Development of an intelligent system based
on ANFIS for predicting wheat grain yield
on the basis of energy inputs
Benyamin Khoshnevisan, Shahin Rafiee
*, Mahmoud Omid, Hossein Mousazadeh
Department of Agricultural Machinery Engineering, Faculty of Agricultural Engineering and Technology, University of Tehran, Karaj, Iran
A R T I C L E I N F O Article history:
Received 25 July 2013 Received in revised form 2 April 2014
Accepted 17 April 2014 Available online 24 April 2014 Keywords: Wheat yield Energy consumption Prediction ANFIS ANN A B S T R A C T
Energy is regarded as one of the most important elements in agricultural sector. During the last decades energy consumption in agriculture has increased, so finding the relationship between energy consumption and crop yields in agricultural production can help to achieve sustainable agriculture. In this study several adaptive neuro-fuzzy inference system (ANFIS) models were evaluated to predict wheat grain yield on the basis of energy inputs. Moreover, artificial neural networks (ANNs) were developed and the obtained results were compared with ANFIS models. For the best ANFIS structure gained in this study, R, RMSE and MAPE were calculated as 0.976, 0.046 and 0.4, respectively. The developed ANN was a multilayer perceptron (MLP) with eleven neurons in the input layer, two hidden layers with 32 and 10 neurons and one neuron (wheat grain yield) in the output layer. For the best ANN model, R, RMSE and MAPE were computed as 0.92, 0.9 and 0.1, respectively. The results illustrated that ANFIS model can predict the yield more precisely than ANN.
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1.
Introduction
Wheat (Triticum spp.) is one of the most-produced cereals which provides 70–90% of all calories and 66–90% of the pro-tein consumed in developing countries and is the leading source of vegetable protein in human food, having a higher
protein content than either maize (corn) or rice and the other major cereals. In terms of total production tonnages used for food, it is currently second to rice as the main human food crop and ahead of maize, after allowing for maize’s more extensive use in animal feeds. It is now cultivated widely all over the world under a wide range of climatic conditions[1]. In 2010 world production of wheat was 651 million tons, mak-ing it the third most-produced cereal after maize (844 million tons) and rice (672 million tons)[2]. Iran with 150 million tons of wheat production in 2010 held the fourth rank among Asian countries.
The role of energy in agricultural production is so signifi-cant and important because different forms of energy are employed during production season and modern agriculture requires an energy input at all stages of agricultural produc-tion such as direct use of energy in farm machinery, water management, irrigation, cultivation and harvesting[3]. Also http://dx.doi.org/10.1016/j.inpa.2014.04.001
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2632808138.
E-mail addresses:[email protected](B. Khoshnevisan), [email protected](S. Rafiee).
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post-harvest energy use includes energy for food processing, storage and in transport to markets. In addition, there are many indirect or sequestered energy inputs used in agricul-ture in the form of mineral fertilizers and chemical pesticides, insecticides and herbicides. Mechanized-crop production and intensive agricultural practices cause that energy consump-tion in agricultural sector increase dramatically[4]. Assessing the relationship between the energy inputs and outputs can help to achieve sustainability in agricultural production[5]. Due to the fundamental importance of energy issue in agri-culture, several studies have been conducted on worldwide production of field crops including wheat [6], potato [7], canola[8], greenhouse crops[9–11], prune[12], soybean[13], etc. to analyze the energy input–output and to investigate their relationship.
To find the relationship between inputs and outputs of a production process artificial intelligence (AI) has drawn more attention rather than mathematical models to find the rela-tionships between input and output variables by training, and produce results without any prior assumptions. Artificial neural network (ANN) models as a form of AI which was inspired by the studies of the human neuron can be applied to overcome the non-linearity problem and to analyze bio-physical data and they are usually used to model complex relationships between inputs and outputs, to find patterns in data, or to capture the statistical structure in an unknown joint probability distribution between observed variables[14]. ANNs have the potential to be better, quicker, and more prac-tical alternative to the traditional methods, for modeling[15]. In the recent years, ANN modeling technique has been employed to show the robustness of AI versus regression methods. Zangeneh et al. [16]drew a comparison between parametric and ANN approaches for economical assessment of potato production. In another study, Safa and Samarasin-ghe[17]used ANN for determination and modeling of energy consumption in wheat production. ANN model and multiple linear regression (MLR) model were compared and it was con-cluded that ANN model can predict energy consumption rel-atively better than the MLR model.
The adaptive neuro-fuzzy inference system (ANFIS), another AI method, is a combination of ANN and fuzzy sys-tems that uses the learning capability of the ANN to derive the fuzzy if-then rules with appropriate membership func-tions worked out from the training pairs, which in turn leads to the inference[18,19]. ANFIS has been employed in various agricultural studies. Akbarzadeh, Mehrjardi[20]developed an ANFIS model for soil erosion estimation. In another research, conducted by Krueger, Prior[21], ANFIS model was evaluated to characterize root distribution patterns under field condi-tions. Kisi and Shiri[22]compared ANN and ANFIS models for prediction of long-term monthly air temperature using geographical inputs. They illustrated that the maximum and minimum determination coefficient values were calculated as 0.995 and 0.921 for ANN model and computed as 0.999 and 0.876 for ANFIS model. Some studies show that there is a positive relationship between energy usage and productivity [10,17,23,24].
The aim of this study was to develop several ANFIS models to predict wheat yield on the basis of energy inputs. Moreover, the ANN models were developed and generalized to predict
wheat grain yield based on the energy inputs and further-more, the results were compared with ANFIS models.
2.
Materials and methods
2.1. Selection of case study region and data processing Initial data for this study were collected from 260 wheat farms in Fereydonshahr region, situated in Isfahan province, Iran. This province is located in the center of Iran within 30–42 and 34–30north latitude and 49–36and 55–32east longi-tude. The average of annual rainfall in this region is 600 mm, the mean annual temperature is 5C and soil texture in the region is typically 48% clay, 40% silt and 11% sand. Data were obtained in the 2011–2012 production year. The sample size was determined using Cochran method which was elab-orated in detail by Mobtaker, Keyhani[25], so 260 wheat farm-ers were randomly selected and inquired using a face to face questionnaire method.
To convert energy inputs to their energy equivalents, energy conversion factors, which are presented in Table 1, were employed. Input energies utilized for wheat production comprises machinery, human labor, diesel fuel, pesticides, chemical fertilizers, farmyard manure (FYM), electricity, water for irrigation and seeds, while the grain produced was regarded as output energy. In questionnaires a question about the agricultural machineries, which were used during the production season, was asked from farmers and then by cal-culating machinery weights and applying the following for-mula, the machinery energy was computed[26].
ME¼ELG
TCa
ð1Þ
where ‘ME’ is the machine energy (MJ ha1), ‘G’ the weight of machine (kg), ‘E’ the production energy of machine (MJ kg1yr1) that is shown in Table 1, ‘L’ the useful life of machine (year), ‘T’ the economic life of machinery (h) and ‘Ca’ the effective field capacity (ha h1)[7].
2.2. Adaptive neuro-fuzzy inference system (ANFIS) Fuzzy inference algorithm as the foundation of ANFIS is a method in which fuzzy rules are employed to deduce a new approximate fuzzy set conclusion while taking fuzzy set as premise. Fuzzy inference system (FIS) is primarily applied to the cases that either the systems are hard to be precisely modeled or the description about the studying issues is vague and equivocal[27]. An ANFIS is used to map input character-istics to input membership functions (MFs), input MF to a set of if-then rules, rules to a set of output characteristics, output characteristics to output MFs, and the output MFs to a single-valued output or a decision associated with the output[28,29]. A typical ANFIS structure, which can be seen in Fig. 1, includes 5 layers. Layer 1: Every nodeiin this layer is an adap-tive node with a node function,
O1
i ¼lAiðxÞ; ð2Þ
wherexis the input to nodei,Airepresents the linguistic label associated with this node function, andO1
iis the membership function ofAithat specifies the degree to which the givenx
satisfiesAi. To the inputy, the node functions in the same layer are of the same function family asx. The most common MFs encompass triangular and bell-shaped. Bell-shaped MF with a maximum equal to 1 and a minimum equal to 0 are calculated as follow:
lðxÞ ¼ 1
1þ jðxcÞ=aj2b ð3Þ
Layer 2: Every node in this layer is a fixed node, and acts as a simple multiplier. The outputs of these nodes are given by O2
i ¼xi¼lAiðxÞ lBiðyÞ; i¼1;2; ::: ð4Þ which are the so-called firing strengths of the rules.
Layer 3: In this layer, each node is an adaptive node labeled as N. The ith node calculates the ratio of the ith rule’s firing strength to the sum of all rules’ firing strengths,
O3 i ¼xi¼
xi x1þx2
; i¼1;2; ::: ð5Þ
For convenience, outputs of this layer are labeled as nor-malized firing strengths.
Layer 4: Every node in this layer is an adaptive node with a function,
O4
i ¼xifi¼xiðpixþqiyþriÞ; i¼1;2; ::: ð6Þ where-is the output of layer 3, and {pi,qi,ri} are referred to as consequent parameters.
Layer 5: In this final layer, the single node is a fixed node labeled as P, which computes the overall output as the sum of all incoming signals, i.e.,
O5 i ¼ X2 i¼1 xifi¼ P2 i¼1xifi P2 i¼xi ð7Þ
It is seen that there are two modifiable parameter sets, {ai, bi,ci} labeled as premise parameters and {pi,qi,ri} labeled as consequent parameters. The aim of the training algorithm for this architecture is to tune the above two parameter sets to make the ANFIS output matches the training data [28,30,31].
ANFIS only supports Sugeno-type systems and these must have the following properties[32]:
Fig. 1 – Adaptive neuro-fuzzy inference system structure.
Table 1 – Energy coefficients of different inputs used and outputs in wheat production.
Inputs Unit Energy equivalent
(MJ unit1)
References A. Inputs
1. Machinery
Tractor and self-propelled kg yra 9–10 [26]
Stationary equipment kg yra 8–10 [26]
Implement and machinery kg yra 6–8 [26]
2. Human labor h 1.96 [8] 3. Diesel fuel L 47.8 [26] 4. Pesticides kg 120 [13] 5. Chemical fertilizers Nitrogen (N) kg 78.1 [26] Phosphate (P2O5) kg 17.4 [26] Potassium (K2O) kg 13.7 [26]
6. Farmyard manure (FYM) kg 0.3 [5]
7. Water for irrigation m3 1.02 [11]
8. Electricity kWh 12 [26]
9. Seed kg 13 [26]
B. Output
1. Wheat kg 13 [26]
• Be first or zeroth order Sugeno-type systems.
• Have a single output, obtained using weighted average defuzzification. All output MFs must be the same type and either be linear or constant.
• Have no rule sharing. Different rules cannot share the same output MF, namely the number of output MFs must be equal to the number of rules.
• Have unity weight for each rule.
The main restriction of the ANFIS model is related to the number of input variables. If ANFIS inputs exceed five, the computational time and rule numbers will increase, so ANFIS will not be able to model output with respect to inputs. In this study, the number of energy inputs were eleven, including machinery, diesel fuel, human labor, nitrogen, potassium, phosphate, electricity, water for irrigation, FYM, pesticides and seed. To investigate which combination of input parame-ters can produce the best ANFIS results with the highest accu-racy, three main schemes were developed. In the first topology, as can be observed inFig. 2, the input parameters were grouped into three parts and each group was chosen as input variable for each ANFIS network. The output results of the ANFIS networks 1–3 were entered to ANFIS 4 to predict grain yield.
The second structure included seven ANFIS networks. At the first stage, energy inputs were clustered into four groups and each group entered to one ANFIS network (Fig. 3). ANFIS 5 was composed of outputs of ANFIS 1 and 2, similarly the outputs of ANFIS 3 and 4 were selected as inputs for ANFIS 6. Eventually, the outputs of ANFIS 5 and 6 composed ANFIS 7 to predict the wheat yield. For the third topology, the inputs were divided into five parts and each part was chosen individ-ually as inputs for an ANFIS network, so at the first stage 5 ANFIS networks were made. The ANFIS 6 was composed of the predicted values of ANFIS 1 and 2 and correspondingly, the output values of ANFIS 3–5 were used in ANFIS 7. At the last stage, ANFIS 8 modeled the yield using the predicted val-ues of ANFIS 6 and 7.
To find the most effective ANFIS model, five necessary modifications can be made to increase the accuracy of the network and decrease the errors. These settings include the number of membership functions, types of MFs (triangular, trapezoidal, bell-shaped, Gaussian and sigmoid), types of output MFs (constant or linear), optimization methods (hybrid or back propagation) and the number of epochs[5]. To develop ANFIS models MATLAB M-file environment version 7.14.0.739 (R2012a) was used to program ANFIS networks.
2.3. Development of ANN model
ANNs are data-processing systems inspired by biological neural system and are used to solve a wide variety of prob-lems in science and engineering, particularly for some areas where the conventional modeling methods fail[33]. Network architecture consists of one input layer, one or more hidden layers and one output layer along with a number of neurons in each layer which transfers information from the input layer to hidden layers and from hidden layers to output layer.
Back propagation algorithm is one of the most popular algorithms which can be used in ANN models. This algorithm has diverse variants which back-propagation training algo-rithms gradient descent and gradient descent with momen-tum are regarded as two important ones. These algorithms are so slow because they need low learning rates for stable learning. Levenberg–Marquardt (LM) is a faster algorithm which employs standard numerical optimization techniques overcomes some of the disadvantages mentioned above[34]. To develop an ANN model, some important modifications should be made including the number of hidden layers, the number of neurons in each layer, the training algorithm along with the type of transfer function. Transfer function deter-mines the relationship between inputs and outputs of a neu-ron and its network. The logistic sigmoid [Eq. (8)], tangent sigmoid [Eq.(9)] and purelin transfer functions were exam-ined in the neurons of hidden and output layers[35]:
fðnetjÞ ¼Oj¼ 1 1þexpðnetjÞ ð8Þ fðnetjÞ ¼Oj¼ 2 1þexpð2netjÞ 1 ð9Þ
where Oj is the output of the jth neuron and netj is the weighted sum of the inputs. Net is obtained by:
netj¼ Xv
i¼1
wijoi ð10Þ
for which netjis the number of input connections, wijis a component of the weighted vector, andOiis the input activa-tion of theithneuron in the preceding layer.
Different program codes were written in MATLAB language version 7.14.0.739 (R2012a), in which distinct number of hid-den layers and various transfer functions were practiced. In other words, at the first step the number of hidden layers was assessed, then the number of neurons were changed from one to thirty. Accordingly, the number of hidden layers was modified and one to thirty neurons were practiced again to generate different results. Eventually, the best results were extracted using statistical parameters. Data were randomized and divided into training (70% of the total data), validation (15% of the total data) and testing data sets (15% of the total data). The best model was selected based on the testing steps because it is possible that a model produces good results in training step but it have been on the basis of over training. Therefore, when the training step was completed the results were validated employing 15% of the data which was not par-ticipated in the model development and eventually the model was tested by the rest of the initial data.
2.4. Performance evaluation of ANFIS and ANN models The performance of the networks was compared using some statistical parameters including root mean square error (RMSE), mean absolute percentage error (MAPE) and correla-tion coefficient (R). These parameters are often defined in terms of the predicting error which is the difference between
the actual and predicted values employing the following equations[35,36]: R¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 Pn i¼1ðPiAiÞ2 Pn i¼1A 2 i ! v u u t ð11Þ RMSE¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 n X ðPiAiÞ2 r ð12Þ MAPE¼1 n Xn i¼1 jPiAij Ai 100 ð13Þ
wherePiandAiare respective predicted and actual yield for theithfarmer andnis the number of the points in the data set.
3.
Results and discussions
3.1. Energy use patternIn order to model the energy consumption pattern, all input materials were converted into their energy equivalent.Table 2 demonstrators the values of energy inputs and their contribu-tions to the total energy input, as well as standard deviation for energy inputs. As can be seen inTable 2the total energy, which was consumed during production season, was calcu-lated as 80173.3 MJ/ha, while the total output energy was computed as 38042.2 MJ/ha. Among the all input energies electricity and chemical fertilizer had the most influential effects on the total energy input. The shares of electricity and chemical fertilizer in the total energy input were esti-mated as 49.3% and 30%, respectively.
All forms of energies utilized in different agricultural prac-tices can be divided into direct and indirect or renewable and non-renewable energy. In the studied area direct energy sources which included human labor, diesel fuel, electricity and water for irrigation, consisted of 62% of the total energy input. Machinery, chemical fertilizer, electricity and diesel fuel which were employed in different agricultural practices were regarded as non-renewable energy sources. 15% of total Fig. 3 – The second topology of ANFIS model to predict wheat grain yield.
energy input was in the form of renewable while the most part of the total energy (85%) was non-renewable energy form.
3.2. Evaluation of ANFIS models
To predict the wheat grain yield based on energy inputs three main ANFIS architectures were evaluated. The first topology included two stages and four ANFIS networks (seeFig. 2). Sev-eral modifications were made in order to achieve the best result. MATLAB’s ANFIS editor offers different types of MFs including: triangular, trapezoidal, generalized bell (Gbell), Gaussian curve, Gaussian combination,-shaped, difference between two sigmoid functions, and product of two sigmoid functions. Correspondingly all these MFs were evaluated and eventually Gbell MF as illustrated inTable 3yielded the best results. The 40 epochs was used to train the model. The hybrid learning method was applied because this algo-rithm uses back propagation for parameter associated with input MF and least square estimation for parameters associ-ated with output MF[37].
One of the most crucial modifications is the number of MFs for input variables which should be chosen carefully. This adjustment assesses the total number of parameters in the network which should not be fewer than the number of training data pairs. According to results presented inTable 4, the total number of parameters for ANFIS 1 and 4 was 104 and for ANFIS 2 and 3 was 135 which show that the number of MFs for inputs was selected appropriately. R, RMSE and MAPE for
the final ANFIS network based on the testing step were calcu-lated as 0.919, 0.083 and 0.8.
The results obtained by the second ANFIS topology (see Fig. 3) are summarized inTable 5. As can be seen the combi-nation of Gbell and linear MFs for input and output layers, respectively, produced the better consequences rather than the application of other combinations. The number of MFs was chosen based on the number of input parameters due to the limitation of the total number of parameters which should be kept fewer than the number of training data pairs. As it was illustrated inFig. 3, ANFIS 1–3 included three input parameters, so the number of MFs was selected to be 4-3-3 and correspondingly the total number of parameters was computed as 174. For ANFIS 4-7 we had only two inputs so the number of MFs was selected as 7-7 and the total number of parameters was calculated as 189. R, RMSE and MAPE for the ANFIS 7 were computed as 0.964, 0.057 and 0.5
Table 3 – The characteristics of the best structure of first ANFIS architecture.
Item Type of MF Number of MF Learning method R RMSE MAPE
(%)
Input Output Input Epoch
ANFIS 1 Gbell Linear 4,3,3 40 Hybrid 0.72 0.149 1.4
ANFIS 2 Gbell Linear 2,2,2,2 40 Hybrid 0.782 0.132 1.3
ANFIS 3 Gbell Linear 2,2,2,2 40 Hybrid 0.784 0.131 1.3
ANFIS 4 Gbell Linear 4,3,3 40 Hybrid 0.919 0.083 0.8
Table 4 – ANFIS information of the first topology.
ANFIS info ANFIS 2&3 ANFIS 1&4
Number of nodes 78 55
Number of linear parameters 108 80 Number of nonlinear parameters 27 24 Total number of parameters 135 104 Number of training data pairs 192 192 Number of checking data pairs 65 65
Number of fuzzy rules 27 16
Table 2 – The input energy values and their percentage of the total energy input.
Input Present use
(MJ/ha) Percentage (%) SD* 1. Human labor (h) 159.4 0.19 98.9 2. Chemical fertilizer a. N (kg) 19265.7 24 5274.6 b. P2O5(kg) 2542.8 3.2 1132.6 c. K2O (kg) 1459.8 1.8 730.1 3. FYM (kg) 1327.1 1.7 1821.3 4. Biocides (kg) 175.3 0.21 136 5. Machinery (kg) 1896.4 2.4 1143.5
6. Water for irrigation (m3) 6171 7.7 325.8
7. Diesel fuel (L) 175.3 4.5 1227.2
8. Electricity (kWh) 39567 49.3 2088.8
9. Seed (kg) 4041 5 5236.4
Total energy input (MJ/ha) 80173.3 100
Total Output energy (MJ/ha) 38042.2
respectively (testing results). Drawing comparisons between the results of the three stages clarifies the statistical parameters of the second stage including ANFIS 5 and 6 are stronger than the first stage and consequently weaker than the final ANFIS network.
Statistical parameters of the performance of third ANFIS topology are presented inTable 5. At the first stage, two inputs were selected for all ANFIS networks except ANFIS 1 which included three inputs, so the number of MFs was selected as 7-7. R, RMSE and MAPE for the ANFIS 7 were calculated as 0.976, 0.046 and 0.4, respectively.
The evaluations illustrated that the third ANFIS topology despite its complexity and employing eight ANFIS networks was able to model energy consumption and predict the wheat grain yield more accurate than other topologies. Coefficient of determination for second ANFIS topology was calculated as 0.921 while for third ANFIS topology it was computed as 0.977 (Fig. 4). Based on the results when the numbers of
combined ANFIS networks are increased the model is able to predict the yield more appropriately and the performance of the model is enhanced.
To make certain that the initial combination of inputs to generate ANFIS sub-networks do not influence on the final results, the inputs were randomly selected and the model was run. For instance if the first ANFIS model (Fig. 2) was con-structed with labor and N-based fertilizers and water instead of N, P and K-based fertilizers how would the output of the system change. To approach this question this examination was performed. The results revealed that the initial synthesis of inputs did not affect the final results.
3.3. ANN models: evaluation and error analysis
Several ANN models were developed to predict a correlation between energy consumption and grain yield. A multi-layer perception (MLP) network along with a LM training algorithm was applied for nonlinear mapping between the input and output parameters. To produce the best results by the net-work, several architectures including different number of hid-den layers, distinct activation functions as well as different combination of neurons in each hidden layer was utilized in training of all ANN models.
Eleven input variables including machinery, diesel fuel, human labor, nitrogen, potassium, phosphate, electricity,
Table 5 – Performance indices of various approaches.
Item R RMSE MAPE
(%) The second ANFIS scheme 0.733 0.146 1.4 The third ANFIS scheme 0.718 0.15 1.4
ANN 0.92 0.1 0.9 1500 2000 2500 3000 3500 1500 2000 2500 3000 3500 Target O u tp u t ~ = 0. 88* T a rg et + 3. 3e+ 02 a: R=0.919 Data Fit Y = T 1500 2000 2500 3000 3500 4000 1500 2000 2500 3000 3500 4000 Target O u tp u t ~ = 0. 93* T a rg et + 1. 7e+ 02 b: R=0.964 Data Fit Y = T 1500 2000 2500 3000 3500 1500 2000 2500 3000 3500 Target O u tp u t ~ = 0. 98* T a rg et + 21 c: R=0.976 Data Fit Y = T 1500 2000 2500 3000 3500 1500 2000 2500 3000 3500 Target O u tp u t ~ = 1. 1* T a rg et + -2 .3e+ 02 d: R=0.92 Data Fit Y = T
Fig. 4 – Cross-correlation between predicted and observed wheat yield for testing datasets. (a) First ANFIS topology, (b) second ANFIS topology, (c) third ANFIS topology (d) ANN.
water for irrigation, FYM, pesticides and seed composed the first layer while wheat yield was selected as output variable. Accordingly the best network was composed of one input layer with eleven neurons, two hidden layers with 32 and 10 neurons and the output layer with one output variable. Three criteria R, RMSE and MAPE which were selected to evaluate the networks performance are presented inTable 5. In the best network architecture the activation function employed in the hidden layers were selected to be tangent sigmoid and a linear function was utilized in the output layer. 3.4. Sensitivity analysis
Sensitivity analysis allows estimation of the sensitivity of the output to changes in each independent variable[17]. In this study a numeric sensitivity analysis proposed by Montano and Palmer[38]has been used to investigate the sensitivity of wheat yield to the Input energies. As can be seen clearly inTable 6, the crop yield is so sensitive to electricity and fol-lowed by water. With the knowledge that electricity is mostly used to extract water from agricultural wells, it can be inferred that these inputs have a meaningful impact on the output of the model. Agricultural machinery, employed in dis-tinctive farm operations, has held the third rank, followed by P-based fertilizers.
3.5. Comparison between ANN and ANFIS model Making a comparison between the gained results from ANFIS and ANN models revealed that ANFIS model was able to fore-cast yield on the basis of input energies with higher correla-tion coefficient and smaller RMSE and MAPE values. R, RMSE and MAPE were calculated as 0.976, 0.046 and 0.4 for ANFIS network and 0.92, 0.9 and 0.1 for ANN. The advantage of ANFIS is that they can use imprecise data especially for agricultural systems. Also, the results of this study showed that employing more ANFIS networks in different stages enhance the accuracy of yield prediction.
4.
Conclusions
Several ANFIS topologies were evaluated in order to predict wheat grain yield based on the energy inputs. To find the best ANFIS network topology, several ANFIS models were
developed. The results illustrated that when the number of inputs for each ANFIS network decreased and simultaneously, the total number of ANFIS networks increased the better results were obtained. The best architecture included five networks at the first stage, two networks at the second stage and one network at final stage. R, RMSE and MAPE of the best ANFIS structure were calculated as 0.976, 0.046 and 0.4, respectively. Furthermore, several ANNs were developed and the ANN model with 11-32-10-1 structure produced the best results. Drawing comparison between ANN and ANFIS models demonstrated that ANFIS networks were able to predict wheat grain yield with more accuracy than ANN models due to their abilities to employ imprecise data.
Acknowledgement
The authors would like to thank the University of Tehran for giving their financial support.
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