# Risk Evaluation Study of Urban Rail Transit Network Based on Entropy-TOPSIS-Coupling Coordination Model

Authors: Fawen Gao; Zhibin Zhang; Mengxing Shang
Journal: Discrete Dynamics in Nature and Society
 (2021)

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## Abstract

As one of the core systems of a city, urban rail transit plays a pivotal role in ensuring the safe, rational, and efficient operation of the city. Therefore, it is of great significance to ensure the safe operation of urban rail transit network to improve the operation efficiency and economic level of the city. The prerequisite to ensure the safety of urban rail transit network is whether the risk situation of urban rail transit network can be reasonably and accurately evaluated. In order to evaluate the risk level of urban rail transit network reasonably and accurately, firstly, with full consideration of the characteristics of urban rail transit, the risk evaluation system of urban rail transit network was established in this paper based on the three levels of regional economy, social resources, and rail transit. Secondly, based on the entropy-TOPSIS-coupling coordination model, the single-factor influence and multifactor coupling influence in the index system are calculated and analyzed, respectively; thus the coupling coordination degree of urban rail transit system is obtained, so as to quantitatively evaluate and analyze the risk situation in urban rail transit network. Finally, based on the actual data of Shanghai from 2000 to 2016, the case simulation and analysis are carried out. The results show that the two indicators of regional economy and social resources are more likely to affect the safety state of urban rail transit. At the same time, the safety factor of urban rail transit coupling system is increasing year by year and gradually develops from disorder to order. This is more in line with current urban rail transit condition, demonstrating the rationality and accuracy of the entropy-TOPSIS-coupling coordination model proposed in this study.


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## Body

## 1. Introduction

Urban rail transit is a kind of public transportation that transports a large number of passenger flows in the form of corresponding vehicles through a dedicated track structure, and it occupies a very important position in the urban system. A reasonable and safe urban rail transit network can greatly improve the efficiency and economic level of urban development. The construction of a reasonable and safe urban rail transit network cannot be achieved without an accurate evaluation of the risk of the existing urban rail transit network. Therefore, in order to establish a reasonable risk evaluation system of urban rail transit network, a risk evaluation method of urban rail transit based on the entropy-TOPSIS-coupling coordination model is proposed in this paper, aiming to accurately evaluate the risk situation of urban rail transit network, so as to lay a solid theoretical foundation for optimizing and perfecting urban rail transit network.Relevant scholars have conducted a series of research on the evaluation of urban rail transit planning and have achieved certain research results. The research content mainly focuses on the exploration, improvement, and optimization of the evaluation model; for example, Yixiu Song [1] used the Analytic Hierarchy Process (AHP) to evaluate the rail transit planning and compared each evaluation index of the transportation planning to obtain its relative importance. Jing Li [2] established a comprehensive evaluation model of traffic network by combining the relative theory of topology and entropy for the shortcomings of the existing urban rail transit network evaluation index system. Chaoxia Su [3] proposed a comprehensive evaluation method of urban traffic network planning and constructed the comprehensive evaluation model of urban rail transit network by fuzzy evaluation method. Yong Jiang [4] believed that the material element analysis model can provide an operable method for VFM evaluation of urban rail transit PPP projects, reduce the subjectivity in the evaluation process, and improve the scientific and reasonable evaluation results. Xin Liu [5] proposed an evaluation model based on the extension cloud theory for the characteristics of urban rail transit safety evaluation, taking advantage of the uncertain reasoning of the cloud model and the quantitative analysis of the extension theory. Xu XD [6] evaluated the potential benefits and limitations of deploying eco-driving strategies on different transit services, service areas, fleet composition, and road terrain. Bin S [7] proposed a quantitative method to evaluate the performance of urban subway network under different damage scenarios. Hy et al. [8] proposed a vague fuzzy matter-element model for the risk assessment of urban rail transit projects by combining vague set and matter-element theory. Hu et al. [9] provided an improved DS/AHP method in this study for the evaluation of hazard source for urban rail transit risk evaluation with incomplete information. Aydin [10] proposed a fuzzy-based multidimensional and multiperiod service quality evaluation outline for rail transit systems. Wang et al. [11] used the grey incidence method for evaluating the hazards of urban rail transit dynamic operating systems and conducting quantitative analysis of risks in the operation process.At the same time, scholars prefer to use various types of evaluation models in combination, so that the evaluation method is more efficient and reasonable. For example, Ying Wang et al. [12] used AHP method and entropy method to determine index weight and applied TOPSIS method to determine the ideal scheme of line network and selected the optimal scheme by comparing the gap between each scheme and the ideal scheme. Bingyi Qian et al. [13] combined entropy method and expert method to determine the evaluation indexes, combined with TOPSIS method to calculate the pros and cons of each scheme and the optimal solution to determine the optimal scheme, and verified by practical case. Zhifeng Zhou [14] proposed the correlation function as the qualitative index for screening in order to evaluate the service level of transfer stations more reasonably. Ruisong Zhao [15] analyzed the basic form of rail network layout and the suitable form of rail network layout, improved the calculating method of existing rail network scale, and also improved the Analytic Hierarchy Process (AHP) network layout method, established the evaluation index system of line network layout, and constructed the evaluation model. Xie [16] constructed an evaluation model based on ISM-ANP-Fuzzy to evaluate the interface risk in urban rail transit PPP projects. Huang et al. [17] proposed a technique for order preference entropy by similarity to ideal solution (TOPSIS) method to evaluate the operational performance of urban rail transit systems from the perspective of operators, passengers, and government. Wu et al. [18] evaluated the urban rail transit operation safety based on an improved CRITIC method and cloud model. Bouraima MB [19] used a combined SWOT matrix and Analytic Hierarchy Process (AHP) to evaluate the priority factors and to employ them in developing strategies for the railway transportation system.Most of the above literature only makes quantitative analysis on the single index factor in the evaluation of urban rail transit; the influence situation and coupling condition between index factors were not calculated and analyzed. Therefore, based on the discussion of the above literature, the entropy-TOPSIS-coupling coordination model evaluation method of urban rail transit is proposed by combining entropy weight method, TOPSIS method, and coupling coordination model. Combined with the relevant traffic system data of Shanghai from 2000 to 2016, the system risk and coordination degree are quantitatively analyzed and comprehensively analyzed, and the development of Shanghai's rail transit system in these ten years is obtained.


## 2. Identification of Evaluation Index

The evaluation index system of the urban rail transit planning network is the key to measuring the results of the traffic system scheme, as well as an important precondition for picking the most reasonable traffic system scheme. This index system needs to comprehensively reflect the traffic system's economic efficiency, social development, network structure, operation effect, and other rail transit characteristics. Based on an analysis of the related literature's index system, combined with the characteristics of the city and the needs of social development, and in accordance with the principles of strong purpose, hierarchy, science, rationality, ease of operation, and the quantitative and qualitative combination, the evaluation index system of urban rail transit network is constructed in this paper from three aspects of regional economy, social resources, and urban rail transit, as shown in Table1.Table 1
System of evaluation indicators for urban rail transit systems.
Target layerCriterion layerIndex layerDescriptionEvaluation of urban rail transit systemsRegional economyTotal GDP (E1)Annual gross regional productInvestment in urban infrastructure (E2)Annual city investment in the engineering and social infrastructure necessary for survival and developmentInvestment in traffic service (E3)Annual investment in necessary tools for transportation, such as machinery and equipment and communication equipmentPopulation density along the rail (E4)Average number of people per unit area of land along urban rail lines per yearSocial resourcesNumber of hospital beds (S1)Total number of people using beds in all hospitals within the urban rail system per yearNumber of park visitors (S2)Total number of people visiting all parks within the urban rail system per yearNumber of mall patrons (S3)Total number of people patronaging all shopping malls within the urban rail system per yearTotal number of jobs along the rail (S4)Total number of jobs along urban rail lines that provide money-making opportunities for citizens per yearTotal number of students enrolled along the rail (S5)Total number of students enrolled in all schools along the urban rail line per yearBuilding area of houses along the rail (S6)Total above-ground floor space along urban rail lines per yearRail transitUrban rail mileage (T1)Total length of lines in normal operation in the urban rail systemDaily average flow of rail transit (T2)Daily passenger volume of urban rail systemPeak hourly cross-sectional flow (T3)The peak number of passengers passing through each section of the rail line in the same direction per unit timeRail transit share (T4)The ratio of trips made by urban residents choosing rail transit to total trips


## 3. Evaluation Modeling

Step 1.
Statistical panel data of three potential variables in Shanghai from 2000 to 2016 are defined askth, where kth denotes the three subsystems of regional economy (E), social resources (S), and urban rail transit (T), respectively; kth is thekth second index under the subsystem, k=1,2,3,…,l,l∈N+; jth is thejth year to be evaluated, j=1,2,3,…,n,n∈N+. The initial matrix of the subsystem Xi=xi,k,jl×n is expressed as(1)Xi=xi,k,jl×n=xi,1,1xi,2,1xi,3,1⋯xi,l,1xi,1,2xi,2,2xi,3,2⋯xi,l,2⋮⋮⋮⋮⋮xi,1,nxi,2,nxi,3,n⋯xi,l,n.Step 2.
For each subsystem separately, the entropy weight method is used to calculate the weight of thekth second index in thejth time period. The smaller the entropy value, the larger the entropy weight, indicating that the more informative the indicator is, the more important the indicator weight will be. Firstly, the initial matrix is normalized to eliminate the dimension problem, and the normalized matrix Yi=yi,k,jl×n of subsystem i is formed as follows:(2)yi,k,j=xi,k,jmax−xi,k,jxi,k,jmax−xi,k,jmin,∀i,k,j,where kth is the value after normalization and kth and kth are the maximum and minimum values of kth, respectively. Calculate the entropy value ei,k of the kth second index under subsystem i as follows:(3)ei,k=−1lnn∑j=1nfi,k,j⋅lnfi,k,j,fi,k,j=yi,k,j∑j=1nyi,k,j,∀i,k,j,when fi,j,k=0; let fi,j,k×Infi,j,k=0. Calculate the entropy weight ϖi,k by using the entropy value of the kth second index under subsystem i as follows:(4)ϖi,k=1−ei,kl−∑i=1lei,k,∀i,k,Step 3.
Using the normalization matrixYi=yi,k,jl×n of subsystem i and the entropy weights ϖi,k of the kth second index under subsystem i, the normalization matrix of the subsystem is weighted as U=ui,jm×n:(5)ui,j=yi,k,j×ϖi,k,U=ui,jm×n=u1,1u1,2⋮u1,nu2,1u2,2⋮u2,nu3,1u3,2⋮u3,n.
Then the probability of subsystemi in the jth year is(6)ti,j=ui,j∑jui,j,∀i,j.Step 4.
Repeat Step2 and calculate the weight of subsystem i for the jth time period using the entropy weight method. Form the normalization matrix R=ri,jm×n,(7)ri,j=ui,jmax−ui,jui,jmax−ui,jmin,∀i,j.
Calculate the entropy weightϖi by the entropy value of subsystem i:(8)ϖi=1−eim−∑i=1mei,∀i.Step 5.
Use the TOPSIS method to solve the comprehensive evaluation indexCj of the urban rail transit system in the jth year, first calculating the weighting matrixO=oi,jm×n:(9)oi,j=ϖi×ri,j,∀i,j.
Determine optimalSi+ and inferior solutions Si− for the weighted value of subsystem i:(10)Si+=maxoi,1,oi,2,oi,3,…,oi,n,∀i,Si−=minoi,1,oi,2,oi,3,…,oi,n,∀i.
Calculate the Euclidean distance between the weighted value for thejth year and the optimal and inferior solutions:(11)sepj+=∑i=1mSi+−oi,j2,∀j,sepj−=∑i=1mSi−−oi,j2,∀j.
Calculate the overall evaluation indexCj=sepj−/sepj++sepj−,∀j,Cj∈0,1 of urban rail transit systems for the jth year:(12)Cj=sepj−sepj++sepj−,∀j,Cj∈0,1.Step 6.
Calculate couplingBj of multiple factors in thejth year. The smaller the deviation between the single factors, the greater the coupling among the factors. Calculate deviation Bv by selecting the formula corresponding to the number of subsystems to be coupled:(13)Bv=Si⋅M∑ti,j×21−∑ti′,j×ti,jM∑ti,j/M2,where Si is the standard deviation of accidents caused by a single factor; M is the number of coupled subsystems to be calculated, 2≤M≤5,M∈N+, let B′=M∑ti′,j×ti,j/∑ti,j2 , ti′,j×ti,j is the product of the probability of two coupled subsystems, and the larger B′, the smaller the deviation. The index is mainly used to evaluate the annual risk coupling strength between the subsystems of urban rail transit coupling model, and at the same time the evaluation results are given to propose decoupling measures. The coupling degree of multifactor risk coupling is calculated by the following formula:(14)Bj=M∑ti′,j×ti,j∑ti,j2M,∀j.Step 7.
Calculate the comprehensive coordination indexVj of probability in the jth year; this index is mainly used to evaluate the orderly and disorderly development of urban rail transit system every year. The more orderly the system develops, the more likely it will lead to safety accidents.(15)Vj=∑i=1mti,j×ϖi∑j=1n∑i=1mti,j×ϖi,∀j.Step 8.
Calculate the coupling coordination degreeKj of the urban rail transit system in the jth year. This indicator comprehensively considers the characteristics of coupling degree and coordination degree and is mainly used to evaluate the annual coupling strength and orderly and disorderly development between subsystems of urban rail transit coupling model. At the same time, the decoupling method is proposed based on the evaluation results.(16)Kj=Bj×Vj,∀j.
The flow chart of the model is shown in Figure1.Figure 1
Entropy-TOPSIS-coupling coordination model flow chart.


## 4. Case Study

Using year as the statistical time period, the panel data of three variables of regional economy (E), social resources (S), and urban rail transit (T) in Shanghai from 2000 to 2016 are counted; the results are shown in Table 2 (see Appendix).Table 2
Initial data on regional economy, social resources, and urban rail transportation in Shanghai, 2000–2016.
YearRegional economySocial resourcesRail transitTotal GDP (E1)Investment in urban infrastructure (E2)Investment in traffic service (E3)Population density along the rail (E4)Number of hospital beds (S1)Number of park visitors (S2)Number of mall patrons (S3)Total number of jobs along the rail (S4)Total number of students enrolled along the rail (S5)Building area of houses along the rail (S6)Urban rail mileage (T1)Daily average flow of rail transit (T2)Peak hourly cross-sectional flow (T3)Rail Transit Share (T4)YearHundred millionHundred millionHundred millionPersons/kmPersonTen thousandPersonTen thousandTen thousandhm2kmMillion passengers/dayPassengers/h%20004771.17449.948.831575.131100.9333.037425303690195.6426.01891762.924262329.620015210.12510.7860.721594.7931141.0983.378192410220202.3826.411147062.92806912720025741.03583.4963.011627.9991162.363.481151470640224.127.01251279062.929875808.820036694.23604.62273.771945.1521183.3714.681288693240240.1327.61514123108.6511180801020048072.83672.58316.962262.3051292.2546.586164759972.3244.8328.217516729121.2313183921120059164.1885.74385.582579.3961492.0246.119151841110290.5328.8218333147.8163886122.5200610366.371125.54589.522699.2951515.0096.392849935715308.5729.422519588169.4180894815200712188.851466.33840.462793.6561557.7488.0241641068480355.0730.02521217234223902618200814275.81733.18838.912786.731451.26710.252471210483374.5730.627521920264.3308.21974522.5200915285.582113.45978.242880.2251775.84610.40956177585537431.2324819355.053611026832201017433.211497.46754.663606.4192015.14112.082822071563377.813229188452.575161105631.8201119533.841157.34595.753702.5112128.82910.624552121537384.3832.8229634454.15761127434.5201220553.521038.61473.433759.09235011.229732364330390.04233.96287735106221191037201322257.661043.31458.73817.8332489.73111.055782509020465.7435.4530277528.96871250138.8201424060.871057.25422.483836.3842566.66711.745012690280452.1136.02317955777751284243201525643.471425.08759.233824.6352751.3211.145752839740438.9436.02332305888411295646.2201628178.651551.87883.813830.8813078.6768.8870143140250440.1936.38354366179291304151http://jtw.sh.gov.cn/jttj/index.html;http://tjj.sh.gov.cn/tjnj/20170629/0014-1000339.html.The statistical results of Table2 show that the economic development of the region is rapid and the investment in infrastructure and transport facilities is increasing, and the growth is increasing over time; in addition, the population density is increasing year by year; the number of times or the number of people using social resources is increasing rapidly; the flow of rail transport resources, the sharing rate, and other characteristic values are also increasing every year.Table3 shows the two-factor and three-factor risk coupling degree; the results show that the coupling degree of E-S and E-T, regional economic and social resources, is larger in the two factors, while the coupling degree of S-T, that is, social resources and rail transit, is small, indicating that regional economic and social resources are easy to cause accidents.Table 3
Results of two-factor and three-factor risk coupling calculations.
YearE-SE-TS-TE-S-T20000.7068482660.7070452250.4776537440.27836350420010.7068402720.7070804230.4769846360.27756383420020.7068660930.7071035810.4758699730.27682527420030.7068866420.7071035550.475702980.27564620420040.7069913120.7071063120.4743701090.27478414420050.7070560310.7071045430.4728563080.27378456520060.7070951620.7071062710.4721083880.2730155920070.7071025990.7071067360.4709175140.27188117220080.7070575350.7070974840.4687297860.27032116820090.70710.7071030570.4712171560.26836808220100.7070906750.7071067590.4702967680.2664582520110.7070301810.707105170.4687240520.26560011720120.7070537560.7071015450.468857660.26437949720130.7069931270.7070856980.4673403770.26303582420140.7069206860.7070829750.4664510610.26173155220150.7067438030.7070938510.4652772970.26048634420160.7065422670.7071066080.4649406130.25872955Table3 shows the two-factor and three-factor risk coupling; its results show that the coupling in E-S as well as E-T, that is, regional economy and social resources, is larger in the two-factor risk, while the coupling in S-T, that is, social resources and rail transportation, is smaller, indicating that both, that is, regional economy and social resources, are prone to accidents.Using (15) to calculate the integrated coordination of urban rail transit coupled system in Shanghai from 2000 to 2016, as shown in Table 4, the integrated system coordination maintains a slowly decreasing trend, indicating that the Shanghai urban rail transit system gradually develops from a disorderly state to an orderly state, and the probability of accidents gradually decreases. This is analyzed because the rapid development of Shanghai brings favorable conditions for the improvement of the safety condition of Shanghai's rail transit system.Table 4
Integrated coordination of urban rail transit coupled systems, 2000–2016.
YearOverall coordination value20000.06431949920010.06391172720020.06357829320030.0627652820040.06221922320050.06164666520060.06108393720070.06028525220080.05942730720090.05789930120100.05677115120110.05629373420120.05556061520130.05483576420140.05405297220150.05326874620160.052080534The coordination degrees between the two-factor and three-factor risk coupling were measured separately using the evaluation model proposed in Part 2, and the degree of coordination of their evolution toward the common system goal (risk) was further analyzed and evaluated objectively, as shown in Table5. From Table 5, it can be seen that the two-factor and three-factor risk coupling coordination degrees maintain a steady decreasing trend, which represents a low degree of interaction and synergistic evolution among the factors and a low possibility of risk occurrence in the system. Meanwhile, Table 5 shows that the coupling coordinations of the two-factor E-S as well as E-T, that is regional economy and social resources and regional economy and rail transit, are both larger, while the risk coupling coordination of S-T, that is, social resources and rail transit, is smaller, indicating that both, that is, regional economy and social resources and regional economy and rail transit, are prone to accidents. E-S-T, that is, the smallest risk coupling coordination among the three factors of regional economy, social resources, and rail transportation, indicates that this scenario is the least likely to lead to accidents.Table 5
Results of two-factor and three-factor risk coupling coordination.
YearE-SE-TS-TE-S-T20000.0454641260.0454767940.0307224490.01790420120010.0451753820.0451907310.0304849120.01773958420020.044941340.0449564390.0302550010.01760007820030.0443679380.0443815530.0298576310.01730101120040.043988450.0439956050.029514940.01709685620050.0435876460.0435906370.0291500140.01687790520060.0431921560.0431928350.0288382390.01667686720070.0426278590.0426281080.0283893810.01639042520080.0420185250.0420208990.0278553490.01606445920090.0409405960.0409407730.0272831440.01553832420100.0401423510.0401432640.0266992890.01512714220110.0398013690.039805590.0263862270.01495162220120.0392843410.0392869970.026050020.01468908720130.0387685080.0387735850.0256269670.0144237720140.0382111640.0382199360.0252130660.01414736820150.0376473560.0376660030.0247847380.01387578120160.0367970980.036826490.0242143550.013474773Table6 shows the annual comprehensive risk index of urban rail transit coupling system based on TOPSIS; the higher the value, the safer the system. The results show that the Shanghai urban rail transit system was the least safe in 2000, and the safety factor of the coupled urban rail transit system is increasing year by year after 2000; that is, the system was gradually safe after 2000.Table 6
Combined risk index and ranking of urban rail transit coupled systems, 2000–2016.
YearTOPSIS valueSorted200001720010.0322911351620020.0555274551520030.1229511411420040.1641843981320050.2085339611220060.2559513771120070.3231014961020080.3892544920090.521650975820100.612688027720110.65000222620120.709916021520130.766845372420140.830907081320150.8969989252201611In the end, the range of the evaluation value obtained by the entropy-TOPSIS-coupling coordination model is 1 and the coefficient of variation is 0.718. The larger the range and coefficient of variation, the greater the dispersion and the higher the degree of discrimination of the evaluation value, where the range reaches the maximum. Therefore, the comprehensive evaluation value of the system obtained by the entropy-TOPSIS-coupling coordination model evaluation method is more beneficial to visually assess the level of urban rail transit risk evaluation.


## 5. Conclusion

(1)
This paper proposes an entropy-TOPSIS-coupling coordination model for urban rail transit by combining the entropy weight method, TOPSIS method, and coupling coordination model. The simulation results show that the risk of urban rail transit system can be reasonably evaluated based on this model, and the conclusions obtained are more in line with the actual situation.(2)
The following results can be obtained from the relevant data of Shanghai from 2000 to 2016: compared with other factors, regional economic and social resources are more likely to cause accidents, so managers need to focus on these two factors for reasonable control.(3)
From Table5, it can be seen that the E-T two-factor coupling coordination degree is the highest in the factor coupling calculation, so managers should try to avoid the coupling condition of regional economic indicators and rail transit indicators.(4)
From Table6, it can be seen that the safety factor of urban rail transit coupling system is increasing year by year, gradually developing from disorderly state to orderly state, and the risk is in a gradually increasing situation. Therefore, relevant government departments should pay attention to the urban rail transit problem and increase the strength of urban rail transit safety construction.Subsequent improvements to the system can be carried out by decoupling methods, and theoretical approaches and practical implementation schemes to decoupling methods for urban rail transit systems should be studied in depth in the future.



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