[american society of civil engineers eighth international conference of chinese logistics and...

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Research for Spatio-temporal Modeling Approach of Railway Safety

System Based on Hybrid Cellular Automata

Qin Yong1 Qiu NingHai1 Jia LiMing1

（1.Key Laboratory of Rail Traffic Control and Safety of Beijing Jiaotong University, Beijing 100044, China)

ABSTRACT: Based on the analysis of the characteristics and the interaction of the safety related factors of the railway transportation system, this paper proposes an modeling approach for the analysis and control of railway transportation safety system based on hybrid cellular automata model. This new spatial-temporal model, simulating dynamic behavior of the system, reveals the essential characteristic and evolution mechanism of railway transportation safety system. Finally, the simulation research results show the effectiveness and efficient of the modeling approach.

Key words: Hybrid cellular automata; Railway transportation safety system; Spatio-temporal Model

0 Introduce

Modern railway transportation, characterized by high-speed, high-density, high-throughput and etc. [1], is faced with a key problem for safety. Therefore, the security, reliability and the evolution mechanism of railway transportation safety system becomes one of hot research issues.

Actually, railway transportation safety system is described as a kind of hybrid system, which is under the influence of the interaction of the safety related factors including people, equipment, environment and etc. The system also has several characteristics of complex system, such as nonlinear, uncertainty, etc. In other words, it is a hybrid system multiple driven by time, location and events. In the past few years, hybrid petri net [2]-[4], hybrid automata [5] [6], etc have been the effective modeling approaches for the hybrid systems. Those modeling approaches including cellular automata [7] [8], hybrid cellular automatic [9], fuzzy cell [10], etc. have gained widespread use for modeling the transport systems.

In this paper, a new modeling approach is proposed to analyze the evolution mechanism and interaction of the safety related factors in railway transportation safety system based on hybrid cellular automata model [13]. The framework of the model and its formal description are presented in this modeling approach. Based on the proposed modeling approach, a simulation system developed on MS Dot.net is constructed to simulate the dynamic behavior of the railway transportation safety

Copyright ASCE 2008 The Eighth International Conference of Chinese Logistics and Transportation Professionals Logistics

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system. Finally, the simulation research results show the effectiveness and efficient of the approach.

1 Characteristics analysis of the railway transportation safety system

Railway transportation safety system which is divided into four safety related factors: people factor, equipment factor, environment factor and management factor is a “people-machine-environment” system. The safety related factors not only include the discrete variables, but also include continuous variables. For example, the state of traction substation discretely changes as normal, break, etc. at a given time, and the value of axle temperature is continuous. In the meantime, the discrete changes of railway track irregularities will arouse the continuous changes of the wheel rail relation. In a word, the evolution and dynamic behavior of the railway transportation safety system is influenced by the interactions of these continuous and discrete variables of the safety related factors, as shown in Figure 1.

Figure 1.the relation between the safety related factors of the railway transportation safety system.

2 Railway transportation safety system model based on hybrid cellular automata

2.1 The framework of the model

Generally, railway transportation safety system essentially is a hybrid system can be modeled by a set of systems with discrete events and continuous time dynamic. The modeling approach which will use here, consider the model of the hybrid system as a discrete cellular automaton augmented with continuous variables. The result of this modeling approach is the model of hybrid cellular automata.


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Therefore, a framework of the model, based on hybrid cellular automate model, is proposed as show in Figure 2.This model is composed of several hybrid cells which denotes block sections or stations. Each hybrid cell has its states, neighbors and rules.

Figure 2. the framework of the model for railway transportation safety system. The states of cells comprise states of people, fixed equipment, moving

equipment, environment and management. Cellular neighbors denote the two neighboring block sections. The basic operating rules, security rules and the bylaw of the railway transportation system are making up of the cellular rules.

2.2 Formal description model of the railway transportation safety system

The hybrid cellular automaton model [12] [13] is generally presented below: HA=(Q,X,V,Ini,f,Inv,R)

(1) The variables in formula (1) are expressed as the safety related factors. In the

meantime, the safety evaluation variables and time variables are added to this formula, so a hybrid cellular automata model for railway transportation system can be described as formula (2):

RS={T,X,U,Y, A,α,β,r,M0 } (2)

X and U particularly refer to the variables of the safety related factors in railway transportation system. Especially, the equipment factors can be subdivided into fixed equipment factors, moving equipment factors. T is a set of times.

X is a state space of the system, where X＝XD∪XL is the final set of states discrete and continuous variables at a given moment, XD is the final set of states discrete variables, and 1 2 1 2( , , , )D n nX s s s S S S= = × × ×LL LL denotes the states of n discrete safety variables of railway transportation safety system, 1 2( , , , )L mX l l l= LL denotes the states of m continuous safety variables in the system.


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U is an input space and U＝UD∪UL, where UD is the set of states discrete input variables of railway transportation safety system and UL is the set of states continuous input variables of the system.

Y is an output space and Y＝YD∪YL, where YD is the set of states discrete output variables of railway transportation safety system and YL is the set of states continuous output variables.

A is a safety decision-making space for railway transportation safety system and l u aA A A A= U U , where lA denotes the safety level, uA means the speed limit and

aA means the control methods for railway transportation safety system. α: X×U→X is the local transition function of the states. β: X→Y is the output

function. r: X∪Y→A is the function of security rules and it can evaluate the safety levels and speed limit and the control methods.

0 1 2 1 2( (0), (0)) ( , , , ) ( , , , )d c n m D CM x x s s s l l l X X= = × ∈ ×LL LL is the initial states of this system.

3 System Simulations

3.1 simulation step

The simulation system was developed on MS Dot.net which is a software product of Microsoft Corporation and the operating system environment is Microsoft

Windows XP. The simulation process is as follows:（Ⅰ）Initialization of cells;（Ⅱ）

Establishing train operation plan;（Ⅲ）Determining train operating rules;（Ⅳ）

Establishing security rules of railway transportation safety system;（Ⅴ）Simulating

railway transportation safety system.

3.2 Initialize Installation

（Ⅰ）Initialization of cells

The block sections and stations of the railway are regarded as cells in this paper. The cell’s state is a set of safety related factors. Table 1 shows the information of railway line.

The railway line, length is 56 kilometers, is divided into 28 cells. Among those cells, there are three stop stations: the first cell (S1), the eleventh cell (S3) and the 28th cell (S6); there are also three intermediate stations: the second cell (S2), the 19th cell (S4) and the 24th cell (S5).

Table 1. the Information of railway line. ID Name Section Distance

（kilometre） Station Type Numbers of

Block


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Section 1 S1 stop station 2 S2 10 Intermediate

Station 5

3 S3 10 stop station 5 4 S4 16 Intermediate

Station 8

5 S5 10 Intermediate Station

5

6 S6 10 stop station 5 Total 56 28

The wind state of the tenth cell is 35m/s, the rainfall state of the twentieth cell is 50mm and the influence time is 120 steps.

（Ⅱ）Establishing train operation plan

In station S1, the departure interval is 10 minutes. When the signal light shows green in front of the station S1, a train is gong to leave with a speed of 0m/s. In the block sections, if the signal shows green, the train can put into the next block section with the highest speed. If the signal shows yellow, the train runs with a limited speed. Otherwise, the train has to stop in the front of the signal.

（Ⅲ）Determining train operating rules

In the simulation ,Train’s speed should be determined by the train operating rules in which the highest speed is 144 km/h, the acceleration and deceleration of the train are both 18km/h, the speed limit is 72km/h.

（Ⅳ）Security rules are the management rules and regulations for railway

transportation system. Table 2. the rules to distinguish the states of the wind.

Wind Speed (m/s) Safety Level Speed Lmit (km/h)

15≤speed＜25 2 ≤200km/h

25≤speed＜30 3 ≤80km/h

30≤speed＜35 4 ≤30km/h

≥35 5 0

Table 3. the rules to distinguish the states of the rain. Hourly Continuous Rainfall Safety Advise of Train


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Rainfall (mm) （24h） Level Operation

25-50 100-140 2 warning

50-70 / 3 170Km/h 70-100 / 4

speed limit 70Km/h

≥100 / 5 stop 0Km/h

（Ⅴ）Simulating railway transportation safety system.

Based on the first four steps, the simulation system simulating the dynamic behavior of the railway transportation safety system can be established by the MS Dot.net.

3.3 Simulation Results

The initialize information, as input set, is carried into the simulation system. Finally, simulation results are provided. Table 4 shows the train’s schedule in process of the simulation.

Table 4.the schedule of the train operation. Sections Distance

（Km） Schedule （Min）

Runtime（Min）

Parking Time （Min）

Average Speed （Km/H）

S1-S2 10 15:56:01-16:00:19 4.3 0 138 S2-S3 10 16:00:19-16:06:38 6.3 0 95 S3-S4 16 16:05:49-16:17:59 12.2 2 78 S4-S5 10 16:17:59-16:23:00 5 0 120 S5-S6 10 16:23:00-16:30:56 8 2 75 Total 56 15:56:01-16:30:56 34.9 4 96

Because the safety level of the cell occupied by the train No.1 is the fifth grade, the train should stop immediately according to the rules to distinguish states of the wind. The red line denotes the track of the train during the process of emergency shutdown. The black line shows the train planed diagram and other lines denote the actual track of the trains, as shows in Figure 3.


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Figure 3. the dynamic spatio-temporal evolution of the railway transportation safety

systems. As shows in Figure 4, safety levels are distinguished by five colors and diverse

safety related factors are distinguished by different types of lines.

Figure 4. the Safety Levels of the Railway Transportation Safety System.

According to Table 2, when the speed of the wind exceeds 35m/s, the safety level is in fifth grade and the safety system should take measure of train withdrawn from schedule. Also according to Table 3, when the rainfall is between 50mm and 70mm, the safety level will be in the third grade and the system should take measure of speed limit.

4 Conclusions

In this paper, a new modeling approach based on hybrid cellular automata model was presented. Based on analyzing the safety related factors and their


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interaction of railway transportation safety system, The framework of the model and its formal description has been established to reveal the essential characteristic and evolution mechanism of the system. Finally, the simulation research results show the effectiveness and efficient of the modeling approach. The modeling approach presented in this paper is the preliminary results of our work that is still in progress. The whole dynamic behaviors and effective security rules of railway will be the further research direction of our research in the future.

5 References

[1] Jiang Guo-Rong, Gu Cai-Xia. Key Notes of China Railway Transportation Safety [M],Beijing, China Railway Publishing House, 2003.

[2] J. L. Bail, H. Alla and R. David, Hybrid Petri Nets, Proceedings of European Control Conference, 1991: 1472-1477.

[3] G. Labinaz, M.M. Bayoumi, K. Rudie, Modeling and Control of Hybrid Systems: a Survey, Proceedings of 13th IFAC triennial World Congress, San Frencisco USA, 1996: 293-304.

[4] Andreu D, Pascal J C, and etc. Batch Process Modeling Using Petri Nets ． Proceedings of 33th IEEE Conference on Decision and Control,1994:314-319.

[5] Alexandru Tiberiu Sava and Hassane Alla, Combining Hybrid Petri Nets and Hybrid Automata, IEEE Transactions on Robotics and Automation, Vol.17, No.5, Oct. 2001:670-678.

[6] Alur R, Courcoubetis C, Henzinger A, Ho Peihsin. Hybrid automata:an algorithmic approach to the specification and verification of hybrid systems. Lecture Notes in Computer Science 736,1993：209-229.

[7] Zheng Rong-sen, Tan Hui-li and etc. Study on a cellular automaton model for pedestrian-vehicle mixing traffic in two-lane system[J]. Journal of Systems Engineering, Vo1.21,No.3,2006:273-279.

[8] Ke-Ping Li, Zi-You Gao, Bin Ning, Modeling the railway traffic using cellular automata model[J], International Journal of Modern Physics C ,Vol. 16, No. 6 (2005) 921-932.

[9] Qin Yong,Wang Ying-Jie,Jia Li-Min, Hybrid cellular automata model for railway transportation system and its implementation on GIS, Intelligent Vehicles Symposium, 2003. Proceedings. IEEE 9-11 June 2003 Page(s):543-546.

[10] Cai Cuo-Qiang. Jia Li-Min, Qin Yong, etc. Railway safety guarantee system risk based on fuzzy cell and its application in Hu-Ning line. Zhongnan Daxue Xuebao(Ziran Kexue Ban)/Journal of Central South University (Scince and Technology), Vol. 36, No. 1 (2005) 610-614..

[11] Wolfram S．Universality and Complexity in Cellular Automata [J]. Physica D, Volume 10, Issues 1-2, January 1984:1-35.

[12] Qin Yong, Wang Zhuo and etc. Research and Application on Comprehensive Monitoring and Control System Center of Qinzang Railway [J]. Journal of Transportation Systems Engineering and Information Technology, vol.7, No.2, 2007(4):129-134.

[13] Harald N. Introduction to Cellular Automata, Seminar “Organic Computing”, 2006:1-19.


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