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Application of Fractal Theory for Prediction of Shrinkage of DriedKiwifruit Using Artificial Neural Network and Genetic AlgorithmMilad Fathia; Mohebbat Mohebbia; Seyed M. A. Razavia

a Department of Food Science and Technology, Ferdowsi University of Mashhad, Iran

Online publication date: 08 June 2011

To cite this Article Fathi, Milad , Mohebbi, Mohebbat and Razavi, Seyed M. A.(2011) 'Application of Fractal Theory forPrediction of Shrinkage of Dried Kiwifruit Using Artificial Neural Network and Genetic Algorithm', Drying Technology,29: 8, 918 — 925To link to this Article: DOI: 10.1080/07373937.2011.553755URL: http://dx.doi.org/10.1080/07373937.2011.553755

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Application of Fractal Theory for Prediction of Shrinkage ofDried Kiwifruit Using Artificial Neural Network andGenetic Algorithm

Milad Fathi, Mohebbat Mohebbi, and Seyed M. A. RazaviDepartment of Food Science and Technology, Ferdowsi University of Mashhad, Iran

In current research, fractal theory has been applied forestimation of shrinkage of osmotically dehydrated and air-driedkiwifruit using a combination of neural network and genetic algor-ithm. Kiwifruits were dehydrated at different conditions and digitalimages of final dried products were taken. Kiwifruit-backgroundinterface lines were detected using a threshold combined with anedge detection approach and their corresponding fractal dimensionswere calculated based on a box counting method. A neural networkwas constructed using fractal dimension and moisture content asinputs to predict shrinkage of dried kiwifruit and a genetic algor-ithm was applied for optimization of the neural network’s para-meters. The results indicated good accuracy of optimal model(correlation coefficient of 0.95) and high potential application offractal theory and described intelligent model for shrinkage esti-mation of dried kiwifruit.

Keywords Artificial neural network; Dried kiwifruit; Fractaldimension; Genetic algorithm; Shrinkage

INTRODUCTION

Drying is one of the oldest preservation methods to pro-long food shelf life by reducing water content.[1,2] Shrink-age is the most important physical change that occursduring the drying of fruits and vegetables. This phenom-enon takes place due to moisture gradient and has somenegative effects on the quality of the dried product, suchas decreasing rehydration ability and consumer’s accept-ance as well as mass transfer rate due to cell structuraldamage.[3,4]

The concept of fractal geometry was first developed byMandelbrot[5] to describe the complexity of natural struc-tures. A fractal object has the following features: (i) it isso irregular that it cannot be easily described in traditionalEuclidean geometry; (ii) it shows a pattern of self-similarity; (iii) it is independent of the unit of measurement;and most important (iv) it has a non-integer dimension(fractal dimension, Df) depending on its irregularity.[6]

Recently, fractal theory has been proposed as a useful toolto quantify irregularity of foodstuff for quality control,non-linear kinetics, and particle and microstructural char-acterization. Chanona et al.[7] applied fractal theory fordescription of drying kinetic and surface temperature dis-tribution and characterization of images of model food(glucose solutions and agar) subjected to dehydration.Based on fractal analysis, the observed drying occurred inthree different stages and fractal dimensions of gray scaleimages increased with drying time. Tang and Marangoni[8]

simulated the rheological properties of fat-structure pro-ducts by determination of fractal dimension of microstruc-ture images of the fat crystal network. The results revealedthat fractal dimension was highly sensitive to differentmicrostructural factors within the fat crystal network.Kerdpiboon and her coworkers[9,10] used fractal dimensionto study and quantify structural changes in dried carrots.The microscopic images were obtained using many differ-ent sample pretreatments (e.g., soaking in isopropylalcohol=water solutions and embedding in paraffin) beforeimage acquiring. Velazquez-Camiloet et al.[11] applied frac-tal theory for monitoring of crystal growth evolution inindustrial processes and reported fractal dimensionincreased with the crystallization time.

In recent years, an artificial neural network (ANN) hasbeen applied as a powerful intelligent modeling tool fornumerous practical applications in food engineering.[12–15]

An artificial neural network model is an interconnectedgroup of functions equivalent to neurons in a biologicalsystem. The power of neural networks lies in their abilityto represent both linear and nonlinear relationshipsbetween inputs and outputs and in their ability to learnthese relationships directly from the modeled data.Mohebbi et al.[16] compared moisture prediction of driedshrimp using multiple linear regression (MLR) and arti-ficial neural network. Their results showed 0.80 and 0.86correlation coefficients for MLR and ANN, respectively.In our previous study we used a multilayer feedforwardneural network to predict the color changes, solid gain,and water loss of osmotically dehydrated kiwifruit. The

Correspondence: Milad Fathi, Department of Food Scienceand Technology, Ferdowsi University of Mashhad, P.O. Box91775 1163, Mashhad, Iran; E-mail: milad.fathi@stu-mail.um.ac.ir

Drying Technology, 29: 918–925, 2011

Copyright # 2011 Taylor & Francis Group, LLC

ISSN: 0737-3937 print=1532-2300 online

DOI: 10.1080/07373937.2011.553755

918

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optimum configuration, which included 16 neurons perhidden layer, could predict these parameters with high cor-relation coefficients.[17]

Determination of neural network architectures, such asthe number of hidden neurons and learning parameterscarried out by a trial and error method, is time-consuming.The use of an optimization technique such as a geneticalgorithm (GA) offers a solution for overcoming this prob-lem. The genetic algorithm mimics the mechanism of thebiological evolution process based on genetic operators.Unlike other optimization techniques, such as linear pro-gramming, genetic algorithms require little knowledge ofthe process itself.[18,19] Liu et al.[20] optimized the neuralnetwork topology for predicting the moisture content ofgrains during the drying process using a genetic algorithm.These authors reported that accuracy of the optimizedmodel with 6 neurons in the hidden layer was satisfactory.

Determination of shrinkage by conventional methodsusing volume measurement is both destructive andtime-consuming. However, fractal geometry can be anopportunity to study irregularity of interfaces as an alter-native method to predict shrinkage. Thus, analysis of theshrinkage as a deformation indicator can be carried outwith fractal dimension determination of the interface line.Therefore, the main aim of this study was to develop aneural network model using a genetic algorithm based onmoisture content and fractal dimension of interface linefor prediction of shrinkage of dried kiwifruit.

MATERIALS AND METHODS

Osmotic Dehydration and Air-Drying Operation

Kiwifruits (cultivar Hayward) were cut into40-mm-diameter and 10-mm-thickness slices and wereosmotically dehydrated with four different sucrose concen-trations (30, 40, 50, and 60� Brix) at temperatures of 20, 40,and 60�C for 2 hours. Osmotic dehydrated samples weresubjected to air drying at 60, 70, and 80�C for 5, 6, and 7hours. Air was injected at the center of the drier (SoroushMedical Company, Khorasan Razavi province, Iran; withoverall dimensions of 85 cm in length, 124 cm in height,and 65 cm in width) at air velocity of 1.5m=s.

Determination of Percentage of Shrinkage and MoistureContent

Percentage of shrinkage (Sh) was determined fromchanges in volume of kiwifruit samples. Volume wasdetermined using the liquid displacement method.[21] Tolu-ene was used instead of water because it caused thereduction of liquid absorption into kiwifruit.[22] Percentageof shrinkage was calculated as:

Sh ¼ V0 � V

V0� 100 ð1Þ

where V0 and V are initial (prior to osmotic dehydration)and final (after air drying) volume of kiwifruit, respectively.

Moisture content (% w.b) was measured by drying in aconvection oven at 90�C until constant weight wasobtained.

Image Acquisition and Fractal Analysis

A color digital camera (Canon Powershot, Model A520,Japan) with 4 Mega Pixels of resolution was placed inside awooden box impervious to light and having internal blacksurfaces. To achieve high uniformity and repeatability, theiris was adjusted in the manual mode and the lens wasoperated with aperture of 4 and speed 1=10 s (withoutzoom and flash). Three illuminating lights (Opple, 8W,model: MX396-Y82; 60 cm in length) with a color index(Ra) close to 95% were fixed into the box at the angle of45� with sample plane to give a uniform light intensity overthe kiwifruit sample.[23] Camera was connected to the USBport of a Pentium IV, 2.4GHz computer. Canon DigitalCamera Solution Software (version 22) was used to acquirethe images in the computer in JPEG format. Images werecaptured at 2272� 1704 pixels.

To measure the fractal dimension of kiwifruit-background interface lines, images were analyzed usingImagJ software version 1.40 g. Red-green-blue (RGB)chromatic space images of kiwifruits were gray-scaledand transformed into binary images. The kiwifruit-background interface lines (edge lines) were found usingautomatic thresholding based on an isodata algorithm[24]

combined with an edge detection approach according tothe Laplacian-of-Gaussian (LoG) filter[25] based on the fol-lowing equation:

LoGðx; yÞ ¼ � 1

prG41� x2 þ y2

2rG2

� �e�x2þy2

2rG2 ð2Þ

Where x and y are coordinates of each pixel and rG is aGaussian standard deviation.

Fractal dimension of kiwifruit-background interface lineswas calculated by means of a box counting method (BCM),which is one of the most widely used techniques in the litera-ture.[26–28] The BCM method consists of carrying out a pro-gressive process by placing a grid of decreasing size over animage and counting the number of boxes that contain someparts of an interface line (Nr), for each grid size (r). The boxsizes of 2, 3, 4, 6, 8, 12, 16, 32, and 64 pixels were chosen andfractal dimension was calculated as:[29]

Df ¼ limr!0

logðNrÞlogð1=rÞ ð3Þ

It is noteworthy that, based on classical Euclidian geometry,a point has a zero dimension, a straight line one, plane two,

FRACTAL THEORY FOR PREDICTION OF SHRINKAGE 919

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and cube three. However, according to fractal geometry anirregular line has a fractal dimension between 1and 2 regard-ing its complexity.

Artificial Neural Network

A feedforward neural network, which is the most com-monly used ANN and can be easily implemented as a soft-ware simulation, was applied for prediction of shrinkage ofdried kiwifruit. This network has one or more hiddenlayers of neurons. Hidden neurons intervene between theinputs and network outputs. In multi-layered perceptronnetwork, the neurons are arranged in three different layers:(i) an input layer with neurons representing input variablesto the problem; (ii) an output layer with neuron(s) repre-senting the dependent variable(s); and (iii) a hidden layer(s)composed of some hidden neurons depending upon com-plexity of the model (Fig. 1).

Each neuron (except the input ones) receives infor-mation from several neurons through connections in pro-portion to their weights, sums them up, and modifies thesum through a non-linear or in some cases linear transferfunction (f) before passing the signal to other neurons.Mathematically, the function of a neuron can be expressedas:

yj ¼Xni¼1

f ðwijxiÞ þ bj ð4Þ

where x and y are input and output of neuron, respectively,n is number of inputs to the neuron, wij is the weight of theconnection between neuron i and neuron j, and bj is the

bias associated with j th neuron, which adds a constantvalue in the weighted sum to improve convergence.

In this research, the fractal dimension of kiwifruit-background interface line and the moisture content ofdried product were applied as inputs, and shrinkage ofdried product was considered as the output. The hyperbolictangent function (Eq. 5), which is the most popular func-tion, was used in a single hidden layer, while a linear func-tion was used in the output layer. The number of hiddenneurons varied from 2 to 20.

tanhðxÞ ¼ ex � e�x

ex þ e�xð5Þ

A total of 324 data were experimentally collected and ran-domly divided into three partitions for training (40% ofdata), validating (30% of data). and testing (30% of data)the developed network. The training process was carriedout for 1000 epochs or until the cross-validation data’smean-squared error (MSE), calculated by Eq. 6, did notimprove for 100 epochs to avoid over-fitting of thenetwork.

A back propagation algorithm was applied as the learn-ing algorithm of ANN. In this method the error of the out-put is back propagated from the output layer to the hiddenlayer and, finally, to the input layer to modify the weights.Evaluation of the performance of the trained network wasbased on the accuracy of the network in the test partition.The test data’s errors were calculated by means of the meansquare error (MSE), normalized mean square error(NMSE), and mean absolute error (MAE) as defined in

FIG. 1. Procedure of optimization using algorithm genetic and artificial neural network.

920 FATHI ET AL.

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TABLE

1Averagevalues

ofshrinkage,

fractaldim

ension,andmoisture

contentofosm

oticallydehydratedandair-dried

kiwifruit

Shrinkage(%

)Fractaldim

ension

Moisture

content(%

w.b.)

Parameter

5h

6h

7h

5h

6h

7h

5h

6h

7h

A1B1C1

65.99�2.41

74.55�1.11

77.75�1.42

1.138�0.0

1.139�0.005

1.149�0.004

53.82�3.04

37.78�2.51

30.7�3.17

A1B1C2

69.55�0.11

74.65�3.09

80.9�0.14

1.154�0.005

1.162�0.003

1.161�0.001

44.02�2.63

32.15�6.27

25.98�0.33

A1B1C3

78.89�0.09

80.34�1.71

80.28�0.72

1.15�0.0

1.153�0.0

1.15�0.002

30.5�2.44

23.4�1.23

17.92�0.51

A1B2C1

69.3�1.90

72.02�2.19

74.36�1.23

1.134�0.0

1.142�0.004

1.152�0.005

42.66�5.64

35.11�4.15

31.21�4.03

A1B2C2

79.01�0.92

78.55�1.02

80.95�1.34

1.139�0.0

1.142�0.0

1.158�0.002

26.85�0.12

22.15�3.04

15.95�0.45

A1B2C3

78.24�1.76

80.69�1.61

78.75�0.45

1.151�0.0

1.128�0.002

1.163�0.001

24.15�2.17

20.95�1.36

13.14�2.46

A1B3C1

68.9�0.46

74.06�0.29

75.65�1.01

1.143�0.002

1.148�0.0

1.152�0.0

37.17�3.53

29.56�2.67

21.54�0.02

A1B3C2

75.42�0.90

76.83�1.25

76.2�0.04

1.145�0.002

1.159�0.003

1.162�0.001

26.46�2.09

20.61�3.59

17.34�1.42

A1B3C3

76.18�0.45

78.5�1.20

77.69�2.03

1.154�0.001

1.151�0.0

1.347�0.001

19.03�0.47

16.76�1.07

12.38�0.22

A2B1C1

69.5�1.65

74.73�2.99

77.99�0.41

1.119�0.002

1.129�0.001

1.147�0.001

49.5�1.01

39.6�6.27

30.25�1.35

A2B1C2

73.47�0.65

77.75�1.68

81.67�0.46

1.15�0.001

1.149�0.001

1.159�0.002

37.21�3.24

26.86�1.30

21.35�4.33

A2B1C3

79.08�0.95

81.5�1.04

81.33�0.62

1.132�0.003

1.154�0.003

1.159�0.001

26.8�0.10

21.35�0.40

17.16�0.94

A2B2C1

75.42�2.14

77.09�1.17

80.38�1.38

1.137�0.001

1.148�0.002

1.148�0.002

33.37�3.64

28.92�2.07

19.82�2.97

A2B2C2

78.02�2.74

78.36�1.29

80.79�0.57

1.148�0.004

1.155�0.001

1.16�0.001

25.2�4.50

21.44�1.87

14.82�3.66

A2B2C3

81.32�0.11

81.35�1.25

83.33�0.43

1.158�0.005

1.244�0.001

1.142�0.0

23.07�2.77

20.24�1.01

12.23�2.12

A2B3C1

72.79�1.92

73.81�1.93

73.68�0.97

1.148�0.001

1.139�0.002

1.143�0.001

33.37�3.64

28.92�2.07

21.01�1.73

A2B3C2

75.08�0.36

75.36�1.11

74.8�0.00

1.136�0.0

1.132�0.002

1.159�0.001

20.01�0.89

18.54�0.41

14.24�0.22

A2B3C3

79.7�0.08

80.36�0.13

78�0.19

1.143�0.0

1.166�0.0

1.135�0.001

18.46�2.41

15.71�3.84

9.82�0.99

A3B1C1

67.45�0.52

70.79�1.65

75.7�2.05

1.129�0.0

1.146�0.007

1.155�0.002

44.68�2.02

35.69�7.78

34.05�0.45

A3B1C2

75.09�0.70

79.28�1.01

80.69�0.02

1.136�0.001

1.15�0.002

1.16�0.001

35.47�0.07

24.68�1.90

21.86�2.58

A3B1C3

81.83�1.33

84.37�0.21

82.79�0.73

1.147�0.004

1.157�0.0

1.161�0.0

21.91�1.64

14.32�0.28

11.72�0.91

A3B2C1

71.82�2.00

75.92�1.37

77.07�0.72

1.143�0.001

1.275�0.002

1.152�0.0

33.62�3.02

27.64�1.70

22.31�2.04

A3B2C2

79.06�1.03

78.32�0.36

79.49�1.70

1.147�0.0

1.152�0.0

1.154�0.001

21.21�2.43

18.46�6.20

15.23�1.16

A3B2C3

81.91�1.08

82.8�0.26

81.06�0.72

1.137�0.0

1.158�0.0

1.166�0.0

14�1.20

13.05�0.01

8.97�1.05

A3B3C1

74.6�0.89

74.58�0.47

77.47�0.55

1.35�0.002

1.16�0.0

1.14�0.0

24.67�1.12

22.06�0.31

18.87�2.59

A3B3C2

78.18�0.55

78.76�0.94

77.16�0.45

1.135�0.001

1.139�0.0

1.161�0.0

20.41�0.99

17.2�1.42

14.16�3.12

A3B3C3

81.05�0.21

78.56�0.89

80.14�0.58

1.149�0.0

1.407�0.0

1.159�0.0

15.36�1.22

12.79�0.34

8.23�0.43

A4B1C1

72.28�5.08

77.1�2.53

79.04�0.56

1.137�0.006

1.152�0.003

1.16�0.0

39.42�0.31

34.31�4.63

27.9�5.62

A4B1C2

78.02�0.36

82.35�1.25

81.28�0.33

1.138�0.0

1.167�0.0

1.155�0.002

36.25�0.72

19.76�3.62

19.06�0.19

A4B1C3

81.3�0.04

83.43�0.06

86.43�5.59

1.152�0.0

1.159�0.002

1.169�0.0

19.01�1.85

11.76�1.57

8.73�5.38

A4B2C1

77.38�0.02

78.52�0.01

79.21�1.54

1.133�0.0

1.135�0.002

1.142�0.0

32.76�3.17

24.93�2.00

23.94�1.90

A4B2C2

76.2�0.90

78.76�1.74

81.58�1.95

1.165�0.0

1.17�0.001

1.165�0.002

21.72�0.57

16.32�0.09

15.33�0.24

A4B2C3

81.79�2.34

80.3�0.38

80.54�1.40

1.145�0.004

1.157�0.0

1.184�0.002

13.17�0.07

11.38�0.91

7.28�0.52

A4B3C1

75.08�1.03

75.61�2.33

74.79�0.74

1.145�0.0

1.378�0.0

1.172�0.006

23.46�1.03

20.44�0.28

16.99�1.30

A4B3C2

75.21�1.64

77.4�0.44

81.46�1.01

1.176�0.003

1.163�0.0

1.179�0.002

23.61�0.02

17.87�1.31

13.21�0.07

A4B3C3

79.91�0.32

79.16�1.18

79.06�1.95

1.153�0.0

1.142�0.001

1.142�0.002

11.02�1.90

10.5�0.57

6.71�1.05

A1,osm

oticconcentrationof30%;A2,osm

oticconcentrationof40%;A3,osm

oticconcentrationof50%;A4,osm

oticconcentrationof60%;B1,osm

otictemperature

of20� C

;B2,osm

otictemperature

of40� C

;B3,osm

otictemperature

of60� C

;C1,airtemperature

of60� C

;C2,airtemperature

of70� C

;C3airtemperature

of80� C

.

921

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Eqs. 6–8:

MSE ¼

PNi¼1

ðOi � TiÞ2

Nð6Þ

NMSE ¼ 1

r21

N

XNi¼1

ðOi � TiÞ2 ð7Þ

MAE ¼ 1

N

XNi¼1

Oi � Tij j ð8Þ

where Oi is the ith actual value, Ti is the ith predicted value,N is the number of data, and r2 is the variance.

Genetic Algorithm

A genetic algorithm, which is based on the principle of aDarwinian-type survival of the fittest in natural evolution,is essentially an iterative, population-based, parallel globalsearch algorithm that has a high ability to find optimalvalue of a complex objective function, without falling intolocal optima.[18] In this optimization method, best indivi-duals can mate with other individuals of the populationand survive for the next generation, and the most excellentindividual, which is the most evolved one, is an optimalvalue. A genetic algorithm optimization method consistsof three principle processes namely selection, crossover,and mutation (Fig. 1). For this purpose, the initial popu-lation of chromosomes is randomly generated. Selectionof individuals to produce successive generations plays anextremely important role in a GA. In this step, each chro-mosome is evaluated by the fitness function. Accordingto the value of the fitness function, the chromosomes

associated with the fittest individuals will be selected moreoften than those associated with unfit ones. In the cross-over step, two individuals (parents) reproduced into anew individual. The mutation operation consists of ran-domly altering the value of each element of the chromo-some according to the mutation probability. It providesthe means for introducing new information into the popu-lation. This cycle is repeated until desired convergence onoptimal or near-optimal of the solutions is achieved.

In current work, the number of hidden neurons andtraining parameters were represented by haploid chromo-somes consisting of three genes of binary numbers. Thefirst gene corresponds to the number of neurons in a single

FIG. 2. True images, interface lines, and corresponding fractal dimen-

sions of kiwifruits undergoing different drying temperatures for 5 h and

for osmotic concentration of 50% and temperature of 60�C.

FIG. 3. Effect of drying temperature and time on the shrinkage (I),

moisture content (II), and fractal dimension (III) of dried kiwifruit at

osmotic concentration and temperature of 50% and 20�C.

922 FATHI ET AL.

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hidden layer and second and third genes represent thelearning rate and momentum of network, respectively.An initial population of 60 chromosomes was randomlygenerated. According to the literature[30–32] the best gener-ation number is set at 50. Therefore, the termination cri-terion of 60 was chosen. The roulette wheel selectionbased on ranking algorithm was applied for the selectionoperator. Uniform crossover and mutation operators withmixing ratio of 0.5 were used and the probabilities of thecrossover and mutation operators were adjusted at 0.9and 0.01, respectively. In this study, the ANN modelingand GA optimization were performed by Neurosolutionsoftware (Version 5.0, NeuroDimension Inc., Gainesville,FL, USA).

Statistical Analysis

Analysis of variance (ANOVA) was performed using acomputerized statistical program called MSTAT versionC, and determination of significant differences of meanswas carried out by ‘‘Duncan’’ test at 99% confidence levelusing the aforementioned software program.

RESULTS AND DISCUSSION

Effect of Drying Conditions

Kiwifruits were dehydrated using sucrose solutions (30,40, 50, and 60%) at different temperatures (20, 40, and60�C) and air-dried at 60, 70, and 80�C for 5, 6, and 7hours. Average values of three replications of moisturecontent, shrinkage, and fractal dimension for different con-ditions were tabulated in Table 1. Results showed increas-ing drying temperatures and times led to more extensiveshrinkage. The percentage of shrinkage changed signifi-cantly (p< 0.01) in the range of 65.99 to 80.38, 69.55 to82.35, and 76.18 to 86.43% at 60, 70, and 80�C, respect-ively. On the other hand, due to increase of driving force,moisture content values of kiwifruits decreased signifi-cantly (p< 0.01) as the concentration and temperature of

osmotic solution and time and temperature of hot air dry-ing increased. Moisture contents had a direct relationshipwith shrinkage values of dried kiwifruits. Increasing themoisture gradient in the fruit due to the increase of dryingtimes and temperatures led to an inability of the kiwifruittissue to hold its structure network and consequentlyshrinkage phenomenon.[33]

Typical images of dried kiwifruits and their correspond-ing interface lines at different temperatures are depicted inFig. 2. It was indicated that fractal dimensions of interfacelines increased as the times and temperatures of air dryingincreased. Applying higher drying times and temperaturesled to more severe microstructure changes of the fruit’stissue, which caused an increase in irregularity of kiwifruitstructure and consequently significantly increasing the frac-tal dimension. Fractal dimension changes followed thesame patterns with shrinkage values (Fig. 2). The effectsof drying temperature and time on the shrinkage, moisturecontent, and fractal dimension of dried kiwifruit at osmoticconcentration and temperature of 50% and 20�C are pre-sented in Fig. 3. The same tendencies were found for otherdehydration conditions. Kerdpiboon et al. calculated frac-tal dimension of cell walls of microscopic images of dried

FIG. 4. Best fitness (MSE) versus generation of optimized neural

network.

TABLE 2Weight and bias values of each neuron of ANN-GA model

for shrinkage prediction of dried kiwifruit

Input neuronsOutputneuron

Number ofhiddenneurons Bias

Fractaldimension

Moisturecontent Shrinkage

1 0.000114 �1.2905 �1.2738 �0.40422 �0.000092 �0.8958 �0.6371 �0.27833 0.000059 0.2199 �0.3236 0.30804 �0.000003 0.4307 0.4513 �0.01985 �0.000024 �0.1338 0.2696 �0.16016 0.000133 �1.2685 �1.3262 �0.47397 �0.000009 0.3831 0.7806 �0.18448 0.000094 1.0047 2.2626 �0.64589 �0.000019 0.0419 0.4692 �0.2090

10 0.000021 �0.0204 �0.5667 0.279311 0.000022 0.1627 �0.2453 0.132712 0.000002 �0.1148 0.0156 0.021813 0.000303 0.6190 �1.6827 �0.299114 0.000005 0.2625 0.1602 0.045915 �0.000039 �0.3130 0.2114 �0.175516 �0.000015 �0.0329 0.3398 �0.128417 �0.000011 0.1767 0.5526 �0.1496Bias 0.000052

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carrot and found that fractal dimension increased with dry-ing time, corresponding to less orderly cell structures.[9]

Neural networks with 2–20 neurons were trained usingGA to find the optimal network configuration and para-meters for prediction of shrinkage. However, since theimage processing and ANN modeling are time-consumingmethods, the application of these techniques are recom-mended for quality control in small-scale production. Theresults showed that the optimized network contained 17hidden neurons and had learning rate and momentumvalues of 0.9022 and 0.9491 in the hidden layer and0.4312 and 0.8212 in the output layer, respectively. Thisconfiguration had MSE, NMSE, and MAE of 1.6762,0.1024, and 1.0146, respectively. The best fitness, which isthe lowest MSE value calculated across all of the networkswithin the corresponding generation, is plotted in Fig. 4.This figure showed that the MSE value achieved a relativeconstant value after 5 generations. The ultimate aim ofANN modeling is determination of connecting weights ofeach neuron. The weight and bias values of optimizedmodel are tabulated in Table 2. Plot of experimental valuesof percentage of shrinkage versus neural network predic-tion is traced in Fig. 5. The high correlation coefficientreveals good agreement between predicted and experi-mental data (correlation coefficient of 0.95) and potentialapplication of fractal theory and ANN-GA model forrapid and non-destructive inspection of osmoticallydehydrated kiwifruit.

CONCLUSIONS

In this study, the moisture content and fractal dimensionof kiwifruit-background interface line of osmotically dehy-drated and air dried kiwifruit were determined and artificialneural network and genetic algorithm approaches wereapplied for estimation of percentage of shrinkage. It wasfound that shrinkage and fractal dimension of dried kiwi-fruit increased as the drying time and temperature increased.

The optimal number of hidden neurons and neural networkparameters (learning rate and momentum) were found usinga genetic algorithm. The optimized neural network modelwith 17 neurons in the hidden layer can estimate shrinkagewith a high correlation coefficient (0.95), showing a highability of the neural network and fractal theory to predictand describe shrinkage of dried kiwifruit.

ACKNOWLEDGMENT

The authors would like to acknowledge Miss Ajori forher assistance during the experiments.

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