Performance Prediction Analysis of Hydraulic Pump Based on
Improved BP Neural Network
Dongyang Zhang
1
, Shaohui Su
2
, Yiting Wang
3
, Chang Chen
4
, Shengran Meng
5
and Guojin Chen
6
1,2,3,4,5,6
College of mechanical engineering,Hangzhou Dianzi University,No. 2 street,Hangzhou,China
Keywords: BP neural network, Algorithm optimization, Performance prediction, Hydraulic pump.
Abstract: Aiming at the disadvantages of standard BP neural network about slow convergence rate and getting into
local minimum value easily, the momentum factor and conjugate gradient method are introduced to
optimize the BP neural network, and the convergence speed and prediction accuracy are improved. The
improved BP neural network is applied to the performance prediction of hydraulic pump with different
characteristic hydraulic oil, and the forecast result is compared with the standard BP algorithm prediction
value and the actual value. The results show that the improved BP algorithm has better prediction results on
the performance prediction of hydraulic pump, which not only improves the calculation speed, but also
improves the prediction precision greatly, and also has a good application prospectin the intelligent
manufacturing industry.
1 INTRODUTION
Hydraulic oil as a kind of liquid working medium,
which is used to transfer the energy in hydraulic
pump transmission and control system. The
hydraulic oil has seven kinds of remarkable
characteristics: lubrication, cooling, rust-proof,
sealing, cleaning, shock absorption. Whether the
hydraulic system can be reliable and effective,
depends largely on the performance of hydraulic oil,
so choosing the suitable hydraulic oil is the key to
improve the performance of the hydraulic pump. In
the production process, the choice of hydraulic oil is
usually dependent on experience, through repeated
experiments to select more suitable hydraulic oil, but
the use of this method will lead to a series of
problems, including the long research cycle and high
cost.
Artificial neural Network (ANN) is a
computational model simulating human
physiological mechanism, which provides an
alternative means for identifying complex and highly
nonlinear problems. BP Neural Network is one of the
most widely used algorithms in artificial neural
networks, and its structure is simple and easy to
understand. Li Ping, Shi Lei used BP neural network
to predict the performance of magnesium alloys
under different deformation parameters and obtained
good results. In the reference, the flow stress of high
speed steels during thermal deformation is predicted
by using BP neural network with 3-9-10-1 structure
based on the parameters of strain rate, temperature
and strain.
However, the BP neural network is similar to a
black box, and the weights of each network affect
each output result. Every time's random assignment
of weights will result in different prediction results,
resulting in the network is not reliable, and cycle
training leads to low learning efficiency, long
learning cycle. Once the algorithm into the local
minimum value, the whole learning convergence
process will be oscillated, it is difficult to get
accurate predictions. Aiming at the defects of
standard BP neural network, this paper first uses
standard BP neural network to predict and analyze
the performance of hydraulic pump with different
properties of hydraulic oil, and obtains the predicted
value which is close to the experimental result. Then
when the convergence speed of BP algorithm
reaches a slow stage, an important unconstrained
optimization method-Conjugate gradient method
(CG) is used to improve the standard BP
algorithm(SBPA). The improved BP algorithm(IBPA)
is used to predict the performance of hydraulic pump,
and the prediction result with higher precision and
smaller error is obtained. This method provides a
new way to consider the product performance and

improve the product benefit in the design stage.
2 MAIN INFLUENCING
FACTORS OF HYDRAULIC
PUMP PERFORMANCE
According to the working environment, working
conditions and hydraulic system of the oil
pump,when selecting hydraulic oil for hydraulic
pump, the following factors should be considered
emphatically:
① Suitable viscosity:Hydraulic pump is the
most sensitive component of hydraulic oil viscosity
reaction in hydraulic system. Under the same
working pressure, the higher the viscosity of
hydraulic oil, the greater the running resistance of
hydraulic moving parts, which causes the hydraulic
pump temperature rising, the self-priming ability
decreasing, the pipeline pressure and power loss
increasing. If the oil viscosity is too low, this will
increase the volume loss of hydraulic pump and the
sliding parts of the oil film thinning, then support
capacity decline.
② Good air release characteristics:The
hydraulic oil always contains a certain amount of air.
When the pressure of the hydraulic oil is below a
certain value, the air dissolved in the hydraulic oil
will be separated to form a bubble. A large number
of bubbles with the oil cycle, not only will reduce
the pressure of the system, but also produces a local
hydraulic impact, emitting noise and vibration. In
addition, the air bubble also increased the contact
area between oil and atmosphere, accelerating the
oxidation of hydraulic oil. Therefore, the hydraulic
oil is required to have good air release
characteristics.
③ Adaptation characteristics of sealing
materials:Because of the poor adaptability of the
hydraulic oil and sealing material, the sealing
material will swell, soften or harden to lose the
sealing ability, so it is required that the hydraulic oil
and sealing material should be adaptable to each
other.
Therefore, this paper will take the hydraulic oil
viscosity, air release characteristics, the adaptability
of sealing materials as variables to predict the
hydraulic pump no-load Force, noise, service life
and other performance effects.
3 BP NEURAL NETWORK
ALGORITHM
3.1 Standard BP Neural Network
The learning and training process of standard BP
Neural network is divided into two parts, including
the forward propagation of signal and the reverse
propagation of error. When the signal is transmitted
forward, the parameters are input from the input
layer, then processed through the hidden layer, and
finally uploaded to the output layer. When the output
result is larger than the desired result, the error is
transmitted backwards until the error is smaller than
the maximum allowable error or the number of
training times reaches the starting preset. The reverse
propagation of error is actually the process of
modifying and adjusting the weight value, and the
weight adjustment formula is as follows:
( )
( )
E
Δ wn η
wn

=−

（1）
In the formula, n is the iteration number, the η is
the learning rateandthe weight adjustment between
the nodes,
( )
E
wn


is the gradient of the error, the
minus sign represents the descent of the gradient.
3.2 Improved BP Neural Network
3.2.1 Introduction of Momentum Factor
Since the standard BP algorithm adjusts the weights,
it only adjusts according to the gradient direction of
the n-th iteration error, but the gradient direction of
the (n-1)-thiteration error is not considered, thus the
training process is concussed and the convergence is
slow. In order to increase the training speed of the
network, momentum items can be added to the
weight adjustment formula. The weight adjustment
formula at this time is:
( )
( )
( )
-1
E
Δ wn η αΔ wn
wn

= − +

（2）
It can be seen that the increased momentum item
is added from the previous weight adjustment
amount to this weight adjustment amount.
α
is a
momentum factor, generally,
( )
01 α ,
.Momentum
terms reflect the accumulation of experience in

weight adjustment during the learning process and
play a dampening role in the current weight
adjustment.
3.2.2 Introduction of Conjugate Gradient
Method
Due to the excessive number of learning and training
times of the standard BP neural network, the error of
the result is large, and the traditional gradient
descent method is easy to cause the disadvantage of
slow convergence speed and easy to fall into the
local minimum of error surface. Therefore, the
conjugate gradient algorithm is introduced into the
BP neural network with momentum added. The basic
idea is to use the gradient of known nodes to
construct a set of conjugate directions and search for
the extremum of the objective function accordingly.
Combining the BP algorithm with the conjugate
gradient method, the training process is divided into
two stages. In the beginning stage, the BP algorithm
is used, when the convergence rate is slow, and the
conjugate gradient method is used to give full play to
the advantages of the two parties.
The process of the conjugate gradient method
introduced is as follows:
( )
dn
is used to represent the gradient direction,
and the minimum value can be obtained by
searching:
( )
( )
( ) ( )
( )
mi n 1 （3）
n
E w n E w n d n

+ = +
The objective function is
( )
mi n Ew
,
wR
, and
n

is the search step, and the expression is shown
in formula (4).
( ) ( )
( ) ( )
T
n
T
n d n
g
n Ad n
d

=
（4）
The A in the upper form is expressed as the
positive definite Hessian matrix of the error function,
and
( )
gn
is expressed as the gradient direction of
the error function. The gradual search by formula (2)
can be obtained:
( ) ( ) ( )
1
n
w n w n d n

+ = +
（5）
( ) ( ) ( )
( ) ( )
1
00
n
d n g n d n
dg

= − + −
=−
（6）
( ) ( )
( )
00g E w=
(7）
n

is expressed as the direction factor of the
error function. The expression is:
( ) ( )
( ) ( )
11
T
n
T
g n g n
g n g n

=−
−−
（8）
When it starts to iterate,
( ) ( )
00dg=−
.
Therefore, the basic idea of the conjugate gradient
can be expressed as a linear combination of the
iterative direction of the N times and the (N-1) times,
and the
( )
dn
and
( )
1dn−
are a pair of
conjugate vectors.
During training, in order to avoid over fitting
phenomenon, the root mean square error (RME) of
the sample is always calculated periodically.












（）
When the root mean square error begins to rise, it
is proved that the over fitting phenomenon appears,
and the neural network obtained by the stop training
at this time has a reasonable reliability for future
prediction.
3.3 Validation of The Effectiveness of
Improved BP Algorithm
In order to study the effect of the improved BP
neural network, the nonlinear function formula (10)
is used to carry out the experiment, and the results
can be compared and analyzed.
( ) ( )
23
2si n 2 cosy x x x= + +
(10)
In the BP neural network, the accuracy of the
error is set to 0.0001, and the Sigmoid function is
used as the activation function. A BP neural network
with a hidden layer is selected for learning and
training, and the output layer has a neural unit，That
is, l=1, the number of nodes in the input layer is set
to 5, that is, n=5; according to formula (11), the
calculation can be obtained:
7 β =
, the number of
nodes with hidden layer can be calculated to be 9,

that is, m=9.
m n l β = + +
（11）
m represents the number of hidden layer nodes, n
indicates the number of input layer nodes, and l
represents the number of nodes in the output layer,
β
is constant and
1，10 



.
According to the above selection, the BP neural
network structure of the experiment is 5-9-1, and the
number of hidden layer nodes is 9. The result of the
improved BP neural network is shown in Table 1.
Table 1:Convergence rate of improved BP algorithm.
No.
Time（s）
Number of
iterations
1
19.34
4681
2
24.51
4963
3
21.67
4826
4
24.03
4901
5
19.41
4689
6
20.89
4736
7
24.18
4930
8
18.37
4597
9
22.15
4885
10
21.14
4782
Average value
21.569
4802.3
Using the improved BP algorithm to train, the
average convergence time is 21.57s and the average
number of iterations is around 4800. The error curve
is recorded as shown below. Figure 1 shows that as
the number of iterations increases, the error
decreases. When the number of iterations reaches
4800 or more, the accuracy can reach 0.0001. During
the iteration process, the error curve remains smooth
and no jitter occurs. The entire learning process is
fast and smooth.
Figure 1: Improved BP neural network algorithm error.
Compare the average time and number of
iterations of the improved BP algorithm with the
standard BP algorithm. The results are shown in
Table 2:
Table 2:Comparison result.
Items
Average
time（s）
Iterations
Error
accuracy
SBPA
52.86
14558.0
0.0009
IBPA
21.57
4802.3
0.0001
According to Table 2, it can be concluded that the
main reason for the slow error convergence rate of
the standard BP algorithm is the defect of the
algorithm itself; however, the improved BP
algorithm can be used to complete the training in a
shorter time and the error accuracy is less than
0.0001. This not only reduces the training time to a
great extent, but also improves the accuracy of the
prediction results.
4 APPLICATION OF IMPROVED
BP ALGORITHM IN
PERFORMANCE PREDICTION
OF HYDRAULIC PUMPS
4.1 Neural Network Model
Construction
① Determine the object of the experiment: in this
paper, YYB1-AA6/14B-Y2 type hydraulic pump is
selected as the research object, and orthogonal test is
used to study and analyze the influencing factors.
According to the relevant theoretical knowledge and

previous experience, the effects of the viscosity of
hydraulic oil, the air release of hydraulic oil and the
adaptability of hydraulic oil and sealing materials on
the no-load force, noise and service life of the
hydraulic pump are considered. In the experiment,
the selected factors are shown in Table 3.
Table 3:Influencing factors.
No.
viscosity
（cst）
air release
(min)
adaptability to
sealing
materials
1
34.7
（class 32）
<5
better
2
46.5
（class 46）
5~10
good
3
63.4
（class 68）
>10
substandard
In orthogonal experiments, in order to reduce the
numberof the selected samples and workload, we
choose the least orthogonal table. The orthogonal
array of hydraulic pump is selected through
influencing factors (shown in Table 4 below). The
number of test samples is 9, that is, the number of
tests is 9 times. Compared with all tests (3
3
=27
times), 18 times of repeated trials can be effectively
reduced. This greatly reduces the time and workload
of the test.
Table 4:Orthogonal test table for hydraulic pump.
No.
A
(Viscosity)
B
(Air release)
C
(Adaptabilit
y)
1
1
1
1
2
1
2
2
3
1
3
3
4
2
1
2
5
2
2
3
6
2
3
1
7
3
1
3
8
3
2
1
9
3
3
2
② Determine the learning rate and
momentum factor: In the training of BP neural
network, the selection of learning rate has an
important influence on the effect of training.
Excessively increasing the learning rate will
fluctuate the error function. If the learning rate is too
small, it will lead to slow convergence. After
repeated experiments, the learning rate in this paper
is 0.035. The momentum factor can effectively avoid
the error surface falling into the minimum value,
reducing the trend of oscillation and improving the
training speed. Its value is 0.65.
③ Determine the number of hidden layer
nodes: The viscosity of the hydraulic oil, the air
release characteristics and the adaptability of the
hydraulic oil and sealing materials are used as the
input level of the input layer, that is, n=3; the output
of the output layer are the no-load force, noise and
service life of the hydraulic pump, that is, l=3.
According to the formula (11), after repeated tests,
the number of nodes in the hidden layer is calculated
to be m=8, so the prediction model of BP neural
network is 3-8-3.
4.2 Comparison and Analysis of The
Results of Training and Learning
4.2.1 The Result of Training
Using Numpy and Matplotlib two library functions
in Python to achieve the prediction of the two
algorithms. The final results obtained by orthogonal
tests are shown in Table 5 below.

Table 5:Training results of standard BP algorithm and improved BP algorithm.
4.2.2 Analysis Results
The training results shown in Table 5 can be shown
in Figures 2, 3, and 4:
Figure 2 :Actual value and training value of the unloaded
force.
According to table 4, it can be seen that when the
viscosity of hydraulic oil is the same, the no-load
force of the hydraulic pump is on the same
horizontal line. When the viscosity of the hydraulic
oil increases, the unloaded force of the hydraulic
pump increases significantly. Thus, it can be seen
that the effect of the unloaded force of the hydraulic
pump on the viscosity of the hydraulic oil is greater
than that of other factors. In addition, the prediction
results obtained by the improved BP algorithm are
closer to the actual values.
Figure 3:Actual value and training value of noise.
The peaks of curves in Figure. 3 appear in third,
sixth, ninth sets of tests. It is shown from table 4 that
the poor air release performance of hydraulic fluids
is the common ground of these three sets of tests.
The trough of the curve appeared in the first, fourth,
seventh group of experiments. The good release of
the hydraulic oil was the common point of the three
groups. It can be concluded that the noise of
hydraulic pump is greatly influenced by the air
release of hydraulic oil, which is also consistent with
the cavitation phenomenon introduced in the
introduction. In addition, the prediction results
obtained by the improved BP algorithm are closer to
the actual values.

Figure4: Actual value and training value.of service life.
The wave peaks in Figure 4 appear in groups 1, 4,
6 and 8. The hydraulic oil used in the four groups
can be well adapted to the sealing material, so the
service life of the products is relatively long. On the
contrary, the hydraulic oil and seal materials used in
other tests can not be well adapted, which causes the
wear and tear of products and the service life greatly
reduced. This is also in line with our daily
experience. In addition, the prediction results
obtained by the improved BP algorithm are closer to
the actual values.
In summary, the prediction results obtained by
the standard BP algorithm are obviously deviated
from the actual value; the predicted value of the
improved BP neural network is basically consistent
with the actual value, and the relative error is smaller
(as shown in Table 6), the learning rate and the
convergence speed are all improved, which can meet
the requirement of prediction precision.
Table6:Relative error of BP algorithm before and after improvement.
Items
Standard BP algorithm
Improved BP algorithm
Relative error
No-load force
（N）
Noise
（db）
Servie
life（a）
No-load force
（N）
Noise
（db）
Servie
life（a）
Average value
0.53%
0.44%
0.51%
0.08%
0.09%
0.09%
5 CONCLUSIONS
1) In this paper, the BP neural network is improved
by introducing momentum factor and conjugate
gradient method, the nonlinear mapping model
between hydraulic oil characteristics and hydraulic
pump performance is established. The model has
shorter prediction time and higher prediction
precision, which effectively solve the shortcomings
of the standard BP algorithm in the slow
convergence speed and easy to fall into the local
minimum.Through the comparison between the
standard BP algorithm and the improved BP
algorithm for the prediction of the performance of
the hydraulic pump, it is concluded that the
improved BP neural network algorithm is effective
and feasible.
2) Based on the product performance prediction
model constructed, the performance of the products
can be predicted during the design period; this
method can instruct the developers to design the
hydraulic pump and choose the required hydraulic
oil quickly and reasonably. At the same time, the
proposed BP neural network provides a new way of
thinking and new means for the performance
prediction of industrial products affected by complex
parameters, which greatly shortens the development
cycle and reduces the research and development cost.
It has high theoretical significance and engineering
application value in the fast intelligent
manufacturing industry.
ACKNOWLEDGEMENTS
Thank the National Natural Science Foundation of
China (Grant No. 51475129,51675148, 51405117)
for its strong support for this paper.In the writing of
this paper, I got the careful guidance of my tutor, Mr.
SuShaohui. At the same time, thanks to the research
platform provided by Anji Intelligent Manufacturing
Research Institute.
REFERENCES
1. Wang Zu’an,1998.The working principle of hydraulic
system and the classification of hydraulic oil. Oil
Technology.
2. Han Liqun,2006. Artificial Neural Network

Tutorial.Beijing:Beijing University of Posts and
Telecommunications Press.
3. Wang Lei,WangRuliang,Qu Hongfeng,2016. BP
Neural Network Algorithm Improvement and
Application. Software Guide,38-40.
DOI:10.11907/rjdk.161429.
4. Li Ping,Shi Lei,2017. Research on prediction of
mechanical properties of AZ31 magnesium alloy based
on BP neural network. Foundry
Engieering,38(11):2721-2723.
5. JiantaoLiu,HongbingChang,T.YHsu,Xueyu Ruan,2000.
Prediction of the Flow Stress of High-Speed Steel
During Hot Deformation Using a BP Artificial Neural
Network. Journal of Materials Processing Tech,103(2)
6. Regelja, M., Regelja, Lončarić,S.,2005. Development
of an inorganic cations retention model in ion
chromatography by means of artificial neural
networks with different two-phase training algorithms.
Journal of Chromatography A, 1085(1):74.
7. Ba. A. J. S.,1997. Second-Order Methods for Neural
Networks.Kybernetes, 27(2):201 - 203.
8. Chen Qiang,2008. Viscosity, viscosity index and
selection of hydraulic oil.Construction Machinery
Technology and Management,123-127.
9. Bao Xiaobing,2008. Selection and maintenance of
hydraulic oi. Hydraulic pneumatic and seal,4-6.
10. Ai Xiaosong,2008. Intelligent control system of
concrete mixing station.Hunan: Central South
University.
11. Li Jie,2015. Research on bearing fault diagnosis
technology based on neural network. University of
electronics technology.
12. Mehmet Engin,SerdarDemirag,Erkan Zeki Engin, et
al,2007.The classification of human tremor signals
using artificial neural network.Expert Systems with
Application,754-761.
13. Ji Li,WangXiaodong,YangXushu,LiuShushen,Wang
Liansheng,2007. Improved BP algorithm artificial
neural network for QSAR research of environmental
estrogen using genetic algorithm combined with
conjugate gradient method. Chinese Science
Bulletin,2116-2121.
14. Ye Bing,Lei Yan,2004. Analysis of selection method of
hidden layer number and node number in BP neural
network. Journal of shangqiu vocational and technical
college,52-53+60.