Train Vehicle Structure Design from the Perspective of Evacuation
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Abstract
The safety of trains, a highly efficient mode of transportation, has attracted significant attention. In the vehicle structure design of a train, the evaluation of the passenger evacuation time is necessary. The establishment of a simulation model is the fastest, most convenient, and practical way to achieve this goal. However, few scholars have focused on the reliability of a passenger train evacuation simulation model. This paper proposes a new validation method based on dynamic time warping and multidimensional scaling. The proposed method validates the dynamic process of a simulation model, provides statistical results, and can be used for smallsample scenarios such as a train evacuation scenario. The results of a case study indicate that the proposed method is an effective and quantitative approach to the validation of simulation models in a dynamic process. Thus, this paper describes the influence of the train structure size on an evacuation based on the results of simulation experiments. The structural size factors include the door width, aisle width, and seat pitch. The experiment results indicate that a wide aisle and reasonable seat pitch can promote a proper evacuation. In addition, a normal train door width has no effect on an evacuation.
Keywords
Simulation Passenger train evacuation Structural size Validation1 Introduction
Because the evacuation capability of a train is vital to the passengers on board, the structural design of a train car must take such a factor into account [2]. This paper studies the effects of the door width, aisle width, and seat pitch on a train evacuation. Some studies have been conducted on the influence of the structural size on the evacuation time in other fields. Wide doors can clearly reduce the evacuation time in building evacuations [3]. McLean and Corbett pointed out that the aisle width has a small but significant impact on airplane evacuations [4]. Nevertheless, McLean and Chittum reported that the aisle width does not affect the flowrate [5]. In addition, the seat pitch has a significant influence on the evacuation time [6]. Because the interior structures of highspeed trains are quite different from those of buildings and airplanes, their results may be unsuitable for highspeed trains.
There are two main research methods for passenger evacuations: real evacuation experiments and simulation experiments [7]. A real experiment recreates the evacuation process under different conditions. However, such experiments are extremely costly and harmful to the subjects [8]. Moreover, this method is for a postdesign evacuation and is not applicable as an ongoingdesign assessment. Therefore, researchers and designers prefer to use simulation experiments. Such experiments are economical and practical if the simulation model is realistic and accurate in comparison with the actual situation. There are numerous commercial software programs available for simulating an evacuation, including EXODUS, LEGION, PATHFINDER, and MassMotion. However, such programs are designed for building evacuations. Few simulation models for railways have been considered. In general, a simulation model is valid only for its specific application [9]. Additionally, it is impossible to achieve a universal validation owing to a lack of sufficient observational data [10]. Hence, it is necessary to validate the simulation models used for a railway system.
There are mainly two methods for validation, namely, a ttest and a graphical comparison [11]. A ttest is mainly used on static indicators. Zhang et al. [12] used a ttest to compare the total time for the model validation in the simulation of alighting and boarding behaviors in metro stations. However, a ttest alone cannot meet the validation requirements for a dynamic process. A visual graphical comparison technique is the most commonly used approach for a validation of simulation models for a dynamic process [13]. The basic validations of many commercial simulation software programs, such as EXODUS [14, 15], LEGION [16], PATHFINDER [17], and MassMotion [18] all use graphical comparisons. A large number of scholars have also used graphical comparisons to validate their simulation models. Chen et al. compared the evacuation behaviors at a Tshaped intersection between a simulation and experiment using the evacuation time series of a pedestrians graph [19]. Zhou et al. [20] compared three evacuation time series to validate their model. Nagai et al. [21] used graphical comparisons to show that the experimental results are consistent with the simulation results. Although this technique is valuable, it is essentially qualitative [22] and inadequate for validation [23]. Other methods have also been used by a few scholars. Woensel and Vandaele used Theil’s inequality coefficient as an evaluation criterion to compare the speeds between the simulation model and reality [24]. However, this coefficient can only be applied to time series of equal length, which rarely occurs during a passenger train evacuation.
A passenger evacuation is a complex and dynamic process. Many factors such as human behavior and train design factors affect the evacuation time [14]. It is insufficient to validate the entire simulation process using only static indicators. Therefore, a comparison between two time series of the dynamic process is usually conducted. However, a graphical comparison is frequently subjective. In addition, only two samples are compared, making it easy for large errors to be produced. An objective comparison between several time series is a problem frequently faced by engineers and scientists [25].
Unlike other simulation processes, a passenger evacuation usually differs in terms of the time series length. The escape time for each passenger is random. This leads to different evacuation times under exactly the same conditions. Owing to the different time series lengths, the difficulty in their quantitative comparison is increased.
This article has two main contributions. First, a new method for validating the simulation model in a dynamic process is proposed. The new validation method compares the time series from several simulations using a real time series in a statistical manner. Specifically, the lengths of the time series may be unequal, which is often the case in reality. Experiments and comparisons show that this method can effectively achieve a quantitative comparison on multiple time series. Second, the influence of three structural train size factors on an evacuation was studied through simulations, namely, the door width, aisle width, and seat pitch. The range of their values in the train design was determined. In addition, singlefactor experiments have been designed to study their effects on a train evacuation.
The remainder of the paper is organized as follows. Section 2 describes the new validation method and provides a case study and comparison between the new validation method and other approaches. Section 3 provides an experimental design of the influence of three structural train size factors on an evacuation. The results and a discussion are provided in Sections 4 and 5, respectively. Finally, Section 6 gives some concluding remarks regarding this research.
2 Preliminary
As previously shown, most validation methods rely on a visual comparison and a subjective evaluation [26]. This section presents a quantitative method for validation. Unlike many other methods that only compare two time series for validation, the proposed method compares numerous time series generated using a simulation model with one or more time series from reality. Because random errors exist in both the simulation model and reality, the validation results from comparing two time series are not credible, and thus a series of successful simulations can be applied to increase the credibility [27]. Moreover, this method can process time series of different lengths, which is suitable for train evacuation scenarios.
2.1 Method Outline
To compare multiple time series, we first need to solve the problem of their different lengths. In this section, we use dynamic time warping to transform two time series with different lengths into a similarity. Then, to reduce the dimensions of the similarity, we use multidimensional scaling. Finally, we use a Hotelling’s One Sample T^{2} Test to check if there is a difference in the position of the samples at a low dimension.
 (1)
Input all time series from the simulation based on a time series from reality. Calculate the distance matrix D through dynamic time warping (DTW).
 (2)
Use multidimensional scaling (MDS) to reduce the dimensions of distance matrix D and determine the position of the samples in the lower dimensions.
 (3)
Propose a hypothesis that there is no difference between the simulation and actual results. Use a Hotelling’s One Sample T^{2} Test for testing.
The details of this method are described below.
2.2 Dynamic Time Warping
Dynamic time warping (DTW) is a widely used algorithm for measuring the similarity between two time series datasets. Its applications include speech recognition, signature verification [28], shape matching, vocalization classification [29], and other time series analyses [30, 31]. As an advantage of DTW, it can compare time series sets of varying length. As the case often rises in simulations, DTW is also suitable for comparing the dynamic processes in simulations.
Given two time series datasets R = r_{1}, r_{2},…, r_{m} and S = s_{1}, s_{2},…, s_{n}, the lengths of R and S may differ. To measure the similarity between R and S, DTW first constructs an \( m \times n \) similarity matrix D between points r_{i} and s_{j} using a cost function. The most commonly used cost function is Euclidean distance. Therefore, the element of the similarity matrix, D, also called a distance matrix, is d(r_{i}, s_{j}) = (r_{i}s_{j})^{2}.
Because DTW assumes that time is continuous and monotonous, the minimum cost path can be calculated from the start point (1, 1) to the end point (m, n) in D without violating this assumption. In addition, the cost of the path divided by the path length can be used as the similarity between R and S.
Therefore, the similarity between R and S is sim_{RS} = (γ(m, n))/K. Clearly, its range is [0, +∞]. The closer sim_{RS} is to zero, the higher the similarity between R and S. However, the DTW distance is not a metric because it does not fully satisfy the triangle inequality. In fact, it is a loose metric of high dimensions [32]. Hence, the following steps are needed for a dimensional reduction.
The above method is used to calculate the similarity between two time series datasets. In the validation of a simulation model, there are many time series datasets from the simulation and at least one practical time series dataset. We merge them and calculate the similarity matrix SIM = (sim_{ij}) between them.
2.3 Multidimensional Scaling
Multidimensional scaling (MDS) is a multivariate data analysis method that expresses the similarity or affinity between objects in the form of a spatial distribution. It belongs to a taxonomy because it is used in geochronology [33], graphbased pattern recognition [34], time series classification [35], and genetics [36]. Unlike other dimensional reduction methods that require raw data, MDS only needs a similarity matrix SIM, which can be provided by the first step.
These two quantities correspond to the cumulative contribution rate in a principal component analysis (PCA). We hope that the value of k is not too large and that a_{1,k} and a_{2,k} are large. Usually, k = 1, 2, or 3. When k is taken, use \( \hat{x}_{\left( 1 \right)} ,\hat{x}_{\left( 2 \right)} , \ldots ,\hat{x}_{\left( p \right)} \)to denote the orthogonalized eigenvector of B corresponding to its eigenvalues λ_{1}, λ_{2},…, λ_{p}. Ensure that \( \hat{x^{\prime}}_{\left( i \right)}\hat{x}_{\left( i \right)} = \lambda_{i} ,\quad i = 1,2, \ldots ,k \). Usually the eigenvalue λ_{k} should greater than zero. If λ_{k} is less than zero, the value of k should be reduced.
Let \( \hat{X} = \hat{x}_{\left( 1 \right)} ,\hat{x}_{\left( 2 \right)} , \ldots ,\hat{x}_{\left( k \right)} \), and the row vector \( x_{1} ,x_{2} , \ldots ,x_{N} ,x_{N + 1} \) of \( \hat{X} \) is then the classical solution. Here, N is the number of time series datasets from the simulation. After using MDS, N simulation results and one sample from reality are placed in a kdimensional space with their DTW distances preserved as well as possible. Hence, the statistical method can be used to test the validation of the simulation results. This will be shown in the next step.
2.4 Hotelling’s One Sample T^{2} Test
In this way, the believability of the simulation system can be verified.
2.5 Case Study: Passenger Train Evacuation Simulation and Validation
This section presents a case study using the proposed method to verify the validation of the Legion simulation model. Legion is a commercial simulation software package, and its core is the microscopic pedestrian interaction model [37]. It has been used in a wide range of large buildings such as metro stations [38], train stations, and stadiums [37]. This section describes the validation of Legion in the dynamic process of a train evacuation. At the same time, a subjective evaluation and ttest are used to verify the effectiveness of the proposed method.
2.5.1 Basic Simulation Model

Step 1: Initialization scenario.

Step 2: Generate passengers and their targets. Set t = 0.

Step 3: Generate paths of passengers randomly.

Step 4: Check whether passengers collide with others or things. If so, go to Step 3. Otherwise, go to the next step.

Step 5: Calculate the overall effort and its reduction.

Step 6: Check whether the reduction is up to the standard. If so, go to Step 3. Otherwise, go to the next step.

Step 7: Passengers move in a time step according to their paths. Set t = t + 1.

Step 8: Check whether all passengers reach their targets. If not, go to Step 3. Otherwise, end the simulation.
2.5.2 Passenger Train Evacuation Experiment
The real sample of a passenger train evacuation was derived from 12 experiment trials conducted by the Volpe Center in 2005 [14, 39]. A series of trials was conducted at North Station, Boston, MA with the cooperation of the Massachusetts Bay Transportation Authority (MBTA). Because the conditions of the 12 experimental trials differ, this paper only uses one for validation of the Legion model. This trial is the trial four, in which passengers are egressed from the car to the high platform through two side doors under normal lighting.
Minimum and maximum free walking travel speeds during egress trials (m/s)
Gender  Average speed  Min speed  Max speed 

Male  1.52  1.22  1.98 
Female  1.31  1.01  1.77 
2.5.3 Simulation
As with trial four, the numbers of male and female passengers were 40 and 44, respectively. Because there is no specific velocity distribution in the egress trial, this study uses a uniform distribution to express the passenger speed. Hence, the male speed distribution is U(1.2, 2), and the female speed distribution is U(1, 1.8). The simulation model was run 25 times.
2.5.4 Analysis of Exit Passenger Flow
Using the DTW algorithm described in Section 2.2, we obtain the similarity matrix SIM of the flow rates from all samples.
The result of Hotelling’s one sample T^{2} test shows that the simulation samples \( \left( {M = \left( {0.233 \times 10^{  3} ,0.195 \times 10^{  3} ,0.423 \times 10^{  3} } \right), SD = \left( {0.083, 0.064, 0.062} \right)} \right) \) do not differ significantly with the real sample, T^{2}(3, 22) = 0.309, p = 0.819. p > 0.05, indicating that there is insufficient statistical evidence to show that the simulation model is not credible. The result indicates that there is an 81.9% level of confidence that the simulation model does not differ from reality.
2.5.5 Comparison
To verify the effectiveness of the proposed method, this paper compares the result with the results of the ttest and a graphical comparison, of which four indicators are used, namely, the first passenger’s evacuation time, the total evacuation time, the passenger flow at the exit, and the evacuation curve [2].
Results of ttests on three indicators
Logarithmic value of reality  Mean logarithmic value of simulation  Standard deviation  Df  t  p  

a) Left door  0.778  0.763  0.067  24  − 1.156  0.259 
a) Right door  0.778  0.778  0.058  24  0.433  0.669 
b) Left door  1.690  1.686  0.015  24  −1.264  0.219 
b) Right door  1.653  1.657  0.019  24  1.007  0.324 
c) Left door  − 0.056  − 0.052  0.018  24  0.606  0.550 
c) Right door  − 0.041  − 0.044  0.019  24  − 0.866  0.395 
It can be seen from the results that there is no significant difference between the simulation results and the actual result for the three static indicators. Furthermore, the evacuation curves between the two have a high consistency. The evacuation simulation is credible in a train environment. This result is consistent with the results of the proposed method. Therefore, the method presented in this paper is effective.
3 Method
Because a train evacuation is a complex process, many factors affect it. The setting of the initial scene has a significant impact on passenger evacuation [40]. To carry out our research, we first need to determine the setting of the control variables and the effective interval of independent variables. The independent variables are the spatial factors, and the control variables mainly include the evacuation scenes and passenger attributes.
3.1 Evacuation Scenarios and Passenger Properties
The number of passengers is the maximum carrying capacity of the train. In other words, the passenger density is four persons per square meter in free space minus the seats [41]. Hence, a total of 130 passengers are in the coach.
Passenger agespeed distribution table
Sex  Age  Proportion (%)  Minimum speed (m/s)  Average speed (m/s)  Maximum speed (m/s) 

Female  Younger than 30  7  0.93  1.24  1.55 
30–50 years old  7  0.71  0.95  1.19  
Older than 50  16  0.56  0.75  0.94  
Older than 50, mobility impaired (1)  10  0.43  0.57  0.71  
Older than 50, mobility impaired (2)  10  0.37  0.49  0.61  
Male  Younger than 30  7  1.11  1.48  1.85 
30–50 years old  7  0.97  1.3  1.62  
Older than 50  16  0.84  1.12  1.4  
Older than 50, mobility impaired (1)  10  0.64  0.85  1.06  
Older than 50, mobility impaired (2)  10  0.55  0.73  0.91 
3.2 Independent and Dependent Variables
The dependent variable is the total evacuation time.
The independent variables are three size parameters of the passenger train structure. The three spatial parameters studied in this paper are the aisle width, door width, and seat pitch.
Main highspeed secondclass space parameters of trains in China
Vehicle type  Aisle width (cm)  Door width (cm)  Seat pitch (cm) 

CRH1  58  110  90 
CRH2  60  66  98 
CRH3  50  90  
CRH3G  58  80  98 
CRH5  57  80  96 
CRH380A  60  72  
CRH380B  45.3  90  
CRH1  58  110  90 
The minimum aisle width is 45 cm, as shown in Table 4. For two persons passing through face to face, the minimum aisle width is 76 cm [46]. Table 4 shows that the minimum and maximum door widths are 66 and 110 cm, respectively. The minimum seat pitch is 90 cm, as shown in Table 4. The maximum seat pitch can reach 101 cm [47].
In conclusion, the minimum reasonable interval of the aisle is [45, 76 cm]. The interval of the door width is [66, 110 cm]. In addition, the maximum reasonable interval of the seat pitch is [90, 101 cm].
3.3 Design Experiment
Six levels of the three spatial parameters
Spatial parameter  1  2  3  4  5  6 

Aisle width (cm)  45  52  59  66  73  80 
Door width (cm)  65  74  83  92  101  110 
Seat pitch (cm)  90  92  94  96  98  100 
In the corresponding model built for the simulation, the value of a single parameter changed while the other factors remain unchanged. The simulation was run 20 times for each spatial parameter at each level.
3.4 Data Analysis
To study the main effects of the various factors, an analysis of the variance was conducted. A curve fitting was applied to observe the influencing trend of various factors on the evacuation. The significance was determined based on a 0.05 level.
4 Results
4.1 Results of Aisle Width
Variance analysis results of aisle width
Model  Sum of squares  df  Mean square  F  Sig. 

Between groups  4174.44  5  834.89  13.67  1.87×10^{−10} 
Within groups  6960.31  114  61.06  
Total  11134.75  119 
The regression equation is y = 0.009x^{2} − 1.63x + 174.65. A regression analysis was carried out on the fitting curve. The overall score of F(2, 3) = 30.76 is significant (p = 0.01 < 0.05). In addition, R^{2} = 0.95 indicates that the fitting equation has a high degree of fit and can be used to explain the effect of the aisle width on the evacuation time.
4.2 Results of Door Width
Variance analysis results of door width
Model  Sum of squares  df  Mean square  F  Sig. 

Between groups  206.62  5  41.32  1.19  0.32 
Within groups  3953.75  114  34.68  
Total  4160.37  119 
4.3 Results of Seat Pitch
Variance analysis results of seat pitch
Model  Sum of squares  df  Mean square  F  Sig. 

Between groups  517.61  5  103.52  2.33  0.047 
Within groups  5058.68  114  44.37  
Total  5576.29  119 
The regression equation is y = − 0.165x^{2} + 30.965x − 1339.3. A regression analysis is carried out on the fitting curve. The overall score of F(2,3) = 21.08 is significant (p = 0.017 < 0.05). In addition, R^{2} = 0.93 indicates that the fitting equation has a high degree of fit and can be used to explain the effect of the seat pitch on the evacuation time.
5 Discussion
5.1 Effects of Aisle Width
The above results show that the change in aisle width has a significant impact on the evacuation time. The fitting curve in Figure 9 shows that the evacuation time decreases as the aisle width increases. At the end of the curve, the reduction rate of the evacuation time also decreases. This result is similar to the results of the building evacuation [19, 48].
5.2 Effects of Door Width
It can be seen from the above experiments that the door width within the interval [65, 110] has no effect on the evacuation time. This conclusion differs from general experience and the research results from other fields.
It is generally believed that the door width affects the crowd evacuation. Research on ships [49] and public buildings [50] has shown that the evacuation time decreases as the door width increases. However, the reduction rate of the evacuation time exponentially decreases as the door width increases [51, 52].
To test whether this fact also occurs in the train evacuation, this study added three levels of testing based on the above experiments. The three levels of door width are 38, 47, and 56 cm, respectively. All other experiment conditions are the same as before. The new experiment results are as follows.
Variance analysis results of door width (2)
Model  Sum of squares  df  Mean square  F  Sig. 

Between groups  4167.23  8  520.90  12.46  5.21×10^{−14} 
Within groups  7147.8  171  41.80  
Total  11315.03  179 
The regression equation is y = −0.0002x^{3} + 0.045x^{2} − 3.816x + 214.77. A regression analysis is carried out on the fitting curve. The overall score of F(3,5) = 23.133 is significant (p = 0.002 < 0.05). Here, R^{2} = 0.93 indicates that the fitting equation has a high degree of fit and can be used to explain the effect of the door width on the evacuation time.
It can be seen from the above results that the functions of the evacuation time and the door width have a roughly Lshaped curve. This result is consistent with experience and other research results. When the door width of the secondclass CRH5 car exceeds 56 cm, the increase in door width cannot effectively reduce the evacuation time. This threshold is much smaller than that of ships and buildings but close to that of aircraft [3, 6, 53]. This is because the aisles of trains and airplanes are narrow and long, and passengers are more likely to be crowded in the aisles and seats. Therefore, if the door width is within a reasonable range, the door will not experience congestion during a train evacuation.
5.3 Effects of Seat Pitch
The change in seat pitch has a significant impact on the evacuation time. The fitting curve in Figure 11 indicates that the evacuation time will increase at the beginning of the increase in seat pitch, and later decreases rapidly. Similar studies have been conducted in the aviation field. However, the seat pitch in the aircraft is less than 90 cm [10]. Because of the different ranges of seat pitch, it is difficult to draw any conclusions.
Because there is insufficient space for direct competition, the evacuation time increases initially. However, as the seat pitch increases, the excess space increases. When the seat pitch is approximately 95 cm, there is space for many people to pass through at the same time. The evacuation time decreases rapidly as the capacity of the seat pitch increases and the passengers become orderly. Therefore, the seat pitch should provide a reasonable space to allow passengers to walk steadily toward the aisle without providing extra space to allow for direct competition.
6 Conclusions
This study analyzed a train vehicle structure design from the perspective of an evacuation. First, a new validation method was proposed and applied to validate the simulation model in a passenger train evacuation. Second, a simulation method was used to analyze the influence of the three structural size factors of a train, namely, the door width, aisle width, and seat pitch, on the evacuation time.
The new validation method begins by constructing a similarity matrix using the DTW. Then, the time series is converted into points in a two or threedimensional space using a similarity matrix with MDS. Finally, a Hotelling’s one sample T^{2} Test is conducted on the points representing the simulation process. In a case study, a simulation model of a passenger train evacuation experiment was built using the Legion model. The results indicate that the simulation model has a high degree of credibility. The ttest and graphical comparison results were compared with these results, which show a level of consistency, indicating the effectiveness of the proposed method.
Three singlefactor experiments were designed to study the effects of the three factors on the evacuation time. The simulation model was applied as the experiment environment. The results indicate that, within the interval of [45, 80] cm, the wider the aisle is, the shorter the evacuation time. When the door width is within a reasonable range, that is, within the [65, 110] cm interval, there is no influence on the evacuation time. However, if the door width is less than approximately 56 cm, the evacuation time will increase rapidly. Approximately 95 cm of seat spacing will cause direct competition among the passengers, thereby reducing the evacuation efficiency. Therefore, the design of the seat pitch within the range of [90, 100 cm] should not result in passenger competition.
Notes
Authors’ Contributions
WF was in charge of the whole trial; HQ wrote the manuscript; HQ assisted with sampling and laboratory analyses. Both authors read and approved the final manuscript.
Authors’ Information
Hanzhao Qiu, born in 1991, is currently a PhD candidate at State Key Lab of Rail Traffic Control & Safety, Beijing Jiaotong University, China. He received his master degree from Beijing Jiaotong University, China, in 2015. His research interests include manmachine system and human factors.
Weining Fang, born in 1968, is currently a professor at State Key Lab of Rail Traffic Control & Safety, Beijing Jiaotong University, China. He received his Ph.D. degree from Chongqing University, China, in 1996. His research interests include human factors, ergonomics and industrial design.
Competing Interests
The authors declare that they have no competing interests.
Funding
Supported by State Key Laboratory Foundation of China (Grant No. RCS2018ZT009).
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