CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 62, 2017 

A publication of 

 

The Italian Association 
of Chemical Engineering 
Online at www.aidic.it/cet 

Guest Editors: Fei Song, Haibo Wang, Fang He 
Copyright © 2017, AIDIC Servizi S.r.l. 

ISBN 978-88-95608- 60-0; ISSN 2283-9216 

Research on the Prediction of Hazardous Chemicals 

Accidents Based on Improved Grey Model 

Minhui Zhanga, Jian Yangb 

aChengdu Normal University, Chengdu 611130, China 
bChengdu College of University of Electronic Science and Technology, Chengdu 611130, China 

newpas521@163.com 

With the rapid development of China's society and economic construction, the production and use of 

hazardous chemicals are increasing. The possibility of hazardous chemicals accidents is increasing. Because 

the hazardous chemicals cause great harm and the accidents affect the normal production and life. Hazardous 

chemicals accidents have become the focus of attention of society and academia. The study of reducing 

hazardous chemicals accidents is an important research field of safety production in china. The prediction of 

hazardous chemicals accidents is of great significance to reduce the number of hazardous chemicals. In this 

paper, we propose an improved grey model for the characteristics of hazardous chemicals accidents to predict 

the numbers of hazardous chemicals accidents. In the experimental section, we predict the number of 

hazardous chemicals accidents in china. The experimental results show that the improved grey model and the 

better fitting result are obtained. 

1. Introduction 

In China, the process of industrialization continues to accelerate (Yang and Shao, 2017). At the same time, 

the scale and quantity of hazardous chemicals enterprises are also gradually. At present, there are about 

7000000 chemicals in the world, of which more than 100 thousand chemicals have been sold in the market. 

Hazardous chemicals are usually explosive, toxic, and are prone to accidents in production, storage and 

transportation. Once a large amount of hazardous chemicals is emitted or leaked, it can cause fire, explosion, 

property damage and environmental pollution (Warnasooriya and Gunasekera, 2017; Benhorma  et al., 2017; 

Gattuso et al., 2016; Cannistraro et al., 2016). At the same time, toxic gases can cause adverse effects on the 

human body, leading to poisoning or death, resulting in greater social and public safety incidents (Slorach, 

2014; Wang et al., 2017; Birungi and Chirwa, 2017; Silva et al., 2017). 

The scope of application of hazardous chemicals in China is more and more extensive. This only promotes the 

development of national economy, but also enriches people's production and life (Li and Hu, 2017). 

Hazardous chemicals accidents involve all aspects of production, storage, transportation, use and so on, and 

the consequences of accidents are serious (Jeremy et al., 2016). The causes of hazardous chemicals 

accidents are mainly including the increase of the number of chemical enterprises, the lack of supervision and 

the lack of safety awareness. In 2002, the State Council issued the “regulations on the safety control of 

hazardous chemicals”, which was revised in 2013. The regulations strengthen the safety management of 

hazardous chemicals, prevent and reduce hazardous chemicals accidents, protect the lives and property of 

the people, and protect the environment. Numbers of hazardous chemicals accidents and deaths in China are 

shown in figure 1. 

Overseas research on risk assessment and prediction of hazardous chemicals accidents started earlier, both 

in theory and in methodology (Marhavilas and Koulouriotis, 2012). Some developed countries have already 

established a perfect safety management system for dangerous chemicals (Bonvicini et al., 2012). At the 

same time, according to the continuous development of the hazardous chemicals industry, the corresponding 

management strategies are also being adjusted (Saidi et al., 2010; Topuz et al., 2010). China is a big country 

in the production and use of dangerous chemicals. Although China has established a safety management 

                                

 
 

 

 
   

                                                  
DOI: 10.3303/CET1762227 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Please cite this article as: Minhui Zhang,  Jian Yang, 2017, Research on the prediction of hazardous chemicals accidents based on improved 
grey model, Chemical Engineering Transactions, 62, 1357-1362  DOI:10.3303/CET1762227   

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system for dangerous chemicals, the management technology is relatively weak and there is still a big gap 

between developed countries and the developed countries. 

 

Figure 1: Numbers of hazardous chemicals accidents and deaths in China 

The grey model was put forward by Professor Deng Julong, a Chinese scholar in 1982 (Wang et al., 2017). 

The naming of grey systems is defined by color. The clarity of information represented by "grey" is between 

"known" and "unknown" (Yu et al., 2017). The modeling of grey system is to use historical data to produce 

new data sequence. Then, the differential equations are established. After accumulating the historical data, 

the grey system turns it into an ascending sequence of exponential growth (Ma et al., 2017). When this new 

theory was born, it has received extensive attention in academic and practical. Many practical workers and 

young and middle-aged scholars have joined the ranks of grey system theory research and exploration, and 

have written a lot of scientific and technological applied papers in this field. The grey system theory in different 

fields of success has been widely recognized by academic circles (Ene et al., 2017). 

In this paper, we study the prediction of hazardous chemicals accidents. In order to better achieve the goal of 

research, we propose an improved grey model. The first part of this article is the introduction. The first part 

introduces the research background. The second part analyzes the dangerous chemicals accident. The third 

part introduces the grey model. In the fourth part, we propose an improved grey model for prediction of 

hazardous chemicals accidents. The fifth part is the experiment and the last part is the conclusion. 

2. Hazardous chemicals accident analysis 

National emergency rescue 

center for hazardous chemical 

accidents

Local emergency rescue 

center for dangerous 

chemicals

Accident scene
Rescue and rescue 

organization
Support system

Police and fireman

The Chemical Corps

Armed police

……

Communication guarantee

Emergency consultation

Material support

Scientific research department

……
 

Figure 2: The emergency organizational relationships about chemical accidents 

Hazardous chemicals accident refers to an accident caused by dangerous chemicals, which endangers 

human life and health, property safety and environmental protection. Hazardous chemicals accident has the 

following characteristics: 

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Abrupt: When many hazardous chemicals accidents happen, there is no warning before. So it is not easy to 

detect 

Multiple: Hazardous chemicals appear in people's life. From the production, storage, transportation, civil, or to 

all aspects of fireworks, it is at any time. 

Susceptibility: Because of the characteristics of hazardous chemicals, it is easily affected by the external 

environment, contact with water, or by the impact, extrusion and so on. These all may lead to accidents. 

Diffusion: When a dangerous chemical accident occurs, it involves a wide range. As the gas continues to 

diffuse, people and surroundings are easily affected. 

The rescue is difficult: Because of the danger of hazardous chemicals accidents, it is necessary to have 

special rescue team and some professionals at the same time 

Social image and economic losses are greater: The occurrence of hazardous chemicals accidents brings a 

series of negative social impacts, and the economy will suffer great losses. 

3. Grey prediction GM(1,1) 

In order to use historical data to predict the future, we call the non negative random sequence X(0)={x(0)(1), 

x(0)(2), …, x(0)(n)} that reflects historical data as parameter sequence. n is called the parameter data length. 

Make an accumulation. 

(1) (0)

1

( ) ( )
k

i

x k x i


   (1) 

The resulting sequence is 

(1) (0) (0) (0)
{ (1), (2), , ( )}X x x x n  (2) 

It is assumed that the accumulated sequence X(0)={x(0)(1), x(0)(2), …, x(0)(n)} is satisfied with the parameter 

sequence X(0)={x(0)(1), x(0)(2), …, x(0)(n)} 

(0) (1)
( ) ( )x k ax k b   (3) 

The equation is called the original form of the model GM(1,1). Generating the sequence X(0)={x(0)(1), x(0)(2), …, 

x(0)(n)} for immediate generation 

(1) (1) (1)1
( ) [ ( ) ( 1)] 1, 2, , 1.

2
z k x k x k k n      (4) 

The lower model is called the basic form of the model GM(1,1), which is called the grey differential equation 

(0) (1)
( ) ( )x k az k b   (5) 

The least squares method is used to estimate the parameters of the upper model 

1
( )

T T
a

A B B B Y
b

 
  
 

 (6) 

Where 

(1) (1)

(1) (1)

(1) (1)

1
( (1) (2)) 1

2

1
( (2) (3)) 1

2

1
( ( 1) ( )) 1

2

x x

x x
B

x n x n

 
  

 
  
 
 
 
 
   
 

 

(0) (0) (0)
[ (2), (3), , ( )]

T

n
Y x x x n  

(7) 

In order to predict the accumulated generating sequence, the set of cumulative generating sequences satisfies 

the differential form (usually called the whitening equation) 

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(1)
(1)dx

ax b
dt

   (8) 

Initial condition 

(1) (0)
(1) (1)x x  (9) 

The solution may be expressed as 

(1) (0) ( 1)ˆ ( 1) ( (1) )
a kb b

x k x e
a a

 
      (10) 

We know 

1
(1) (0) (0) (0) (1) (0)

1 1

ˆ ˆ ˆ ˆ ˆ ˆ( ) ( ) ( ) ( ) ( 1) ( )
k k

i i

x k x i x i x k x k x k


 

        (11) 

A regressive fitting sequence obtained reduction. Fitting sequence of X(0) is �̂�𝑜 

(0) (1) (1)ˆ ˆ ˆ( ) ( ) ( 1)x k x k x k    (12) 

4. Improved grey model 

The cumulative formula of (1,1)GM  model is rewritten as 

1
(1) (0) (0) (0) (1) (0)

1 1

( ) ( ) ( ) ( ) ( 1) ( )
k k

i i

x k x i x i x k x k x k


 

        (13) 

We know 

(0) (1) (1)
( ) ( ( ) ( 1))

2

a
x k x k x k b     (14) 

The parameters a and b  are still given.  

Grey prediction iterative equation 

2
(0) (0)

1

( )
( ) ( (1) )

n

n

m a
x n ax b

m






    (16) 

Bring a, b and m into the upper model 

2
(0) (0)

1

2(2 )
( ) ( (1))

( 2)

n

n

a
x n b ax

a






 


 (17) 

Since the genetic algorithm has good search performance, it can automatically accumulate and acquire the 

knowledge about the search space. The search process of the adaptive control algorithm is used to obtain the 

optimal solution. Therefore, the genetic algorithm is used to optimize the parameters. Firstly, the genetic 

algorithm encodes the solution of the problem with the proper coding method. Then the algorithm measures 

the fitness values of the current group. A series of genetic manipulations such as selection, crossover and 

mutation is applied to the present group. New population is generated. The specific steps are as follows. 

The steps of the improved grey model are as follows: 

(1) Initial population generation. A series of grey model parameters are generated randomly. The binary 

encoding scheme is adopted to encode each grey model parameter. The initial population of the genetic 

algorithm is formed. 

(2) Calculate the fitness. Calculate the prediction error of each individual in the colony and then determine the 

fitness of the individual. 

(3) Select individuals. The genetic algorithm uses the selection operator to select the fittest of the population, 

and chooses the fitness of each individual according to the size of each individual. The basic genetic algorithm 

employs proportional selection operators.  

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(4) Individual crossover. Randomly select two individuals from a group as cross objects to exchange one or 

more bits of two individuals and form two individual individuals. Crossover operations produce offspring, which 

inherit the basic features of the parent. 

(5) Variation. The genetic algorithm uses a small probability to change the individual gene code in the 

population and creates a variant of the offspring, which makes the genetic algorithm have a broader search 

space. 

(6) Repeat step 2-5 and keep the grey model parameters evolving until the training target meets the 

termination condition. Finally, the optimal solution of the parameters is substituted into the grey model and a 

grey prediction model based on genetic algorithm optimization is obtained. 

Model building

Create initial population

Calculate the fitness 

function

 Meet the 

conditions?

N

Selection operator, 

crossover operator, 

mutation operator

Progeny population

Y Optimal model

 

Figure 3: The specific steps of improved grey model 

5. Experiment 

In order to illustrate the superiority of the improved grey model in the prediction of hazardous chemicals 

accidents, we use the model to predict the numbers of hazardous chemicals and the numbers of fatalities. We 

use 2006-2010 of the data as a training set and 2011-2014 years of data as the prediction set. 

From Figure 4, we can see that the improved grey model curve is more similar to the actual value, which 

shows that the improved grey model has a good effect on the prediction of the number of hazardous 

chemicals accidents. 

From Figure 5, we can get the result of the improved grey model. The fitting result is basically consistent with 

the actual value. It shows that the improved grey model obtains the good result in the prediction of the death 

toll of hazardous chemicals. 

  

Figure 4: Number of accidents                   Figure 5: Accident death toll 

6. Conclusion 

The use of chemicals has brought a great convenience to people's life and improved the quality of life. The 

increase of kinds and quantities of chemicals increases the probability of chemical accidents. Hazardous 

chemicals are prone to accidents and such accidents can not only cause direct bodily harm, but also pose a 

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great threat to the environment. In order to reduce the occurrence of hazardous chemicals accidents and 

control the accidents of hazardous chemicals, we predict the number of hazardous chemicals accidents. In 

this paper, we propose an improved grey model and use the model to predict hazardous chemicals accidents. 

The main work of this paper includes: (1) Introducing the research background; (2) Analyzing the 

characteristics and causes of hazardous chemicals accidents; (3) Introduction of grey model; (4) Putting 

forward an improved grey model and the model being used to predict hazardous chemicals accidents. 

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