Evaluation of Flooding Disaster Risks for Subway Stations Based on the PSR Cloud Model

Abstract

This study aims to scientifically evaluate the risk of rainstorm waterlogging disasters in urban subway stations, improve the management of disaster prevention and control, and mitigate the impact of such disasters. To achieve this, a risk assessment analysis was conducted using the Pressure-State-Response (PSR) cloud model. The analysis involved examining the components of the subway station rainstorm waterlogging disaster system, including the disaster-prone environment, disaster-affected body, and disaster-causing factors. Based on the PSR framework, a risk assessment index system for rainstorm waterlogging disasters in subway stations was developed. The entropy weight method and cloud model algorithm were then combined to establish a risk assessment method. By utilizing a cloud generator, the digital characteristics of the risk cloud were calculated, and a risk cloud map was generated to determine the level of risk. Finally, an empirical analysis was carried out at Jin’anqiao Station of the Beijing Subway, providing valuable insights for the evaluation of rainstorm waterlogging disasters in subway stations.

1. Introduction

Extreme heavy rainfall is one of the most common and disaster-prone natural disasters in the context of global climate change [1]. Climate change has increased the frequency and intensity of extreme rainfall. Additionally, rapid urbanization and development processes have further exacerbated the risk of flooding, threatening global urban development and the safety of residents’ lives and property [2]. In low-lying areas, heavy or persistent rainfall leads to the inundation of buildings on the ground and underground infrastructure [3]. Due to their rapid onset, wide range of impacts, and high frequency of recurrence, heavy rainfall disasters cause serious casualties and economic losses globally [4,5]. Consequently, research on urban flooding has gained significant interest among experts and scholars, with a noticeable growth in the citation frequency of the related literature. Notably, cities may not be fully aware of the flooding hazards that their subway systems are vulnerable to [6]. The “7.20” heavy rainstorm disaster in Zhengzhou’s subway system served as a painful lesson, further drawing people’s attention to the risks of subway flooding disasters.

The subway system has become an increasingly important element for sustainable urban development due to its large capacity, energy efficiency, environmental friendliness, and high level of safety. Furthermore, with accelerated urbanization and the continual growth of urban populations, the significance of the subway system in urban construction has greatly increased. However, being an underground infrastructure [7], the subway is susceptible to the issue of flooding during heavy rainfall, especially in low-lying areas where water cannot be promptly drained from nearby locations, leading to its entry into subway stations through the entrances. In such cases, stagnant water within the station cannot be easily discharged into the city’s pipe network if solely relying on the weight of the water flow. If the flow of water is substantial or if the drainage system fails, effective pumping becomes difficult, resulting in a rapid rise in water levels and the occurrence of large-scale flooding, further exacerbating the challenges of evacuation and rescue efforts during emergencies. Given the relatively limited construction area and the significant number of people it transports, the subway system is considered a high-risk target for flooding [8]. Instances of subway systems around the world being forced to suspend operations due to heavy rainfall are numerous and have had significant consequences. For example, on 22 May 2020, heavy rainfall in Guangzhou led to flooding at multiple stations on Metro Line 13. Similarly, on 18 July 2021, heavy rainfall in Beijing caused flooding at Jin’anqiao Metro Station. Moreover, on 21 July 2021, continuous heavy rainfall in Zhengzhou resulted in flooding on Line 5, leading to the loss of 14 lives. International cities have also experienced flooding incidents, such as a sudden rainstorm in London on 25 July 2021, which caused flooding on several subway lines. Subsequent examples include the flooding of the subway station hall at Shenzhou Road Station on Line 21 in Guangzhou during a sudden rainstorm on 30 July 2021 and the flooding of several subway tunnels in New York due to torrential rain from Hurricane Ida on 1 September 2021. Undoubtedly, metropolitan subway systems face a high risk of flooding during heavy rainfall events.

Implementing the concept of waterlogging risk management and conducting rainstorm waterlogging disaster risk assessments are crucial steps in urban disaster prevention and mitigation. As the subway system continues to expand rapidly and extreme weather events become more frequent, assessing the risk of rainstorm waterlogging in major cities’ subway systems has become an urgent challenge. In order to effectively prevent the risk of rainstorm waterlogging and ensure the safety of the subway system, it is essential to employ scientific methods that can objectively evaluate the disaster risk status of the subway system [9].

This study proposes a PSR cloud model for evaluating the disaster risk associated with heavy rain and flooding in subway stations. The research begins by utilizing the disaster risk theory and the PSR theoretical framework to establish an index system based on the following three dimensions: pressure, state, and response. The index system is then used to construct a cloud model for evaluating the disaster risk of heavy rainfall and flooding in subway stations. To demonstrate the practical application of this model, a case study of the Jin’anqiao subway station in Beijing, China, was conducted. This study is organized as follows: Section 2 provides an overview of relevant studies in the field. In Section 3, the methodology of the PSR cloud model is explained in detail. Section 4 presents the findings of a case study conducted to validate the effectiveness and applicability of the proposed methodology. Finally, Section 5 concludes the study and outlines potential future research directions.

2. Literature Review

Indeed, the study of flood hazards affecting metro systems is still a developing field, and relatively few studies have been conducted in this area [8]. However, existing studies have focused on the risk assessment of stormwater flooding hazards in metro systems using the following two main approaches: the simulation approach and the multi-criteria analysis (MCA) approach.

Simulation methods are commonly used to assess the risk of flooding disasters in subway systems. These methods involve the use of topographic information and drainage system data to establish mathematical models that can consider various factors and perform sensitivity analysis. There are two main types of simulation methods used in subway system flood analysis: physical modeling and statistical modeling. In physical modeling, researchers utilize hydrodynamic models to simulate flooding scenarios. For example, Edwar Forero-Ortiz [6] employed a 1D/2D hydrodynamic model, Zhiyu Lin [10] developed a 3D numerical simulation model based on the VOF (Volume of Fluid) model, Colombo [11] used a stochastic model that transformed a 3D numerical model, and Lyu [12] combined the stormwater management model SWMM (Storm Water Management Model) with the GIS (Geographic Information System) to simulate flood hazards in metro systems. On the other hand, statistical modeling approaches involve analyzing data and performing simulations based on statistical analysis. For instance, some scholars use weather warning signals and passenger flow elasticity curves [13], census and metro smart card data [14], and sequence-probability matrices [15] to perform statistical analysis and then conduct simulation studies. However, simulation-based approaches require a large amount of data and computational resources, which can be costly.

The MCA (multi-criteria analysis) method offers a comprehensive approach to assessing the risk of metro systems by considering and quantifying various evaluation criteria. This method integrates different factors and provides an objective assessment by assigning weights to different criteria. In recent years, scholars have utilized and improved various MCA methods for flood risk assessment in metro systems. For example, YU et al. [16] constructed an AHP (Analytic Hierarchy Process) fuzzy comprehensive evaluation model to assess the flood risk of metro stations using the combined assignment method. Lyu et al. [17] used the interval FAHP-FCA (fuzzy comprehensive assessment) method to assess the flood risk of metro systems in subsidence environments. Wang G P et al. [2,18] successively proposed the fuzzy hierarchy analysis (FAHP) and Geographic Information System (GIS) combined method, as well as the improved Trapezoidal Fuzzy Hierarchy Analysis (TF-AHP) method to assess the flood risk of subway systems. Wu H et al. [19]. Based on linguistic intuitionistic fuzzy sets and TOPSIS, the decision making of an emergency plan for waterlogging disasters in subway station engineering was studied. Many scholars have proposed more comprehensive flood risk assessment methods based on AHP and TOPSIS, which offer practical decision making significance. However, these methods also have limitations, such as subjectivity, data incompleteness, and the determination of weights, which require specialized knowledge and experience for support.

In summary, the simulation approach and the multi-criteria analysis (MCA) approach have their own strengths and weaknesses. However, they also share common shortcomings, including data uncertainty, subjectivity, and limitations in real-time and complex parameter selection. To enhance the accuracy and credibility of risk assessments, it is necessary to combine these methods with other approaches and tools for a comprehensive assessment.

It is worth noting that recent studies have shown a strong interest in using learning techniques to predict disasters [20]. For example, Cheng et al. [21] developed efficient parameter-flexible fire prediction algorithms by integrating machine-learning algorithms and parameter tuning through forward and inverse modeling. Zhong et al. [22] also utilized JULES-INFERNO-based digital twin fire models with ROM techniques and deep-learning prediction networks to achieve more accurate fire prediction. Junwu Wang et al. [23,24] used the projection-seeking method and particle swarm algorithm for evaluation and developed an emergency response input-efficacy system dynamics model for simulation optimization. Bai Lian and Liu Ping [25] employed the Random Forest-Recursive Feature Elimination (RF-RFE) algorithm combined with a DNN neural network model for flood hazard prediction in subway stations. LIU [26] conducted a vulnerability evaluation of flood hazards in subway station engineering based on a projection tracing model, among other studies. In conclusion, with the continuous development and application of machine-learning technology, we can anticipate significant breakthroughs and progress in predicting heavy rainfall and flooding disasters. These advancements could provide more effective means to reduce disaster losses and protect people’s lives and properties.

Among the existing research methods, neural network models, Bayesian network models, and particle swarm optimization are prediction and evaluation models that require a large number of training samples. However, these models do not possess a distinct advantage in addressing the randomness and fuzziness associated with the risk assessment of rainstorm waterlogging disasters. While the Analytic Hierarchy Process (AHP) fuzzy comprehensive evaluation considers the fuzzy nature of the problem, it fails to account for randomness in the risk assessment of rainstorm waterlogging disasters in subway stations. To address this limitation, this study proposes the utilization of the cloud model and risk cloud map to analyze the risk of rainstorm waterlogging disasters. The cloud model is capable of mapping fuzziness and randomness, enabling the conversion between qualitative language and quantitative values. This approach has been successfully applied in various domains, including a rail transit operation safety evaluation [27], fire risk evaluation [28], water conveyance capacity evaluation [29], ecological safety [30], construction site stability [31], engineering safety risk evaluation [32], and lining construction quality evaluation [33]. By employing the cloud model, this study aims to transform abstract qualitative risk concepts into concrete quantitative values, thereby enhancing the accuracy and comparability of risk assessments and facilitating a better understanding and management of risks by decision makers.

Scholars often face challenges when constructing flood disaster index systems due to a lack of theoretical foundation and weak systematicity. These systems are often developed solely based on questionnaires, expert interviews, an analysis of the literature, and actual case selection. For example, He et al. [34] established an index system that considers the influencing factors of risk, exposure, and vulnerability. Building upon this foundation, Tu et al. [35] incorporated rescue into the criterion system and utilized the SMAA-2-FFS-H method to validate the evaluation framework using real-life cases. The selection of indices can be broadly categorized into disaster-causing factors, disaster-prone environments, and disaster-affected entities. For instance, some studies have constructed index systems for subway flood disasters based on flood factors, personnel, facilities, and emergency response [36]. Other studies have developed evaluation index systems based on natural factors surrounding the environment and flood control capacity [37]. Additionally, some studies have constructed subway flood disaster accident trees based on the unsafe behaviors of personnel, unsafe subway, and environmental conditions, and management deficiencies [38]. Furthermore, other studies have taken a broader approach by constructing index systems that include multiple dimensions such as people, equipment, the environment, safety management, and emergency responses [39,40]. Furthermore, indicators are selected from the following four aspects: flood disaster risk, sensitivity, vulnerability, and disaster prevention and mitigation ability [41].

This study aims to analyze the rainstorm waterlogging disaster in subway stations from the perspective of disaster risk. Utilizing the Pressure-State-Response (PSR) theory, this research examines the waterlogging disaster system in subway stations, which consists of the disaster-prone environment, the vulnerable elements, and the factors contributing to the disaster. The PSR model is widely employed in ecological security research [42], including the assessment of ecological environmental impacts in the Yellow River source region [43], risks associated with mining groundwater [44], the evaluation of wetland ecological health [45], the urban spatial ecosystem health status [46], the resilience of rural ecosystems [47], and the assessment of sustainable water use [48]. As the understanding of disaster risks has deepened, the PSR model has also been applied in various disaster risk assessments, such as flood risk assessment [49] and the vulnerability assessment of rainstorm waterlogging [50]. Therefore, this study adopts the PSR framework to establish an index system encompassing the aspects of pressure, state, and response.

3. Research Methodology

This study proposes a method for evaluating the risk of storm flood disasters in subway stations by combining the entropy weight method and cloud modeling algorithm.

The first step involves establishing an evaluation index system. Based on the theory of disaster risk, the subway station rainstorm flooding disaster system was analyzed, including the disaster-bearing environment, disaster-bearing body, and disaster-causing factors. The Pressure-State-Response (PSR) model was used to construct the evaluation index system. In this model, the risk of disaster-causing factors measures the degree and potential threat of external factors that trigger disasters. In the PSR model, pressure indicators are used to describe the external factors that trigger a disaster, so the degree of pressure can be measured using the risk of disaster-causing factors. The vulnerability of the disaster-bearing body describes the resistance and adaptive capacity of the disaster system. In the PSR model, state indicators are used to describe the internal state prior to a disaster, so the degree of state can be measured using the vulnerability of the disaster-bearing body. The sensitivity of the disaster-conceiving environment describes the post-disaster recovery and coping capacity. In the PSR model, response indicators are used to describe the capacity for response after a disaster, and thus, the degree of response can be measured using the sensitivity of the disaster-conceiving environment. By incorporating these concepts into the model, a comprehensive assessment of the disaster risk can be achieved.

The next step was to identify the criteria cloud. These indicators were classified into hierarchical criteria, and the standard cloud digital features were calculated. The forward cloud generator was used to generate the standard cloud map. Then, the risk evaluation cloud was determined. The inverse cloud generator was utilized to calculate the cloud digital features of each indicator’s risk cloud. The entropy weight method was applied to determine the weight of each indicator, and the weights were used to calculate the comprehensive evaluation of cloud digital features. The forward cloud generator was then used to generate the comprehensive risk evaluation cloud diagram. By comparing the comprehensive evaluation cloud map with the standard cloud map, the risk level could be determined based on its closeness.

Finally, an empirical analysis was conducted using the Beijing Metro Jin’anqiao Station. The proposed method was applied to assess the storm flood disaster risk of the subway station. We evaluated this risk level based on the generated comprehensive risk evaluation cloud diagram and compared it with the standard cloud map. The empirical analysis of the Beijing Metro Jin’anqiao Station demonstrates the practical application of the proposed method (Figure 1).

3.1. Constructing an Indicator System Based on PSR

The PSR model is used to establish the risk assessment framework for waterlogging disasters in subway stations. The Pressure (P) aspect refers to the risk pressure that the disaster risk receptor faces due to various disaster-causing factors. In the context of this study, the risk pressure of rainstorm waterlogging disasters in subway stations includes factors such as the frequency, duration, and intensity of rainstorms, as well as unfavorable geological conditions and surrounding environmental factors around the subway station. The State (S) aspect represents the condition of the disaster risk receptor and the disaster-bearing environment, which is primarily influenced by the vulnerability of the disaster-bearing bodies. In this study, the focus was on the water retention capacity and drainage capacity of subway stations, including factors such as the height of water retention walls, the drainage capacity coefficients of drainage ditches, and the density of the drainage pipe network. The Response (R) aspect refers to the countermeasures taken in response to the pressure of disaster risk. This study primarily considers pre-disaster flood prevention and early warning and emergency rescue measures, including the preparation and practice of flood prevention emergency plans, traffic management, and coordination, and the allocation of material reserves.

The risk assessment index system for rainstorm waterlogging disasters in subway stations was developed, comprising the following three layers: the target layer, criterion layer, and index layer. The target layer focuses on the overall risk of rainstorm waterlogging disasters in subway stations. The criterion layer primarily considers the PSR framework, while the index layer consists of specific characteristics related to the risk of rainstorm waterlogging disasters in subway stations. The construction of the index system is based on the relevant literature and is presented in

Table 1. Disaster risk assessment indicator system.

Valuation Indicators		Very Low-Risk Level I [0, 2]	Low Risk Level II (2, 4]	Medium Risk Level III (4, 6]	High Risk Level IV (6, 8]	Very HighRisk Level V (8, 10]
A1	A11 Rainstorm frequency/event [23]	[0, 2)	[2, 4)	[4, 5)	[5, 7)	[7, 26]
	A12 Rainstorm duration/h [50]	[0, 1)	[1, 1.5)	[1.5, 3)	[3, 8)	[8, 10]
	A13 24 h maximum rainfall/mm [23]	[0, 50)	[25, 50)	[50, 100)	[100, 200)	[200, 2000)
	A14 Adverse geological conditions [23]	Not have	Lesser	General	More	Much
	A15 Adverse neighborhood elements [23]	Not have	Lesser	General	More	Much
	A16 Runoff coefficient [23]	[0.1, 0.2)	[0.2, 0.3)	[0.3, 0.45)	[0.45, 0.6)	[0.6, 0.85]
A2	A21 Retaining wall height/m [23]	[1.5, 3.0]	[1.0, 1.5)	[0.5, 1.0)	[0.3, 0.5)	[0, 0.3)
	A22 Flood control barrier height/m [51]	[1.5, 1.8)	[1.2, 1.5)	[1.0, 1.2)	[0.8, 1.0)	[0.5, 0.8)
	A23 Terrain around entrances and exits [38]	Higher	High	General	Low	Lower
	A24 Drainage capacity factor for drains [23]	[1.5, 100]	[1.25, 1.5)	[1.0, 1.25)	[0.75, 1]	[0, 0.75)
	A25 Drainage network density/(km·km−2) [23]	[3.17, 10]	[2.78, 3.17)	[2.39, 2.78)	[2, 2.39)	[0, 2)
	A26 Standing water detection alarm system [50]	Very sensitive	Sensitive	General	Insensitive	Defunct
	A27 Surveillance equipment [24]	Very complete	Complete	General	Incomplete	Not have
A3	A31 Number of safety inspections (times/month) [23]	[8, 30]	[6, 8)	[4, 6)	[1, 4)	[0, 1)
	A32 Flood control emergency preparedness [23]	Vigorous	Strong	General	Weaker	Weak
	A33 Flood emergency drills (times/month) [23]	[4, 12]	[3, 4)	[2, 3)	[1, 2)	[0, 1)
	A34 Timeliness and accuracy of flood information [24]	Very complete	Complete	General	Incomplete	Not have
	A35 Proportion of professional rescuers/% [23]	[30, 100]	[20, 30)	[10, 20)	[5, 10)	[0, 5)
	A36 Traveling command and dispatch level [24]	Excellent	Good	General	Poor	Worse
	A37 Stockpiling of rescue materials [23]	Very complete	Complete	General	Incomplete	Not have

.

3.2. Defining the Standard Cloud

3.2.1. Cloud Digital Features and Cloud Diagrams

A cloud consists of a number of cloud droplets, each of which is a point in the space of a number of fields to which this qualitative concept is mapped. Let $U$ be a quantitative domain expressed in terms of exact numerical values and $C$ be a qualitative concept on $U$. If the value $x\in U$ and $X$ is a one-time random realization of the qualitative concept $C$, and the degree of certainty (degree of affiliation) of $X$ with respect to $C$ is a random number $\mu C(x)\in [0,1]$, then the distribution of $X$ over domain $U$ is called a cloud, and $x$ is called a cloud droplet $(x,\mu C(x))$, and the cloud droplets converge to a cloud diagram.

The cloud uses numerical features to reflect the quantitative characteristics of qualitative concepts. The cloud numerical features $(E_x,E_n,H_e)$ of the cloud model include $E_x$(expected Value), $E_n$ (entropy), and $H_e$ (hyper entropy). $E_x$ is the central or standard value, which is the cloud drop that best represents that qualitative concept; $E_n$ is ambiguity; and $H_e$ is the randomness and discrete nature.

3.2.2. Computing Standards Cloud Digital Features

The standard cloud is the baseline reference for risk evaluation, and there are bilateral constraints on the rubric $\left[Z_{min}{Z}_{max}\right]$ that are derived from the numerical characteristics of the standard cloud using the following equation.

$$\overline{E_x}=\frac{Z_{min}+Z_{max}}{2}$$

(1)

$$\overline{E_n}=\frac{Z_{max}-Z_{min}}{6}$$

(2)

$$\overline{H_e}=C$$

(3)

where $C$ is a constant, which is specifically adjusted according to the fuzziness of the rubric itself. In this study, it was taken as 0.1. Based on the rating criteria in Table 1, the standard cloud numerical characteristics are calculated, as shown in

Table 2. Digital characteristics of the standard cloud.

Level	Interval	Standard Cloud Digital Features	Description
Level I	[0, 2]	(1, 0.33, 0.1)	Very low risk
Level II	(2, 4]	(3, 0.33, 0.1)	Low risk
Level III	(4, 6]	(5, 0.33, 0.1)	Medium risk
Level IV	(6, 8]	(7, 0.33, 0.1)	High risk
Level V	(8, 10]	(9, 0.33, 0.1)	Very high risk

.

3.2.3. Generate a Standard Cloud Map

A forward cloud generator is used to generate cloud maps. The algorithm is as follows:

• Generate a normal random number with $E_n$ as the expected value and $H_e^2$ as the variance, denoted $E_n{}^{\prime }~N(E_n,H_e^2)$;
• Generate a normal random number X with $E_x$ as the expected value and $E_n{{}^{\prime }}^2$ as the variance, denoted as $X~N(E_x,E_n^2)$;
• Calculate the affiliation of a cloud droplet $\mu (x)=e^{-\left[\frac{-{(x-E_x)}^2}{2{(E_n)}^2}\right]}$;
• Generate $(x,\mu (x))$ as a cloud droplet in the domain of the theory;
• Repeat steps 1 to 4 until the desired number of cloud droplets are generated.

The standard cloud diagram generated using the forward cloud generator MATLAB programming is shown in Figure 2.

The cloud model is a useful tool for displaying different risk levels and their ranges. It achieves this by utilizing the digital eigenvalues of the cloud model. These eigenvalues represent various risk levels, such as Level I (extremely low risk), Level II (low risk), Level III (medium risk), Level IV (high risk), and Level V (extremely high risk). In practical applications, the measured data of different evaluation indicators can be used to generate a comprehensive evaluation cloud map for the entire evaluation object’s risk. This cloud map provides a visual representation of the risk distribution. To determine the risk level of the evaluation object, the comprehensive evaluation cloud map can be compared with the standard cloud model’s comprehensive evaluation cloud map. By analyzing the similarities and differences between these two maps, the risk level of the evaluation object can be determined. This comparison helps understand the level of risk associated with the evaluated object and enables appropriate risk management strategies to be implemented.

3.3. Identify the Evaluation Cloud

3.3.1. Calculate Metrics to Evaluate Cloud Digital Features

Evaluating the numerical characteristics of the cloud can be computed using an inverse cloud generator. The steps are as follows:

• Calculate the mean $E_x$:

  $$E_x=\overline{x}=\frac{1}{n}{\displaystyle \sum _{i=1}^n{x}_i}$$

  (4)
• Calculate the variance $S^2$:

  $$S^2=\frac{1}{n-1}{\displaystyle \sum _{i=1}^n{(x_i-\overline{x})}^2}$$

  (5)
• Calculate entropy:

  $$E_n=\sqrt{\frac{\pi }{2}}\times \frac{1}{n}{\displaystyle \sum _{i=1}^n\left|x_i-\overline{X}\right|}$$

  (6)
• Calculate hyper entropy:

  $$H_e=\sqrt{S^2-E_n^2}$$

  (7)
• Output cloud digital features $(E_x,E_n,H_e)$.

3.3.2. Determine the Entropy Weight of the Metric Information

$$e_j=-k{\displaystyle \sum _{i=1}^n{p}_{ij}}\ln (p_{ij})$$

(8)

$$k=\frac{1}{\ln (n)}$$

(9)

$e_j$ denotes the information entropy value of the i-th information indicator; $k$ is a random coefficient related to the number of indicators $n$; $p_i$ denotes the value after standardizing the i-th indicator, and if $p_i$ is 0, it is defined $\ln p_i=0$.

According to the size of the information entropy of different indicators, its weight performance can be obtained, which is the entropy weight size. It can be expressed as follows:

$$w_j=\frac{1-e_j}{n-{\displaystyle \sum _{i=1}^n{e}_j}}$$

(10)

3.3.3. Determine the Weighted Evaluation of Cloud Digital Characteristics

By weighted aggregation, comprehensive cloud digital features can be obtained for evaluation.

$$F=(w_1,w_2,\dots ,w_n)\left[\begin{array}{ccccc}& E_{x_1}& E_{n_1}& h_{e_1}& \\ & .& .& .& \\ & .& .& .& \\ & .& .& .& \\ & E_{x_n}& E_{n_n}& h_{e_n}& \end{array}\right]=(E_x{}^{\prime },E_n{}^{\prime },H_e{}^{\prime })$$

(11)

The formula $(w_1,w_2,\dots ,w_n)$ is the weight $w_j$ determined using the entropy weighting method.

3.3.4. Generate an Evaluation Cloud Map

Evaluation cloud plots are generated by forward cloud generator MATLAB programming.

3.4. Compare the Cloud Graph Judgment Results

The risk evaluation cloud map can be compared with the standard cloud map to determine the risk status. In order to avoid the problem that visual discrimination may not be precise enough, closeness is introduced to determine the risk status.

$$T=\frac{1}{\left|E_x-\overline{E_x}\right|}$$

(12)

In the formula, T is the closeness and $\overline{E_x}$ is the expectation of the standard cloud.

4. Case Analysis

4.1. Introduction to the Study Object

The Beijing Metro Jin’anqiao Station serves as the western terminus of Line 6 and functions as a three-line interchange station for Beijing Metro Line S1, Line 11, and Line 6. The station has a total of eight entrances and exits, namely A, B, C, D, E, F, H, J, and K. The name “Jin’anqiao” refers to four locations in close proximity: Jin’anqiao on the Fushilu Viaduct, Jin’anqiao on the S1 railroad, Jin’anqiao on the railroad, and Jin’anqiao Station on the subway. Notably, Jin’anqiao acts as an intersection that connects five roads, making it a unique location. The Fushilu-elevated viaduct runs east–west above Jin’anqiao. To the south of Jin’an Bridge lies Beixing’an Road, a newly constructed two-way, three-lane urban arterial road. It connects to Shijingshan Road (the Chang’an Street extension) in the east–west direction. On the north side of Jin’an Bridge is Jindingxi Street, which gradually curves northwest to connect with Shimen Road. Located to the east of Jin’an Bridge is Jinding South Road, which links Apple Park South Road and Fushilu Road. To the west of Jin’an Bridge is Guangning Road, extending northwest toward the Fushilu Viaduct and Shuangyu Bridge. To the southwest of Jin’an Bridge is the Shougang Industrial Ruins Park. This area experiences warm temperate conditions with a semi-arid and semi-humid continental monsoon climate. Rainfall is unevenly distributed throughout the year, with fewer rainy days but high-intensity rainfall when it does occur. Localized heavy rainfall events are frequent, with a short duration but high intensity. The spatial distribution of rainfall is also uneven in this area.

The Jinanqiao subway station area is surrounded by natural low-lying terrain, particularly Exit B and Exit C of the subway station. This topography makes the surrounding roads susceptible to waterlogging. Jinanqiao itself is a depressed overpass, which means it has a significant amount of water underneath the bridge during heavy rainfall events. This can lead to a large area of water, prolonged flooding, and significant disruptions to traffic. On 18 July 2021, during heavy rainfall in Beijing, water backflow occurred at the subway entrance of Jinanqiao station. Several areas within the subway station experienced water accumulation, with the deepest point reaching 90 cm. To address this issue, a total of 4 stations, 10 cars, 45 commanders, 10 hand pumps, 5 floating tappet pumps, and rescue equipment were mobilized. A total of 40 firefighters worked continuously for 3 h to drain the water. Following this incident, the Metro implemented a series of flood control emergency measures to mitigate the risk of flooding disasters during heavy rainfall events (Figure 3).

4.2. Identify the Evaluation Cloud

Six experts from metro operation units and universities were invited to comment and score according to Table 1. Each value of the expert scoring was substituted into the entropy weight method to calculate the indicator weights. Using the cloud inverse generator formula MATLAB programming to calculate the risk evaluation cloud of the indicator layer, we then used Formula (11) to summarize upward to identify the risk evaluation cloud of the guideline layer and further find out the risk evaluation cloud of the target layer, as shown in

Table 3. Risk evaluation cloud digital features.

Objective Layer	Cloud Digital Features	Criteria Layer	Weights	Cloud Digital Features	Indicator Layer	Weights	Cloud Digital Features
A	(4.4548, 0.1947, 0.1237)	A1	0.316	(4.61, 0.21, 0.13)	A11	0.170	(4.66, 0.20, 0.11)
					A12	0.180	(4.92, 0.27, 0.17)
					A13	0.129	(3.54, 0.26, 0.14)
					A14	0.171	(4.68, 0.18, 0.11)
					A15	0.164	(4.48, 0.11, 0.10)
					A16	0.186	(5.08, 0.23, 0.13)
		A2	0.307	(4.04, 0.18, 0.13)	A21	0.170	(4.52, 0.23, 0.11)
					A22	0.135	(3.58, 0.15, 0.14)
					A23	0.178	(4.74, 0.24, 0.17)
					A24	0.170	(4.50, 0.15, 0.12)
					A25	0.168	(4.48, 0.11, 0.10)
					A26	0.094	(2.52, 0.20, 0.19)
					A27	0.084	(2.24, 0.20, 0.11)
		A3	0.377	(4.66, 0.19, 0.11)	A31	0.148	(4.80, 0.25, 0.13)
					A32	0.139	(4.52, 0.08, 0.11)
					A33	0.144	(4.70, 0.25, 0.11)
					A34	0.150	(4.88, 0.11, 0.07)
					A35	0.138	(4.05, 0.25, 0.13)
					A36	0.139	(4.52, 0.27, 0.12)
					A37	0.143	(4.66, 0.15, 0.09)

.

The comprehensive evaluation cloud feature values were (4.4548, 0.1947, 0.1237). We used a forward cloud generator to program in MATLAB, generate evaluation cloud droplets, and ultimately generate a comprehensive evaluation cloud map.

4.3. Comparison of Cloud Diagrams to Determine the Results

Figure 4 shows a comparison between the comprehensive evaluation risk cloud and the standard risk cloud map. By overlaying these two cloud maps, the different risk levels of the subway station could be clearly determined. This comparison provides a visual representation that helps in assessing and understanding the risk level associated with the subway station.

Judging by the comprehensive cloud map, the evaluation cloud map is closer to level III and between the level II standard cloud and level III standard cloud. According to Equation (12), the closeness between the comprehensive evaluation cloud and the standard cloud of each grade was calculated to be 0.289, 0.687, 1.834, 0.393, and 0.220, respectively, so it is judged that the comprehensive risk is at level III and is a medium risk.

4.4. Result Analysis

The characteristic values of the three criteria stratus clouds of PSR were A₁ (4.61, 0.21, 0.13), A₂ (4.04, 0.18, 0.13), and A₃ (4.66, 0.19, 0.11), all of which were at moderate risk, and the risk ranking A₃ > A₁ > A₂. Response risk A₃ and Pressure risk A₁ were greater. The evaluation results obtained through this method were verified and found to align with the empirical analysis conclusions of on-site experts. This further demonstrates the accuracy and effectiveness of the evaluation model.

The risk of heavy rainfall is greater in pressure layer A₁, and there are several adverse environmental factors in the surrounding area. Waterlogging induced by short-duration heavy rainfall mainly occurs in local low-lying urban areas [16]. The natural terrain around the Jin’anqiao subway station area is low-lying, making it prone to water accumulation. This is especially true for entrances B and C of the subway station, and the surrounding roads are more likely to accumulate water. On 18 July 2021, during heavy rainfall in Beijing, there was water accumulation at the subway entrance, and a phenomenon of subway station backflow occurred.

In state layer A₂, the subway company learned from the heavy rainstorm disaster in Zhengzhou, Henan Province, on 20 July and reflected on the rainwater irrigation problem in the subway station on 18 July. Consequently, significant hardware improvements were carried out by the subway company. The plaza outside the station was renovated, and rainwater grates and drainage ditches were added to level the square in front of the station. Moreover, a 1.2 m high concrete retaining wall was constructed in the square. Additionally, at the entrance and exit of the subway station, a one-meter-high flood control baffle made up of five layers of high-strength, water-resistant material was installed. The drainage facilities under the Jin’an Bridge on North Xin’an Road surrounding the subway station were also renovated to enhance their instantaneous drainage capacity. As a result of these improvements, the risk of state layer A₂, such as retaining wall height, flood control baffle height, drainage network density, and the drainage capacity coefficient of the drainage ditch, was reduced.

As for response layer A₃, several measures were reinforced, including prevention, drills, and rescue efforts. The flood prevention emergency plan was revised and improved, and plans for vehicle flow restrictions, guidance, and temporary road closures in case of water accumulation were established. Furthermore, comprehensive flood control drills and safety inspections are being conducted. Although these measures have improved flood control capabilities and reduced disaster risk to some extent, flood control remains a pressing concern. Therefore, it is necessary to continue enhancing comprehensive emergency management systems before flood disasters occur. This includes strengthening early warning systems for flood disasters and providing timely, rapid, and accurate information services. In addition, the flood control emergency plans should be improved, and simulation drills should be carried out. To enhance flood prevention and emergency response efficiency, the comprehensive command system for flood emergency responses should be improved. This can be achieved through the comprehensive use of modern computer network technology to conduct hazard analysis and risk assessments and develop intelligent auxiliary programs for emergency decision making and commands. Moreover, the construction of emergency management teams should be strengthened, particularly in subway stations, by establishing professional emergency response teams and professional fire rescue teams. This can enhance the efficiency of flood prevention and emergency handling.

5. Conclusions

The subway system plays a crucial role in mitigating urban transportation challenges. However, rainstorm waterlogging disasters significantly impact the operation of urban subways, posing serious security risks. This study analyzes the risk of heavy rainfall flooding in subway stations using the Pressure-State-Response (PSR) framework. It considers the pressure, state, and response system formed by the disaster-prone environment, the disaster-bearing body, and the factors causing the disaster. A comprehensive risk assessment system was constructed based on this analysis. The entropy weighting method was employed to determine the indicator weights, enhancing objectivity and reducing the influence of extreme values. A risk analysis was conducted using cloud modeling, generating cloud digital features, cloud drops, and risk cloud diagrams. Risk levels are determined by comparing with a standard cloud map, and the evaluation results align with the actual situation, validating the effectiveness of this approach. The main conclusions are as follows:

• By combining disaster risk theory with the PSR model, this study establishes a risk assessment index system for rainstorm waterlogging disasters in subway stations. This approach provides new ideas and methods to scientifically assess the risk of such disasters. The integration of disaster-causing factors, the vulnerability of disaster-bearing bodies, and the sensitivity of disaster-prone environments into the evaluation index allows for the greater comprehensive evaluation of the risk level of rainstorm waterlogging disasters in subway stations. This theoretical support contributes to disaster prevention and reduction efforts in subway stations.
• The entropy weight method is utilized to determine the weight of indicators, ensuring that subjective factors do not influence the evaluation results and improve the accuracy of the assessment. The use of cloud model algorithms to generate risk assessment cloud maps provides intuitive displays of evaluation results, making them easily understandable and operable. The evaluation method combining the entropy weight method and cloud model algorithm can more accurately and comprehensively evaluate the risk level of subway flood disasters, providing a scientific basis for disaster prevention and the reduction work of the subway system. This approach has the potential for application in other disaster risk assessments, offering universality and promotional value.
• Through an empirical analysis of the Jin’anqiao subway station in Beijing, this study presents a novel idea and method for evaluating rainstorm waterlogging disasters in subway stations. The findings can serve as a reference for evaluating such disasters in other subway stations and can contribute to enhancing the overall safety and disaster resilience of subway systems.
• However, it is important to note that the risk factors of rainstorm waterlogging disasters in subway stations are complex. In this study, the correlation between risk indicators was not investigated. Additionally, due to limitations in data collection, only Beijing Subway’s Jin’anqiao Subway Station was selected as the research object, which limits the generalizability of these results.

To improve the indicator grading and allow for a more comprehensive evaluation of risks, future research can delve into an in-depth exploration of the indicator system and study the quantitative relationship between various disaster risk indicator elements. This can be further enhanced by including more examples to validate research conclusions, thus enhancing the reliability and universality of the results. To further enhance the accuracy and reliability of the assessment results, it is recommended that more risk assessment methods be employed, such as machine-learning methods, to conduct empirical analyses on the risk of rainstorm waterlogging disasters in subway stations. Through these studies and applications, targeted recommendations for flood prevention and emergency measures at subway stations can be provided. This can ensure the safety of people’s lives and property, help urban planners and decision makers better respond to flood disaster risks, and contribute to the sustainable development of cities.