANN) are used. ANN is an alternative for this application because modeling is carried out by using data recorded during normal productions. ANN is general non-linear model inspired on a simplified model of human brain function. More than other modeling strategies, they have the capability to internally self-adapt and relate complex non-linear relationships between input and output variables, without the need for rigid a priori models (Thibault & Grandjean, 1992). This makes them particularly useful when a phenomenological model of the process is not available or would be far too complex to derive. ANN concepts have been used in many food and agricultural applications such as psychrometry (Sreekanth, Ramaswamy, & Sablani, 1998), drying (Huang & Mujumdar, 1993), thermal processing (Sablani, Ramaswamy, & Prasher, 1995) rheology (Ruan, Almaer, & Zhang, 1995) and sensory science (Park, Chen, Whittaker, Miller, & Hale, 1994). The objective of this research was to develop a model of water sorption isotherms using an ANN as a tool. The model should be able to predict the equilibrium moisture content of the data variety given the aw, temperature. The performance of the ANN model was then compared to the empirical and semi-empirical equations. Furthermore, the influence of the independent factors on the dependent variable EMC was determined. 2. Materials and methods 2.1. Experimental procedure Corn starch (0.4% protein, 0.1% ash, 0.1% fat) used for the experiments were obtained from Jilin region of China.
563
The equilibrium moisture contents of corn starch were determined by a gravimetric technique, in which the weight was monitored discontinuously within a standard static system of thermally stabilized desiccators. This method was recommended by the COST 90 project (Wolf, Spiess, & Jung, 1985). For adsorption a 1.5 ± 0.001 g sample of the bone dry powder was placed in a petri-dish (diameter is 40 mm) inside a desiccator (the distance from petri-dish to sulphuric acid solutions is 100 mm). Schematic diagram of the equipment for determination of equilibrium moisture content is presented in Fig. 1. For desorption a 2.5 ± 0.001 g sample of 0.75 kg/kg dry basis powder was used. Each experiment was carried out in triplicate. Sulphuric acid solutions were used to maintain the specified relative humidity inside the desiccators. The effect of temperature and acid concentration on the equilibrium relative humidity values of sulphuric acid solutions are presented in Table 1 (Ruegg, 1980). The prepared desiccators were then placed in temperature controlled cabinets maintained at 30, 45 and 60 ± 1 °C. The samples were weighed interval 24 h, the samples were allowed to equilibrate until there was no discernible weight change, as evidenced by constant weight values (±0.001 g). This involved a period of approximately 10 days for corn starch powder. The total time required for removal, weighing and replacing the samples in the desiccators was approximately 30 s. This minimized the degree of atmospheric moisture sorption during weighing. Each experiment was carried out in triplicate. The bone dry mass was determined gravimetrically by drying in a convectional oven at 105 °C for 8–10 h (AOAC, 1980).
Fig. 1. Schematic diagram of the equipment for determination of equilibrium moisture content. Table 1 Water activity of sulphuric acid solutions at selected concentrations and temperatures H2SO4 solution % (v/v) 5 20 30 40 50 60 70 80
Water activity (aw) 30 °C
45 °C
60 °C
0.9808 0.8814 0.7549 0.5711 0.3574 0.1677 0.0470 0.0059
0.9812 0.8839 0.7629 0.5866 0.3765 0.1834 0.0548 0.0077
0.9818 0.8882 0.7711 0.5989 0.3936 0.1988 0.0611 0.0103
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2.2. Data analysis
3. Results and discussion
The isotherm models and artificial neural network used to fit the data. The adsorption and desorption experimental data for corn starch powder at 30, 45 and 60 °C are shown in Figs. 2 and 3. A non-linear least square regression analysis was used to evaluate the model parameters. To evaluate the goodness-of-fit of each model, the mean relative percentage deviation modulus (E) was used, which is defined by n mi mpi 1 X E¼ m 100% N
3.1. Traditional models
i¼1
i
Equilibrium Moisture Content(d.b.)
where mi is the experimental value, mpi is the predicted value, and N is the number of experimental data. The mean relative percentage deviation modulus (E) is widely adopted throughout the literature, with a modulus value below 10% indicative of a good fit for practical purposes (Lomauro, Bakshi, & Labuza, 1985).
0.3
3.2. Neural network predicted model 3.2.1. ANN configuration The experiment consisted of two inputs that were water activity and temperature and one output that was equilibrium moisture content. In order to find optimal configuration of neural networks, based on repeating tryout, two
0.2
0.1
0.0 0.0
0.2
0.4 0.6 Water Activity 30ºC
45ºC
0.8
1.0
60ºC
Fig. 2. Experimental adsorption isotherms for corn starch powder.
0.4
Equilibrium Moisture Content(d.b.)
The parameters for the sorption models for corn starch powder are shown in Tables 2 and 3, together with the mean relative percentage deviation module (E). Examination of the results in Tables 3 and 4 indicate that the GAB model best describes the experimental adsorption and desorption data for corn starch powder throughout the entire range of water activity. The GAB model gives E values ranging from 3.43% to 7.05%, with average values of 4.73% for adsorption and 6.28% for desorption. Van den Berg (1984), McMinn and Magee (1999) and Timmermann, Chirife, and Iglesias (2001) reported that the GAB model adequately represented the sorption isotherms of potato, wheat starch, potato and starchy materials. In the range of water activity 0.35 < aw < 0.9, Al-Muhtaseb, McMinn, and Magee (2004) reported GAB and model adequately represented the sorption isotherms of potato, highly amylopectin and highly amylose starch.
Table 2 Estimated values of coefficients and mean relative percentage deviation module obtained for sorption models applied to experimental adsorption data Model
Constants
30 °C
GAB
X0 C K E (%)
0.0446 14.1646 0.8536 3.4291
0.0411 9.3075 0.8591 6.1045
0.0373 5.5678 0.8682 4.665
Peleg
K1 K2 n1 n2 E (%)
0.1685 0.1344 9.7702 0.7774 6.409
0.1570 0.1331 10.8348 0.9241 5.9002
0.1433 0.1344 12.4142 1.1966 11.4637
Ferro-Fontan
c a r E (%)
0.0252 1.1271 1.3058 10.0964
0.0296 1.1396 1.1933 15.5580
0.0385 1.1591 1.0398 14.2398
Henderson
A B E (%)
23.9261 1.3726 8.8795
23.0711 1.2958 6.2403
21.1248 1.1884 5.1775
Oswin
A B E (%)
0.0787 0.3233 27.5716
0.0707 0.3363 31.2188
0.0616 0.3562 39.1051
Smith
A B E (%)
0.0259 0.1479 14.55
0.0195 0.1427 18.6828
0.0119 0.1383 13.6546
0.3
0.2
0.1
0.0 0.0
0.2
0.4
0.6
0.8
1.0
Water Activity 30ºC
45ºC
60ºC
Fig. 3. Experimental desorption isotherms for corn starch powder.
45 °C
60 °C
G. Peng et al. / Journal of Food Engineering 80 (2007) 562–567 Table 3 Estimated values of coefficients and mean relative percentage deviation module obtained for sorption models applied to experimental desorption data Model
Constants
30 °C
45 °C
60 °C
GAB
X0 C K E (%)
0.0556 19.6845 0.8264 5.1938
0.0480 19.3915 0.8453 6.6047
0.0450 19.7003 0.8506 7.0525
K1 K2 n1 n2 E (%)
0.1682 0.1563 9.7839 0.6722 4.8581
0.1697 0.1478 11.5091 0.7333 5.3209
0.1666 0.1419 11.7917 0.7504 6.6539
c a r E (%)
0.0232 1.1290 1.4625 10.5026
0.0165 1.0990 1.5153 11.7335
0.0146 1.0919 1.5313 10.954
Henderson
A B E (%)
27.8275 1.5728 7.9837
26.0649 1.4643 9.6351
26.3568 1.4349 9.2097
Oswin
A B E (%)
0.0960 0.2925 17.2208
0.0861 0.3072 16.8931
0.8206 0.3094 17.0344
A B E (%)
0.0397 0.1541 17.7311
0.0329 0.1484 14.7806
0.0309 0.1432 12.9687
Peleg
Ferro-Fontan
Smith
aw EMC T Input layer
3.2.2. Pretreatment of data In the process of network learning, it is necessary to pretreat the sample data to make training easy and to reflect better correlations among them. The general weight value of each network output is between [0, 1]. To make bigger inputs lie in the region of higher neural activation function gradient, it’s better to make the weight value of each net-
Hidden layers
Ouput layer
Fig. 4. Schematic of a multilayer ANN used in adsorption isotherm.
aw EMC
T Input layer
Hidden layers
Ouput layer
Fig. 5. Schematic of a multilayer ANN used in desorption isotherm.
work input at [0, 1] too. Therefore before training networks, input and output samples are normalized as follows: X 0i ¼
and three neurons were respectively assigned to two hidden layers in the adsorption models, and one and three neurons were respectively assigned to two hidden layers in the desorption models. Transfer functions among hidden layers and output layers were designed based on Elman network. That is, transfer function between hidden layers and output layers is sigmoid function of f ðxÞ ¼ 1þe1 x , and transfer function between hidden layers and output layers is a kind of linear function. BP network configuration of adsorption isotherm is shown in Fig. 4, and BP network configuration of desorption isotherm is shown in Fig. 5.
565
X i X i min X i max X i min
where Ximax and Ximin is, respectively, the maximum and minimum of weight value of each neural; Xi and X 0i is, respectively, the weight value before and after pretreatment of neutral i. 3.2.3. Network learning Choose the sorption data of 30 °C and 60 °C as training samples of sorption model. The square sum of error of sorption model attains to 2.06E29 after training the samples 2336 times. The square sum of error of desorption model attains to 1.52E5 after training the samples 10,000 times. 3.2.4. Fitting analysis As Table 4, Figs. 6 and 7 show predicted values by BP neural network model are compared with the measured sorption and desorption values at 45 °C. The average relative error of sorption BP network model is 2.96% and
Table 4 Predicted values by BP neural network model compared with equilibrium values Water activity
0.9812 0.8839 0.7629 0.5866 0.3765 0.1834 0.0548
Adsorption data
Desorption data
Experimental values
Predicted values
Relative error
Experimental values
Predicted values
Relative error
0.2591 0.1572 0.1184 0.0769 0.0533 0.0286 0.0119
0.2597 0.1598 0.1192 0.0777 0.0500 0.0281 0.0130
0.22 1.67 0.70 1.09 6.14 1.69 9.18
0.2828 0.1728 0.1367 0.0945 0.0714 0.0418 0.0219
0.2845 0.1713 0.1408 0.1033 0.0675 0.0413 0.0249
0.62 0.87 3.02 9.28 5.41 1.23 13.48
Equilibrium Moisture Content(d.b.)
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0.3
0.2
0.1
0.0 0.0
0.2
0.4
0.6
0.8
1.0
Water Activity Experimental Values
A new sorption model of corn starch powder on BP neural network is established. Analysis showed that BP neural network model not only accommodated temperature and water activity parameter, but also is more accurate than other mathematical models. The average relative error of sorption BP network model is 2.96% and desorption BP network model is 4.84% at 45 °C. The GAB model is considered to be the most versatile sorption model available in the literature, however the average relative error of GAB model is 6.10% and 6.60% at 45 °C. So within the temperature range investigated, BP network model can be used to describe sorption isotherms of corn starch powder.
Predicted Values
References
Equilibrium Moisture Content (d.b.)
Fig. 6. Predicted values by BP neural network model compared with experimental values for adsorption data.
0.3
0.2
0.1
0.0 0.0
0.2
0.4 0.6 Water Activity
Experimental Values
0.8
1.0
Predicted Values
Fig. 7. Predicted values by BP neural network model compared with experimental values for desorption data.
determination coefficients (R2) value between the experimental value and predicted value is 0.9996. The average relative error of desorption BP network model is 4.84% and determination coefficients (R2) value between the experimental value and predicted value is 0.9979. BP neural network model includes two parameters of temperature and water activity with higher determination coefficient and lower average relative error, while the other models only include one parameter of water activity and therefore have to establish different models to adapt to different temperature parameter. Myhara, Sablani, Al-Alawi, and Taylor (1998) reported the ANN model was able to capture water sorption isotherm crossing due to temperature effects. Therefore, BP neural network can be used to effectively describe the isothermal sorption of corn starch powder within temperature range investigated. 4. Conclusion On the basis of this work the following conclusions can be drawn.
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