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 CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 46, 2015 

A publication of 

 
The Italian Association 

of Chemical Engineering 
Online at www.aidic.it/cet 

Guest Editors: Peiyu Ren, Yancang Li, Huiping Song 
Copyright © 2015, AIDIC Servizi S.r.l., 
ISBN 978-88-95608-37-2; ISSN 2283-9216 
 

Application of Grey Neural Network Forecasting Model Based 
on Background Value Improvement in Enterprise Network 

Security Evaluation 
Limin Zhao*, Peng Yue 

College of Management, Xinxiang Medical University, Xinxiang, Henan, 453002, China. 
zhaoxxmu@163.com 

Network security is related to the proper protection of the network system hardware, software, and the data in 
the system. They are not subjected to accidental or malicious destruction, alteration and disclosure to make 
the system run continuously and reliably. Then, the network service is not interrupted. As we all know, BP 
neural network is used more fully in the network security. It has a strong nonlinear approximation ability, the 
algorithm is simple and easy to implement, but it is easy to fall into local extreme value, which is difficult to 
ensure that the algorithm converges to the global minimum point, and the global search ability is not strong. 
Based on this, this paper makes an improvement on the background value of grey model, and uses the output 
value of the gray model to establish the neural network forecasting model. In addition, this paper presents a 
decision method of the importance degree of the enterprise network security evaluation index which is based 
on BP neural network. The main feature of this method is that the evaluation index is extracted directly from 
the network connection weights. Finally, this article proves that the grey neural forecasting model based on 
background value improvement can be used to evaluate the development trend of enterprise network security 
more accurately. 

1. Introduction 

Network security is related to the proper protection of the network system hardware, software, the data in the 
system. They are not subjected to accidental or malicious destruction, alteration and disclosure. So as to 
make the system run continuously and reliably. Then, the network service is not interrupted. Because the 
network has the characteristics of connectivity, users enjoy the convenience of the network. At the same time, 
their information resources will be exposed. Due to the network information related to the national 
government, military, cultural and educational fields, so much of the information stored in the network is 
classified. If this information is violated, it will bring immeasurable loss to the country's political and economic. 
Therefore, our research on network security is especially important (Zhang Jun, Luo Baoqing (2010), Zhao, 
Qiu Xiaofeng (2010), and Zhang Yunyong, Chen Qingjin (2010)). 
Domestic and foreign scholars pay much attention to the study of computer network security. The agent theory 
is a frontier theory of computer science and artificial intelligence. Using Agent technology, many scholars had 
proposed many models or some basic application system in the network security. The scholars had carried 
out a lot of research, such as virus detection (Jieh-Sheng Lee, Jieh Hsiang (1997)), intrusion detection 
(Balasubramaniyan, J.S.et al (1998), Crosbie M, Spaford E H (1995), and Jai S B., Jose O., Isacof D, et al 
(1998)), log audit (Ling-yu Chou, Timon Du (2007)), and security management and monitoring (Michalas, A., 
Kotsilieris, T., Kalogeropoulos, S., et al (2001), Satoh, I (2002)). They were based on the basic features of 
Agent to build their own network security system. More importantly, artificial neural network model can 
effectively overcome the defect of the traditional statistical model. By adjusting the weights of the connections 
between neurons, they can capture the nonlinear rules between the computer network security and the 
attributes, so as to realize the accurate evaluation of the computer network security (Gong Hui, Feng Xin 
(2010), Wang Gang, Zhang Zhiyu (2006), and Kaufmann K W (2010)). Ren Wei (2006) proposed a method 
based on RBF neural network to carry out the situation prediction. He used the neural network to deal with the 

                               
 
 

 

 
   

                                                  
DOI: 10.3303/CET1546205

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Please cite this article as: Zhao L.M., Yue P., 2015, Application of grey neural network forecasting model based on background value 
improvement in enterprise network security evaluation, Chemical Engineering Transactions, 46, 1225-1230  DOI:10.3303/CET1546205

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chaos and nonlinear data, so as to solve the problem of network security situation prediction. In order to 
improve the precision of computer network security evaluation, Wu Renjie (2011) proposed a particle swarm 
optimization neural network model for the evaluation of computer network security.    
To sum up, this paper makes an improvement on the background value of grey model, and uses the output 
value of the gray model to establish the neural network forecasting model. Moreover, this paper presents a 
decision method of the importance degree of the enterprise network security evaluation index which is based 
on BP neural network. The main feature of this method is that the evaluation index is extracted directly from 
the network connection weights. Finally, this article proves that the grey neural forecasting model based on 
background value improvement can be used to evaluate the development trend of enterprise network security 
more accurately. 

2. Related concepts 

2.1 Gray model 
GM (1, 1) model is the most commonly used in gray modeling. First of all, it makes an accumulation of the 
original data sequence 0iX . After the accumulation, the data has a certain exponential growth trend. Then, we 

get the sequence 1iX . The specific method is shown as follows: 

(1) (0)

1
( ) ( )

k

i

x k x i
=

=      (1) 

Let the background value series be  

(1) (1) (1)1( ) [ ( 1) ( )]
2

z k x k x k= − + , 2, 3, ,k n=      (2) 

The grey differential equation is constructed with (1)x  by formula (1). 

(1)
(1)dx ax u

dt
+ =      (3) 

Which a  is called development coefficient. u  is called grey action variable. 
The discrete form of formula (3) is  

(0) (1)( ) ( )x k az k u+ =     (4) 

Put parameters into grey differential equation (4), the solution is 

ˆ(1) (1) ˆ ˆ( ) [ (1) ]
ˆ ˆ

atu ux t x e
a a

−= − +     (5) 

In the end, we get the recursive formula of the gray prediction model. 

ˆ ˆ(0) (1) (1) ( 0) ˆˆ ˆ ˆ( 1) ( 1) ( ) (1 )( (1) )
ˆ

a akux k x k x k e x e
a

−+ = + − = − − , 1, 2,k =       (6) 

2.2 Neural network model 
BP neural network is a mature model of artificial neural network technology. It is a multilayer feed forward 
neural network, which is composed of input layer, hidden layer and output layer, It has the ability to learn from 
the back propagation, and its mathematical expression is:  

1 1
( )

l n

ij i j j
j i

y f x a bω ω
= =

= − −     (7) 

Where, y is the Output value of BP neural network, ( 1, 2, , )ix i n=   are input values, ijω  represents the 
connection weights of the input layer and the hidden layer, jω  represents the connection weights between the 

hidden layer and the output layer, f  is a function of the implicit layer, ja  is the threshold of j  th neural node 

for the hidden layer, and b  is the threshold for the output layer. 

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2.3 The excitation function 
The excitation function is the input-output relationship between the neurons in the neural network. So, the type 
of the excitation function determines the characteristics of the neuron. It has been proved that the three layer 
feed forward neural network can approximate any continuous function with arbitrary precision when the 
excitation function of neuron satisfies the condition of monotone increasing, bounded and differentiable. The 
BP algorithm usually uses the sigmoid function as the excitation function. Next, we give several commonly 
used excitation functions. 

(1) Threshold excitation function: 1 , 0( )
0 , 0

x
f x

x

≥
= 

≤
    (8) 

(2) Sigmoid excitation function: 1( )
1 x

f x
e−

=
+

     (9) 

(3) Linear excitation function: ( )f x kx=                (10) 

(4) Hyperbolic tangent excitation function: ( ) tan( )
x

f x
T

=                (11) 

Below, we give a graph of four excitation functions. 
 

 

Figure 1: The excitation function 

By means of an effective way, gray neural network combined with the gray system and neural network . With 
the gray model and neural network in series, we can get a gray neural network model of n  input values and 1 
output value. Its structure is shown in figure 2. 
 

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Figure 2: Topology of the grey neural network 

3. Improvement of grey mode 

The parameters a  and u  in the formula 3 are the key parameters to ensure the accuracy of the gray model 
prediction. In the traditional gray model, a  and u  can be obtained by formula 2 and the least square method. 
But the curve of Formula 1 is smooth in a very short time interval. Using sequences to estimate parameters is 
more appropriate. The sequence is generated within 1 second. Otherwise, the generated sequence will make 
the prediction error, and reduce the prediction accuracy of the model. In order to guarantee the accuracy of 
the model, we adopt adaptive methods to determine the grey parameters in this paper. According to the 

function of the S type curve and the existing risk index limit, it can be amended as 1 1( )
dk

x k
ce

= . When, the 

1k + , 1
( 1)

1
( 1)

d k
x k

ce +
+ = . 

Simultaneous above two equations, We can get:   
1

11

1

1

( 1)

( )

( )
ln

( 1)

k

x k
c

x k

x k
d

x k

+

 +
=
   


= +

               (12) 

The, we put the formula (12) into the 
(1) (1) (1)1( ) [ ( 1) ( )]

2
z k x k x k= − + . The formula 2 is modified as follows: 

1 1
(1)

1 1

( ) ( 1)
( 1)

ln ( ) ln ( 1)
x k x k

z k
x k x k

− +
+ =

− +
               (13) 

4. Simulation experiment and result analysis 

4.1. Network security evaluation index system 
Network and information system is a complex system engineering, which includes the external factors and the 
internal factors, and they are mutually restricted. Therefore, we must have a standard, unified, objective 
criteria to measure network security. According to the domestic and foreign network security evaluation 
standard, and the basic requirements of the network and information system security, we should fully consider 
the various factors that affecting the security of the network, such as physical security factor, operation safety 
factor, information security factors, factors of safety technical measures and security system. Therefore, we 
give the network security evaluation index system. As shown in table 1: 
 
 
 
 

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Table 1: The network security evaluation index system 

First level index Second level index safety index Variable 

network security 

physical security 
Equipment safety X1 

Environmental safety X2 
Media security X3 

operation safety 

Risk analysis X4 
Access control measures X5 

Audit measures X6 
Emergency technology X7 

information security 

Information transmission security X8 
Defense Technology X9 

Data integrity X10 
Data encryption X11 

safety technical 
measures 

Anti-virus measures X12 
System operation log X13 

Server backup X14 

security system 
measures 

Organization X15 
Regulations X16 

Accident emergency plan X17 

4.2 Setting of computer network security level 
According to the comprehensive score of the index, we can evaluate the computer network security.  
According to the relevant research, the computer network security level is divided into 4 levels. They include 
that safety (A), basic safety (B), insecurity (C) and extreme insecurity (D).  We set the total score of security 
level to 1, then the corresponding security level and the corresponding score is shown in table 2.  

Table 2: Computer network security level 

level A B C D 
Score 1-0.85 0.85-0.7 0.7-0.6 0.6-0 

4.3 Simulation experiment 
In this paper, we select a company's computer network security data as sample data.  Then, all the indicators 
of 36 months has to be marked by the experts. We put the results of the score as the input value of the gray 
neural network. Through this paper's excitation function, we can output the computer network security score of 
the enterprise in the next six months. According to figure 2, we can know that the gray neural network model is 
a 17-5-1 model. Then, we use this algorithm to compare with other methods which are artificial neural network 
prediction algorithm and gray prediction model. Experimental results show that the prediction results are more 
close to the expected output value of the enterprise. 
 

 

Figure 2: Comparison chart of the assessment result  

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5. Conclusions 

This article makes an improvement on the background value of grey model, and uses the output value of the 
gray model to establish the neural network forecasting model. In addition, this paper presents a decision 
method of the importance degree of the enterprise network security evaluation index which is based on BP 
neural network. The main feature of this method is that the evaluation index is extracted directly from the 
network connection weights. Finally, this article proves that the grey neural forecasting model based on 
background value improvement can be used to evaluate the development trend of enterprise network security 
more accurately. 

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