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Computers and Electronics in Agriculture 66 (2009) 209–214

Contents lists available at ScienceDirect

Computers and Electronics in Agriculture

journa l homepage: www.e lsev ier .com/ locate /compag

eural network modeling of sorption isotherms of longanDimocarpus longan Lour.)

. Janjai a,∗, P. Intaweea, K. Tohsinga, B. Mahayotheeb, B.K. Balac,.A. Ashrafd, J. Müllere

Solar Energy Research Laboratory, Department of Physics, Faculty of Science, Silpakorn University, Nakhon Pathom 73000, ThailandDepartment of Food Technology, Faculty of Engineering and Industrial Technology, Silpakorn University, Nakhon Pathom 73000, ThailandDepartment of Farm Power and Machinery, Bangladesh Agricultural University, Mymensingh 2202, BangladeshDepartment of Farm Structure, Bangladesh Agricultural University, Mymensingh 2202, BangladeshInstitute of Agricultural Engineering, University of Hohenheim, Stuttgart 70593, Germany

r t i c l e i n f o

rticle history:eceived 21 May 2008eceived in revised form 1 December 2008ccepted 7 February 2009

eywords:onganryingorption isothermNN model

a b s t r a c t

A multilayer neural network model was developed to predict the equilibrium moisture content of longan(Dimocarpus longan Lour.) and the model was trained using a back-propagation algorithm. The predictivepower of the model was found to be high (R2 = 0.9998) after it was adequately trained. The artificial neuralnetwork (ANN) model was better than the well known phenomenological Guggenheim, Anderson, andde Boer (GAB) model previously developed by the authors [Janjai, S., Bala, B.K., Tohsing, K., Mahayothee,B., Heawsungcharern, M., Muhlbauer, W., Muller, J., 2006. Equilibrium moisture content heat of sorptionof longan (Dimocarpus longan). Drying Technology 24, 1691–1696]. The ANN model was programmed inC++. The isosteric heat of sorption of longan is predicted by a power law model developed in this study,which was found to have better fit than the exponential model previously developed by the authors[Janjai, S., Bala, B.K., Tohsing, K., Mahayothee, B., Heawsungcharern, M., Muhlbauer, W., Muller, J., 2006.Equilibrium moisture content heat of sorption of longan (Dimocarpus longan). Drying Technology 24,1691–1696]. Also a power law model was developed for entropy of sorption. The net isosteric heats ofsorption were compared for longan (D. longan Lour.), litchi (Litchi chinensis Sonn.) and mango (Mangiferaindica L. cv. Nam Dok Mai). Longan and litchi have the same pattern of variation in heat of sorption

with moisture contents which might be due to similar biological structure of both of these two fruits.However, at a moisture content of above 50% (d.b.) the isosteric heat of sorption of longan is lower thanand it is higher at a moisture content below 50% (d.b.) when compared with that of mango. This set oftwo equations (isosteric heat and entropy) would be useful in the simulation of storage of dried longan.The artificial neural network model predicts equilibrium moisture contents more accurately and hencebetter equations for heat of sorption and entropy are developed based on data from the neural network model.

. Introduction

Dried longan fruit is an important export product in Thailandnd it is mainly grown in the Chiang Mai and Lumpun provinces.he annual production of fresh longan is about 500,000 tons and thexport volume is 80,000 tons of dried fruit. More than 3000 driers

n Thailand are now in operation for production of dried longansor export.

Many studies have been reported to suggest numerous isothermodels for food materials (Van den Berg, 1984; Lomauro et al., 1985;

∗ Corresponding author. Tel.: +66 34 270 761; fax: +66 34 271 189.E-mail address: serm@su.ac.th (S. Janjai).

168-1699/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.compag.2009.02.003

© 2009 Elsevier B.V. All rights reserved.

Sun and Woods, 1994; Mir and Nath, 1995; Reddy and Chakraverty,2004; Lahsasni et al., 2004; Kaymak-Ertekin and Gedik, 2004).Of these models the GAB (Guggenheim, Anderson and de Boer)model is the most widely used and versatile model. More recentlyPhomkong et al. (2006) fitted the Chung Pfost, Oswin and GAB mod-els to the desorption isotherm data of peach, plum and nectarineand the GAB model was found to give the best representation ofthe data. More recently Janjai et al. (2006) determined the isothermdata of longan using dynamic method and fitted data to five selectedmathematical models. The GAB model was found to be the best to

fit the experimental isotherm data of longan.

Isotherms of agricultural products are usually sigmoid-shapecurves which are even difficult to draw and manipulate (Bala,1997). Several complex mathematical models have been devel-oped to describe these curves (Van den Berg, 1984 and Janjai et

210 S. Janjai et al. / Computers and Electronics

Nomenclature

C intercept of ln(RH) versus 1/Tab�G Gibbs free energy (J/mol)�H heat of sorption (kJ/mol)Me equilibrium moisture content (% d.b.)R coefficient of determination (decimal)R0 universal gas constant (8.315 kJ/kmol K)RH relative humidity (%)�S entropy of sorption (J/mol K)

amutrhppn

bnpiM2aattm

tspThci

bcb

nMtMoiaha

ghATohh

T Temperature (◦C)Tab absolute temperature (K)

l., 2006) and the estimations of the parameters of these mathe-atical models require non-linear direct optimization techniques

sing computer. However, such estimations of the parameters limithe accuracy and the correct shape of the isotherms and also theeliability of the predictions over the whole range of the relativeumidity. Therefore, researchers are searching for alternative com-uter models to describe the isotherm relationships of agriculturalroducts for accuracy and reliability in predictions. Artificial neuraletwork is an alternative for such applications.

Artificial neural network (ANN) is a general non-linear modelased on a simplified model of human brain function and this tech-ique is particularly useful when a phenomenological model of arocess is not available or would be too far complex. Several stud-

es have been reported ANN on modeling of drying (Huang andujumdar, 1993; Bala et al., 2005; Movagharnejad and Nikzad,

007; Poonnoy et al., 2007; Lertworasirikul and Tipsuwan, 2008)nd thermal processing (Sablani et al., 1995). ANN technique haslso been applied for modeling of water sorption isotherms of blackea (Panchariya et al., 2002) and corn starch (Peng et al., 2007) andhe ANN models were found to be better than other mathematical

odels.The net isosteric heat of sorption is also important informa-

ion for drying and it gives a measure of the water–solid bindingtrength. It can be used to determine the energy requirements androvide information on the state of water within the dried product.he moisture content level of a product at which the net isostericeat of sorption reaches the value of latent heat of sorption is oftenonsidered as the indication of the amount of bound water existingn the product (Wang and Brennan, 1991).

Tsami (1994) proposed an empirical exponential relationshipetween the net isosteric heat of sorption and material moistureontent for some fruits. Hossain et al. (2001) found isosteric heat toe a power function of equilibrium moisture content for pineapple.

The differential entropy of a material is proportional to theumber of sites at a specific energy level (Madamba et al., 1996).adamba et al. (1996) adopted an exponential relation to describe

he entropy of garlic sorption as a function of moisture content.cMinn and Magee (2003) reported that the net isosteric heat

f sorption and differential entropy of potato decreased with thencreasing moisture content and were adequately characterized bypower law model. A knowledge of the equations of net isostericeat of sorption and differential entropy is essential in the modelingnd simulation of drying and storage of longan fruit.

Although mathematical modeling of sorption isotherm of lon-an has been reported by the authors (Janjai et al., 2006), no studyas been reported on ANN modeling of sorption isotherm of longan.

lso no information is available on the isosteric entropy of longan.he objectives of this study were to develop a neural network modelf sorption isotherm, an improved empirical model for net isostericeat of sorption and also a new empirical model for the net isostericeat of entropy.

in Agriculture 66 (2009) 209–214

2. Materials and methods

2.1. Determination of the sorption isotherm of longan

Equilibrium moisture contents of longan were determinedexperimentally using the dynamic method. The sample box wasessentially an airtight plastic box containing saturated salt solu-tion to maintain constant relative humidity inside the sample box.The samples were placed inside the perforated sample containersand the sample containers were placed on the perforated plasticsupports just above the salt solution. Electric fans were fitted to cir-culate the air inside the sample box to accelerate moisture transferbetween the samples and air inside the sample box. The sampleboxes were placed inside the hot air chamber equipped with anelectrical heater and an electronic temperature controller to main-tain the temperature.

In conducting the experiments, 50 g of the longan was placedinside the sample containers which were placed inside the sam-ple boxes and the sample boxes were placed inside the hot airchamber. The samples were weighed regularly until they reachedequilibrium. The selected temperatures for sorption isothermdetermination were 30, 40, and 50 ◦C and the relative humiditywas 11–97%. The values of the relative humidity were controlledby various saturated salt solutions as described in Bala (1997). Inaddition, these values were also checked by using a hygrometer.Details of the experimental set up and the dynamic method usedfor determination of isotherm data of longan are given in Janjai etal. (2006).

2.2. Structure of neural network model

The neurocomputing techniques are shaped after biological neu-ral functions and structures. Therefore, they are popularly known asartificial neural networks. Similarly as for their biological counterparts, functions of ANN are being developed not by program-ming them but by exposing them to carefully selected data onwhich they can learn how to perform the required processingtask. In such a modeling approach, there is no need to formu-late analytical description of the process. Instead, a black-boxprocess model is constructed by interacting the network with rep-resentative samples of measurable quantities characterizing theprocess.

An independent multilayer ANN model for equilibrium moisturecontent of longan is developed. The model has a four-layered net-work, which has large number of simple processing elements, calledneurons (Fig. 1). The input layer of the model consists of two neu-rons which correspond to the two input variables, while the outputlayer has one neuron, which represents the equilibrium moisturecontent (EMC) in the model. Selection of the number of neurons foreach hidden layer is optional. Larger number of neurons can rep-resent the system more precisely but complication arises to attainproper training. The number of neurons in the hidden layer-1 andhidden layer-2 of the model are five and three, respectively. Theinput variables are temperature and water activity.

ANN can modify their behavior in response to their environ-ment. This factor, more than any other, is responsible for the interestthey have received. Unlike mathematical model, the structure ofANN model itself cannot represent the system behavior, unless it isproperly trained. The objective of training the network is to adjustthe weights of the interconnecting neurons of the network so thatapplication of a set of inputs produces the desired set of outputs.

Initially, random values are used as weights. For reason of brevity,one input–output set can be referred to as vector. Training assumesthat each input vector is paired with a target vector representingthe desired output; together these are called a training pair. Usuallya network is trained over a number of training pairs. A total of 10

S. Janjai et al. / Computers and Electronics in Agriculture 66 (2009) 209–214 211

ork m

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tively while these values for the GAB model developed by Janjai etal. (2006) are 1.6008, 1.8788 and 0.992, respectively. Thus, the ANNmodel prediction is the best as its prediction is better than GABmodel. Also the ANN model prediction demonstrates that training

Fig. 1. The structure of the artificial neural netw

raining pairs are used to train the model, which were the observedata obtained from two independent experimental runs.

A wide variety of training algorithms has been developed, eachith its own strengths and weakness. The ANN drier models are

rained by backpropagation algorithm so that application of a setf input would produce the desired set of output. The steps of theraining procedure are summarized as follows: (i) an input vector ispplied; (ii) the output of the network is calculated and comparedo the corresponding target vector; (iii) the difference (error) is fedack through the network; and (iv) weights are changed accord-

ng to an algorithm, called delta rule (Wasserman, 1989) that tendso minimize the error. The vectors of the training set are appliedequentially. This procedure is repeated over the entire traininget for as many times as necessary until the error is within somecceptable criteria, or until the outputs do not significantly changeny more. After the end of training, simulations were done withhe trained model to check the accuracy of the model. Experimen-al input values were used in the simulation. The artificial neuraletwork model was programmed in C++.

.3. Determination of isosteric heat and entropy of longan

The net isosteric heat of sorption phenomenona can bexplained by the Clausius–Clayperon equation (Hossain et al., 2001;ohamed et al., 2005; Phomkong et al., 2006) as follows:

∂ ln(RH)∂Tab

= �H

R0T2ab

(1)

here RH = relative humidity (%); Tab = absolute temperature (K),H = isosteric heat of sorption (kJ/mol); R0 = universal gas constant

8.315 kJ/kmol K).Integrating Eq. (1) and assuming that the isosteric heat of sorp-

ion (�H) is independent of temperature, gives the following Eq.2):

n(RH) = −(

�H

R0

)1

Tab+ C (2)

here C = intercept of the Eq. (2).The value of �H is calculated from the slope of the Eq. (2).From the thermodynamic relationship (Rizvi, 1995):

G = �H − Tab�S (3)

here �G = Gibbs free energy (J/mol) and �S = entropy (J/mol K).For moisture sorption, it can be shown that:

G = −R0Tab ln(RH) (4)

Substitute �G from Eq. (3) into Eq. (4), the following equations obtained:

ln(RH) =(

�H

R0

)1

Tab− �S

Ro(5)

odel of equilibrium moisture content of longan.

When ln(RH) are plotted against 1/Tab a straight line graph isobtained, with the y-intercept of �S/R0. From the values of thisy-intercept and R0, �S can be computed.

3. Results and discussion

3.1. Neural network model

Equilibrium moisture contents of longan were determinedexperimentally using a dynamic method developed by the authors(Janjai et al., 2006). Data on isotherms of longan is shown in Fig. 2.Sorption isotherms (points) of longan are at three temperature lev-els of 30, 40, and 50 ◦C, in the range of 11–97% relative humidity. TheANN model of equilibrium moisture content of longan was devel-oped by training it with experimental sorption data at temperaturesof 30 and 50 ◦C. The isotherm data at 40 ◦C were reserved for test-ing the model. After 500,000 times iteration steps of training, thesquare sum of difference (error) between the observed output andpredicted output reached a significantly low level (3.337 × 10−7).The comparison between the model-predicted and measured equi-librium moisture contents of longan, at the temperature of 40 ◦C isshown in Fig. 3. From this figure it is found that the agreementbetween the predicted and observed equilibrium moisture contentfor longan is excellent (R2 = 0.9998). The standard error of estimate,the relative mean error and the coefficient of determination (R2)of the ANN model at 40 ◦C are 0.8045, 0.1052 and 0.9998, respec-

Fig. 2. Sorption isotherms of longan from the experiments at a temperature of 30,40, and 50 ◦C.

212 S. Janjai et al. / Computers and Electronics in Agriculture 66 (2009) 209–214

F

ohao

3

p6mtmt

rhsdtemusim2tf

�

F

Fig. 5. Net isosteric heat of sorption of longan at different equilibrium moisturecontents.

Table 1Equations of net isosteric heat of sorption of longan, litchi and mango.

Product Equation for theheat of sorption

Coefficient ofdetermination

Source

explained by the fact that at a moisture content above 50% (d.b.) the

ig. 3. Predicted and measured sorption isotherms of longan at 40 ◦C (ANN model).

f the model with more sets of isotherm data between 30 and 50 ◦Cave little to contribute to the further refinement of the ANN modelnd the ANN model can be used to describe the sorption isothermsf longan within the temperature range investigated.

.2. Isosteric heat of sorption and entropy of longan

The values of the equilibrium moisture content at the three tem-erature levels (30, 40, and 50 ◦C) and four moisture levels (40,0, 80, 100 and 120%) for longan were determined using the ANNodel. The plot of ln(RH) as a function of 1/Tab at constant mois-

ure content is shown in Fig. 4. The slopes of the lines at constantoisture contents were determined by regression analysis to find

he net isosteric heat of sorption of longan.The isosteric heat of sorption was derived from the slope of the

egression of ln(RH) versus 1/Tab at constant moisture content. Theeat of sorption for longan at different moisture contents is pre-ented in Fig. 5. The net isosteric heat of sorption was found toecrease with increase in moisture content. At low moisture con-ents, water is absorbed on the most accessible locations on thexterior surface of the solid. As the moisture content increases, theaterial swells and therefore, new high-energy sites are opened

p for water to get bound to. This causes the net isosteric heat oforption to increase as with moisture content decreases. This trends similar to those reported in studies on agricultural, food, and

edicinal and aromatic plants (Hossain et al., 2001; Lahsasni et al.,

004; Mohamed et al., 2005; Phomkong et al., 2006). The net isos-eric heat of sorption was found to fit a power law relation. Theollowing Eq. (6) was developed:

H = 2181.6M−1.2802e R2 = 0.99 (6)

ig. 4. Plot of ln(RH) as a function of 1/Tab at different moisture contents Me (% d.b.).

Longan �H = 2181.6M−1.2802e 0.99 This study

Litchi �H = 50.892 e−0.0232Me 0.95 Janjai et al. (2009)Mango �H = 22.596e−0.0087Me 0.97 Janjai et al. (2007)

This relation showed that the net isosteric heat of sorption oflongan increases following a power law relationship. This rela-tionship has a better fit than the exponential relation previouslydeveloped by the authors (Janjai et al., 2006) for longan. The equa-tion for the net isosteric heat of sorption for longan obtained fromthis study and the net isosteric heat of sorption equations for mango(Janjai et al., 2007) and litchi (Janjai et al., 2009) are shown inTable 1. The comparisons of net isosteric heat of sorption in eachof these species are shown Fig. 6. The variations of the net isostericheat of sorption of longan and litchi with moisture contents arealmost identical (Fig. 6). This might due to the fact that the phys-iochemical structures of the flesh of longan and litchi are similar.However, at moisture contents above 50% (d.b.) the net isostericheat of sorption of longan is lower than that of mango, while at amoisture content below 50% (d.b.) the reverse is true. This can be

water is loosely bound in longan as compared to mango while at amoisture content below 50% it is more tightly bound. This impliesthat longan needs less energy at higher moisture content for dry-

Fig. 6. Comparison of net isosteric heat of sorption of longan with that of litchi andmango.

S. Janjai et al. / Computers and Electronics

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4

obaRuagig

CmtbodTaosatmiwca

ig. 7. Net isosteric entropy of sorption of longan at different equilibrium moistureontents.

ng but more energy at lower moisture contents as compared to thenergy requirements of drying mango.

The differential entropy of longan is plotted as a function ofoisture content and the following power law relationship is fittedith the entropy data of longan, as shown in Fig. 7.

S = 704.5M−0.5576e R2 = 0.97 (7)

From Fig. 7, it is observed that the predicted entropy fitsell with the measured data. This result shows that the entropyecreases with increase in moisture content. Similar trends haveeen reported on the entropy of potato and melon seed and cas-ava (McMinn and Magee, 2003; Aviara and Ajibola, 2002). Theet isosteric heat and entropy equations are essential to computehe humidity during simulation of stored dried longan. The artifi-ial neural network model provides more accurate data to developetter equations for heat of sorption and entropy.

. Conclusions

An ANN model with two inputs (temperature and relative), oneutput (moisture content) and two hidden layers was found toe able to predict the equilibrium moisture content after it wasdequately trained. The ANN model has a predictive power of2 = 99.98%. This is higher than the predictive power of the widelysed phenomenological GAB model previously developed by theuthors (Janjai et al., 2006). Within the temperature range investi-ated, the neural network model can be used to describe sorptionsotherms of longan. The artificial neural network model was pro-rammed in C++.

The net isosteric heat of sorption of longan calculated using thelausius–Clapeyron equation showed a power law relation withoisture content. The isosteric heat of sorption of longan charac-

erized by a power law model developed in this study was found toe more predictive than the exponential model previously devel-ped by Janjai et al. (2006). Differential entropy of dried longaneveloped in this study was also described by a power law model.he net isosteric heats of sorption were compared for longan, litchind mango fruits. Longan and litchi have same pattern of variationf heat of sorption with moisture contents which might be due toimilar biological structure of both of these two fruits. However,t a moisture content above 50% (d.b.) the isosteric heat of sorp-ion of longan is lower than that of mango and the reverse true at a

oisture content below 50% (d.b.). The net isosteric heat equations suggested for use in the computation of heat of sorption of longan

hile both the isosteric heat and entropy equations are essential toompute the humidity during simulation of stored dried longan. Ifrtificial neural network models are developed using experimen-

in Agriculture 66 (2009) 209–214 213

tal equilibrium moisture content data of agricultural products, themodels developed can be used to predict more accurately the equi-librium moisture contents using computers and also can be used topredict the isosteric heat and entropy more accurately for modelingand simulation of drying and storage of agricultural products.

Acknowledgements

This research is part of the research project SFB 564 (Researchfor Sustainable Land Use and Rural Development in MountainousRegions of Southeast Asia), funded by Deutsche Forschungsgemein-schaft (DFG), Germany, and co-funded by the National ResearchCouncil of Thailand and the Ministry of Science, Technology andEnvironment, Vietnam. We would like to thank these organizationsfor the financial support to this project. We also gratefully acknowl-edge Silpakorn University Research and Development Institute forsupporting the experimental part of this work under the projecton determination of equilibrium moisture content of agriculturalproducts in Western Thailand.

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