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Article

Resilience Measurement and Enhancement of Subway Station Flood Disasters Based on Uncertainty Theory

by
Jingyan Liu
1,2,*,
Shuo Zhang
3,
Wenwen Zheng
3 and
Xinyue Hu
3
1
Key Laboratory of Building Collapse Mechanism and Disaster Prevention, China Earthquake Administration, Institute of Disaster Prevention, Sanhe 065201, China
2
Hebei Technology Innovation Center for Multi-Hazard Resilience and Emergency Handling of Engineering Structures, Sanhe 065201, China
3
School of Civil Engineering, Institute of Disaster Prevention, Sanhe 065201, China
*
Author to whom correspondence should be addressed.
Appl. Sci. 2024, 14(23), 10930; https://doi.org/10.3390/app142310930
Submission received: 5 October 2024 / Revised: 9 November 2024 / Accepted: 23 November 2024 / Published: 25 November 2024
Browse Figures
Figure 1
<p>Resilience framework for flooding at subway stations.</p> "> Figure 2
<p>Specific analysis process.</p> "> Figure 3
<p>Unascertained measure function.</p> "> Figure 4
<p>Results of the obstacle degree analysis at the index Layer.</p> ">
Versions Notes

Abstract

:
To address the uncertainty of influencing factors in measuring the resilience of subway stations to flood disasters, this study introduces Unascertained Measurement Theory to assess the resilience of subway stations against flood disasters. Initially, the research involves a thorough examination and analysis of past subway flood disaster incidents, which elucidates the disaster system and its resilience processes, thereby facilitating the construction of a resilience analysis framework specific to subway stations. Subsequently, a measurement index system is developed to evaluate the resilience of subway stations against flood disasters, drawing upon relevant literature, and resilience levels are categorized according to established standards. Following this, an unascertained measurement model is formulated to assess the resilience of subway stations in the face of flood disasters. This model incorporates the development of an unascertained measurement function and an unascertained measurement matrix, yielding comprehensive results that inform the determination of resilience levels through credible degree assessment. Furthermore, the SPSSAU obstacle degree model is utilized to analyze the resistance factors that influence the resilience of subway stations to flood disasters, leading to the formulation of strategies aimed at enhancing this resilience. This approach offers novel insights into the measurement of subway station resilience in the context of flood disasters.

1. Introduction

Flooding represents a significant threat to the advancement of human society, characterized by extensive repercussions and considerable economic losses. The phenomenon of global warming has contributed to an increase in both the frequency and unpredictability of urban rainstorms, while the accelerated pace of urbanization has further heightened the risk of flooding events. Subway stations, as subterranean infrastructures [1], are particularly susceptible to the adverse effects of heavy rainfall and flooding, which can result in substantial economic damages and loss of life. Given their underground location, subway stations are at risk of inundation when water accumulates in adjacent low-lying areas and is unable to be drained efficiently. This accumulation can lead to water entering the station through its entrances and exits. The topographical limitations of these stations complicate the drainage of water into the urban drainage system, as gravity alone is often insufficient. In instances where the volume of incoming water is excessive or when drainage systems fail to operate effectively, the water level within the station can rise rapidly, potentially causing widespread flooding. The subway system plays a crucial role in urban transportation; thus, flooding incidents can severely impair its operational efficiency and may result in significant service disruptions. The socio-economic ramifications of such flooding are profound, with indirect economic losses likely surpassing the direct financial impacts.
In recent years, there have been several severe subway flood disasters both domestically and internationally. We have listed some typical incidents, as shown in Table 1.
The transition from a focus on risk to an emphasis on resilience signifies a significant evolution in the academic discourse surrounding disaster prevention and mitigation. Disaster resilience [2,3] is an important research direction following engineering resilience [4] and ecological resilience [5]. Presently, there exists a paucity of literature examining subway flood disasters through the lens of resilience [6]. Yan Xuxian [7] conducted an analysis of the causes of subway flood disasters from the perspective of resilient urban environments, employing a Bayesian network model for risk assessment. However, this study primarily centers on disaster risk analysis and does not delve into the specific characteristics or mechanisms of resilience. Resilience theory advocates for proactive adaptation to change, positing that the enhancement of disaster resilience is integral to sustainable development. While disasters are frequently instigated by extreme weather events, deficiencies in emergency command responses are often evident [8].
Subway stations exist within a multifaceted urban framework, wherein a variety of uncertain variables influence their resilience to flood disasters. The interplay between controllable and uncontrollable factors complicates the decision-making process, as decision-makers frequently encounter limitations stemming from their own knowledge, experience, and capabilities. This situation hinders their ability to thoroughly evaluate all factors that contribute to resilience. Furthermore, the challenge of quantifying subjective human influences necessitates that risk assessments be conducted through the integration of objective realities and experiential knowledge. This approach inherently introduces a degree of subjective uncertainty, thereby characterizing the flood disaster resilience evaluation system as an uncertain system. The theory of uncertainty measurement offers a robust framework for evaluating the uncertainty associated with assessment indicators.
This research presents the principles of uncertainty measurement theory and introduces a novel method for assessing the resilience of subway stations in the face of flood disasters. Grounded in resilience theory, this study examines the evolution of resilience within the subway system as it responds to the risks posed by sudden fluctuations in disaster-inducing factors, the instability of environments prone to disasters, and the vulnerabilities of entities affected by such disasters. An indicator system is developed, encompassing three dimensions: resistance, recovery, and adaptability. Subsequently, an uncertainty measurement model tailored to the resilience of subway stations during flood events is formulated, and its practical applicability is demonstrated through a case study of the Jin’anqiao subway station in Beijing, China.

2. Theoretical Framework and Methods

2.1. Subway Station Flood Resilience System

2.1.1. Causes of Flood Disasters in Subway Stations

The causes of subway station flood disasters are the sudden changes in disaster-causing factors and the destabilization of the disaster-prone environment under the impact of sudden events such as heavy rain, which lead to losses or damage to the disaster-affected bodies. Disasters result in varying degrees of consequences for the subway, including operational disruptions, damage to facilities and equipment, and casualties. For instance, during the incident involving Zhengzhou Line 5, significant water accumulation at the tunnel entrance of the Wulongkou parking lot breached the water barrier, causing water to flow into the subway station at Yueji Park. Conversely, at the Jin’anqiao subway station in Beijing, the area’s relatively low elevation causes rainwater from surrounding roads to converge at this location during heavy rainfall, resulting in the backflow of rainwater.

2.1.2. Flood Resilience Process for Subway Stations

The resilience process is comprised of three primary components: Resistance, Recovery, and Adaptation [9]. Correspondingly, resilience is expressed through three distinct capacities: resistance capacity, recovery capacity, and adaptation capacity. “Resistance capacity” pertains to the system’s ability to withstand adverse effects resulting from disturbances, thereby safeguarding its essential functions from total disruption. In the context of this study, this concept pertains to the subway station’s defensive mechanisms against heavy rainfall disturbances, which include factors such as the elevation of flood walls, the height of flood barriers, the topography of access points, and the accessibility of flood-related information. “Recovery capacity” is a critical element of resilience, denoting the system’s capability to swiftly restore its compromised components to their intended operational state following disturbances, such as natural disasters. This aspect primarily encompasses the efficiency of drainage systems, the density of drainage networks, the ratio of trained rescue personnel, and the availability of emergency supplies. “Adaptation capacity” refers to the system’s ability to modify its structure through either active or passive learning processes to better address future uncertainties. This includes the development of flood emergency response plans, the execution of flood preparedness drills, the conduct of safety inspections and training, and the improvement of flood information management systems.
The processes of resistance and recovery in response to each disturbance create opportunities for adaptation. The enhancement of adaptive capacity, in turn, reinforces both resistance and recovery capabilities when confronted with disturbances. Collectively, resistance, recovery, and adaptation facilitate the system’s continuous dynamic evolution.

2.1.3. Resilience Framework for Flooding at Subway Stations

This study primarily identifies the factors influencing the resilience of subway stations to flood disasters by reviewing and referring to relevant literature, combining actual cases of subway station flood disasters, and conducting expert interviews. These experts include one engineer from the construction department of a rail transit company under China Railway Construction Corporation, one engineer from the operation department of Beijing Rail Transit, one engineer from the Beijing Flood Control Command, and two professors from universities.
According to disaster system theory, the formation and evolution of a disaster are the result of the combined effects of the hazard-pregnant environment, disaster-inducing factors, and the disaster-bearing body within a specific spatial context [10,11].
In the study of subway flood disasters, scholars have conducted extensive research from the perspective of traditional disaster risk. Among them, based on the Pressure-State-Response (PSR) theory, an evaluation index system is constructed, and methods such as the entropy weight cloud model [12], DNN neural network model [13], IOWA operator, and vector angle cosine method [14] are used to assess the risk and vulnerability of subway waterlogging. Some scholars have analyzed the vulnerability of subway projects to waterlogging using projection pursuit methods and particle swarm optimization [15]. In addition, interval FAHP-FCA methods and AHP combined with GIS technology [16] are used to assess the flood risk of subway systems. Other studies include the proposal of evidence-based reasoning methods to measure the worst-case flood risk and identify key influencing factors [17]. By considering flood hazards, subway travel exposure, and population vulnerability, a comprehensive assessment of subway flood disaster risk is conducted [18]. Some scholars have also used improved trapezoidal fuzzy analytical hierarchy process [19] and fuzzy analytical hierarchy process (FAHP) combined with geographic information systems (GIS) [20] to assess the flood risk of urban subway systems. These research outcomes provide a scientific basis and effective tools for the assessment and management of flood risks in subway systems.
Resilience theory has been applied in research on flood disasters. Some studies have comprehensively analyzed the issues faced by old urban communities in the face of flood disasters [21] based on the connotation, characteristics, and mechanisms of action of urban disaster resilience and combined with the causal logic of the “Pressure-State-Response” model, effectively assessed the resilience of mountain towns to disasters [22]. Others have conducted research on the resilience of cities in Hubei Province to flood disasters, aiming to accelerate the construction of resilient cities in the region and promote the sustainable and healthy development of cities [23]. In addition, a resilience assessment method for urban flood disasters based on a combined weighting-cloud model has been proposed using resilience theory [24]. There are also studies that explore the intelligent transformation and implementation path of urban flood resilience governance systems, aiming to enhance the city’s ability to cope with flood disasters [25]. These studies together have promoted the scientific and systematic assessment and management of urban flood disaster resilience.
How to enhance the resilience of subway stations in the face of flood disasters has become an urgent issue that needs to be addressed. To effectively guard against the risks of subway flood disasters and ensure the safety of the subway system, it is necessary to use scientific methods to objectively assess the resilience status of the subway system, combining the resilience process and the disaster development process and fully considering the subway station’s response to flood disasters. Referring to the above literature, a framework for the analysis of subway station flood disaster resilience is constructed.
The resilience analysis framework for subway station flood disasters is shown in Figure 1. The figure was created by the author.
Subway stations serve as significant hubs characterized by extensive underground structures and equipment, as well as sites of high-density, dynamic activities and interactions. Flood disasters represent a complex interplay between the natural water cycle and human societal factors. Consequently, the analysis of flood resilience emphasizes the adaptive responses of disaster-affected entities to the evolving nature of such disasters. Achieving resilience in the face of flood disasters necessitates not only robust engineering systems, such as buildings and infrastructure, but also the collaborative support of various interconnected systems, including economic, social, and informational frameworks.

2.2. Uncertainty Measurement Principle

To accurately grasp the specific conditions of things within a system, it is necessary to quantify uncertainty and calculate numerical values for in-depth analysis. L.A. Zadeh introduced the concept of a fuzzy membership function in his paper “Fuzzy Sets”, describing the “phenomenon of vague boundaries” [26]. This concept expanded research from deterministic sets to uncertain sets, and, on this basis, the emerging discipline of fuzzy mathematics was established. Polish scholar Z. Pawlak, in his paper “Rough sets”, based on the study of “indiscernible relations”, constructed the theory of rough sets to describe uncertain information [27]. Furthermore, Professor Liu Kaidi and his research team conducted an analysis of the distinctions between fuzzy sets and rough sets, leading to the proposal of the concept of uncertainty sets, operational rules, and methods for constructing uncertainty functions. The uncertainty measurement theory is predicated on the premise that decision-makers assess the uncertainty inherent in phenomena within uncertain states and translate this level of understanding into a quantitative ratio.
Uncertainty measure theory, as an effective method for dealing with uncertain information, can fully utilize the inherent information value carried by data. It not only eliminates the subjective bias in the decision-making process but also avoids the limitations of other mathematical methods. Therefore, it has been widely applied in evaluation studies across various fields. In the field of urban real estate investment risk assessment, the theory has pioneered a new evaluation model [28]. Furthermore, the combination of uncertainty measure and entropy weight method has provided a more precise perspective for urban rail construction risk assessment [29]. In the field of tunnel gas risk assessment, the combination of uncertainty measure theory and entropy-weight-analytic hierarchy process has formed a more accurate evaluation method [30]. In rockburst risk assessment, uncertainty measure theory, by quantifying uncertain information and combining it with the analytic hierarchy process, has offered a novel evaluation approach [31]. In the subway engineering field, uncertainty measure theory has been introduced to establish a surrounding rock quality evaluation model, and its feasibility and effectiveness have been verified through comparative analysis with cloud models [32]. The stability analysis of foundation pit slopes has also been deeply studied using uncertainty measure evaluation methods [33]. The risk assessment method for high-temperature operations in underground mines has also been constructed through uncertainty measure theory [34]. Additionally, by combining uncertainty measure theory with dynamic, comprehensive weighting methods of fuzzy analytic hierarchy process-entropy weight method and set pair analysis theory, an improved UM-SPA coupling model has been proposed for landslide susceptibility assessment [35]. In the comprehensive evaluation of construction project safety risks, the analytic hierarchy process and information entropy are used to determine weights, and then uncertainty measure theory is applied for evaluation [36]. The normal cloud model optimizes the uncertainty measure theory to enhance the accuracy of rockburst prediction [37]. Set pair analysis theory has also been used to optimize the attribute recognition standards in uncertainty measure theory, and based on this, an optimized comprehensive prediction model for tunnel rockburst trends has been constructed [38]. These studies demonstrate the wide application and effectiveness of uncertainty measure theory in the field of risk assessment.
Subway stations are located in complex urban systems where there are many uncertain factors affecting flood disaster resilience, and controllable and uncontrollable factors are intertwined. Decision-makers are often limited by their own knowledge, experience, and capabilities and cannot fully consider all resilience-affecting factors. At the same time, due to the difficulty in quantifying the subjective influences of individuals, risk judgments can only be made in combination with objective realities and experiential cognition, which inevitably generates subjective, uncertain information, making the flood disaster resilience evaluation system an uncertain system.
Uncertainty measure theory provides an effective solution for problems with uncertain assessment indicators. In the evaluation of flood disaster resilience, by orderly dividing the resilience levels, the confidence recognition criterion based on orderliness can more accurately reflect the actual situation compared to the maximum membership degree criterion. Furthermore, while fully utilizing the orderliness of the evaluation space, the “non-negativity”, “normalization”, and “additivity” exhibited by the indicator data perfectly align with the connotations of uncertainty measure.

2.2.1. Uncertainty Set

The establishment of uncertain sets is aimed at studying uncertain mathematics, inheriting the characteristics of fuzzy sets and gray sets. When 0 ≤ a ≤ b ≤ 1  is satisfied, there exists a non-negative uncertain number F ( x ) less than 1 on [ 0 , 1 ] , mathematically represented as { [ a , b ] , F ( x ) } . The set composed of all F ( x ) is called an uncertain set, denoted as H [ 0 , 1 ] , as shown in Equation (1):
H [ 0 , 1 ] = [ a , b ] , F ( X ) | a ≥ 0 , a ≤ b ≤ 1
If C is an uncertain set, U is the domain, and C is mapped (membership function) μ : U → H [ 0 , 1 ] , u → μ u ∈ H [ 0 , 1 ] , and u ∈ U represent the combination of elements u in the domain U with the uncertain numbers in the uncertain set H [ 0 , 1 ] , the membership degree of u for C is denoted as μ u , and the uncertain set C with μ ( u ) as the membership function is denoted as C μ ( μ ) .

2.2.2. Uncertainty Measurement

1. Measurable space
In the domain U , there exists a property domain F , and on the property domain F , there exists a topology E . Then F , E is called a measurable space on the domain U when F i ∈ F i = 1 , 2 , 3 , … and satisfies Equations (2) and (3).
F i ∩ F j = ∅ , i ≠ j
∪ i = 1 F i = F
F 1 , F 2 , F 3 , … is a classification of F .
Assuming F 1 , F 2 , F 3 , … , F m is a partition of F , when the condition (4) is satisfied, E is called the topology of F .
E = E i | E i = ∪ j = 1 i F j , F j ∈ { ∅ , F 1 , F 2 , … , F m } , 1 ≤ i ≤ m
2. Uncertainty measurement
Assume F , E is a measurable space on the domain U , for any B ∈ E , μ ∈ U , there exists a mapping u such that μ B μ satisfies conditions (5)–(7).
0 ≤ μ B ( u ) ≤ 1 , ∀ u ∈ U , B ∈ E
μ F ( U ) = 1
μ ∪ i B i ( u ) = ∑ i μ B i ( u ) , B i ∈ E , B i ∩ B j = ∅ ( i ≠ j )
When the three conditions of non-negativity and boundedness (Equation (5)), normalization (Equation (6)), and additivity (Equation (7)) are satisfied, μ B μ is referred to as an uncertain measure on the measurable space F , E . μ B μ is the uncertain measure of u with respect to B , and the uncertain measure essentially represents the degree of distribution of the property B i in the decision-maker’s mind regarding u , which is highly subjective.
Assuming there exists a property domain F on the universe U , and E is the topology of F , μ B μ represents the uncertain measure of u regarding B , then D , E , μ is referred to as the uncertain measure space. When μ B μ is used as the membership function, there exists a fixed B ∈ E such that an uncertainty set B ˜ in the deterministic domain U , then B ˜ is called an uncertain subset of the universe U regarding property B ˜ .
3. Uncertainty measurement of Single Indicator
The evaluation space is the set X composed of all evaluation influencing factors of the evaluation object A . Let x 1 , x 2 , … , x n be the evaluation influencing factors of the evaluation space X , denoted as X = x 1 , x 2 , … , x n . When there are m indicators, the influencing factor x i i = 1 , 2 , … , m is measured, and the set P = P 1 , P 2 , … . P m composed of m evaluation indicators is called the indicator space.
x i j represents the i -th evaluation factor for the j -th indicator P j ’s measurement value, so x i can be represented as an m dimensional vector:
x i = ( x i 1 , x i 2 , … , x i m )
When there are Z evaluation levels in x i j , the space is denoted as C = c 1 , c 2 , … , c z , and the k -th evaluation level is denoted as c k . When the k -th level is higher than the k + 1 level, then c k > c k + 1 k = 1 , 2 , … , z − 1 . When c 1 < c 2 < … < c z or c 1 > c 2 > … > c z , then c 1 , c 2 , … , c z is referred to as an ordered partition class on the evaluation level space C . The space C is a closed measurable space that satisfies the basic operations of set intersection, union, and complement, and can be represented as follows:
C = B | B = ∪ i = 1 k b i , b i ∈ { ∅ , 1 , c 1 , c 2 , … c z } , 1 ≤ i ≤ k
Assume μ i j k = μ x i j ∈ c k is the measurement value x i j belonging to the evaluation level c k , and it is required that μ meets the following conditions:
0 ≤ μ ( x i j ∈ c k ) ≤ 1
μ ( x i j ∈ Y ) = 1
μ x i j ∈ ∪ l = 1 k c l = ∑ l = 1 k μ ( x i j ∈ c l )
μ λ x i j ∈ ∪ l = 1 k c l = λ ∑ l = 1 k μ ( x i j ∈ c l )
i = 1 , 2 , … , n ; j = 1 , 2 , … , m ; k = 1 , 2 , … , z
When Equations (10) to (13) are simultaneously satisfied, μ is referred to as the uncertain measure.
Based on the defined construction of the uncertain measurement single index measurement function μ x i j ∈ c k , where j = 1 , 2 , … , m ;   i = 1 , 2 , … , n ;   k = 1 , 2 , … , z , the measurement values μ i j k of each index of the influencing factor x i are obtained. The matrix composed of μ i j k is called the single index measurement matrix, denoted as follows:
μ i j k m × z = μ i 11 μ i 12 ⋯ μ i 1 z μ i 21 μ i 22 ⋯ μ i 2 z ⋮ ⋮ ⋮ ⋮ μ i m 1 μ i m 2 ⋯ μ i m z
4. Multi-Indicator Comprehensive Measurement
Let ω j be the importance of evaluation index P j of evaluation factor x i compared to other evaluation indices, and it satisfies the following:
0 ≤ ω j ≤ 1
∑ j = 1 m ω j = 1
ω j is the weight of evaluation index P j .
When there exists μ i k such that 0 ≤ μ i k ≤ 1 and
μ i k = ∑ j = 1 m ω j μ i j k
μ i k is an uncertain measurement, and the matrix μ i j n × z is referred to as the multi-index comprehensive evaluation matrix, represented as follows:
μ i k n × z = μ 11 μ 12 ⋯ μ 1 z μ 21 μ 22 ⋯ μ 2 z ⋮ ⋮ ⋮ ⋮ μ z 1 μ z 2 ⋯ μ n z
When μ k = μ x i k ∈ c indicates the degree to which evaluation factor x i belongs to level k , then
μ k = ∑ i = 1 n ω i μ i k ( k = 1 , 2 , ⋯ , z )
In Equation (19), ω i is the weight of evaluation factor x i , 0 ≤ μ k ≤ 1 , ∑ k = 1 z μ k = 1 , so μ k is determined as an uncertain measure, and the vector μ k = ( μ 1 , μ 2 , … , μ z ) is referred to as the multi-criteria comprehensive evaluation vector.

2.3. Analysis Process

This research integrates the theories of uncertainty measurement and obstacle degree to assess and improve the resilience of subway stations in the context of flood disasters. The primary steps involved in this study are as follows:
(1) Establish the evaluation framework for assessing the resilience of subway stations against flood disasters. This involves analyzing the underlying causes of flood events and the resilience mechanisms of subway stations, thereby delineating the resilience system pertinent to flood disasters and subsequently defining the evaluation framework.
(2) Develop a classification standard for the resilience of subway stations in relation to flood disasters. This classification will be informed by the distinctive characteristics of flood disaster resilience observed in subway stations, alongside relevant standards and regulations.
(3) Construct uncertainty measurement functions and matrices. Utilizing the established resilience classification standards, uncertain measurement functions will be developed, observed values will be incorporated, and a single-index uncertain measurement matrix will be created.
(4) Determine the weights for the evaluation criteria. The measure of information entropy will be employed to ascertain the weights, culminating in the formation of a weight vector.
(5) Calculate the comprehensive uncertainty measurement. A weighted calculation of the comprehensive uncertainty measurement will be performed using a multi-indicator measurement matrix.
(6) Establish the measurement results. Categories will be determined based on established confidence criteria.
(7) Identify critical obstacle factors through an analysis of obstacle degree.
(8) Recommend strategies to enhance resilience.
See Figure 2 for the specific analysis process.

2.3.1. Defining the Resilience Evaluation Space and Grading Criteria

The resilience indicator system for flood disasters at subway stations is divided into three levels: the goal level, the criterion level, and the indicator level. The goal level is the resilience of subway stations to flood disasters, while the criterion level mainly considers three aspects of resilience: resistance, recovery, and adaptability. The indicator level consists of the specific characteristics of resilience to flood disasters at subway stations. The division of resilience levels is an important tool for assessing and enhancing the adaptability and recovery capabilities of systems, organizations, or communities when facing challenges. By categorizing resilience into levels, entities can self-assess against standards, identify their strengths and weaknesses, and thus make targeted improvements. The division of resilience levels is not only a technical assessment tool but also an important means of promoting social progress and sustainable development [15,39,40].
Based on the characteristics of resilience to flood disasters at subway stations and referencing the “Subway Design Code GB50157-2013” [41], “Waterproofing Technical Code for Underground Engineering GB50158-2008” [42], “Outdoor Drainage Design Code GB50014-2021” [43], and relevant literature [44,45,46], five levels of resilience are defined, as shown in Table 2.

2.3.2. Constructing the Uncertainty Measurement Function

Based on the resilience grading standards, an uncertain measurement function is constructed. In this study, the C k ( k = 1 , 2 , … , 5 ) classification space C = C 1 , C 2 , … , C 5 is classified into Level I, Level II, Level III, Level IV, and Level V. The standard values are set at 1, 3, 5, 7, and 9, respectively. That is, when the actual value of the indicator equals the standard value, the indicator will completely belong to the resilience level corresponding to that standard value; when the indicator value falls within the interval defined by two standard values, it will belong to the two adjacent resilience levels to varying degrees. A single indicator measurement function is constructed, as shown in Figure 3.

2.3.3. Constructing the Uncertainty Measurement Matrix

Substituting the observation value t i j into the uncertainty measurement function μ ijk = μ ( t i j ∈ C k ) , we obtain the degree of uncertainty measurement μ i j k (a real number between [0, 1]) that t i j belongs to the category C k , resulting in a single-index uncertainty measurement vector μ i j = μ ij 1 , μ ij 2 , … , μ ij p , which forms the single-index uncertainty measurement matrix ( μ i j k ) m × p .
Using measured information entropy to determine indicator weights
v i j = 1 + 1 log p ∑ k = 1 p μ i j k log μ i j k
w j ( i ) = v i j ∑ j = 1 m v i j
In the formula, 0 ≤ w j ( i ) ≤ 1 , ∑ j = 1 m w j ( i ) = 1 , The weight vector obtained is as follows:
w ( i ) : w ( i ) = w 1 ( i ) , w 2 ( i ) , … , w m ( i )
Calculate the multi-indicator uncertain measurement vector and measurement matrix ( μ i k ) m × p
( μ i k ) m × p = ∑ j = 1 m w j ( i ) μ i j k = ∑ j = 1 m w 1 w 2 … w m T μ 11 μ 12 … μ 1 p μ 21 μ 22 … μ 2 p … … … … μ m 1 μ m 2 … μ m p
In the above formula, the following is true:
w j ( i ) is the weight of the j -th indicator y j of x i . 0 ≤ μ i k ≤ 1 , i = 1 , 2 , … n ; j = 1 , 2 , … m ; k = 1 , 2 , … p .
Layered upward aggregation results in a comprehensive measure of uncertainty.

2.3.4. Confidence Level Determination Category

Determine categories based on confidence criteria. λ predetermined confidence threshold λ is set to judge whether sample x i belongs to category k 0 , with a confidence level of λ . The range of λ is 0.5 ≤ λ < 1.0; the larger the λ value, the more conservative the result (Ruan Chao et al., 2021) [29].
k 0 = min k ∑ k = 1 p μ i k ≥ λ , 1 ≤ k ≤ p

2.3.5. Obstacle Degree Analysis

Through the obstacle degree model, it is possible to accurately quantify the degree of obstacles posed by various evaluation indicators in the resilience of subway stations to flood disasters, thereby identifying key factors that significantly constrain resilience performance. At the same time, it clarifies the core factors affecting evaluation results and specifies the extent to which key constraints impact the overall evaluation. Based on this, it can precisely diagnose the issues faced by subway stations’ resilience to flood disasters and propose targeted measures for enhancing resilience.
The core of the obstacle degree model lies in its three main measurement indicators: obstacle degree, factor contribution degree, and indicator deviation degree. The calculation process of this model is as follows:
F j = V j × w j
D j = 1 − A j
O j = F j × D j ∑ F j × D j
In the formula, A j represents the standardized value of the indicator, V j represents the weight of the j -th criterion layer indicator, and W j represents the weight of the i -th individual indicator to which the j -th criterion layer indicator belongs.

3. Case Analysis

3.1. Introduction to the Research Subject

Jin’anqiao Metro Station serves as the western terminus of Line 6 and functions as a transfer hub for Line S1, Line 11, and Line 6. The station is notable for its substantial scale, featuring a total of eight entrances and exits. The designation “Jin’anqiao” not only refers to a bridge located on the elevated Fushi Road but also identifies the station associated with Line S1, thereby establishing it as a critical junction for both railways and the metro system (Jin’anqiao Station). These interconnected elements collectively contribute to the station’s status as a distinctive landmark within the region.
As a transportation nexus, the Jin’anqiao intersection links five significant thoroughfares, underscoring its vital geographical importance. The Fushi Road overpass, which runs east–west, is elevated above the surrounding area, while, to the south of Jin’anqiao lies Beixin’an Road, a newly constructed two-way, three-lane urban arterial road that extends southward to Shijingshan Road, an extension of Chang’an Avenue. To the north, Jinding West Street meanders northwest, connecting with Shimen Road. On the eastern side, Jinding South Road intersects with Apple Garden South Road and Fushi Road, while Guangning Road, located to the west, also extends northwest, reaching Shuangyu Bridge in conjunction with the Fushi Road overpass. Additionally, the Shougang Industrial Heritage Park is situated to the southwest of Jin’anqiao.
The region is characterized by a warm temperate semi-arid and semi-humid continental monsoon climate, which features distinct rainfall patterns that are unevenly distributed throughout the year. The area experiences a limited number of rainy days, yet the intensity of rainfall is high, particularly with frequent localized instances of intense, short-duration precipitation, resulting in significant spatial variability in rainfall distribution.
The low-lying topography surrounding the Jin’anqiao subway station, particularly near exits B and C, predisposes the roads to water accumulation during periods of rainfall. As a depressed interchange, the water accumulation issue at Jin’anqiao becomes particularly pronounced during heavy rain events, characterized by considerable depth, extensive area, and prolonged duration, which severely disrupts traffic flow. On 18 July 2021, Beijing experienced significant rainfall that resulted in water accumulation at the entrance of the Jin’anqiao subway station, leading to backflow phenomena and flooding in multiple areas within the station, with water levels reaching depths of up to 90 cm. In response to this emergency, relevant authorities promptly mobilized resources, deploying ten vehicles and 45 personnel from four stations, equipped with ten hand pumps, five floating pumps, and various rescue apparatus. Following three hours of intensive drainage operations conducted by 40 firefighters, the water accumulation issue was effectively mitigated.
In the aftermath of this incident, the subway company undertook a thorough review of the situation, enhancing its flood prevention and emergency response protocols. The organization has actively addressed the risks associated with heavy rainfall and waterlogging disasters, thereby improving flood control and drainage capabilities to ensure the safety of passengers and the uninterrupted operation of subway services.

3.2. Resilience Measurement

Inviting the aforementioned five experts to evaluate and obtain the resilience scores for each indicator. Calculated based on the principles described in Formulas (1)–(19) in Section 2.2. The arithmetic mean of the experts’ scores is used as t i j to substitute into the uncertain measurement function, resulting in the single indicator measurement vector μ i j = μ ij 1 , μ ij 2 , … , μ ij 5 composed of each factor’s single indicator measurement. μ i j k ( 4 × 5 ) calculates the indicator weights and computes the uncertain measurement vector of A i . Use Formulas (20)–(23) to calculate the index weights and determine the uncertainty measure vector for A i .
The uncertain measurement vector of A1
μ 1 = w 1 × ( μ 1 ) 4 × 5 = w 11 w 12 w 13 w 14 T × μ 11 μ 12 μ 13 μ 14 = 0.233 0.274 0.28 0.245 × 0 0 0.24 0.76 0 0 0 0.88 0.12 0 0.19 0.81 0 0 0 0 0 0.2 0.8 0
Similarly, we obtain the uncertain measurement vectors and weight vectors for A2 and A3, which are filled in Table 3.
The final calculation of the comprehensive uncertainty vector for target layer A is as follows.
μ = w × ( μ ) 3 × 5 = w 1 w 2 w 3 T × μ 1 μ 2 μ 3 = 0.217 0.388 0.395 × 0.047 0.201 0.346 0.406 0 0 0.467 0.549 0.384 0 0.054 0.465 0.481 0 0
Set the confidence threshold λ = 0.7 . The probability that the sampled value of the random variable falls within one standard deviation is 68.3%, so λ is generally taken as 0.6 to 0.7 [47], which indicates a high reliability of the evaluation results. According to the confidence determination Formula (24), by substituting the threshold λ , we obtain Formula (30).
k 0 = min k ∑ k = 1 p μ i k ≥ 0.7 , p = 1 , 2 , … , 5
Because μ 1 + μ 2 + μ 3 = 0.032 + 0.253 + 0.478 = 0.763 > 0.7 , k = 3 has moderate resilience.

3.3. Resilience Enhancement

Using the Statistical Product and Service Software Automatically 24.0 (SPSSAU 24.0) obstacle degree model (25)–(27) for analysis, the results are shown in Table 4 and Figure 4.
The primary factors identified as obstacles within the guideline layer are ranked as follows: recovery (A2), adaptability (A3), and resistance (A1).
Within the specific indicator layer, the highest-ranked items include A32, which pertains to the quality of flood emergency plans; A23, which addresses the proportion of professional rescue personnel; A33, which focuses on safety inspections and training; A31, which involves flood emergency drills; A24, which relates to the reserves of rescue materials; and A34, which concerns flood information management.
The vicinity of Jin’anqiao Metro Station is characterized by low-lying topography, particularly at exits B and C, where adjacent roadways are susceptible to water accumulation. During the significant rainfall event in Beijing on 18 July 2021, water accumulation was observed at the metro entrance, resulting in backflow into the station. In response, the metro company evaluated the issue of rainwater backflow and drew lessons from the severe flooding incident that occurred in Zhengzhou, Henan, on 20 July. Consequently, a series of remedial measures were implemented. In terms of resistance, renovations were made to the outdoor plaza, the pavement in front of the station was leveled, and a 1.2 m-high concrete flood wall was constructed at the front plaza. Additionally, high-strength flood barriers, measuring one meter in height, were installed at the station’s entrances and exits. Regarding recovery, supplementary rainwater grates and drainage ditches were introduced, and the drainage infrastructure beneath Jin’anqiao on Beixin’an Road was upgraded to improve instantaneous drainage capacity. In terms of adaptability, lessons learned were documented, the flood emergency response plan was revised and enhanced, and comprehensive flood prevention drills and safety inspections were conducted.
To further bolster the resilience of subway stations, it is imperative to enhance and implement the following measures:
1. Enhancing Resistance Measures
To improve flood resistance, it is essential to establish additional flood prevention barriers. This includes the installation of waterproof gates at the entrances of subway stations and critical passageways, similar to the practices implemented in the London Underground, to prevent rainwater ingress. Concurrently, it is imperative to conduct annual safety inspections of the station’s drainage outlets and their connections to the municipal pipeline network and drainage facilities prior to the flood season. Any outdated or defective components should be promptly replaced to ensure the effective functioning of the drainage system. In the event of extreme rainfall, it is advisable for each site to maintain an adequate supply of materials and equipment, such as sandbags and flood barriers, to implement temporary self-protection measures. This may involve sealing entrances, exits, ventilation ducts, and transfer passage interfaces. The adoption of advanced automated electric flood prevention gates, such as those installed at Jinan Metro stations, can significantly enhance flood prevention efficiency. Additionally, waterproofing measures should be implemented, including the application of waterproof coatings to tunnel walls and subway stations, as well as the construction of waterproof barriers within the station to mitigate water infiltration and intrusion, thereby safeguarding subway station infrastructure.
2. Enhancing Resilience Measures
To bolster resilience, it is crucial to refine the emergency response plan. This involves enhancing the comprehensive command system for flood emergencies by leveraging modern computer network technology for hazard analysis and risk assessment. Responsibilities and tasks for rescue teams should be clearly delineated, fostering close collaboration with relevant departments, including the subway company, public security, and fire services. Regular training and drills focused on flood prevention emergency protocols should be conducted to enhance rescue capabilities. Upgrading the drainage system is also necessary, which entails increasing pipe diameters and drainage capacity to accommodate heavy rainfall during extreme weather events. The design of a multi-layer drainage system is recommended, incorporating surface drainage, underground drainage, and deep drainage strategies. This layered approach will help alleviate water accumulation pressure within the subway station.
3. Enhancing Adaptability Measures
To improve external flood discharge capacity, the construction of low-lying gardens, underground runoff systems, and rainwater retention basins is recommended, which is akin to the strategies employed by the New York subway system following Hurricane Sandy. The introduction of the “sponge city” design concept in the landscaping around station entrances and exits is also advisable. This may include the implementation of grassed ditches, permeable pavements, and sunken green spaces to enhance the environment’s capacity for water absorption and infiltration. Furthermore, the establishment of an information-based dynamic monitoring and early warning system is essential for real-time monitoring and warning analysis. This system should include flood prevention water level warning markers and alert levels within the camera observation range, enabling the monitoring of water levels through surveillance cameras and facilitating timely flood prevention emergency drills. By implementing these measures, the resilience, recovery, and adaptability of subway stations will be significantly improved, thereby enhancing their capacity to effectively respond to the challenges posed by flood disasters.

4. Conclusions

In this research, we analyzed the characteristics of flood disasters in subway stations, constructed a measurement index system for the resilience of subway stations to flood disasters based on the resilience theory analysis framework, and introduced uncertainty measure models and obstacle degree models to measure and enhance the resilience of subway stations to flood disasters.
(1) Firstly, in this study, we analyzed the resilience system of subway station flood disasters. By examining the causes and processes of subway floods, a framework for analyzing the resilience of subway stations to flood disasters was constructed. The resilience of subway stations to flood disasters is reflected in their ability to maintain functionality, recover promptly, and continuously learn and adjust in the face of risk impacts from sudden changes in disaster-inducing factors, instability in the disaster-prone environment, and the vulnerability of the disaster-bearing body. In dealing with flood disasters, subway stations need to possess the following capabilities: first, the ability to resist disasters; second, the ability to recover quickly after a disaster; and third, long-term adaptation and learning mechanisms. Secondly, this study introduced uncertainty theory to measure the resilience of subway stations to flood disasters. By establishing grading standards for the resilience of subway stations to flood disasters, constructing uncertainty measure matrices and functions, and measuring the resilience of Jin’anqiao Subway Station in Beijing, the result was found to be moderate resilience. Thirdly, the obstacle degree model was introduced to identify key obstacle factors, and the results showed that indicators A32, A23, A33, A31, A24, and A34 ranked at the forefront. Finally, based on the resilience evaluation results and obstacle degree analysis, strategies for enhancing resilience were proposed.
(2) Due to the complexity of factors affecting the resilience of subway stations to flood disasters, the current analysis does not consider the interrelated membership of various indicators. Future research should further improve the indicator system and deeply explore the quantitative relationships between indicators. The identification and analysis of disaster-causing factors are based on relevant literature, expert interviews, and case collection, and the obtained disaster-causing factors are limited, which may not fully reflect the overall picture of the disaster-causing factors of flood disasters in subway stations. Subsequent research should continue to supplement and refine the data samples of disaster-causing factors. This study mainly focuses on flood disasters during the operational period of subway stations, while flood disasters may occur at different stages of subway stations. Therefore, follow-up research can comprehensively analyze the disaster-causing factors of flood disasters in subway stations from multiple stages, such as the construction period and operational period.

Author Contributions

Conceptualization, J.L. and W.Z.; software, J.L.; validation, J.L., S.Z. and W.Z.; formal analysis, J.L.; investigation, S.Z.; resources, W.Z.; data curation, J.L. and X.H.; writing—original draft preparation, J.L.; writing—review and editing, S.Z.; supervision, W.Z.; project administration, J.L.; funding acquisition, J.L. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Fundamental Research Funds for the Central Universities (ZY20220206), and the National Natural Science Foundation of China (52278489).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data are contained within the article.

Conflicts of Interest

The authors declare no conflicts of interest.

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Applsci 14 10930 g001
Figure 1. Resilience framework for flooding at subway stations.
Figure 1. Resilience framework for flooding at subway stations.
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Figure 2. Specific analysis process.
Figure 2. Specific analysis process.
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Figure 3. Unascertained measure function.
Figure 3. Unascertained measure function.
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Figure 4. Results of the obstacle degree analysis at the index Layer.
Figure 4. Results of the obstacle degree analysis at the index Layer.
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Table 1. Rainstorm flood disaster of subway station.
Table 1. Rainstorm flood disaster of subway station.
TimePlaceCauseDisaster Situation
8 August 2007New YorkRainstormThe subway is severely flooded, and New York’s 4, 5, 6, E, F, R, and V lines are suspended
28 October 2012New YorkHurricane SandySeven subway tunnels were flooded
25 September 2014NagoyaConcentrated rainstormThe platform of Nagoya Station on the Higashiyama Line of the subway was submerged in water, and all the lines were submerged in water. Some sections of trains on the Higashiyama Line stopped operating
30 June 2015NanjingContinuous rainfallSubway Line 3’s Mozhou East Road Station is submerged
21 June 2016WashingtonRainstormThe accumulated water rushed into the Cleveland Park subway station, causing the escalator to turn into a waterfall and temporarily closing the subway
19 July 2016BeijingHeavy rainfallThe subway stations of Line 4, Line 6, Line 7, Line 13, Line 14, and Line 15 have been temporarily closed. The Yihezhuang section of Line 4 has serious water seepage and has been suspended from operation
13 June 2017ShenzhenTyphoonMetro Line 1 Chegongmiao Station is flooded with rainwater
28 June 2018ChengduContinuous rainfallA large amount of rainwater has infiltrated Guangfu Station on Metro Line 1, causing water accumulation in the station hall
21 June 2019WuhanRainstormSubway Line 11 Guanggu 7th Road Station Passage
17 July 2019New YorkFloodFloods poured into the 23rd Street subway station in Queens due to rainstorm, and the subway cars were soaked
12 February 2020SydneyContinuous rainfallThe drainage pump in the underground tunnel is unable to cope with the heavy rain that poured down last weekend, and hundreds of meters of Sydney Metro is currently submerged in water
29 June 2020ShijiazhuangHeavy rainfallHeavy rainfall caused water to enter the equipment room of Berlin Station on Metro Line 3, and the station was closed
18 July 2021BeijingHeavy rainfallRainwater poured into Jin’anqiao Station on Metro Line 6, causing severe waterlogging
20 July 2021ZhengzhouContinuous rainfallThe accumulated water washed over the water retaining wall and entered the subway station, causing a train on Line 5 to come to a forced stop. A major accident resulting in 12 deaths and 5 injuries
1 September 2021New YorkHurricane IdaAbout 46 locations in the subway system have experienced flooding
1 June 2022NanchangEncounter extremely heavy rainstormThe water barrier of Metro Line 2 has been washed away
8 August 2022SeoulContinuous rainfallThe subway station has been shut down due to water ingress, ground subsidence, and platform power outage
5 September 2023FuzhouTyphoon HaikuiMultiple subway stations have accumulated water, and multiple lines have been flooded
21 August 2024TokyoSudden rainstormThe subway station leaked rain like a waterfall, and multiple subway lines were flooded
20 September 2024ShanghaiTyphoon PrasangMultiple subway lines flooded
Table 2. Resilience measurement index system and grading of flood disasters.
Table 2. Resilience measurement index system and grading of flood disasters.
Measurement IndicatorsVery Low
Resilience
I Graed
[0,2]		Low
Resilience
II Grade
(2,4]		Medium
Resilience
III Grade
(4,6]		High
Resilience
IV Grade
(6,8]		Very High
Resilience
V Grade
(6,8]
A1
Resistance		A11 Height of water retaining wall/m[0,0.3)[0.3,0.5)[0.5,1.0)[1.0,1.5)[1.5,3.0]
A12 Height of flood control barrier/m[0.5,0.8)[0.8,1.0)[1.0,1.2)[1.2,1.5)[1.5,1.8)
A13 Terrain conditions at the entrance and exitLowVery lowmediumhighVery high
A14 Flood situation informationnot haveincompleteGenerallycompleteVery complete
A2
Recovery		A21 Drainage capacity coefficient of drainage ditch[0,0.75)[0.75,1)[1.1.25)[1.25,1.5)[1.5,100]
A22 Dense drainage network/(km·km−2)[0,2)[2,2.39)[2.39,2.78)[2.78.3.17)[3.17,10]
A23 Proportion of professional rescue personnel/%[0,5)[5,10)[10,20)[20,30)[30,100]
A24 Reserve situation of rescue suppliesnot haveincompleteGenerallycompleteVery complete
A3
Adaptability		A31 Flood control emergency drill (times/month)[0,1)[1,2)[2,3)[3,4)[4,12]
A32 Quality of flood prevention emergency planVery lowlowmediumhighVery high
A33 Safety inspection and training (times/month)[0,1)[1,4)[4,6)[6,8)[8,30]
A34 Flood prevention information managementVery lowlowmediumhighVery high
Table 3. Calculation of unascertained measure.
Table 3. Calculation of unascertained measure.
Target LayerUncertainty Measurement VectorCriteria LayerWeightUncertainty Measurement VectorIndex LevelWeightUncertainty Measurement Vector
A(0.032,0.253,0.478,0.237,0)A10.217(0.047,0.201,0.346,0.406,0)A110.233(0,0,0.24,0.76,0)
A120.274(0,0,0.88,0.12,0)
A130.248(0.19,0.81,0,0,0)
A140.245(0,0,0.2,0.8,0)
A20.388(0,0.0467,0.549,0.384,0)A210.249(0,0.16,0.84,0,0)
A220.221(0,0,0.26,0.74,0)
A230.274(0,0.1,0.9,0,0)
A240.256(0,0,0.14,0.86,0)
A30.395(0.054,0.465,0.481,0,0)A310.225(0,0.46,0.54,0,0)
A320.278(0,0.18,0.82,0,0)
A330.227(0,0,0.42,0.58,0)
A340.270(0.2,0.8,0,0,0)
Table 4. Resilience obstacle degree to flood disasters.
Table 4. Resilience obstacle degree to flood disasters.
Criteria Layer
Obstacle FactorMean of Obstacle Degree %Sort
A118.793
A241.841
A339.372
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Liu, J.; Zhang, S.; Zheng, W.; Hu, X. Resilience Measurement and Enhancement of Subway Station Flood Disasters Based on Uncertainty Theory. Appl. Sci. 2024, 14, 10930. https://doi.org/10.3390/app142310930

AMA Style

Liu J, Zhang S, Zheng W, Hu X. Resilience Measurement and Enhancement of Subway Station Flood Disasters Based on Uncertainty Theory. Applied Sciences. 2024; 14(23):10930. https://doi.org/10.3390/app142310930

Chicago/Turabian Style

Liu, Jingyan, Shuo Zhang, Wenwen Zheng, and Xinyue Hu. 2024. "Resilience Measurement and Enhancement of Subway Station Flood Disasters Based on Uncertainty Theory" Applied Sciences 14, no. 23: 10930. https://doi.org/10.3390/app142310930

APA Style

Liu, J., Zhang, S., Zheng, W., & Hu, X. (2024). Resilience Measurement and Enhancement of Subway Station Flood Disasters Based on Uncertainty Theory. Applied Sciences, 14(23), 10930. https://doi.org/10.3390/app142310930

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