Estimating soybean yields with artificial neural networks

The complexity of the statistical models used to estimate the productivity of many crops, including soybeans, restricts the use of this practice, but an alternative is the use of artificial neural networks (ANNs). This study aimed to estimate soybean productivity based on growth habit, sowing density and agronomic characteristics using an ANN multilayer perceptron (MLP). Agronomic data from experiments conducted during the 2013/2014 soybean harvest in Anápolis, Goiás State, B razil, were used to conduct this study after being normalized to an ANN-compatible range. Then, several ANNs were trained to choose the best-performing one. After training the network, a performance analysis was conducted to select the ANN with a performance most appropriate for the problem, and the selected network had a 98% success rate with training data and a 72% data validation accuracy. The application of the MLP to the data used in the experiment shows that it is possible to estimate soybean productivity based on agronomic characteristics, growth habit and population density through AI.

Keywords:
Glycine max (L.) Merrill; agronomic characteristics; modeling; MLP; perceptron

Authorship

Guiliano Rangel Alves ^**Author for correspondence. E-mail: guiliano@gmail.com

Departamento de Engenharia Agrícola, Universidade Estadual de Goiás, Campus Henrique Santillo, BR-153, Fazenda Barreiro do Meio, 75132-400, Anápolis, Goiás, Brazil. Universidade Estadual de GoiásBrazilAnápolis, Goiás, BrazilDepartamento de Engenharia Agrícola, Universidade Estadual de Goiás, Campus Henrique Santillo, BR-153, Fazenda Barreiro do Meio, 75132-400, Anápolis, Goiás, Brazil.

Itamar Rosa Teixeira

Francisco Ramos Melo

Raniele Tadeu Guimarães Souza

Alessandro Guerra Silva

Departamento de Agronomia, Universidade de Rio Verde, Rio Verde, Goiás, Brazil. Universidade de Rio VerdeBrazilRio Verde, Goiás, BrazilDepartamento de Agronomia, Universidade de Rio Verde, Rio Verde, Goiás, Brazil.

*Author for correspondence. E-mail: guiliano@gmail.com

SCIMAGO INSTITUTIONS RANKINGS

Figures | Tables | Formulas

Figures (6)
Tables (6)
Formulas (2)

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Figure 1
Graphical representation of network training with 19 neurons and 806 repetitions.

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Figure 2
Graphical representation of network training with 2 neurons and 212 repetitions.

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Figure 3
Comparative graphical representation of the estimated and observed values of the validation set for the network with one neuron and 340 repetitions.

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Figure 4
Comparative graphical representation of the estimated and observed values of the validation set for the network with 9 neurons and 963 repetitions.

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Figure 5
Graphical representation of linear R training, validation, testing and the overall network with 9 neurons and 963 trainings.

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Figure 6
Comparative graphical representation of the observed and estimated training values for the network with 9 neurons and 963 repetitions.

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Table 1
Values used for X_min and X_max by variable.

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Table 2
Variables presented to the input neuron layer.

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Table 3
Description of the columns in the file containing the information network training data.

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Table 4
Descriptive statistics of the variables used to train the ANN.

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Table 5
ANN training data.

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Table 6
Analysis of network errors with nine neurons and 963 repetitions.

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(1)

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(2)

Figure 1 Graphical representation of network training with 19 neurons and 806 repetitions.

Figure 2 Graphical representation of network training with 2 neurons and 212 repetitions.

Figure 3 Comparative graphical representation of the estimated and observed values of the validation set for the network with one neuron and 340 repetitions.

Figure 4 Comparative graphical representation of the estimated and observed values of the validation set for the network with 9 neurons and 963 repetitions.

Figure 5 Graphical representation of linear R training, validation, testing and the overall network with 9 neurons and 963 trainings.

Figure 6 Comparative graphical representation of the observed and estimated training values for the network with 9 neurons and 963 repetitions.

Table 1 Values used for X_min and X_max by variable.

Variable	Unit	X_min	X_max
Plant height (PH)	cm	20	200
Number of branches per plant (B)	un	1	15
Number of pods per plant (P)	un	10	150
Number of seeds per pod (S)	un	1	4
Weight of 1,000 seeds (WTS)	kg	5	40
Productivity (Prod)	kg ha^-1	1000	6000

Table 2 Variables presented to the input neuron layer.

Variable	Transformation	Description
C2	Category/type	Growth habit
C3	Category/type	Growth habit
D2	Category/type	Density
D3	Category/type	Density
PH	Linear transformation	Plant height
B	Linear transformation	Number of branches per plant
P	Linear transformation	Number of pods per plant
S	Linear transformation	Number of seeds per pod
WTS	Linear transformation	Weight of 1,000 seeds

C2, C3: Growth habit identification. D2, D3: Density identification.

Table 3 Description of the columns in the file containing the information network training data.

Column index	Column name	Formula	Information
66	BN	-	Overall network performance
67	BO	-	Performance in joint training
68	BP	-	Performance in the validation set
69	BQ	-	Performance in the test set
70	BR	-	R linear training set
71	BS	=(BRnn)²	R² training set
72	BT	-	R linear validation set
73	BU	=(BTnn)²	R² validation set
74	BV	-	R linear training set
75	BW	=(BVnn)²	R² training set
76	BX	-	R linear general set
77	BY	=(BXnn)²	R² from general set
78	BZ	-	Pearson correlation of the training set
79	CA	-	Pearson correlation of the validation set
80	CB	-	Pearson correlation of the test set
81	CC	-	Epoch that was the training stop (convergence)
82	CD	-	Number of neurons in the hidden-layer training
83	CE	-	Training number held in the architecture

nn: the line number.

Table 4 Descriptive statistics of the variables used to train the ANN.

Characteristic	N	Average	Min	Max	Standard deviation	C.V.
Plant height	65	92.37361	78.80	112.18	8.87538	10 %
Branches per plant	65	4.81704	2.00	11.30	2.09585	44 %
Grains mass per plant	65	18.18143	10.00	30.57	5.32825	29 %
Nº pods per plant	65	59.63328	27.60	119.80	19.28325	32 %
Seeds per pod	65	2.18204	1.82	2.67	0.27201	12 %
Productivity (kg ha^-1)	65	4347.56436	2958.72	5248.17	477.41305	11 %

N: number of samples; Min: minimum value; Max: maximum value.

Table 5 ANN training data.

Training			Performance				R²				Pearson's correlation
NN	NT	C	Gen	Tra	Val	Test	Gen	Tra	Val	Test	Gen	Tra	Val	Test
14	124	18	0.009	0.001	0.03	0.03	0.743	0.980	0.240	0.203	0.862	0.990	0.490	0.451
9	963	19	0.03	0.001	0.033	0.155	0.611	0.987	0.727	0.033	0.782	0.993	0.852	0.181
19	806	48	0.044	0.000	0.138	0.092	0.357	0.999	0.145	0.045	0.598	0.999	0.381	0.212
2	212	926	0.028	0.022	0.046	0.021	0.239	0.423	0.000	0.991	0.489	0.650	0.013	0.996
6	336	42	0.029	0.034	0.009	0.048	0.195	0.283	0.264	0.151	0.441	0.532	0.513	0.389
1	340	119	0.033	0.038	0.032	0.003	0.107	0.244	0.041	0.090	0.328	0.494	0.203	0.300

C: cycles or epoch at which the architecture training was finalized; NN: -number of neurons in the hidden layer; NT: training number held in the NN architecture; Tra: training; Val: validation; Performance: mean squared error (MSE) = 7.

Table 6 Analysis of network errors with nine neurons and 963 repetitions.

	Samples	Min	Max	Average	Mean Absolute Error	Deviation
General	65	-841.23	1398.14	122.28	203.78	380.75
Training	42	-216.42	167.81	1.17	30.42	55.85
Validation	16	-351.78	1246.33	193.32	340.56	427.76
Test	7	-841.23	1398.14	686.57	926.92	761.56

Min: minimum; Max: maximum; Mean Absolute Error: average of the absolute error values. Minimum values below zero indicate that the network was estimated above that value. All values are in kg.

(1)

X = \frac{(s c a l e d X - d 2) (X_{m a x} - X_{m i n})}{d 2 - d 1} + X_{m i n}

(2)

M S E = \frac{1}{N} \sum_{i = 1}^{N} {(e_{i})}^{2} = \frac{1}{N} \sum_{i = 1}^{N} {(t_{i} - \propto_{i})}^{2}

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Estimating soybean yields with artificial neural networks

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[1] *Author for correspondence. E-mail: guiliano@gmail.com