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Pelagia Research Library European Journal of Experimental Biology, 2013, 3(3):712-721

ISSN: 2248 –9215 CODEN (USA): EJEBAU

Mathematical and neural networks modeling of thin-layer drying of peach (Prunus persica) slices and their comparison [6]Majid Yazdani1*, Ali Mohammad Borghaee1, Shahin Rafiee2, Saeid Minaei1 and Babak Beheshti1 1

Department of Agricultural Machinery Eng., College of Agriculture, Science and Research Branch, Islamic Azad University (IAU), Tehran, Iran 2 Department of Agricultural Machinery Engineering, Faculty of Agricultural Engineering and Technology, College of Agriculture and Natural Resources, University of Tehran, Karaj, Iran _____________________________________________________________________________________________ ABSTRACT Fast ripening and decay after harvesting are the factors limiting peach storage, so drying peach slices is a solution for this problem. To introduce an accurate model to simulate the drying curves under different conditions, peach slices were dried to equilibrium moisture in thin-layer dryer set using different air temperatures (40, 50, 60, 70 and 80°C) and velocities (1, 1.5 and 2 m/s). In this research, 13 mathematical equations have been used to fit peach slices drying curve. Results indicated that Midilli et al. model with RMSE between 0.01273 to 0.00463 and r2 0.9996 to 0.9982 was the best mathematical model that satisfactorily represented the experimental values. Artificial neural network is a well-known tool for solving complex, non-linear biological systems. The Multi-layer perceptron network was used for modeling drying kinetics. With regard to the results, the network with LOGSIG-TANSIGPURELIN activation function and 3-6-4-1 topology showed the best performance, in which RMSE was 0.00196 and r2 was 0.99996. At last, by comparing final unique neural network model with Midilli et al. model for the whole range of experiments, it was clear that neural network model is more accurate than Midilli model in each experiment conditions. Keywords: Neural Network model, Empirical model, peach, moisture ratio, Multi-layer perceptron. _____________________________________________________________________________________________ INTRODUCTION Fruits and vegetables are regarded as highly perishable food due to their high moisture content [[41]]. Drying is one of the most widely used primary methods for food preservation [[4]]. It provides longer shelf-life, smaller space for storage and lighter weight for transportation [[3]]. Drying is defined as a process of moisture removal due to simultaneous heat and mass transfer [[35]]. This complicated process depends on different factors such as air temperature and velocity, relative air humidity, air flow rate, physical nature and initial moisture content of the drying material, exposed area and pressure [[5]]. The importance of achieving quality specifications and conserving energy, emphasize the need for a thorough understanding of drying process [[4]]. In order to improve the control the operation of this unit, it's important to provide precise models for simulating the drying curves under different conditions. Thin-layer drying models that describe the drying phenomenon of agricultural products fall mainly into three categories, namely theoretical, semi-theoretical and empirical [[38]]. The theoretical approach is concerned with diffusion or simultaneous heat and mass transfer equations. The semi-theoretical approach is concerned with approximated theoretical equations. Empirical equations are easily applied to drying simulation as they depend only

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Majid Yazdani et al Euro. J. Exp. Bio., 2013, 3(3):712-721 ____________________________________________________________________________ on experimental data [[1]]. Several investigators have proposed numerous mathematical models for thin layer drying of many agricultural products. For example, tomato [[35]], Golden apples [[30]], eggplants [[4]], Mango Slices [[3]], sesame seeds [[26]], prickly pear fruit [[27]], eggplant [[16]], kiwi fruit[[42]], tarragon [[7]], red chillies [[24]], apricots [[11]], apple [[40]], orange skin [[19]], figs [[10]], parboiled paddy [[43]], hazelnuts [[37]], red pepper [[6]], pistachio nuts [[25]], pistachio [[32]], banana [[9]]. Empirical mathematical correlations usually give very accurate results for each specific experiment. But there isn't any valid equation for other conditions and there is no way to obtain a general equation for a range of drying parameters. Artificial Neural Networks (ANN) models have been successfully used in prediction of problems in bioprocessing and chemical engineering [[35]]. Artificial neural network is a well-known tool for solving complex, non-linear biological systems and it can give reasonable solutions even in extreme cases or in the event of technological faults [[26]]. An ANN is a computer program capable of learning from examples through iteration, without requiring prior knowledge of the relationships between process and product parameters [[13]]. The selection of an appropriate ANN topology to predict the drying process is important in terms of model accuracy and model simplicity [[29]]. This technique has been successfully applied to the prediction of drying kinetics of seeds, vegetables, and fruits by investigators [[35], [26], [29], [18], [12], [33], [16], [31], [20], [36], [34], [13]]. No investigations have been reported on the thin-layer drying kinetics of peach slices in literatures. Peach (Prunus persica) is a source of fiber, vitamins, and minerals, and now we found that it is a good source of antioxidants [[28]]. Iran is the world's eighth peach producer [[1]]. Fast ripening and decay after harvesting are the factors limiting peach storage life, thus drying peach slices is a solution for the problem. A large-sized peach has only 70 calories which makes it a fantastic snack or dietetic dessert [[15]]. This research is based on thin layer drying process with heated air. The objectives of the study were to determine the effect of drying air temperature and air flow rate on the drying kinetics of peach slice, and to select the best mathematical model and artificial neural network topology for predicting the drying curves and to compare them.

Fig. 1. Experimental dryer: 1.Fan; 2.Preheating element; 3.Interface canvas; 4.Dryer chamber stand; 5.Heating elements; 6.Straightener; 7.Relative humidity and Temperature sensors; 8.Air velocity and Temperature sensors; 9.Top camera; 10.Fluorescent lamps; 11.Side camera; 12.Halogen lamp; 13.Load cell; 14.Platform; 15.HMI; 16.Computer; 17. Keyboard.

MATERIALS AND METHODS Drying equipment The dryer used in present study was a thin layer dryer manufactured based on machine vision at Farm Machinery Department, Agricultural Faculty, Tehran University, Karaj, Iran [[21]]. The dryer was consisted of a centrifugal fan, ventilator, four electrical heater elements (a 750 W element beside centrifugal fan for preheating and three 2000 W elements beside ventilator for heating the inlet air flow), air flow straightener, control unit, lighting and imaging chamber, a digital color camera, a single point load cell with 0.001 g accuracy, drying chamber, product samples tray and temperature, air velocity and relative humidity sensors. Two temperature sensors with ± 1°C accuracy were placed before and after the sample tray as well as another sensor to measure ambient air temperature. The schematic view of this dryer is shown in figure 1. All parts of dryer are covered by fiberglass insulation. The control system including a programmable logic controller (PLC, FATEK, Fbs-20MA), analog digital converter (FATEK, Fbs-6AD), digital analog converter (FATEK, Fbs-4AD), 12 V power supply (Acro, AD1048-24FS), load

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Majid Yazdani et al Euro. J. Exp. Bio., 2013, 3(3):712-721 ____________________________________________________________________________ cell transmitter (ESiTT, TR-3, Turkey), an inverter to control fan speed (Rhymebus, RM5E-2002), a power controller using to control the elements voltage (Autonics, SPCI-35) and electronic circuit consist of air relative humidity and temperature measurement sensors, were used to control the dryer during drying process. PLC controller was connected to a computer (Intel-Pentium 4, 3.06 GHz, 512MB RAM, 200GB hard disk) by a RS-232 cable. All the measured data during drying process (temperatures, relative humidity, air velocity, sample weight and time) were transferred to computer and saved in it by PLC controller and a program which was written in MATLAB software (MATLAB 7.7). A control panel (HMI, FV035ST-C10) was applied to input drying condition and load cell, fluorescent lamps and camera adjustment to choose data recording interval. Fresh and ripe Haji Kazemi variety peach fruits were purchased at local market in Karaj (an agricultural area in west of Tehran). Variety selection was done based on cutting ability, proper color and availability. During the experiments, fruits were stored in a refrigerator at 4°C. First, the peaches were washed, their pits were removed, then were sliced into 4 mm thickness using a stainless steel sausage cutter. The initial moisture content and dry-based material weight of samples were determined at 78°C after 48 hours in an oven dryer (AOAC, 1984) . Drying procedure The dryer was run without the sample for about 30 min to set the desired conditions before each drying experiment [[35]]. Drying process started when drying conditions were achieved. The peach slices samples were spread on mesh trays and placed into the tunnel of the dryer and measurement started at this point. The amounts of samples weight, ambient air relative humidity, air temperature before and after the tray and time were recorded and saved in PC at 1 minute intervals. The final moisture content of the product was determined while the product reached the fixed weight in the drying chamber [[30]]. Drying experiments were run at 3 levels of drying air velocity and 5 levels of drying air temperature (Table 1). Three sets of drying experiments were conducted during September 2012 under Karaj (a city in center of Iran) weather conditions. Table 1. Experimental conditions Experiment No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Air temperature °C 40 40 40 50 50 50 60 60 60 70 70 70 80 80 80

Air velocity m/s 1 1.5 2 1 1.5 2 1 1.5 2 1 1.5 2 1 1.5 2

Table 2. Empirical mathematical equations used for peach slices drying modeling Model no. 1 2 3 4 5 6 7 8 9 10 11 12 13

Model equation MR = exp(-kt) MR = exp(-ktn) MR = exp[-(kt)n] MR = a exp(-kt) MR = a exp(-kt) + c MR = a exp(-k0t) + b exp(-k1t) MR = a exp(-kt) + (1 - a)exp(-kat) MR = 1 + at + bt2 MR = a exp(-kt) + (1 - a)exp(-kbt) MR = a exp(-kt) + (1 - a)exp(-gt) MR = a exp(-kt) + b exp(-gt) + c exp(-ht) MR = a exp(-ktn) + bt t = a ln(MR) + b[ln(MR)]2

Name Newton Page Modified Page Henderson and Pabis Logarithmic Two term Two term exponential Wang and Singh Diffusion approach Verma et al. Modified Henderson and Pabis Midilli et al. Thompson

Mathematical modeling of drying curves In thin layer drying model, the rate of change in material moisture content at falling rate drying period is proportional to instantaneous difference between material moisture content and the expected one when it reaches

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Majid Yazdani et al Euro. J. Exp. Bio., 2013, 3(3):712-721 ____________________________________________________________________________ equilibrium level by the drying air. It is assumed that the material layer is thin enough or the air velocity is high so that the conditions of the drying air (humidity and temperature) are kept constant throughout the material [[30]]. Table 2 consists of 13 mathematical equations which are frequently used to fit empirical correlations for describing the drying behavior of natural products. These equations which express the moisture ratio (MR) as a function of time have been used to fit the drying curve of the peach slices. The moisture ratio is usually expressed as: (1) Where M0 and Me are the initial and equilibrium moisture contents(% dry basis) respectively. However, the value of equilibrium moisture content (Me) for natural products is usually small relative to M or M0 Thus, equation 1 may be simplified to M/M0 [[35]]. The regression analysis was performed using the MATLAB software toolbox (MATLAB 9.2). The models constants were calculated. Root Mean Square Error (RMSE) and correlation coefficient (r2) were the criterions for selection of the best equation in each experimental condition. RMSE may be calculated as follows:

(2) Where MRexp,i is the ith experimental moisture ratio, MRpre,i is the ith predicted moisture ratio, N is the number of observations and n is the number of constants in the drying model. The results of the regression analysis for the drying data are shown in Table 3. It is assumed that the model with lowest RMSE and highest r2 is best suited for each condition. Artificial neural networks modeling of experiment data The type of network used in this work is multi-layer perceptron (MLP) network. Multi-layer perceptron networks are one of the most popular and successful neural network architectures, which are suited to a wide range of applications such as prediction and process modeling [[26]]. An MLP network comprises a number of identical units organized in layers, with those on one layer connected to those on the next layer, so that the outputs of one layer are regarded as inputs to the next layer. MLP neural networks are normally trained using a supervised training algorithm. Figure 2 illustrates the topology of a simple, fully connected three-layer MLP network. Different types of activation functions can be utilized for this network; however the common ones, which are sufficient for most applications, are the Logarithmic Sigmoid, Tangent Sigmoid and Purelin functions. Normally, the back-propagation method is the first order gradient method used to train neural networks to correlate between input and output variables [[22]]. The training of a back-propagation network consists of two phases: a forward pass during which the processing of information occurs from the input layer to the output and a backward pass when the error from the output layer is propagated back to the input layer and the interconnections are modified [[39]]. Experimental data from this study were used to train and test an Artificial Neural Networks model for prediction of peach slices moisture ratio during the drying process. The experimental data were randomly divided into two sets. One set was used as training data and the other was used for testing the model. Applying MATLAB Neural Network Toolbox, MATLAB 9.2 software, a feed-forward ANN model was designed using back-propagation training algorithm. The number of neurons in input and output layers depend on independent and dependent variables, respectively. Since one dependent variable (the moisture ratio of the dried peach slices) depends on three variables including drying air temperature and velocity and time, one and three neurons were respectively devoted to output and input layers. The number of hidden layers and their neurons depends on the complexity of the problem to be investigated [[23]]. The Root Mean Square Error (RMSE) and correlation coefficient (r2) of the models were calculated and used for selecting an optimal ANN model and comparing with different empirical correlations in Table 3.

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Majid Yazdani et al Euro. J. Exp. Bio., 2013, 3(3):712-721 ____________________________________________________________________________ Table 3. Statistical results of 13 models at 15 different drying conditions Experiment No. 1 Model No. statistical criterions RMSE 0.02959 1 0.09886 r2 RMSE 0.01251 2 r2 0.998 RMSE 0.01251 3 r2 0.998 RMSE 0.02492 4 r2 0.9919 RMSE 0.02492 5 r2 0.9919 RMSE 0.02498 6 r2 0.9919 RMSE 0.02964 7 r2 0.9886 RMSE 0.03401 8 r2 0.985 RMSE 0.02948 9 r2 0.9887 RMSE 0.0248 10 r2 0.992 0.02659 RMSE 11 r2 0.9909 RMSE 0.0074 12 r2 0.9993 RMSE 0.1168 13 r2 0.8223

2

3

4

5

6

7

8

9

10

11

12

13

14

15

0.03603 0.9842 0.01258 0.9981 0.01258 0.9981 0.02942 0.9895 0.02942 0.9895 0.02947 0.9895 0.03608 0.9842 0.02552 0.9921 0.03614 0.9842 0.03606 0.9842 0.02982 0.9893 0.0072 0.9994 0.1238 0.8135

0.01901 0.9944 0.00907 0.9987 0.00907 0.9987 0.01635 0.9959 0.01635 0.9959 0.01637 0.9959 0.01904 0.9944 0.07891 0.904 0.01904 0.9944 0.01903 0.9944 0.04282 0.9719 0.0067 0.9993 0.09758 0.853

0.02376 0.9895 0.00676 0.9991 0.00676 0.9991 0.01877 0.9934 0.01877 0.9934 0.0188 0.9934 0.02378 0.9895 0.1303 0.6839 0.02378 0.9895 0.02377 0.9895 0.04253 0.9665 0.0046 0.9996 0.08869 0.8533

0.02214 0.9924 0.00961 0.9986 0.00096 0.9986 0.01871 0.9946 0.01871 0.9946 0.01874 0.9946 0.02217 0.9924 0.07921 0.9033 0.02217 0.9924 0.02215 0.9924 0.08864 0.8797 0.0075 0.9991 0.09698 0.8548

0.0313 0.9866 0.01184 0.9981 0.01184 0.9981 0.02585 0.9909 0.02585 0.9909 0.02605 0.9908 0.03135 0.9866 0.06046 0.9501 0.0312 0.9867 0.02562 0.9911 0.02898 0.9886 0.009 0.9989 0.1073 0.8423

0.03445 0.9855 0.01371 0.9977 0.01371 0.9977 0.0287 0.99 0.0287 0.99 0.02879 0.99 0.03452 0.9855 0.02074 0.9948 0.03435 0.9857 0.02848 0.9902 0.03534 0.985 0.0077 0.9993 0.1184 0.8292

0.04079 0.9805 0.01485 0.9974 0.01485 0.9974 0.03359 0.9868 0.03359 0.9868 0.0337 0.9868 0.04087 0.9804 0.02166 0.9945 0.04092 0.9805 0.04085 0.9805 0.03898 0.9824 0.0093 0.999 0.1207 0.8289

0.04037 0.9804 0.01405 0.9976 0.01405 0.9976 0.03324 0.9867 0.03324 0.9867 0.09218 0.8987 0.04045 0.9804 0.02864 0.9902 0.04029 0.9805 0.03284 0.9871 0.04303 0.9781 0.0096 0.9989 0.1166 0.8362

0.04871 0.9738 0.01558 0.9973 0.01558 0.9973 0.03929 0.983 0.03929 0.983 0.03944 0.983 0.04881 0.9738 0.0076 0.9994 0.04888 0.9738 0.04871 0.9738 0.04424 0.9788 0.00856 0.9992 0.1314 0.8093

0.03986 0.9815 0.01358 0.9979 0.01385 0.9979 0.03241 0.9878 0.03241 0.9878 0.03254 0.9878 0.03996 0.9815 0.01505 0.9974 0.04002 0.9815 0.03994 0.9815 0.08124 0.9248 0.0076 0.9993 0.1198 0.8333

0.03094 0.986 0.0086 0.9989 0.0086 0.9989 0.0243 0.9914 0.0243 0.9914 0.02437 0.9914 0.03099 0.986 0.07553 0.917 0.03098 0.986 0.03098 0.986 0.03829 0.9789 0.0066 0.9994 0.09905 0.8569

0.05013 0.972 0.01576 0.9972 0.01576 0.9972 0.04012 0.9821 0.04012 0.9821 0.1007 0.8884 0.05026 0.972 0.0062 0.9996 0.05007 0.9722 0.03952 0.9827 0.05291 0.9695 0.00773 0.9993 0.1293 0.8136

0.05221 0.9702 0.02152 0.995 0.02152 0.995 0.04417 0.9788 0.04417 0.9788 0.04549 0.9778 0.05238 0.9702 0.0059 0.9996 0.0522 0.9704 0.04364 0.9795 0.04825 0.9754 0.01097 0.9987 0.1251 0.8292

0.04816 0.974 0.01602 0.9971 0.01602 0.9971 0.03955 0.9826 0.03955 0.9826 0.0398 0.9826 0.04832 0.974 0.01313 0.9981 0.04814 0.9742 0.03883 0.9833 0.0432 0.9797 0.0127 0.9982 0.117 0.8467

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Majid Yazdani et al Euro. J. Exp. Bio., 2013, 3(3):712-721 ____________________________________________________________________________ Activation Function 1

Activation Function 2

Activation Function 3

Drying air Temp.

Drying air Vel.

Moisture ratio

Drying time

Input layer

Output layer

Hidden layers

Fig. 2. Topology of a simple, fully connected three-layer MLP network

In the first stage of determining optimal ANN topology, models with same number of neurons and activation functions and different number of layer were compared. Results showed that predicting accuracy in networks with more than two hidden layers had not significant differences. Thus two hidden layers were selected for network. In second stage, various combinations of activation functions were investigated and seven combinations between them which had significant difference with the other were chosen for investigating and determining the number of neurons of each layer. At final stage, by changing the number of neurons of each layer from one to ten and comparing their statistical result, the simplest ANN topology which shown optimal statistical criteria, was introduced. Table 4. Statistical results of Midilli et al. model and its constants and coefficients at different drying conditions MR =a exp(-ktn) + bt Experiment No. a 1 0.9646 2 0.9664 3 0.9654 4 0.9614 5 0.9614 6 0.9543 7 0.9689 8 0.9606 9 0.09576 10 0.9678 11 0.9707 12 0.965 13 0.9708 14 0.9671 15 0.9912

k 1.261E-05 8.317E-06 2.182E-05 8.992E-06 1.805E-05 8.964E-06 1.911E-05 1.107E-05 9.692E-06 8.781E-06 0.0000193 1.306E-05 1.218E-05 2.083E-05 3.859E-05

n 1.224 1.278 1.186 1.315 1.234 1.331 1.235 1.327 1.359 1.345 1.275 1.335 1.334 1.301 1.252

b -4.316E-07 -4.957E-07 -1.128E-07 5.509E-09 -6.409E-08 -6.253E-08 -0.000001041 -8.849E-07 -5.889E-07 -0.000001553 -0.000001469 -3.612E-08 -0.000002358 0.00002083 -0.000003053

RMSE 0.007364 0.007203 0.006732 0.004629 0.007476 0.008991 0.007694 0.009343 0.009562 0.008558 0.007578 0.006566 0.007728 0.01097 0.01273

r² 0.9993 0.9994 0.9993 0.9996 0.9991 0.9989 0.9993 0.999 0.9989 0.9992 0.9993 0.9994 0.9993 0.9987 0.9982

RESULTS AND DISCUSSION Peach slices with 5.85 g water g-1 dry matter and average initial moisture content were dried to equilibrium moisture using different air temperatures (40, 50, 60, 70 and 80°C) and velocities (1, 1.5 and 2 m/s). In order to modeling, the experimental moisture content data were used on the dry weight basis. These moisture content data were converted to the moisture ratio values at any time of drying process and fitted against the drying time (figure 3). This Figure demonstrates the influence of the air temperature and velocity on the change of moisture content of the peach slices over time, and shows that air temperature had a significant effect, while air velocity had a small effect. This matter confirms Islam and Flink (1982) studies results that at air velocities of 2.5 m s-1 or less, the external mass transport resistance is significant and needs to be considered in analyzing drying data [[26]]. The present study has shown this to be the case for air velocity in the range 1–2 m s-1.

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Majid Yazdani et al Euro. J. Exp. Bio., 2013, 3(3):712-721 ____________________________________________________________________________

Fig. 4. Experimental and predicted moisture ratio at different drying conditions.

Thirteen thin layer drying models were compared according to their statistical results such as RMSE and r2 (Table 3). The results indicated that the lowest values of RMSE and the highest values of r2 were obtained at Midilli et al. model. This model could be shown as MR =a exp(-ktn) + bt

(3)

Where MR is the moisture ratio, k drying rate constant (min-1), t time (min), a, n and b are experimental constants. RMSE changed between 0.01273 and 0.004629 and r2 between 0.9996 and 0.9982. This model represented the experimental values of moisture ratio satisfactorily. The accuracy of the established model was evaluated by comparing the computed moisture ratios with the observed values in Figure 4. The closeness of the plotted data to the straight line represents equality between the experimental and predicted values at drying air temperatures of 40-80°C and velocities of 1.0-2.0 ms-1. When the Midilli et al. model analyzed according to the different drying air temperature and velocity conditions, individual constants could be obtained (Table 4). It is clear from Table 4 that the values of constants for each correlation vary considerably from one experimental condition to another.

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Majid Yazdani et al Euro. J. Exp. Bio., 2013, 3(3):712-721 ____________________________________________________________________________ Table 5. Best activation function combinations for 3-5-5-1 topology based on statistical results activation functions tan-log-pur tan-tan-tan log-tan-pur tan-log-tan log-log-tan tan-tan-pur log-tan-tan pur-log-tan pur-tan-tan tan-pur-tan

RMSE 0.002129648 0.003717257 0.003651164 0.004194163 0.00547476 0.006408432 0.007516316 0.012206556 0.013449907 0.013985707

r² 0.99997 0.9999 0.99991 0.99989 0.99981 0.99971 0.9996 0.99908 0.99892 0.99854

Table 6. Top ten ANN models and their statistical criterions Model No. 1 2 3 4 5 6 7 8 9 10

Activation function log-tan-pur log-tan-tan log-tan-pur tan-tan-pur tan-log-tan tan-tan-pur log-tan-tan tan-tan-tan tan-log-pur log-tan-tan

Topology 3-6-4-1 3-4-8-1 3-8-2-1 3-4-8-1 3-8-2-1 3-8-2-1 3-10-2-1 3-10-2-1 3-8-2-1 3-4-4-1

RMSE 0.001955 0.00347 0.004059 0.004003 0.004058 0.004082 0.004182 0.003977 0.004676 0.004498

r2 0.999956 0.999824 0.999805 0.999796 0.999796 0.999781 0.999785 0.999782 0.999719 0.99973

Table 7. Comparison between neural network and Midilli et al. model Experiment No. 1 2 3 4 5 6 7 Midilli et al. model 8 9 10 11 12 13 14 15 ANN model

RMSE 0.007364 0.007203 0.006732 0.004629 0.007476 0.008991 0.007694 0.009343 0.009562 0.008558 0.007578 0.006566 0.007728 0.01097 0.01273 0.0019547

r² 0.9993 0.9994 0.9993 0.9996 0.9991 0.9989 0.9993 0.999 0.9989 0.9992 0.9993 0.9994 0.9993 0.9987 0.9982 0.999956

In the present study, an ANN model was developed to predict the moisture ratio of peach slices based on the drying time and conditions (drying air temperature and velocity). It is evident that the learning ability of the two-hidden layer networks was significantly higher than that for one-hidden layer. More hidden layers had no significant effect on learning ability. This indicated that seven optimum combinations of all the possible ones from activation functions with RMSE 0.002-0.008 and r2 0.9996-0.9999 had significant difference compared to the other one (table 5). In investigating the number of neurons in each layer, ten top situations were obtained (table 6). Among this various structures, models of good training performance were produced. With regard to the results, the MLP network with LOGSIG-TANSIG-PURELIN activation function and 3-6-4-1 topology showed the best performance, where RMSE was 0.001955 and r2 was 0.99996. The RMSE and r2 values from Midilli et al. model for whole range of experiments were compared with the results of the unique ANN model in table 7. The values in table 7 clearly show that although the constants of the Midilli et al. model are allowed to change from one experimental condition to another, the results of the ANN model are more accurate than each of them. The RMSE and r2 for Midilli et al. model changed to 0.0046-0.0127 and 0.9982-0.9996 respectively when describing the drying behavior of peach slices, while the RMSE and r2 of the ANN model was found to be 0.00195 and 0.99996 for testing data.

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Majid Yazdani et al Euro. J. Exp. Bio., 2013, 3(3):712-721 ____________________________________________________________________________ CONCLUSION The time needed to dry peach slices with initial moisture content of 58.5% d.b in drying experiment conditions vary from 150 min to 540 min. The influence of air temperature on drying behavior of the peach slices was more significant than that of the air velocity. Among these thirteen thin-layer drying mathematical models which comparatively tested according to their RMSE and r2 values, the Midilli et al. model best described the drying behavior of the peach slices. A multi-layer perceptron ANN was able to learn the correlation between moisture ratio of peach slices with drying air velocity and temperature and drying time. The optimal ANN model was found to be a network consist of 3 neurons and LOGSIG activation function in the input layer, 6 neurons and TANSIG activation function in the first hidden layer and 4 neurons and PURELIN activation function in the second hidden layer. This optimal model was capable of predicting the moisture ratio with R2 higher than 0.9998 and RMSE less than 0.002. It is clear from Table 7 that the ANN model describes the drying behavior more accurately. However, the main superiority of ANN models is not its accuracy, but their generality. ANN models are able to describe a range of experiments while the application of mathematical models is limited to a specific experiment. The ANN model is also able to be retrained and the range of experimental conditions may be expanded by addition of new sets of experiments. So it can be concluded that the application of ANN models may be considered as an alternative for description of drying behavior of peach slices. 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