Abstract: This article establishes the estimate&apos;s mathematics model of the soybean&apos;s yield, using the artificial nerve network&apos;s knowledge, and by the model we can increase accuracy of the Soybean Yield Forecast

Guoqiang Qi

Lishu Wang

Qiang Fu

Yan Liu

CiteSeerX

The Journal of American Science, 2(3), 2006, Wang, et al, Soybean Yield Forecast Application Based  
 
Soybean Yield Forecast Application Based on HOPFIELD ANN 
Model  
 
Lishu Wang1, Guoqiang Qi1, Qiang Fu2, Yan Liu3 
 
1. School of Engineering, Northeast Agriculture University, Harbin, Heilongjiang 150030, China 
2. School of Water Conservancy & Civil Engineering, Northeast Agriculture University, Harbin, 
Heilongjiang 150030, China 
3. Harbin Tie Ling Primary School, Harbin, Heilongjiang 150001, China 
 
Abstract: This article establishes the estimate's mathematics model of the soybean’s yield, using the artificial nerve 
network's knowledge, and by the model we can increase accuracy of the Soybean Yield Forecast. [The Journal of 
American Science. 2006;2(3):85-89].  
  
Keywords: ANN；Soybean ；Hopfield ； Yield Forecast  
 
1. Foreword 
By setting up simulation model , we can get some  
relevant conclusions and realize  predict function in 
order to assist people making decision [1]． In general 
situation, it is very difficult to set up relative and 
accurate mathematics  model reflect objective systems, 
it is even impossible sometimes, but there are certain 
relations between various kinds of factors[3] [4]． If we 
can find the mathematics model which reflect the 
realistic input and output system, it has very important 
significance in Yield Forecasting． 
Assume the system mathematics model as follow： 
),(ˆˆ ,21 nxxxfy ⋅⋅⋅=  
Set up the mathematics model: 
),,( 21 nxxxfy ⋅⋅⋅=  
 
If 0),(),,(ˆˆ 2121 →⋅⋅⋅−⋅⋅⋅=−= nn xxxfxxxfyyQ  
 
Then we think that the model 
 is successful, and we can 
use it in Forecasting. In numerous artificial nerve 
network models, Hopfield nerve network is widely used, 
this text apply this model to soybean predict field, In 
order to improve utilization ratio of fertilizer, impel the 
soybean excellent quality, high yield , reach the unity of 
economy, the ecology and social benefit. 
),,( 21 nxxxfy ⋅⋅⋅=

 
2. Brief introduction of the Hopfield Nerve network  
Hopfield Nerve network Mathematics model as 
follow[2]: 





⋅⋅⋅==
++−= ∑
=
NiugV
VTI
R
u
dt
du
C
ii
N
j
jiji
ii
,2,1)(
1  
ijT —join Proportion Number value between neuron 
member i and j 
g(ui) — monotony Increase progressively Continuous 
function, and =T  ijT ji
 85
The Journal of American Science, 2(3), 2006, Wang, et al, Soybean Yield Forecast Application Based  
 
ui——Inputting value of i, —Exporting value of i. iV
Simplify models. 






⋅⋅⋅==
+= ∑
=
NiugV
IVT
dt
du
ii
N
j
ijij
i
,2,1)(
1  
define systematical energy function is: 
∑∑ ∑
= = =
−−=
N
i
N
j
N
i
iijiij IVVVTE
1 1 12
1
 
 
We can prove dE/dt≤0, only when dVi/dt=0 that 
dE/dt=0 (i=1,2,…,N), that is to say that the system’s 
Stable and Balanced point is extreme small point of 
Energy Function E, so the operation course on this 
network is a course seeking excellent the extreme small 
point in fact. Goal function is the energy function of this 
network system[5]. 
 
 
3. Setting-up The predicted and Simulation model of 
soybean’s Yield 
As mentioned above, it is the more difficult thing 
to set up its intact prediction mathematics model for the 
realistic system. So is the relation of Yield with the 
balance of soybean applies fertilizer, because six 
indexes which can influence the balance of the soybean 
to apply fertilizer. As there is a relation between a great 
deal of factors (the independent variable) and the yield 
of soybean. Set mathematics model systematically as: 
),(ˆˆ ,21 nxxxfy ⋅⋅⋅=  
1x  ， … ——Influence factors of the output of 
soybean，Such as：Soil organic matter、The ammonium 
form nitrogen、The nitre form nitrogen、Quick-acting 
phosphorus、Quick-acting potassium、pH value etc，
which can instruct the balance of soybean to apply 
fertilizer。 
2x nx
We can make use of following model to fit, and get[6] 
 
 
∑ ∑∑ ∑∑∑
= = ≤ = ≤ ≤
⋅⋅⋅++++=
N
j
N
j ji
N
j ji ik
kjiijkjiijjj xxxxxxy
1 1 1
0 ββββ  
 
In above formula,β0,βj,βij,βij k,…, parameters to be estimate; Under normal conditions, it is enough to use 
two steps to fit, after every parameter appeared in the estimation that we can predicted the function. 
Assume P is the sample number, ),2,1( ppy p ⋅⋅⋅=
)
 is variable, N),1,2,(j ⋅⋅⋅=pjx  is number 
∑
=
=
P
1p
2
pp )y-(y2
1Q )  reach extremely small. 
py ——The output of the fitting model；Define the energy function : 
∑ ∑ ∑∑ ∑ ∑ ∑
∑
= ≤ ≤= = = ≤
=
−⋅⋅⋅++++=
==
N
j ji ik
ppkpjpiijk
p
p
N
j
n
j ji
pjpiijpjj yxxxxxx
E
1
2
1 1 1
0
P
1p
2
pp
)(
2
1
)y-(y
2
1Q
)
)
ββββ
take two steps, and get 
 86
The Journal of American Science, 2(3), 2006, Wang, et al, Soybean Yield Forecast Application Based  
 
2
1 1 1
0 )(2
1
p
p
p
N
j
n
j ji
pjpiijpjj yxxxE
)−++= ∑ ∑ ∑ ∑
= = = ≤
βββ  
so we know 
∑ ∑ ∑ ∑∑
∑ ∑ ∑ ∑
= = ≤ ==
= = = ≤
−⋅++=
−++=
∂
∂
N
j
N
j ji
p
P
P
p
ppjpiij
P
p
pjj
p
p
p
N
j
N
j ji
pjpiijpjj
yxxxP
yxxxE
1 1 11
0
1 1 1
0
0
)()(
)(
)
)
βββ
βββ
β
∑
=1
 
pj
N
j
N
j ji
p
P
P
p
ppjpiij
P
p
pjj
P
p
pj
pjp
p
p
N
j
N
j ji
pjpiijpjj
j
xyxxxx
xyxxxE
∑ ∑ ∑ ∑ ∑∑∑
∑ ∑ ∑ ∑
= = ≤ ===
= = = ≤
−⋅++=
−++=
∂
∂
1 1 1
2
1
2
1
0
1 1 1
0
)()(
)(
)
)
βββ
βββ
β
=1
 
pjpi
N
j
N
j ji
p
P
P
p
ppjpiij
P
p
pjpij
P
p
pjpi
pjpipjp
p
p
N
j
N
j ji
pjpiijpjj
ij
xxyxxxxxx
xxxyxxxE
∑ ∑ ∑ ∑ ∑∑∑
∑ ∑ ∑ ∑
= = ≤ = ===
= = = ≤
−⋅++=
−++=
∂
∂
1 1 1 1
22
1
2
1
0
1 1 1
0
)()(
)()(
)
)
βββ
βββ
β
 
0
0
β
β
∂
∂
−=
E
dt
d
,
j
j E
dt
d
β
β
∂
∂
−= ,
ij
ij E
dt
d
β
β
∂
∂
= , and order  




<
≥
=
00
0
)(
x
xx
xg
Hopfield nerve network necessary parameters are： 
∑∑
==
==
P
p
pjpj
P
p
p xyIyI
11
0 ,
))
， ，Tpjpi
P
p
pij xxyI ∑
=
=
1
) P−=00 ，T ，T  ∑
=
−=
P
p
pjij x
1
2 ∑
=
⋅ −=
P
p
pjpjijij xx
1
22
∑
=
−==
P
p
pjjj xTT
1
0..0 , ,  ∑
=
−==
P
p
pipjijij xxTT
1
0..0 ∑
=
−==
P
p
pjpijijijj xxTT
1
2
..
To the high-order situation, we can get: 
)(,
11
0 pk
P
p
pjpipkij
P
p
p xxxyIyI ∑∑
=
⋅⋅⋅
=
⋅⋅⋅== )) ,T  ∑
=
⋅⋅⋅•⋅⋅⋅ ⋅⋅⋅−=−=
P
p
pkpjpikijkij xxxTP
1
222
)()(00 )(,
∑
=
⋅⋅⋅⋅⋅⋅⋅⋅ ⋅⋅⋅−==
P
p
pkpkpikijkij xxxTT
1
0)()(0 )( ,T  ∑
=
⋅⋅⋅⋅⋅⋅⋅⋅ ⋅⋅⋅−==
P
p
pkpkpiikijkiji xxxT
1
2
)()( )(
Among them, p=1,2,…,P；j=1,2,…N; k≤…≤i≤j. 
Utilize above-mentioned parameter values we can construct soybean apply fertilizer Hopfield nerve network 
which predicts yield conveniently, This network reach a stable equilibrium of states, exports value which fit the 
parameter values of curved surface are what we need estimate promptly. The state of stable equilibrium at this 
 87
The Journal of American Science, 2(3), 2006, Wang, et al, Soybean Yield Forecast Application Based  
 
moment, is the state of the soybean of relatively high yield[7] [8]. 
 
4. The experiment of the computer 
Choose a group of data as Form 1 shows are single factors, adopt 1 step to fit the relations of yi and xi, Yi is the 
average yield of soybean, xi is the amount of application of nitrogen, i.e y = a + bx, and i =1,2, …., 12, use ahead 
derived result, we can construct necessary every parameter respectively for network nerve Hopfield: 
8.14242,3.2074,78,390,12 ==−==−=−= babaabbbaa IITTTT  
This system dynamic equation is: 









=
=
+−−=
+−−=
b
a
ba
b
ba
a
ub
ua
uu
dt
du
uu
dt
du
8.1424239078
3.20747812
 
use Euler method to solve, take initial value ua=0, ub=0, step h=1.0E-7, Change and take the place of a=2.5822887, 
b=5.0504757, to accelerate simulation operation disappear speed by, we change step h=1.0E-6, in the end we get 
steady result 
a=138.26, b=5.322 
So, the fitting equation received is: y=138.26+5.322x 
 
 
 
 
i
x
Y
 
 
 
U
y
F
U
 
 
 
 
 
 
 
5
y
 
                           Form 1. Experimental data                           
  1      2     3     4     5      6      7     8      9      10     11    12 
i 1     2     3     4     5      6      7     8      9      10     11    12 
i 143.5  148.9  154.2  159.5  164.8  170.2  175.5  180.8  186.2   191.5  196.8  202.1   tilize least square method, Get equation: 
=139.26+5.822x 
orm 2: It is these two kinds of methods that export the comparison of the result.  
sing least square method get y=139.26+5.822x. Form 2 is export results to compare.  
.
ie                             Form 2. Export results to compare                          
The method Absolute error 
Total 
Average 
absolute error 
Square Error Standard deviation  
error 
Nerve  network 2.853 0.319 0.258 0.628 
Least square method 3.05 0.33 0.228 0.567  Conclusion 
This paper has put forward a model to predict the 
lds of soybean with Hopfield nerve network raise the 
predicting accuracies of soybean yield, improve 
utilization ratio of fertilizer also, achieve the goal of 
increasing production[9]。 
88
The Journal of American Science, 2(3), 2006, Wang, et al, Soybean Yield Forecast Application Based  
 
 
Acknowledge 
   This article is from dissertation of Heilongjiang 
province education office “research and exploitation of 
crop DSS in high-cold area”; dissertation of 
Heilongjiang province science and technology office 
“Design on information service project in village”. 
 
Correspondence to: 
Lishu Wang, Guoqiang Qi, Qiang Fu, Yan Liu  
School of Engineering 
Northeast Agriculture University 
Harbin, Heilongjiang 150030, China 
Telephone: 01186-451-89971785 
Email: wanglishu@neau.edu.cn  
 
References 
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house, 1989.  
2. Jiao Li-cheng. The network system theory of nerve. The 
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3. Eugene Chamik, Introduction to Artificial Intelligence, 
Addison-Wesley Publishing Company Inc. 1985:12-44.  
4. Subrahmanian. S. Jajodia. Data base system of multimedia. 
1998.8：35-46.  
5. Deck S H , Mokow C T, Heinemann P H, et al. Sommer Com 
parison of a neural network and traditional classifier for machine 
vision inspection [J]. Applied Engineering in Agriculture, 1995, 
11.  
6. Zhang Xin, Cai Wei-guang  utilize ANN realize forecast 
modeling. 1997.  
7. Haykin S. Neural Networks: A Comprehensive Foundation[M]. 
Macmillan College Publishing Company, Inc, New York, NY, U 
SA. 1994.  
8. Zhang Ning, Zheng Junli. An Artificial Neural-Based A/D 
Converter Using Asymmetric Hopfield Network ICCAS-91. 
Shenzhen, China. 1999. 
9. Muller B, Reinhardt J. Neural Networks An Introduction. 
Spinger-Verlag, 1990.
 
 
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Soybean Yield Forecast Application Based

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