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Prediction of rheological properties of Iranian bread dough from chemical composition of wheat flour by using artificial neural networks
Journal of Food Engineering 81 (2007) 728–734 www.elsevier.com/locate/jfoodeng
Prediction of rheological properties of Iranian bread dough from chemical composition of wheat flour by using artificial neural networks E. Razmi-Rad a, B. Ghanbarzadeh b,*, S.M. Mousavi a, Z. Emam-Djomeh a, J. Khazaei c a
Food Science and Engineering Group, Faculty of Biosystem Engineering, Agricultural Campus of Tehran University, P.O. Box 4111, Karadj, Iran b Department of Food Science and Technology, Faculty of Agriculture, University of Tabriz, P.O. Box 51666-16471, Tabriz, Iran c Department of Agricultural Technical Engineering, Faculty of Agricultural Engineering, Abouraihan Campus, University of Tehran, P.O. Box 11365-7117, Pakdasht, Iran Received 19 September 2006; received in revised form 16 January 2007; accepted 17 January 2007 Available online 27 January 2007
Abstract This paper shows the ability of artificial neural network (ANN) technology for predicting the correlation between farinographic properties of wheat flour dough and its chemical composition. The input parameters of the neural networks (NN) were the four most important chemical parameters influencing farinographic properties, namely protein content, wet gluten, sedimentation value and falling number. The output parameters of the NN models were six farinographic properties including water absorption, dough development time, dough stability time, degree of dough softening after 10 and 20 min and valorimeteric value. Results showed that, the Multi Layer ANN with training algorithm of back propagation (BP) was the best one for creation of non-linear mapping between input and output parameters. The ANN model predicted the farinographic properties of wheat flour dough with average RMS 10.794. These results show that the ANN can potentially be used to estimate farinographic parameters of dough from chemical composition. This development may have significant potential to improve product quality and reduce time and costs by minimizing farinographical experiments. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Artificial neural network; Dough; Prediction; Rheological (Farinographic) properties
1. Introduction Dough rheological properties are important for both product quality and process efficient. The ability to measure the rheology of every batch of dough enables online process control by modifying subsequent process conditions. Rheological properties of dough can be related to bakery products specific volume and textural attributes. These attributes subsequently determine consumer acceptance (Menjvar, 1990). Therefore, accurate prediction of dough rheology can have many benefits for the baking industry. However, measuring rheology of every batch is impractical, while predicting these rheological properties has historically proved to be complex (Ruan, Almear, & *
Corresponding author. E-mail address: [email protected] (B. Ghanbarzadeh).
0260-8774/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2007.01.009
Zhang, 1995). Within the cereal industry, there has been a long history of using descriptive empirical measurements of rheological properties. Empirical tests are easy to perform and are often used in practical factory situations, providing data which is useful in evaluating performance during processing and for quality control. Several empirical devises are used in cereal industries including Farinograph, Amylograph, Mixograph, Extensograph and Alveograph. Farinograph is most frequently used equipment for empirical rheological measurements. An artificial neural network (ANN) is a form of analysis which is based on the simulation of living nervous systems. A neural network is a parallel distributed processing system composed of two components: the node (also called processing element, artificial neuron or unit) and the connection (Khazaei & Shahbazi, 2005). A parameter Wij (known as weight) is associated with each connection
E. Razmi-Rad et al. / Journal of Food Engineering 81 (2007) 728–734
between two cells. Thus each cell in the upper layer receives weighted inputs from each node in the layer below and then processes these collective inputs before the unit sends a signal to other layers (Li & Bridgwater, 2000). One of the major advantages of ANN is efficient handling of highly non-linear relationships in data, even when the exact nature of such relationship is unknown. Therefore, ANNs are well suited for food quality prediction, because of the complex nature of interrelationships among various quality parameters, composition and processing conditions in foods (Ni & Gunasekaran, 1998). The most popular ANN is the feed forward multi-layer ANN which uses back-propagation learning algorithm. This type of network consists of three layers of nodes namely an input layer, hidden layers and an output layer. Feed forward neural network usually has one or more hidden layers, which enable the network to model non-linear and complex functions. Scaled data are introduced into the input layer of the network and then is propagated from input layer to hidden layer and finally to the output layer (Hussain & Shafiur, 2002). Each node in hidden or output layer firstly acts as a summing junction which combines and modifies the inputs from the previous layer using i X yi ¼ xi wij þ bj ð1Þ where yi is the net input to node j in hidden or output layer, xi are the inputs to node j (or outputs of previous layer), wij are the weights representing the strength of the connection between the ith node and jth node, i is the number of nodes and bj is the bias associated with node j. Each neuron consists of a transfer function expressing internal activation level. Output from a neuron is determined by transforming its input using a suitable transfer function. Generally, the transfer functions for function approximation (regression) are sigmoidal function, hyperbolic tangent and linear function, of which the most widely used for non-linear relationship is the sigmoidal function. The general form of this function is as follows (Razavi, Mortazavi, & Mousavi, 2003): 1 1 þ ey j
ANN modeling has been successfully applied to the prediction of dough rheological properties (Ruan et al., 1995), physical properties of ground wheat (Fang, Bibi, Haque, Hanna, & Spillman, 1998), thermal conductivity of fruits and vegetables (Hussain & Rahman, 1999), isotherms of dates (Myhara, Sablani, Al-Alawi, & Taylor, 1998), food quality (Ni & Gunasekaran, 1998) prediction of heat penetration parameters in stumbo’s method of thermal process calculations (Sablani & Shayya, 2001) and prediction of thermal conductivity of bakery products (Sablani, Baik, & Marcotte, 2002). Wheat flour dough is one of the most complicated systems for rheological evaluation because it simultaneously possess viscous and elastic characteristics. In previous work on application of ANN modeling for prediction of dough rheological properties, relation between extensographical and farinographical data were studied. The purpose of this article was to discover the dependence of rheological parameters of dough, (farinographical parameters) on the chemical composition of wheat flour and develop a neural network model for the dynamic prediction of frinographical factors from chemical composition of wheat flour. 2. Materials and methods 2.1. Procedures
i¼1
zj ¼
729
Different Iranian cultivars of wheat seeds were selected for testing. These cultivars were conveniently used in bread making. These seeds were milled and obtained flours were used for measurements of four chemical variables (total protein, wet gluten, sedimentation value and falling number) and also for providing of 132 batches of dough, for measurement of six farinographical parameters. For these measurements, Standard Methods of the International Association for Cereal Science and Technology, (ICC) procedures, were followed. Those standard numbers were: 105/2: total protein, 107/1: falling number, 116/1: sedimentation value, 137/1: wet gluten, and 115/1: farinographical measurement. Four replicate were done for any experiment.
ð2Þ
zj, the output of node j, is also an element of the inputs to the nodes in the next layer. The values of the interconnection weights are determined by a neural network training or learning procedure using a set of data. The objective is to find the value of the weight that minimizes differences between the actual output and the predicted output in the output layer in order to minimize the mean square errors (MSE). In the learning process, there are several variables that have an effect on the ANN training. These variables are the number of iterations, learning rate (g), the momentum coefficient (a), number of hidden layers (L) and the number of hidden neurons (H). To find the best set of these variables and parameters, all of those must be varied and the best combination chosen.
2.2. ANN model development A feed forward multi-layered ANN trained by back propagation (BP) algorithm was selected to develop rheological (farinographic) properties models. The back-propagation algorithm firstly adjusts weights connected to the output layer. Then, working backward towards the input layer, the algorithm adjusts weights in each successive layer to reduce the errors at each level. In this study the inputs were: total protein, wet gluten, sedimentation value and falling number and six farinographic variables (water absorption, dough development time, dough stability time, degree of dough softening after 10 and 20 min and Valorimeteric value) were selected as the outputs of the network (Fig. 1).
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E. Razmi-Rad et al. / Journal of Food Engineering 81 (2007) 728–734
Fig. 1. Structure of feed forward multi-layer ANN for calculating farinographical parameters.
The data sets of 132 cases obtained from our experiments and then they were divided in two sets. The first set consisted of 106 (80%) cases for training/testing and 26 (20%) cases for validation data set were chosen randomly from the set of 132 cases. From the first set consisted of 106 cases, 85 cases were selected for training and 21 cases for testing. Adjustments of ANN parameters were included the number of hidden layers and neurons, and the number of iteration. The delta learning rule was selected in this research work. It is one of the well-known weight update rules, which is based on the simple idea of continuously modifying the strengths of the connections to reduce the difference the (delta) between the desired output value and the current output value of a processing element (Li & Bridgwater, 2000). It is expressed as Dwij ðn þ 1Þ ¼ gd j xi þ aDwji ðnÞ
ð3Þ
where Wij is the connection weight between nodes i and j, n is discrete time cycle number, g is the learning rate, dj is the difference between actual and predicted values, xi is the current output of processing element i and a is momentum value. The larger the learning rate, the larger the weight changes on each training cycle, and the quicker the network learning. However, the size of the learning rate can also influence whether the network achieves a stable solution. Momentum weights the importance of previous iteration (previous changes in the connection weights) to the next connection weight modification (Li & Bridgwater, 2000). The performances of the various ANN configurations were compared using the mean absolute error (MAE) and root mean square error (RMSE). Final errors of vari-
ous ANN structures were average of six out put errors. The coefficient of determination, R2, of the linear regression line between the predicted values from the neural network model and the desired output was also used as a measure of performance. The two error measures used to compare the performance of various ANN configurations were n 1X MAE ¼ jxd xp j; ð4Þ n i¼1 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n 1X 2 ð5Þ ðxd xp Þ ; RMSE ¼ n i¼1 where n is the number of data points, and xd and xp are the desired and predicted values of farinographical parameters, respectively. A commercial software package, Neural works professional II/plus simulator (Ware, Pittsburgh, USA), was used in this study. 3. Results and discussion The ANN parameters used for prediction of dough rheological properties are shown in Table 1. Table 1 shows the optimum value of the final selected ANN used to predict to rheological properties of wheat flour dough. The error measures associated with different ANN configurations for prediction of rheological properties are presented in Table 2. The optimal number of hidden layers and number of neurons in the hidden layers were selected by using a trial and error method and keeping the learning coefficient and momentum constant (chosen as 0.3 for learning coefficient and 0.4 for momentum). Results showed that ANN configuration included one
Table 1 The best structure and optimum values of the ANN produced in testing stage ANN structure
Learning rate
Momentum
Transfer function
Average testing RMSE
Average testing MAE
Iteration 1000
Average testing R2
4-17-6 with back propagation algorithm
0.3
0.4
Sigmoid
8.841
7.029
75
0.8251
E. Razmi-Rad et al. / Journal of Food Engineering 81 (2007) 728–734
731
Table 2 Average testing error parameters and average coefficient of determination for predicting of rheological properties with different neural network configurations Number of hidden layer
Neuron in first hidden layer
Neuron in second hidden layer
MAE
RMSE
R2
1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
1 3 5 7 9 11 13 15 17 19 1 1 1 1 1 3 3 3 3 3 5 5 5 5 5 10 10 10 10 10 15 15 15 15 15 20 20 20 20 20
0 0 0 0 0 0 0 0 0 0 3 5 10 15 20 3 5 10 15 20 3 5 10 15 20 3 5 10 15 20 3 5 10 15 20 3 5 10 15 20
9.9494 8.7937 7.9402 7.4997 7.3800 7.3160 7.0550 7.0597 7.0290 7.0656 15.9652 12.3052 10.3270 10.5354 10.2475 11.2447 23.6597 9.2111 8.8182 8.6198 9.3480 9.1010 8.7606 8.0853 8.4429 8.5736 8.4334 8.4632 7.7002 7.8034 9.2071 8.0983 8.0108 7.7679 7.8584 9.3035 7.6781 7.7954 7.5746 7.3559
30.7708 22.2769 9.4274 9.2138 8.9961 9.0139 8.8794 8.8835 8.8411 9.0998 19.3673 15.2885 13.0718 13.2809 12.8069 13.8462 27.2799 11.2758 10.7170 10.3961 11.4514 11.2031 10.6469 9.8267 10.2679 10.2751 10.2594 10.3013 9.4031 9.4300 11.3222 9.8053 9.7071 9.4301 9.4653 11.4512 9.3171 9.4996 9.1957 8.9835
0.7920 0.8168 0.8243 0.8157 0.8126 0.8155 0.8071 0.8136 0.8251 0.7718 0.7693 0.7562 0.7852 0.7813 0.7955 0.7649 0.7960 0.8038 0.8093 0.8183 0.7450 0.7936 0.8055 0.8129 0.8133 0.8147 0.8135 0.8193 0.8153 0.8226 0.8199 0.8120 0.8211 0.8100 0.8233 0.7607 0.8114 0.8161 0.8234 0.8207
30 MAE RMSE
RMSE, MAE
25 20 15 10 5 0
100000 95000 90000 85000 80000 75000 70000 65000 60000 55000 50000 45000 40000 35000 30000 25000 20000 15000 10000 5000 1000
hidden layers with 17 neurons in hidden layer had best structure for prediction of rheological properties. The MAE and RMSE for this optimal configuration were 7.029 and 8.841, respectively. Fig. 2 shows the RMSE and MAE as a function of the number of the iteration for the final structure. RMS and MA error proceeded toward minimum value to 75 000 iterations and then increasing trend was observed in higher iteration (over training). To reveal the credibility of prediction from the optimal ANN (trained with 75 000 iteration) presented in Table 2, predicted data versus actual data for testing data set were plotted (Fig. 3) and the determination coefficients (R2) were determined. As well as, average determination coefficient for different ANN configurations were calculated and presented in Table 2. Average R2 value for optimal ANN was acceptable (0.8251) and the results showed relatively good agreement between the predicted and the actual values.
Iteration Fig. 2. Effect of iteration on average RMSE and MAE of optimal ANN.
The performance of the optimal neutral network was validated using a second data set consisting of 26 cases that not previously used in the training and testing stage. The
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E. Razmi-Rad et al. / Journal of Food Engineering 81 (2007) 728–734
a
b
Water Absorption(%)
Dough development time 250
64
Predicted Data
Predicted Data
66
62 60 58 R2 = 0.6157 Testing data
56
55
60
65
150 R2 = 0.8910 Testing data
100 50
54 50
200
0
70
0
50
100
Actual Data
c
200
250
d Degree of Dough Softening after 10 Minutes (BU)
Dough Stability Time (min)
8
150
Actual Data
250
6
Predicted Data
Predicted Data
7
5 4 3 R2 = 0.8301 Testing data
2
200 150 R2 = 0.9071 Testing data
100 50
1 0
0 2
0
6
4
0
8
50
100
Actual Data
e
Degree of Dough Softening after 20 Minutes (BU) 300
f
200
250
Valorimeter Value (mm) 70
Predicted Data
250
Predicted Data
150
Actual Data
200 2
R = 0.9377 Testing data
150 100 50
60 50 R2 = 0.9284 Testing Data
40 30 20 10
0
0 0
50
100
150
200
250
300
Actual Data
0
20
40
60
80
Actual Data
Fig. 3. Predicted rheological data versus actual data for testing data set.
objective of this step was to evaluate the competence of the trained network. The optimal neural network predicted rheological parameters with MAE 8.638 and RMSE 10.794. Correlations between predicted and actual data for validation data set were demonstrated in Fig. 4. Average R2 value for validation data set was 0.801. These results are implying that the designed ANN was able to properly learn the relationship between the input and output data. 4. Conclusion The possibility of artificial neural network approach was investigated to model dough rheological (farinographic)
properties as a function of protein content, wet gluten, sedimentation value and falling number. Due to the complexity of dough rheological (farinographic) properties prediction using conventional methods, these alternative models allow a unified approach that can be used in baking industry. From this study, the following conclusions were drawn: The ANN technology has been shown to be a useful tool to investigate, approximate and predict rheological (farinographic) properties with a large number of parameters. It learned the relationship between the chemical input parameters (four factors) and rheological (farinographic) properties as output successfully. The results showed that, model consisted of one hidden layers with 17 neurons, was
E. Razmi-Rad et al. / Journal of Food Engineering 81 (2007) 728–734
a
Water Absorption(%)
66
b
62
Predicted Data
Predicted data
64
60 58
2
R = 0.629 validation data
56 54 52 50
733
Dough development time 250 200 150
R2 = 0.8810 Testing data
100 50 0
50
55
60
65
70
0
50
100
c
150
200
250
Actual Data
Actual Data
d Degree of Dough Softening after 10 Minutes (BU)
Dough Stability Time (min) 7
250 5
Predicted Data
Predicted Data
6
4 3
2
R = 0.6261 Validation data
2
200 150
R2 = 0.9098 Validation data
100 50
1 0
0 2
0
6
4
0
8
50
Actual Data
150
200
250
Actual Data
300
70
250
60
Predicted Data
e
200 150
R2 =
0.8603 Validation data
50
Valorimeter Value (mm)
80
Predicted Data
f Degree of Dough Sotening after 20 Minutes (BU)
100
100
50 40 R2 = 0.8901 Validation data
30 20 10
0 0
50
100
150
200
250
300
Actual Data
0 0
20
40
60
80
Actual Data
Fig. 4. Predicted rheological data versus actual data for validation data set.
able to produce rheological data with acceptable error (MAE 8.638 and RMSE 10.794). Acknowledgements We are thankful to the University of Tehran and Cereal Chemistry Center of Iran Agriculture Investigation Institute for supporting the facilities for this research work. The authors also thank Dr. Javad Khazai and Dr. Afshin Ashrafzadeh for their helpful guidance in ANN software and Mr. Rashmekarim for his technical assistance. References Fang, Q., Bibi, G., Haque, E., Hanna, M. A., & Spillman (1998). Neural network modeling of physical properties of ground wheat. Cereal Chemistry, 75(2), 251–253.
Hussain, M. A., & Rahman, M. S. (1999). Thermal conductivity prediction of fruits and vegetables using neural networks. International Journal of Food Properties, 2, 121–138. Hussain, M. A., & Shafiur, R. M. (2002). Prediction of pores formation (porosity) in foods during drying: generic models by the use of hybrid neural network. Journal of Food Engineering, 51(3), 239–248. Khazaei, J. & Shahbazi, F. (2005). Modelling physical and physiological damage to wheat seeds under impact loading using artificial neural networks. International Conference on Agrophysics, Lublin, Poland. Li, Y. Y., & Bridgwater, J. (2000). Prediction of extrusion pressure using an artificial neural network. Powder Technology, 108, 65–73. Menjvar, J. A. (1990). Fundamental aspects of dough rheology. In H. Levine, L. Slade, H. Faridi, & J. M. Faubion (Eds.), Dough Rheology and Baked Product Texture. New York: AVI-Van Nostrand Reinhold. Myhara, R. M., Sablani, S. S., Al-Alawi, S. M., & Taylor, M. S. (1998). Water sorption isotherms of dates: modeling using GAB equation and artificial neural network approaches. Lebensmittel Wissenschaft und Technologie, 31(7/8), 699–706. Ni, H., & Gunasekaran, S. (1998). Food quality prediction with neural networks. Food Technology, 52(10), 60–65.
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Razavi, M. A., Mortazavi, A., & Mousavi, M. (2003). Dynamic modelling of milk ultrafiltration by artificial neural network. Journal of Membrane Science, 220, 47–58. Ruan, R., Almear, S., & Zhang, J. (1995). Prediction of dough rheological properties using neural networks. Cereal Chemistry, 72(3), 308–311.
Sablani, S. S., & Shayya, W. H. (2001). Computarization of Stumbo’s method of thermal process calculations using neural networks. Journal of Food Engineering, 47, 233–240. Sablani, S. S., Baik, O. D., & Marcotte, M. (2002). Neural networks for predicting thermal conductivity of bakery products. Journal of Food Engineering, 52(3), 299–304.
Prediction of rheological properties of Iranian bread dough from chemical composition of wheat flour by using artificial neural networks E. Razmi-Rad a, B. Ghanbarzadeh b,*, S.M. Mousavi a, Z. Emam-Djomeh a, J. Khazaei c a
Food Science and Engineering Group, Faculty of Biosystem Engineering, Agricultural Campus of Tehran University, P.O. Box 4111, Karadj, Iran b Department of Food Science and Technology, Faculty of Agriculture, University of Tabriz, P.O. Box 51666-16471, Tabriz, Iran c Department of Agricultural Technical Engineering, Faculty of Agricultural Engineering, Abouraihan Campus, University of Tehran, P.O. Box 11365-7117, Pakdasht, Iran Received 19 September 2006; received in revised form 16 January 2007; accepted 17 January 2007 Available online 27 January 2007
Abstract This paper shows the ability of artificial neural network (ANN) technology for predicting the correlation between farinographic properties of wheat flour dough and its chemical composition. The input parameters of the neural networks (NN) were the four most important chemical parameters influencing farinographic properties, namely protein content, wet gluten, sedimentation value and falling number. The output parameters of the NN models were six farinographic properties including water absorption, dough development time, dough stability time, degree of dough softening after 10 and 20 min and valorimeteric value. Results showed that, the Multi Layer ANN with training algorithm of back propagation (BP) was the best one for creation of non-linear mapping between input and output parameters. The ANN model predicted the farinographic properties of wheat flour dough with average RMS 10.794. These results show that the ANN can potentially be used to estimate farinographic parameters of dough from chemical composition. This development may have significant potential to improve product quality and reduce time and costs by minimizing farinographical experiments. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Artificial neural network; Dough; Prediction; Rheological (Farinographic) properties
1. Introduction Dough rheological properties are important for both product quality and process efficient. The ability to measure the rheology of every batch of dough enables online process control by modifying subsequent process conditions. Rheological properties of dough can be related to bakery products specific volume and textural attributes. These attributes subsequently determine consumer acceptance (Menjvar, 1990). Therefore, accurate prediction of dough rheology can have many benefits for the baking industry. However, measuring rheology of every batch is impractical, while predicting these rheological properties has historically proved to be complex (Ruan, Almear, & *
Corresponding author. E-mail address: [email protected] (B. Ghanbarzadeh).
0260-8774/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2007.01.009
Zhang, 1995). Within the cereal industry, there has been a long history of using descriptive empirical measurements of rheological properties. Empirical tests are easy to perform and are often used in practical factory situations, providing data which is useful in evaluating performance during processing and for quality control. Several empirical devises are used in cereal industries including Farinograph, Amylograph, Mixograph, Extensograph and Alveograph. Farinograph is most frequently used equipment for empirical rheological measurements. An artificial neural network (ANN) is a form of analysis which is based on the simulation of living nervous systems. A neural network is a parallel distributed processing system composed of two components: the node (also called processing element, artificial neuron or unit) and the connection (Khazaei & Shahbazi, 2005). A parameter Wij (known as weight) is associated with each connection
E. Razmi-Rad et al. / Journal of Food Engineering 81 (2007) 728–734
between two cells. Thus each cell in the upper layer receives weighted inputs from each node in the layer below and then processes these collective inputs before the unit sends a signal to other layers (Li & Bridgwater, 2000). One of the major advantages of ANN is efficient handling of highly non-linear relationships in data, even when the exact nature of such relationship is unknown. Therefore, ANNs are well suited for food quality prediction, because of the complex nature of interrelationships among various quality parameters, composition and processing conditions in foods (Ni & Gunasekaran, 1998). The most popular ANN is the feed forward multi-layer ANN which uses back-propagation learning algorithm. This type of network consists of three layers of nodes namely an input layer, hidden layers and an output layer. Feed forward neural network usually has one or more hidden layers, which enable the network to model non-linear and complex functions. Scaled data are introduced into the input layer of the network and then is propagated from input layer to hidden layer and finally to the output layer (Hussain & Shafiur, 2002). Each node in hidden or output layer firstly acts as a summing junction which combines and modifies the inputs from the previous layer using i X yi ¼ xi wij þ bj ð1Þ where yi is the net input to node j in hidden or output layer, xi are the inputs to node j (or outputs of previous layer), wij are the weights representing the strength of the connection between the ith node and jth node, i is the number of nodes and bj is the bias associated with node j. Each neuron consists of a transfer function expressing internal activation level. Output from a neuron is determined by transforming its input using a suitable transfer function. Generally, the transfer functions for function approximation (regression) are sigmoidal function, hyperbolic tangent and linear function, of which the most widely used for non-linear relationship is the sigmoidal function. The general form of this function is as follows (Razavi, Mortazavi, & Mousavi, 2003): 1 1 þ ey j
ANN modeling has been successfully applied to the prediction of dough rheological properties (Ruan et al., 1995), physical properties of ground wheat (Fang, Bibi, Haque, Hanna, & Spillman, 1998), thermal conductivity of fruits and vegetables (Hussain & Rahman, 1999), isotherms of dates (Myhara, Sablani, Al-Alawi, & Taylor, 1998), food quality (Ni & Gunasekaran, 1998) prediction of heat penetration parameters in stumbo’s method of thermal process calculations (Sablani & Shayya, 2001) and prediction of thermal conductivity of bakery products (Sablani, Baik, & Marcotte, 2002). Wheat flour dough is one of the most complicated systems for rheological evaluation because it simultaneously possess viscous and elastic characteristics. In previous work on application of ANN modeling for prediction of dough rheological properties, relation between extensographical and farinographical data were studied. The purpose of this article was to discover the dependence of rheological parameters of dough, (farinographical parameters) on the chemical composition of wheat flour and develop a neural network model for the dynamic prediction of frinographical factors from chemical composition of wheat flour. 2. Materials and methods 2.1. Procedures
i¼1
zj ¼
729
Different Iranian cultivars of wheat seeds were selected for testing. These cultivars were conveniently used in bread making. These seeds were milled and obtained flours were used for measurements of four chemical variables (total protein, wet gluten, sedimentation value and falling number) and also for providing of 132 batches of dough, for measurement of six farinographical parameters. For these measurements, Standard Methods of the International Association for Cereal Science and Technology, (ICC) procedures, were followed. Those standard numbers were: 105/2: total protein, 107/1: falling number, 116/1: sedimentation value, 137/1: wet gluten, and 115/1: farinographical measurement. Four replicate were done for any experiment.
ð2Þ
zj, the output of node j, is also an element of the inputs to the nodes in the next layer. The values of the interconnection weights are determined by a neural network training or learning procedure using a set of data. The objective is to find the value of the weight that minimizes differences between the actual output and the predicted output in the output layer in order to minimize the mean square errors (MSE). In the learning process, there are several variables that have an effect on the ANN training. These variables are the number of iterations, learning rate (g), the momentum coefficient (a), number of hidden layers (L) and the number of hidden neurons (H). To find the best set of these variables and parameters, all of those must be varied and the best combination chosen.
2.2. ANN model development A feed forward multi-layered ANN trained by back propagation (BP) algorithm was selected to develop rheological (farinographic) properties models. The back-propagation algorithm firstly adjusts weights connected to the output layer. Then, working backward towards the input layer, the algorithm adjusts weights in each successive layer to reduce the errors at each level. In this study the inputs were: total protein, wet gluten, sedimentation value and falling number and six farinographic variables (water absorption, dough development time, dough stability time, degree of dough softening after 10 and 20 min and Valorimeteric value) were selected as the outputs of the network (Fig. 1).
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E. Razmi-Rad et al. / Journal of Food Engineering 81 (2007) 728–734
Fig. 1. Structure of feed forward multi-layer ANN for calculating farinographical parameters.
The data sets of 132 cases obtained from our experiments and then they were divided in two sets. The first set consisted of 106 (80%) cases for training/testing and 26 (20%) cases for validation data set were chosen randomly from the set of 132 cases. From the first set consisted of 106 cases, 85 cases were selected for training and 21 cases for testing. Adjustments of ANN parameters were included the number of hidden layers and neurons, and the number of iteration. The delta learning rule was selected in this research work. It is one of the well-known weight update rules, which is based on the simple idea of continuously modifying the strengths of the connections to reduce the difference the (delta) between the desired output value and the current output value of a processing element (Li & Bridgwater, 2000). It is expressed as Dwij ðn þ 1Þ ¼ gd j xi þ aDwji ðnÞ
ð3Þ
where Wij is the connection weight between nodes i and j, n is discrete time cycle number, g is the learning rate, dj is the difference between actual and predicted values, xi is the current output of processing element i and a is momentum value. The larger the learning rate, the larger the weight changes on each training cycle, and the quicker the network learning. However, the size of the learning rate can also influence whether the network achieves a stable solution. Momentum weights the importance of previous iteration (previous changes in the connection weights) to the next connection weight modification (Li & Bridgwater, 2000). The performances of the various ANN configurations were compared using the mean absolute error (MAE) and root mean square error (RMSE). Final errors of vari-
ous ANN structures were average of six out put errors. The coefficient of determination, R2, of the linear regression line between the predicted values from the neural network model and the desired output was also used as a measure of performance. The two error measures used to compare the performance of various ANN configurations were n 1X MAE ¼ jxd xp j; ð4Þ n i¼1 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n 1X 2 ð5Þ ðxd xp Þ ; RMSE ¼ n i¼1 where n is the number of data points, and xd and xp are the desired and predicted values of farinographical parameters, respectively. A commercial software package, Neural works professional II/plus simulator (Ware, Pittsburgh, USA), was used in this study. 3. Results and discussion The ANN parameters used for prediction of dough rheological properties are shown in Table 1. Table 1 shows the optimum value of the final selected ANN used to predict to rheological properties of wheat flour dough. The error measures associated with different ANN configurations for prediction of rheological properties are presented in Table 2. The optimal number of hidden layers and number of neurons in the hidden layers were selected by using a trial and error method and keeping the learning coefficient and momentum constant (chosen as 0.3 for learning coefficient and 0.4 for momentum). Results showed that ANN configuration included one
Table 1 The best structure and optimum values of the ANN produced in testing stage ANN structure
Learning rate
Momentum
Transfer function
Average testing RMSE
Average testing MAE
Iteration 1000
Average testing R2
4-17-6 with back propagation algorithm
0.3
0.4
Sigmoid
8.841
7.029
75
0.8251
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Table 2 Average testing error parameters and average coefficient of determination for predicting of rheological properties with different neural network configurations Number of hidden layer
Neuron in first hidden layer
Neuron in second hidden layer
MAE
RMSE
R2
1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
1 3 5 7 9 11 13 15 17 19 1 1 1 1 1 3 3 3 3 3 5 5 5 5 5 10 10 10 10 10 15 15 15 15 15 20 20 20 20 20
0 0 0 0 0 0 0 0 0 0 3 5 10 15 20 3 5 10 15 20 3 5 10 15 20 3 5 10 15 20 3 5 10 15 20 3 5 10 15 20
9.9494 8.7937 7.9402 7.4997 7.3800 7.3160 7.0550 7.0597 7.0290 7.0656 15.9652 12.3052 10.3270 10.5354 10.2475 11.2447 23.6597 9.2111 8.8182 8.6198 9.3480 9.1010 8.7606 8.0853 8.4429 8.5736 8.4334 8.4632 7.7002 7.8034 9.2071 8.0983 8.0108 7.7679 7.8584 9.3035 7.6781 7.7954 7.5746 7.3559
30.7708 22.2769 9.4274 9.2138 8.9961 9.0139 8.8794 8.8835 8.8411 9.0998 19.3673 15.2885 13.0718 13.2809 12.8069 13.8462 27.2799 11.2758 10.7170 10.3961 11.4514 11.2031 10.6469 9.8267 10.2679 10.2751 10.2594 10.3013 9.4031 9.4300 11.3222 9.8053 9.7071 9.4301 9.4653 11.4512 9.3171 9.4996 9.1957 8.9835
0.7920 0.8168 0.8243 0.8157 0.8126 0.8155 0.8071 0.8136 0.8251 0.7718 0.7693 0.7562 0.7852 0.7813 0.7955 0.7649 0.7960 0.8038 0.8093 0.8183 0.7450 0.7936 0.8055 0.8129 0.8133 0.8147 0.8135 0.8193 0.8153 0.8226 0.8199 0.8120 0.8211 0.8100 0.8233 0.7607 0.8114 0.8161 0.8234 0.8207
30 MAE RMSE
RMSE, MAE
25 20 15 10 5 0
100000 95000 90000 85000 80000 75000 70000 65000 60000 55000 50000 45000 40000 35000 30000 25000 20000 15000 10000 5000 1000
hidden layers with 17 neurons in hidden layer had best structure for prediction of rheological properties. The MAE and RMSE for this optimal configuration were 7.029 and 8.841, respectively. Fig. 2 shows the RMSE and MAE as a function of the number of the iteration for the final structure. RMS and MA error proceeded toward minimum value to 75 000 iterations and then increasing trend was observed in higher iteration (over training). To reveal the credibility of prediction from the optimal ANN (trained with 75 000 iteration) presented in Table 2, predicted data versus actual data for testing data set were plotted (Fig. 3) and the determination coefficients (R2) were determined. As well as, average determination coefficient for different ANN configurations were calculated and presented in Table 2. Average R2 value for optimal ANN was acceptable (0.8251) and the results showed relatively good agreement between the predicted and the actual values.
Iteration Fig. 2. Effect of iteration on average RMSE and MAE of optimal ANN.
The performance of the optimal neutral network was validated using a second data set consisting of 26 cases that not previously used in the training and testing stage. The
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E. Razmi-Rad et al. / Journal of Food Engineering 81 (2007) 728–734
a
b
Water Absorption(%)
Dough development time 250
64
Predicted Data
Predicted Data
66
62 60 58 R2 = 0.6157 Testing data
56
55
60
65
150 R2 = 0.8910 Testing data
100 50
54 50
200
0
70
0
50
100
Actual Data
c
200
250
d Degree of Dough Softening after 10 Minutes (BU)
Dough Stability Time (min)
8
150
Actual Data
250
6
Predicted Data
Predicted Data
7
5 4 3 R2 = 0.8301 Testing data
2
200 150 R2 = 0.9071 Testing data
100 50
1 0
0 2
0
6
4
0
8
50
100
Actual Data
e
Degree of Dough Softening after 20 Minutes (BU) 300
f
200
250
Valorimeter Value (mm) 70
Predicted Data
250
Predicted Data
150
Actual Data
200 2
R = 0.9377 Testing data
150 100 50
60 50 R2 = 0.9284 Testing Data
40 30 20 10
0
0 0
50
100
150
200
250
300
Actual Data
0
20
40
60
80
Actual Data
Fig. 3. Predicted rheological data versus actual data for testing data set.
objective of this step was to evaluate the competence of the trained network. The optimal neural network predicted rheological parameters with MAE 8.638 and RMSE 10.794. Correlations between predicted and actual data for validation data set were demonstrated in Fig. 4. Average R2 value for validation data set was 0.801. These results are implying that the designed ANN was able to properly learn the relationship between the input and output data. 4. Conclusion The possibility of artificial neural network approach was investigated to model dough rheological (farinographic)
properties as a function of protein content, wet gluten, sedimentation value and falling number. Due to the complexity of dough rheological (farinographic) properties prediction using conventional methods, these alternative models allow a unified approach that can be used in baking industry. From this study, the following conclusions were drawn: The ANN technology has been shown to be a useful tool to investigate, approximate and predict rheological (farinographic) properties with a large number of parameters. It learned the relationship between the chemical input parameters (four factors) and rheological (farinographic) properties as output successfully. The results showed that, model consisted of one hidden layers with 17 neurons, was
E. Razmi-Rad et al. / Journal of Food Engineering 81 (2007) 728–734
a
Water Absorption(%)
66
b
62
Predicted Data
Predicted data
64
60 58
2
R = 0.629 validation data
56 54 52 50
733
Dough development time 250 200 150
R2 = 0.8810 Testing data
100 50 0
50
55
60
65
70
0
50
100
c
150
200
250
Actual Data
Actual Data
d Degree of Dough Softening after 10 Minutes (BU)
Dough Stability Time (min) 7
250 5
Predicted Data
Predicted Data
6
4 3
2
R = 0.6261 Validation data
2
200 150
R2 = 0.9098 Validation data
100 50
1 0
0 2
0
6
4
0
8
50
Actual Data
150
200
250
Actual Data
300
70
250
60
Predicted Data
e
200 150
R2 =
0.8603 Validation data
50
Valorimeter Value (mm)
80
Predicted Data
f Degree of Dough Sotening after 20 Minutes (BU)
100
100
50 40 R2 = 0.8901 Validation data
30 20 10
0 0
50
100
150
200
250
300
Actual Data
0 0
20
40
60
80
Actual Data
Fig. 4. Predicted rheological data versus actual data for validation data set.
able to produce rheological data with acceptable error (MAE 8.638 and RMSE 10.794). Acknowledgements We are thankful to the University of Tehran and Cereal Chemistry Center of Iran Agriculture Investigation Institute for supporting the facilities for this research work. The authors also thank Dr. Javad Khazai and Dr. Afshin Ashrafzadeh for their helpful guidance in ANN software and Mr. Rashmekarim for his technical assistance. References Fang, Q., Bibi, G., Haque, E., Hanna, M. A., & Spillman (1998). Neural network modeling of physical properties of ground wheat. Cereal Chemistry, 75(2), 251–253.
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