Electronic Journal of Polish Agricultural Universities (EJPAU) founded by all Polish Agriculture Universities presents original papers and review articles relevant to all aspects of agricultural sciences. It is target for persons working both in science and industry,regulatory agencies or teaching in agricultural sector. Covered by IFIS Publishing (Food Science and Technology Abstracts), ELSEVIER Science - Food Science and Technology Program, CAS USA (Chemical Abstracts), CABI Publishing UK and ALPSP (Association of Learned and Professional Society Publisher - full membership). Presented in the Master List of Thomson ISI.
Volume 20
Issue 1
Agricultural Engineering
Available Online: http://www.ejpau.media.pl/volume20/issue1/art-05.html


Adel Bakhshipour, Dariush Zare
Biosystems Engineering Department, Faculty of Agriculture, Shiraz University, Iran



In order to estimate the moisture content variations of paddy in a deep bed dryer, an Artificial Neural Network (ANN) simulation model was developed from a validated partial differential equation (PDE) model. Different ANN structures were developed and evaluated to obtain the best simulation model. Subsequently, the best network was selected based on the highest value of coefficient of determination (R2=0.9979), and the lowest value for the mean squared error (MSE=0.0732).The mean relative deviation between PDE data and the verified network outputs was obtained to be close to zero (MRD=0.51%). The performance of the proposed ANN was also evaluated by a set of experimental data. Good agreement was found between experimental and network predicted values (MRD=8.29%). Results indicated that the developed ANN is capable of predicting drying process with reasonable accuracy.

Key words: Deep bed, Artificial Neural Networks, Modeling, Paddy drying.


Rice (Oryza Sativa L.), one of the major staple food sources in the world, is among the oldest cultivated crops and ranks as the most widely grown food grain crop [12].

The management of paddy grain after harvesting has been reported to play an essential role in posterior maintenance of rice yield and quality [40].

At the stage of harvesting, grains are usually moist and their moisture content is much higher than such adequate level which prevents the product from deterioration during storage. The storage life of grains depends mainly on two physical factors: temperature and moisture content [19]. Safe storage requires rapid decrease in moisture to preserve quality [35]. Drying of agricultural products is the most widespread preservation technique that has been of much interest by the producers for many years. Drying is used in order to preserve and store agricultural products for longer periods by removing some of their moisture content [22].

The main goal in each drying process is to achieve the desired moisture content. Evaluation of dehydration level is necessary in food quality control. It should be considered that if the moisture is not brought down to desired limit, this encourages the growth of molds and poses a danger to the safe storage of grains [36]. On the other side, overdrying requires excessive energy and even can damage the quality of the dried material, especially in case of seeds [10].

Knowledge of drying behavior is important in the design, simulation and optimization of the drying process [31].

Nowadays, moisture content measurement is commonly performed by sampling at different intervals of time, which is usually tedious, costly, laborious, invasive and destructive. In order to design new optimized batch dryers or improve existing dryers, the moisture content of the grain should be predicted at different locations of the drying chamber at any moment [43].

Investment in new methodologies in various stages of drying can help to improve the dehydration process and increase quality of the dried foods.

Already, several experiments have been conducted to develop mathematical models for thin layer drying of rough rice [3, 8, 9, 13, 20, 32]. Also there are some mathematical models such as logarithmic [29], heat and mass balance [33, 44] and partial differential equation (PDE) [34, 42] reported for batch drying of grains. Although the drying behavior of the product can be predicted using these models, such models are not widely used because of their complexity and long computing times required [38].

Artificial Neural Networks have been successfully used in the prediction and optimization problems in bioprocess and chemical engineering [5, 37]. The ANN has been developed as a generalization of mathematical models of human cognition and neural biology [4, 30].

Neural network is a calculative approach that correlates input data with desired outputs by means of special learning processes. After training process, the ANN models have faster response than mathematical and numerical models. Higher accuracy and stability are two of the most important specifications of artificial neural networks.

Drying process is a complex treatment which can be affected by a large number of factors including drying temperature, air velocity, relative humidity, physical nature and initial moisture content of the drying material.

Against this complexity, ANN as a nonlinear calculation method can overcome the limitations of the conventional approaches by extracting the desired information using the input data by means of special learning processes.

Some applications of ANN models in several types of drying processes can be found in published articles [2, 7, 11, 16–18, 26–28]. The artificial neural network models were reported to be more accurate than empirical models and able to predict the moisture ratio quite well for thin-layer drying of Canola [24] as well as drying of apple slices pretreated with high intensity ultrasound [21].

Few studies have been done to investigate the use of ANN in drying process simulation of fixed bed agricultural dryers. It was reported that the ANN was capable to simulate the moisture distribution in the drying bed as well [10]. Zhang et al. developed and evaluated an ANN model for prediction of performance indices and optimal parameters in the rough rice drying [45].

Moisture variation during the drying process in different layers of deep bed depends on many drying parameters including drying air temperature and humidity, mass flow rate of drying air, initial grain temperature and moisture content, physical properties of grain in the dryer and so on. To develop a generalized ANN model a comprehensive drying experiment is needed to consider all important drying factors which is a tedious and time consuming work. The PDE model is more detailed and having the capability of survey different drying parameters. It is desirable to utilize the PDE model as a fundamental model for generating data to develop a comprehensive ANN drying simulation model.   

As far as we know there is no information about such an ANN model in the literature. Therefore the aim of the present study is to develop a comprehensive ANN simulation model obtained from validated PDE drying model.


Development of basic model
Zare et al. have developed a PDE model for drying process of paddy in a deep-bed batch dryer. The model was obtained based on principles of mass and energy balance as follows [44]:


The unknown drying variables in the above three equations are M(x, t), h(x, t), H(x, t), and T(x, t). A modified empirical thin-layer drying equation for paddy [39] was applied to solve the set of equations [44]:



X = 0.01579 + 0.0000176T + 0.078867(RH)

Y = 0.6545 + 0.002425T + 0.078867(RH)

The developed model was solved by considering initial and boundary conditions. More details information about solving approaches was presented elsewhere [44]. The model was validated by a set of experimental data [42].

In the further researches, Zare et al., have investigated to develop a generalized dimensionless model according to the numerical solution of the PDE model that can be applied in the industry and used operationally for precise controlling of the deep bed drying systems. So they have found the effects of important factors on the rate of moisture content changes in the paddy bed and derived the generalized model by determining the dimensionless terms. The accuracy of the developed model was evaluated and reported to be acceptable [43].

In the present research, an artificial neural network was designed to predict drying behavior of paddy kernels in deep bed drying process. As the network needs large amount of input data for training and the experimental data were not enough to perform a adequate network training, the PDE model numerically solved and evaluated previously was used to produce data for various combinations of drying parameters as follows:

Table 1. Average physical properties for different types of rough rice (paddy) [6]
Rice type
Equivalent radius [mm]
Bulk density[kg·m-3]
Specific surfacearea [m2·m-3]
Short grain
Medium grain
Long grain

By running the PDE simulation model for different drying conditions, totally 97200 values of M(x, t) were obtained at different drying conditions which were then used to develop the ANN model.

Neural networks
The feed-forward multi-layer perceptron (MLP) network with back-propagation learning algorithm was developed in this study. MLP is one of the most common feed-forward networks. Its structure consists of processing elements and connections [23]. A schematic of feed-forward two-layer neural network is illustrated in Figure 1. Values of ten input variables including; inlet drying air temperature, inlet drying air humidity, inlet drying air mass flow rate, grain initial moisture content, grain initial temperature, batch depth, drying time, grain bulk density, specific surface area of grain, and equivalent radius of grain, were supplied as input neurons. The moisture content values computed by PDE model were supplied as target vector.

Fig. 1.

The Levenberg-Marquardt (LM) Back-propagation training function was used for networks. LM is known to be very efficient when applied to ANN.

The network training process was based on the Levenberg-Marquardt (LM) back-propagation training function which is known to be very efficient when applied to ANNs [14]. During the training process, the input layer distributes input signals to the next layer, which is the first hidden layer. Each node in this layer sums its input from all input nodes, multiples the new value by a weight, attaches a bias to the resulting value then shifts the final value through a transform function to the next layer. This process is repeated in next hidden layer (if exist) until the training process reaches to the output layer. The hyperbolic tangent sigmoid function was used as the activation function [15]. The transfer function of output layer was considered linear. The goal of training pattern is to produce outputs that match the target values so that low errors can be computed [25]. Target values are experimental data and the training algorithm should reduce the overall error between targets and output by adjusting the weights and biases.

One of the most important parameters in networks is determination the optimize number of hidden layer neurons or the size of each hidden layer. Setting too few hidden units causes high training errors and high generalization errors due to under-fitting, while too many hidden units results in low training errors but still high generalization errors due to over-fitting [41]. A compromise should be made when structuring an ANN model.

Tangent sigmoid and logarithm sigmoid functions were used as transfer function of hidden layers. As the sigmoid function ranges between -1 and 1, the input and output data must be normalized to this range. This reduces the training time and improves the accuracy of the network. The following equation was used:


Where, Vnor is normalized value, Vi is actual input or output value and Vmax and Vmin are maximum and minimum values in the data set respectively.

Input data were divided to three parts randomly, 60% for training, 20% for validation and 20% for network test. Several topologies, with both one and two hidden layers were tested. The best network was selected based on two statistical indices, namely, mean squared error (MSE) and coefficient of determination (R2) given by equations (6) and (7).

R2 corresponds to the fraction of variance in the observations (target) which can be explained by the network model (ANN output). MSE measures the average magnitude of the differences between the observed and predicted values. The highest value of the R2 and the lowest value of the MSE are indications of the best performance of the developed ANN model [1].



Where, is the number of samples, is output of ANN for sample, and  is the actually observed value for sample .

The error of the best network was also determined using the following equation [43]:



Results of developed networks are shown in Table 2. Logarithmic sigmoid transfer function resulted in less error and more determination coefficient compared to tangent sigmoid function. The network with two hidden layers (10-8-10-1) and logarithmic sigmoid transfer function showed the best results with maximum value of the R2 (99.79%) and the lowest value of the MSE (0.0732). In the case of test data, this network predicted the moisture content of paddy with high accuracy of over 99.45%. These statistical indicators show that ANN model was capable to predict the moisture content of paddy during deep bed drying process with very high accuracy.

Table 2. Statistical results of some of the most promising ANNs for prediction of grain moisture content
Transfer Function
R2 [%]
R2 [%]
0. 0921

The plot of ANN predicted data versus the PDE numerical data training and testing data set has been illustrated in Figure 2. The points are laid closely around the X=Y line which also which emphasizes the goodness of fit between the developed ANN and validated PDE model. The estimating ability of the developed ANN model was also assessed by plotting moisture content variation from the ANN and PDE model. Figures 3–8 shows the changes of average moisture content values for both ANN and PDE models for different drying conditions. In the figures the two curves have the same trends and follow each other very closely. The same results were observed for other drying conditions. For all treatments the mean relative values were less than 0.51% which shows the reasonable deviation between PDE model and those predicted by the ANN model.

Fig. 2.

Fig. 3.

Fig. 4.

Fig. 5.

Fig. 6.

Fig. 7.

Fig. 8.

Modeling efficiency of the developed network was also evaluated by comparing the ANN model by a set of independent experimental data presented before in the literature [44]. Figures 9–12 illustrate the moisture content variation curves during drying time for experimental, PDE model and ANN predicted data in some drying conditions.

Fig. 9.

Fig. 10.

Fig. 11.

Fig. 12.

As it can be seen from these figures, the PDE model and ANN data are exactly laying on each other but there is some deviation from the experimental data. This is due to the fact that the ANN was developed based on the PDE model. The mean relative deviation between experimental moisture content values and ANN outputs was 8.29% which shows the good accuracy of the developed ANN. Therefore the ANN has the capability of predicting the drying behavior of paddy during in a deep-bed batch dryer.


The capability of ANN for predicting the paddy drying behavior in a deep-bed dryer was tested in this study. The PDE model as a fundamental model was successfully applied for generating data to develop a comprehensive ANN drying simulation model. The developed ANN model was capable to predict grain moisture variation during the drying process with good accuracy.


ca Specific heat capacity of air [J·kg-1·K-1]
cv Specific heat capacity of water vapor [J·kg-1·K-1]
cw Specific heat capacity of water [J·kg-1·K-1]
G Mass flow rate of air [kg·m-2·s-1]
H Absolute humidity of air [kg·kg-1]
Hi Absolute humidity of inlet air [kg·kg-1]
ha Grain bed volumetric heat transfer coefficient [J·m-1·K-1·s-1]
hv Latent heat of vaporization [J·kg-1]
M Moisture content of grain [dry basis] [kg·kg-1]
Me Equilibrium moisture content of grain [dry basis] [kg·kg-1]
N Total number of samples
RH Relative humidity of air [decimal]
T Air temperature [°C]
Ti Inlet air temperature [°C]
t Time [s]
x Depth in bed from air inlet [m]
YANN,i ith Predicted parameter by ANN
YPDE,i ith PDE resulted parameter
Vnor Normalized value used for network training
Vmax Maximum input or output value introduced to network
Vmin Minimum input or output value introduced to network
Vi ith actual input or output data in the network dataset
Greek Letters
ε Porosity of grain bed [decimal]
θin Grain temperature [°C]
ρp Grain bulk density [kg·m-3]
ANN Artificial neural networks
PDE Partial differential equation
MLP Multi-layer perceptron
MSE Mean Squared error
R2 Coefficient of determination
MRD Mean relative deviation


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Accepted for print: 26.03.2017

Adel Bakhshipour
Biosystems Engineering Department, Faculty of Agriculture, Shiraz University, Iran
Former Ph.D. Student

Dariush Zare
Biosystems Engineering Department, Faculty of Agriculture, Shiraz University, Iran
P.O. Box 7144165186, Shiraz, Iran
Phone: +98 711 6138192; Fax: +98 711 2286104
email: dzare@shirazu.ac.ir

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