RESEARCH ON SAFETY EVACUATION IN METRO UNDER UNCERTAIN CONDITIONS
Weili FANG，Yawei QIN，Xianguo WU，Wenli LIU，Jingbing ZHONG
School of Civil Engineering& Mechanics，Huazhong University of Science and Technology，Wuhan 430074
Abstract：This paper is based on the background of evacuation in subway.A method based on support vector machine（SVM）and EFAST is proposed，and the influence of uncertainties such as person-density，speed of movement，distance of exit，outlet width and width of stair on the evacuation time was analyzed.The results show that the speed of movement takes a leading part in the simulation，and interactions between factor v and factor L is the largest，followed by v and B1.Therefore，the uncertainty of the three parameters should be considered in the actual evacuation design.
Keywords：subway evacuation，support vector machine，uncertainty analysis，sensitivity analysis
Email：fwl0923@126.com
1 Introduction
The many indefinite exists in the design parameters and influence factors of subway evacuation.It is neither feasible nor desirable to consider every factor of all the time[1].Therefore，parameter sensitivity analysis was adopted to research the influence degrees of each parameter on evacuation time.The factors which had little influence in the evacuation model，these parameters will be considered as constant.
The global sensitivity analysis is the important methods that was used to analysis effect of the uncertain inputs to the output[2].It is mainly to decompose the total variance into partial variance which was caused by individual parameters and the interaction among factors，and then calculate the interaction among the parameters to the output of the total variance contribution.While，this method requires a lot of data samples，through the simulation of Pathfinder can’t complete it in a short time.Hence，in this paper，a method based on support vector machine（SVM）and EFAST is proposed，as well as analyzed the uncertainties of person-density，speed of movement，distance of exit，outlet width，and width of stair on the influence of the evacuation time.The result of phosphorus accumulate conditions provides a theoretical basis for research of subway evacuation design.
2 Methodology
2.1 Description of SVM simulation
SVM is a popular method of pattern recognition with many applications[3].It is mainly used to solve pattern recognition and function fitting problems.The input space is nonlinearly transformed into a high-dimensional space by the inner product function in SVM，and then the non-linear relationship between the input variables and output variables is fitted in this higher dimensional space.
2.2 Description of EFAST simulation
Saltelliet al.[4，5]unified the merits of the Sobol method and the FAST method，and proposed the extended Fourier amplitude sensitivity test（EFAST）.First-order sensitivity has only reflected the uncertain influence of each parameter to the total variance，while the total sensitivity has included the uncertainty influence of each parameter and the interaction influence of this parameter with other parameters，and the first-order sensitivity Siis as Equation（1），and the total sensitivity STiis as Equation（2）.
2.3 Description of SVM-EFAST simulation
Step 1：Establishes the simulation model based on Pathfinder，and calculates the evacuation time.
Step 2：Prediction model based on SVM is set up.In order to get forecast samples，through the Pathfinder simulation，the results with the sample size of 200 are intended as classification，applied to the SVM.
Step 3：Uncertainty and Sensitivity analysis.The uncertainty of the index factors was quantified by using Simlab simulation.
The entire flow is illustrated in Figure 1.
Figure 1 Illustration of procedure of uncertainty and sensitivity analyses
3 Pedestrian Evacuation Simulations under Fire
3.1 Model construction
Subway station is 120 m×20 m，with a height of 4.5 m.In the middle of station has some sign pillar with 800 mm long and 800 mm wide.There have 2 stairs and 2 elevators，and the width of stair and escalator is 4.5 m and 1.5 m respectively.There are three exit A，B and C，in which the width of A and B exit is 4.0 m，width of C exit is 6.0 m.Layout of subway station is shown in Figure 2.
Figure 2 Layout of subway station
3.2 Influential factors
In this paper，five parameters were selected from many uncertain factors，as described next.
（1）Person-density（q）：person-density related with many factors，thus the result show some uncertainty.For example，it has different person-density for different time sections.
（2）Speed of movement（v）：the speed of movement vary with person-density，etc.
（3）Distance of exit（L）：There are many uncertain in location of accidents.
（4）Outlet width（B1）：To optimize the export width has a great influence on subway safety design.
（5）Width of stair（B2）：It is beneficial on evacuation for optimizing the stair width.
Combined with engineering case，the distribution and the value range of five kinds of uncertain parameters are shown in Table 1.
Table 1 distribution of risk factor
4 Sensitivity Analyses
4.1 Uncertainty analysis
Through the process of generation and propagation of a sample，the CDF and CCDF of the evacuation time of subway evacuation with sample size of 2000 are shown in Figure 3 and Figure 4.
Figure 3 Probability distribution of evacuation time
Figure 4 Cumulative probability curve
As shown in Figure 3，the probability distribution of the evacuation time of subway evacuation in this case study follows a unimodal，positively skewed distribution，which is because the skewness is 0.9654.Furthermore，the evacuation time in this study ranges from 140 s to 360 s.More than 78％of the evacuation time lies within the range 160 s to 240 s，which indicates that in this study，people most likely to escape safety in this range.According to this result，engineers can judge whether the people can escape safety in urgent condition.For example，the CCDF is shown in Figure 4，the confidence level of a predicted evacuation time of not more than 240 s is 78 ％.That is to say，the probability of the evacuation time of subway evacuation in the case not more than 240 s is 0.78.With these confidence levels，engineers can not only judge whether people can escape safety in the conditions，but also provide a reasonable basis for risk assessment.
4.2 Sensitivity analysis
By using SIMLAB，the sensitivity of each factor during the development is determined together with the interactions among all of them.The results are shown in Table 2.It is showed that the first-order sensitivity index and the total sensitivity index have the same influence on evacuation time.Relationships between factors are as follows，v>L>q>B1>B2.Thus，we can get a conclusion that the speed of movement takes a leading part in the simulation.In addition to the factor of B2，evacuate the results of first-order sensitivity index of the four parameters are the same order of magnitude.This indicates that there are some differences among four factors on evacuation，but an insignificant difference.So，the uncertainty of four parameters should be considered in the actual evacuation design.
Table 2 Value of first-order sensitivity index，total sensitivity index and relative value
It can be seen from Table 2，speed of movement has a great interaction among the parameter.In order to find out the relationship of these factors with the speed of movement，the second order index of Sobol to confirm it，the results are shown in Table 3.
Table 3 Second order sensitivity index of Sobol
According to Table 3，it can be seen that interactions between factor v and factor L is the largest，followed by v and B1.In addition，the second order sensitivity index of Sobol are negative number，the interactions among the other parameters could be neglected.
5 Conclusions
By this simulation，conclusions are as follows.
（1）A method based on SVM and EFAST is proposed.With confidence levels，engineers can not only judge whether people can escape safety in the conditions，but also provide a reasonable basis for risk assessment.
（2）the speed of movement takes a leading part in the simulation，and interactions between factor v and factor L is the largest，followed by v and B1.
Acknowledgement
This research was financially supported by the National Natural Science Foundation of China（No.51378235）and Hubei Provincial Natural Science Fund（No.2014DFA117）.
References
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ICRE2016-International Conference on Railway Engineering