MATERIALS AND METHODS

Data collection and preparation: The study area included an industrial complex for dairy cattle farming in Tehran province of Iran. Tehran province is located within 35°34' and 35°50' N latitude and 51°02' and 51°36' E longitude. This province with 4,443 industrial dairy and beef cattle farms plays an important role in producing milk and meat for the population of Iran. The milk yield for the first three months of 2010 was announced as 265,501 t yielded from 1,897 dairy cow farm units (Anonymous, 2010). "Dam-Gostar Dairy Cattle Farms Complex" was established in this province for the purpose of drawing dairy farms off the residential areas inside the city. Currently, there are about 200 industrial and semi-industrial dairy farms producing milk in this complex. This survey was made in 2011-2012 by interviewing the dairy cattle farmer of 50 units. The sample size was determined by using the random sampling method (Cochran technique) (Cochran, 1977). Some assumptions were made essentially in order to have a much more precise computation such as the period for which energy consumption was estimated for. A lactation period of a cow is approximately 305 days and cows are dry in about 60 days. Therefore, input consumptions assigned to a production year were considered. More specific characteristics of the target farms and cows are given in Table 1.

The culled data was transformed into energy equivalents. To achieve this, gained energy coefficients from various references (Table 2) were applied. The references of each energy coefficient have also been cited in third column. These energy coefficients were multiplied by the inputs consumption quantities to compute the energy use equivalents.

Table 1:	Characteristics of the dairy cattle farms and cows of the studied area
*Dry matter

Table 2:	Energy equivalent coefficients of inputs and outputs
a*: Economic life of machine (year)

Based on the energy equivalent computation results, various energy indices including Energy Use Efficiency (EUE) or Energy Ratio (ER), Energy Productivity (EP), Specific Energy (SE) and Net Energy Gain (NEG) were estimated as follows (Eq. 1-4) (Pishgar-Komleh et al., 2011):

(1)

(2)

(3)

(4)

Artificial neural networks model: The acronym ANNs which stands for artificial neural networks, is an information processor with identical characteristics as biological and behavioral neural networks of human brain (Movagharnejad and Nikzad, 2007). Multi-Layer Perceptron (MLP) is a widely used ANNs architecture. It consists of one input layer, one or more hidden layers and one output layer and each layer employs several neurons. To run the model, data was divided into three groups. One of these groups was used for training (training set) and the other was used for testing (testing set) of the network and the third is for validation measuring network generalization. The artificial neural network model with back propagation is the most widely used multi-layered prediction model.

In this study, in order to forecast milk yield in the studied region, five energy inputs were chosen as input parameters to the ANNs model. Milk yield of the target farms was selected as output variable. Different hidden layers and different number of neurons in each hidden layer were examined to determine the best topology of the network. Networks with different activation functions were also developed to attain the best results. To perform ANN models, MATLAB M-le environment version 7.1 (R2012a) was employed. Moreover, various required modifications were applied to the program. These modifications included number of hidden layers, number of neurons in each hidden layer. After making each modification, the model was run for forty iterations.

Adaptive neuro-fuzzy inference system: A Fuzzy Inference System (FIS) forms a useful computing framework based on the concepts of fuzzy set theory, fuzzy if-then rules and fuzzy reasoning. The ANFIS is a FIS implemented in the framework of an adaptive fuzzy neural network. This is a rule-based system with three components: membership functions of input-output variables, fuzzy rules and output characteristics and system results. A Neuro-fuzzy network is the combination of neural networks with the fuzzy logic; this combination has the explicit knowledge representation of a FIS with the learning power of ANNs. The ANFIS is capable of simulating and analyzing the mapping relation between the input and output data through a hybrid learning to determine the optimal distribution of membership function. It is mainly based on the fuzzy "if-then" rules from the Takagi and Sugeno type (Jang et al., 1997).

In general, the algorithm first requires the establishment of fuzzy sets and rules over the number of inputs (N). By defining appropriate membership functions the input data would change from crispy into the non-crispy manner through a process called fuzzification. Then, the non-crispy data were analyzed in the fuzzy inference engine based on the pre-defined if-then rules, before being converted back to the crispy output through the defuzzification process. the basic block diagram of the fuzzy system is illustrated in Fig. 1 (Hou and O'Brien, 2006).

The FIS, whose membership function parameters are tuned (adjusted) using either a back propagation algorithm alone or in combination with a least squares type of method (hybrid), is applied to a given input/output data set. This allows the fuzzy systems to learn from the data they are modeling. The ANFIS uses either back propagation or a combination of least squares estimation and back propagation (hybrid) for membership function parameter estimation. In some cases, data is collected using noisy measurements and the training data cannot be representative of all the features of the data that will be presented to the model. This is where model validation comes into play.

In order to create ANFIS models, MATLAB M-file environment version 7.1 (R2012a) was utilized. In running the ANFIS models, we faced two major constraints. One was the number of input parameters and other the number of units (fifty dairy cattle farms). The total number of inputs was five including: diesel fuel, electricity, machinery, human labor and feed supply energy equivalents. The milk yield was regarded as the output of the model. When the number of ANFIS inputs exceeds 5, increased computational time and rule numbers cause ANFIS to run out of analysis (Naderloo et al., 2012). To overcome this constraint, input clustering was performed so that they were classified into two clusters based on their share in energy consumption.

Fig. 1:	Fuzzy block diagram

Fig. 2:	ANFIS network diagram

Correspondingly, three ANFIS sub-networks were developed (Fig. 2). Hence, an individual ANFIS network was employed for each category and two predicted values were used as inputs to ANFIS 3. Eventually the output of the last model was milk yield. Applying this procedure the problem of limited number of samples (dairy cattle farms) was also solved and the total number of parameters did not exceed the number of training data pairs.

Moreover, in order to achieve the best and effective model with minimum errors, five significant and important adjustments were made in the structure of ANFIS network. These settings include types of membership function (mf) (including triangular, trapezoidal, bell-shaped, Gaussian and sigmoid), the number of membership functions, the number of epochs, types of output membership function (constant or linear) and optimization methods (hybrid or back propagation). The ANFIS performance was validated using some statistic parameters such as the coefficient of determination (R²), the Root Mean Square Error (RMSE) and the Mean Absolute Percentage Error (MAPE) (Eq. 5-7):

(5)

(6)

(7)

where, x_i is the observed value, is the predicted value, is the mean of each observed or predicted values and n is the number of samples (Khoshnevisan et al., 2014a). Therefore, these parameters indicate the agreement between the actual and forecast values and are used as evaluation criteria for comparing this model with others.

RESULTS AND DISCUSSION

Energy consumption estimation: Energy input-output analysis was carried out in order that we could model the energy use pattern in milk production process. In Table 3, the energy equivalents of inputs and output, their contribution in total energy consumption and some of the energy indices are presented.

Table 3:	Energy inputs and output equivalents for studied dairy cattle farms
NEG: Net energy gain, EP: Energy productivity, ER: Energy ratio

Based on the findings, feed supply, fossil fuel and electricity energy inputs had highly contributed in total energy consumption as 41548.7 (78.24%), 8655.8 (16.3%) and 1699.2 (3.2%) MJ cow^–1 in a production period (365 days), respectively. The shares for human labor and machinery energy in total energy input was less than 1% indicating their less importance in energy optimization programs. It should be noted here that electricity energy was observed to be highly applied for operating dairy farming equipment. Based on the results, energy is used efficiently to produce milk in the studied region while, this index is used to measure the system efficiency. Energy productivity index was calculated as 0.16. In other words, to produce 8089.12 kg cow^–1 milk per year, 0.16 MJ cow^–1 energy is consumed.

Development of ANNs model: The program written in MATLAB environment was modified from different viewpoints. Different number of hidden layers, number of neurons, activation functions and training algorithms were attempted to obtain the best network topology. Finally, the best ANNs architecture was 5-18-16-1 which composed of one input layer with five input variables, two hidden layers each consists of eighteen and sixteen neurons and one output layer with one parameter. The abovementioned structure gained the best statistical parameters, too. The coefficient of determination (R²) between the observed and predicted milk yield was estimated 0.85. The RMSE and MAPE were calculated as 1052.413 and 0.0702, respectively. The relatively high correlation between measured and predicted yield for testing data set indicated that the developed ANNs model can accurately predict milk yield amount of studied farms on the basis of energy inputs (Fig. 3).

Khoshnevisan et al. (2014b) reported the best prediction of the ANNs network with 11-30-2-1 structure that consisted of an input layer with eleven parameters, two hidden layers each one consisted of 30 and 2 neurons, respectively and one output layer including one output variable (potato yield). In another study by Sharma et al. (2007), an Artificial Neural Network (ANNs) model is proposed to predict the first lactation 305-day milk yield. several training algorithms such as gradient descent algorithm with adaptive learning rate, Fletcher-Reeves conjugate gradient algorithm, Polak-Ribiére conjugate gradient algorithm, Powell-Beale conjugate gradient algorithm, Quasi-Newton algorithm with Broyden, Fletcher, Goldfarb and Shanno (BFGS) update and Levenberg-Marquardt algorithm with Bayesian regularization along with various network architectural parameters, i.e., data partitioning strategy, initial synaptic weights, number of hidden layers, number of neurons in each hidden layer, activation functions, regularization factor, etc., were experimentally investigated to arrive at the best model for modeling and predicting the milk yield. The results of this study emerged that the performance of ANNs model seems to be slightly superior to that of the conventional regression model.

Fig. 3:	Correlation plot between actual and predicted values of milk yield for the testing data

Assessment of ANFIS modeling: In situations that there is uncertainty about data for approximation problems, fuzzy logic is a proper tool to apply modeling and predicting techniques such as ANFIS in imprecision environment. As, it is mentioned in previous section and depicted in Fig. 2, inputs were divided into two clusters based on their energy share. This classification was undertaken to overcome constraints on the number of input parameters (five energy input elements) and simultaneously number of samples in each variable (fifty dairy cattle farms). Therefore, feed supply of cows, electricity and fossil fuel energies were considered as input parameters to ANFIS 1 network; while machinery and human labor energy inputs were considered as inputs to ANFIS 2. Accordingly, three ANFIS networks were developed to predict and model milk yield in dairy cattle farms. In ANFIS editor, there are different input membership functions including triangular, trapezoidal, generalized bell, Gaussian curve, Gaussian combination, q-shaped, difference between two sigmoid functions and product of two sigmoid functions. The best results were derived from triangular membership function. It is worth nothing that, in this study, three membership functions were applied to each input variable. The type of output membership function was considered to be linear. In Fig. 4, the structure of the ANFIS 2 network with two input parameters and also the number of fuzzy rules are illustrated.

The number of epochs was another modification to the written program. One to forty epochs were tested in training step and the results of their variation against the number of epochs for ANFIS 1 and ANFIS 2 are depicted in Fig. 5. As it can be observed, the amount of error is diminishing by increasing the number of epochs. The same trend was observed for ANFIS 3 network.

Some statistical parameters were calculated for the purpose of best model validation including R², RMSE and MAPE. The validation results are given in Table 4. As, it is presented in Table 4, the correlation coefficient (R²) of ANFIS 1 and ANFIS 2 were 0.75 and 0.65, respectively; while it has improved to 0.93 for ANFIS 3 network. So, it can be concluded that the MLANFIS model was able to predict and model the milk yield successfully based on the energy use. The correlation results of each three ANFIS networks in contrast with ANNs model is presented in Fig. 6.

Fig. 4:	General structure of the ANFIS 2 network

Fig. 5(a-b):	Relation between training error and the number of epochs in (a) ANFIS 1 and (b) ANFIS 2

Table 4:	Characteristics of the best structure
mf: Membership function, RMSE: Root mean square error, MAPE: Mean absolute percentage error, R2: Correlation co-efficient and ANFIS: Adaptive neuro-fuzzy inference system, Trimf: Triangular membership function

Due to the lack of similar studies to our research criteria (use of MLANFIS in modeling milk yield based on energy use), the results of this study are compared with other agricultural fields but in similar geographical zone.

Fig. 6(a-d):	Correlation between predicted and observed milk yield for (a) ANFIS 1, (b) ANFIS 2, (c) ANFIS 3 and (d) ANN models

Naderloo et al. (2012) developed an Adaptive Neuro-Fuzzy Inference System (ANFIS) to predict the grain yield of irrigated wheat in Abyek town of Ghazvin province, Iran. The R² and RMSE values were found 0.996 and 0.013 for ANFIS 1 and 0.992 and 0.018 for ANFIS 2, respectively. Hence, this emerged the fact that ANFIS 1 and ANFIS 2 could well predict the yield based on energy use pattern. Also, the R² and RMSE values for ANFIS 3 were 0.013 and 0.996, respectively. These results showed that the final network (ANFIS 3) could predict the grain yield with good accuracy. Khoshnevisan et al. (2014a) found ANFIS technique with multiple layers more precise than artificial neural network in predicting potato yield on the basis of energy inputs in Isfahan province of Iran. According to their results, the best ANNs model had a topology with 11-30-2-1 structure. In their study labor, machinery, diesel fuel, seeds, biocides, chemical fertilizers (N, P₂O₅), farmyard manure, irrigation water and electricity were energy variables and potato yield was considered as output parameter. Correlation coefficient (R), Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE) for the best ANNs model were 0.925, 0.071 and 0.5, respectively while, the corresponding R, RMSE and MAPE values for the best ANFIS topology were reported as 0.987, 0.029 and 0.2, respectively. Finally, it was concluded that MLANFIS model gives better results than does ANNs model in imprecise and fuzzy conditions.

Finally, there would be one more query on why the proposed ANFIS model was developed by clustering input variables to two groups based on their energy share. As the first step, we examined various networks using logical relationships between inputs and the MATLAB written program was run. For instance, electricity and fossil fuel were considered as a cluster and the model was tested. Correspondingly, the gained results were not effective on the final ANFIS network performance. Therefore, based on energy use analysis, clustering was performed using the share for each input variable in total energy use of studied dairy cattle farms. In addition, Khoshnevisan et al. (2014b) expressed identical findings.

CONCLUSION

In this study, artificial intelligent techniques including Multi-Layered Adaptive Neural Fuzzy Inference System (MLANFIS) and Artificial Neural Network (ANNs) were employed to model and predict the milk yield of some dairy cattle farms based on energy consumption in Tehran province, Iran. Using the input use amounts and their related energy coefficients, energy equivalents of inputs were computed. Also, energy indices in the studied region were estimated. Total energy use was calculated as 5310.98 MJ cow^–1 and among all inputs, cows’ feed with 41548.76 MJ cow^–1 (78.24%) of total energy use had the highest share; moreover fossil fuels and electricity energy with 8655.82 MJ cow^–1 (16.3%) and 1699.21 MJ cow^–1 (3.2%) shares were in the second and third rank, respectively. The average total milk yield of the target production process was about 8089.12 kg cow^–1 during one production year. The ANNs model with two hidden layers based on energy inputs was applied to model milk yield. The best ANNs model was 5-18-16-1. Furthermore, ANFIS model was developed and in order to have an accurate ANFIS model performance and to overcome the constraints of this method (number of input variables and samples for each variable), inputs were divided into two clusters based on their energy share in total energy input and the output for each cluster (ANFIS 1 and 2) was assumed as the input to the final ANFIS network (ANFIS 3). The outcomes of these two methods were compared in this study. Firstly, R² value of ANFIS 1 (0.75), ANFIS 2 (0.65) and ANFIS 3 (0.93) networks indicated that input clustering had been effective in the ANFIS performance as data were not crisp and precise. Secondly, results revealed that MLANFIS model was relatively better in prediction capability of milk yield rather than ANNs model and it is suggested to be considered as an alternative technique in the same situations for other future studies. Indeed it is simple for programming though it seems extremely complicated. To extend this model for further studies, it is recommended to assess other production factors in dairy farms like socio-economic conditions, economical productivity and other management parameters to investigate their effects on milk yield. Moreover, researchers can develop this model with more layers and draw a comparison between its outcomes and the results of this study.

ACKNOWLEDGMENTS

The financial support provided by the University of Tehran, Iran, is duly acknowledged. Also, thanks are due to board of directors of Dam-Gostar Dairy Cattle Farms Complex for granting permission to collect data for this study. Last but not the least, the authors wish to sincerely appreciate the anonymous reviewers of this paper for their time and effort to review the manuscript and for their valuable and useful comments to improve the study.