Application of neural network for estimation of pistachio powder sorption isotherms

H. Tavakolipour^† and M. Mokhtarian^‡

^† Department of Food Engng, Sabzevar Branch, Islamic Azad University, Sabzevar, Iran. Email: h.tavakolipour@gmail.com
^‡ Young Researchers and Elite Club, Sabzevar Branch, Islamic Azad University, Sabzevar, Iran.

Abstract— Moisture sorption isotherms for pistachio powder were determined by gravimetric method at temperatures of 15, 25, 35 and 40°C. Some mathematical models were tested to measure the amount of fitness of experimental data. The mathematical analysis proved that Caurie model was the most appropriate one. As well, adsorption-desorption moisture content of pistachio powder were predicted using artificial neural network (ANN) approach. The results showed that, MLP network was able to predict adsorption-desorption moisture content with R² values of 0.998 and 0.992, respectively. Comparison of ANN results with classical sorption isotherm models revealed that ANN modeling had greater accuracy in predicting equilibrium moisture content of pistachio powder.

Keywords— Pistachio; Modeling; Sorption Isotherm; Neural Network Approach; Isosteric Heat of Sorption.

I. INTRODUCTION

The pistachio (Pistacia vera L.) is cultivated in the Middle East, United States, and Mediterranean countries (Tavakolipour and Mokhtarian, 2012). Pistachio is one of the most important Iranian horticultural products with high export value for the country and Persian cultivars have different taste and flavour. According to Food and Agricultural Organization (FAO), Pistachio production in 2010 was reported 446647 MT, which Iran is dedicated of about 47.3% of the global production of pistachio in this year (FAO, 2010). According to position of this product in the country economy, suitable preservation and storage conditions is necessary to prevent spoilage.

During various postharvest processes such as drying, storage and packaging, water adsorption and desorption processes play an important role on deteriorative reactions (DRs) such as browning, lipid oxidation and microbial growth of pistachio nuts. The influence of moisture on DR has been explained in terms of a_w, and this approach is now well established in controlling reaction and predicting food stability. Because a_w is the most important parameter for the stability of raw and processed agricultural products, the sorption isotherms can be used to obtain their optimum residual moisture content and end point of a drying process, which is useful to design their suitable packaging systems and storage conditions, and to select proper ingredients for preparing a formulated intermediate moisture food (Tavakolipour and Kalbasi Ashtari, 2008).

Maskan and Karatas (1997) determined the sorption characteristics of whole pistachio nuts at 10, 20 and 30°C, and evaluated their data for fitting to some sorption equations. They found some important parameters such as monolayer moisture content and heat effects on water sorption. Additionally, the adsorption studies were done on few pistachio varieties and their products, e.g., raw pistachio (Pistacia terebinthus L.) and its protein isolate by Ayrancy and Dalgic (1992), pistachio nut paste at different T values (Hayoglu and Gamli, 2007). However, very limited data are available on sorption isotherms and other characteristics of different Persian pistachio varieties.

Presently, neural networks enact an important key as a powerful analysis machine in predicting the process parameters. The scientists were used ANN in various field of food processing. For example, using an ANN approach as intelligent tools for prediction of food drying parameters (Tavakolipour and Mokhtarian, 2012), freezing and thawing times (Goñi et al., 2008), osmotic dehydration parameters such as solid gain (SG) and water loss (WL) (Lertworasirikul and Saetan, 2010), anthocyanin concentration (Fernandes et al., 2011), antioxidant activity (Cimpoiu et al., 2011) and equilibrium moisture content (Amiri Chayjan and Esna-Ashari, 2010).

The aim of this study were: (1) evaluation of feasibility of neural network to predict adsorption and desorption moisture content of pistachio powder in order to momentarily monitor the storage conditions, (2) to determine the sorption isotherms and hysteresis effects and (3) to evaluate the suitability of various mathematical models for fitting the isotherms and determine the isosteric heat of sorption.

II. MATERIALS AND METHODS

A. Materials

Raw and dried Kerman variety pistachios were purchased from a local market. They were sorted and separated to split and nonsplit samples. Medium-sized and splitted pistachio nuts with a moisture content of 4.5% (d.b.) were selected for the tests. After harvesting, the pistachio nuts should be dried from a moisture content of about 40% to safe storage moisture of less than 7% wet basis (w.b.). Pistachio nuts dried to a range of 4-6% (w.b.) are graded higher in organoleptic quality indicators such as crispness and sweetness, and lower in bitterness and rancidity than those dried in the range of 6-11% (w.b.) moisture content. Pistachio powder was produced by weighing 10 g of pistachio kernels crushed in a home mill (Black and Decker, London, U.K.) for 30 s until its average particle size reached 250 microns. Various saturated salt solutions including LiCl, CH₃COOK, MgCl₂, K₂CO₃, Mg(NO3)₂, NaNO₂, NaCl and KCl were used to obtain constant relative humidity (Tavakolipour and Kalbasi Ashtari, 2008).

B. Determination of equilibrium moisture content

Sorption isotherms of pistachio powder were determined by a static gravimetric method at 15, 25, 35 and 40°C. According to Tavakolipour and Kalbasi Ashtari (2008), eight saturated salt solutions were prepared to provide a range of 0.11, 0.23, 0.36, 0.49, 0.62, 0.75 and 0.88 for a_w values. After transferring 150 mL of each salt solution into separate glass jars, the jar grids were suspended. About 2 g sample of pistachio powder was weighed separately and placed on grids in the jars, which were tightly closed, and kept in convective ovens at different temperatures for equilibration. The required time to reach equilibrium moisture content for sample of pistachio powder was close to 18 day. Equilibration was achieved when the changes in moisture content (d.b.) did not exceed 0.1%, and it was less than 0.001 g/g dry solids for three consecutive weighting at 3-day intervals. Moisture content of pistachio samples was measured by vacuum oven at 70°C and 150 mbar for 6 h (AOAC, 1990). For the adsorption process, pistachio samples were placed on suspended dishes in jars containing silica gel. Again, the same procedure was repeated to reach the equilibrium moisture content. Desorption isotherms were determined on samples hydrated in a glass jar over distilled water. At high a_w values (a_w > 0.7), a small amount of toluene was placed in a capillary tube fixed to the inner wall of different jars to prevent microbial spoilage of the pistachio samples (Tavakolipour and Kalbasi Ashtari, 2008).

Ten mathematical models were used for fitting of sorption isotherm curves of pistachio powder at different temperatures (Noshad et al., 2012; Shivhare et al., 2004). The equations of these models are shown in Table 1.

Table 1. Mathematical models for fitting of sorption data to pistachio powder

The goodness of the fitting was evaluated by calculating two statistical parameters namely coefficient of determination (R²) and mean relative error (MRE). Each model with highest R² value and lowest MRE value is the best model for fitting of sorption moisture isotherm data of pistachio powder (Tavakolipour and Mokhtaran, 2012). The R² and MRE parameters can be calculated as follows:

	(1)
	(2)

where X_e,i is experimental data, X_p,i is predicted data, is average of predicted data and N is number of observations.

C. Design of artificial neural network

An artificial neural network was composed of simple processing elements called neurons that are connected to each other by weights. The neuron is grouped into distinct layers and interconnected according to a given architecture.

A multilayer perceptron (MLP) networks is one of the most popular and successful neural network architectures, suited to wide range of engineering application involved drying. Mathematically:

(3)

where y_j is the net input of each neuron in the hidden and output layers, x_i is input, n is number of inputs to the neuron, w_ij is the weight of the connection between neuron i and neuron j and b_j is the bias associated with j^th neuron. Each neuron consists of a transfer function that express of its internal activation level. Output from a neuron is determined by transforming its input using a suitable transform function.

In this work, Number of 1-2 hidden layers with 2-34 neurons per hidden layer, learning rate= 0.4, momentum coefficient=0.9, activation functions of sigmoid logarithms (Eq.4) and hyperbolic tangent (Eq.5) in each hidden and output layer and training period (epoch)=5000 were used in order to find the best configuration.

	(4)
	(5)

In this network, air temperature and water activity (a_w) were selected as input parameters and equilibrium moisture content (absorption/desorption) was selected as output parameter (see Fig. 1). Data randomly divided into two groups, 70% used for training and 30% for testing of network. Data modeling accomplished by using SPSS statistical software version 19 (2011). In order to evaluate the network performance and select the best topology, two statistical criteria of R² and MRE were used.

Figure 1. Schematic structure of ANN, x₁: air temperature, x₂: water activity (a_w), y: adsorption/desorption moisture content.

III. RESULTS AND DISCUSSION

A. The effect of temperature on the isotherm curves Pistachio powder adsorption and desorption isotherm curves at different temperatures are presented in Fig 2. These curves are shown as a function of temperature where temperature increased the equilibrium moisture content of pistachio powder decreased for both adsorption and desorption. This behavior is consistent with thermodynamic laws and showed the reverse effect of increasing of moisture content or temperature on sorption enthalpy. However, some of sugars and low molecular weight food components are exceptions and by, increasing temperature they will more hygroscopic (Ayrancy and Dalgic, 1992). The study of the curves observed that for water activity in range of 0.2-0.7 corresponding to the capillary condensation region, when adsorption and desorption temperature at minimum (15°C) its hysteresis reached to the highest value. By increasing temperature hysteresis was reduced and for water activity lower than 0.2 and higher than 0.7, it reached to the lowest value (Tavakolipour and Kalbasi Ashtari, 2008).

Figure 2. The adsorption and desorption isotherm curves of pistachio powder at different temperatures.

B. Empirical modeling

In this study the BET, GAB, Oswin, Smith, Halsey, Henderson, Kuhn, Freundlich, Harkins and Jura, Iglesias and Chirife, and Caurie equations were used to fit the sorption data for pistachio powder. Statistical and model parameters are shown in Table 2. The calculation of R² and MRE values for the ten models showed that the highest R² (average 0.982 for adsorption and 0.990 for desorption) and the lowest MRE values (average 5.599 for adsorption and 4.920 for desorption) were related to Caurie equation in the first order and Smith equation with R² (average 0.982 for adsorption and 0.988 for desorption) and MRE values (average 5.599 for adsorption and 4.920 for desorption) in the second order for fitting sorption data in all storage temperatures.

Table 2. The model constants and statistical parameters for experimental adsorption/desorption data at different temperatures.

C. Isosteric heat of sorption

Isosteric heat of sorption or binding energy is defined as the amount of energy required to remove water from the substrate in excess of the amount of energy required for free water vaporization. It's a valuable tool for understanding the water sorption mechanism. Generally, sorption phenomena can be explained by the differential form of the Clausius-Clapeyron equation:

(6)

where Q_s is isosteric heat and R is universal gas constant. Some selected values of isosteric heat of sorption were estimated from the slope of ln a_w versus 1/T plots at various moisture content values. The slope of the line (-Q_s/R) decreases to zero as moisture content in agricultural commodity increases which is an indicative of reduced water interactions, i.e., less binding energy (Tavakolipour and Kalbasi Ashtari, 2008). Furthermore, the isosteric heat of sorption shown in Fig. 3 is a function of moisture content and it varies inversely with the amount of water vapor absorbed by the solid. The higher the moisture content, the lesser energy was required to remove water molecules from the pistachio powder, as observed in Fig 3. At moisture content more than 60%, the binding energy in pistachio powder decreases to zero, because water characteristics of pistachio approaches to free water. Also, results obtained from binding energy of moisture adsorption and desorption showed that binding energy for adsorption isotherm is larger than desorption isotherm and causes some structural changes during drying process. When moisture content in pistachio powder reduced from 10% to 1% (dry basis), the binding energy increased from 0.299 to 33.01 kJ/mol.

Figure 3. Isosteric heat of sorption of pistachio powder at different equilibrium moisture contents.

D. Artificial neural network modeling

In order to predict adsorption and desorption moisture content of Persian pistachio powder, artificial neural network model was used. To this end, a combination of layers and neurons with different activation functions were used for modeling perceptron of neural network. Neural network include one and two hidden layers, 2 to 34 neuron were selected randomly and network power was estimated to predict adsorption and desorption moisture content of Persian pistachio powder. Suitable learning epoch was selected according to previous study in field of ANN. The results showed that, the best learning epoch for logarithm sigmoid (logsig) and hyperbolic tangent (tanh) activation function is 5000 (Tavakolipour and Mokhtarian, 2012). The best learning epoch for each activation function was chosen in order to achieve the lowest mean relative error.

The obtained result of MLP network with 'logsig' and 'tanh' activation function and different configurations are shown in Table 3. Investigation of obtained result for MLP with logsig and tanh activation function with one and two hidden layers has been shown, topology of 2-10-10-2 (i.e. network with 2 inputs, 10 neurons in the first and second hidden layer and 2 output) with logsig had the best result to predict adsorption moisture content. On the other hand, result of perceptron neural network with same activation functions (logsig and tanh) with one and two hidden layers indicated that, neural network with structure of 2-6-2 (i.e. network with 2 inputs, one hidden layer with six neurons and two output) and tanh activation function had acceptable result in terms of predicting desorption moisture content of Persian pistachio powder. This network was able to predict adsorption and desorption moisture content with relative error values 0.0029 and 0.0095, respectively. Likewise, R² values for adsorption and desorption moisture content were obtained 0.998 and 0.992, respectively. The similar results in field of sorption isotherm were reported by another scientist in cases of raisin (Amiri Chayjan and Esna-Ashari, 2010).

Table 3. ANN results to predict equilibrium moisture content (EMC) of pistachio powders with different activation functions at various temperatures and a_w.

Figure 4 shows model sensitivity diagram of predicted values by MLP network vs. experimental values for the best configurations (i.e. structure of 2-10-10-2 with logsig activation function and structure of 2-6-2 with tanh activation function for predicting adsorption and desorption moisture content, respectively). The result indicated that, data were randomly located around the regression line. This could be a reason for carefully evaluating the neural networks to predict adsorption and desorption moisture content of Persian pistachio powder.

Figure 4. Predicted and experimental values of MLP network to predict EMC of pistachio powder, (a) Adsorption moisture content with logsig activation function and (b) Desorption moisture content with tanh activation function

IV. CONCLUSION

The moisture sorption isotherms and isosteric heat of sorption are important in optimization of storage conditions and packaging of pistachio powder. The hysteresis was the highest value, when a_w was in range of 0.2-0.7 and it reduced when it was less or more than 0.2 and 0.7, respectively.

As well, in this study, possibility of implementing ANN to on-line monitoring of equilibrium moisture behavior of pistachio powder during drying and storage was evaluated. The results demonstrated that, neural network with logsig threshold function could predict adsorption moisture content with 10 nodes in first and second hidden layer each, with R² value equals to 0.998. On the order hand, the results showed that, this network with tanh activation function with 6 neuron in first hidden layer had the best result in terms of predicting desorption moisture content of pistachio powder (R²=0.992). Comparison of ANN results with classical models revealed that ANN modeling had greater accuracy for predicting adsorption-desorption moisture content of pistachio powder.

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Received: February 28, 2013
Accepted: November 19, 2013
Recommended by Subject Editor: Orlando Alfano