Fire Resilience Assessment and Application in Urban Rail Transit Systems

Abstract

With the rapid development of urban underground rail transit, its enclosed and densely populated environment significantly increases fire risks, posing serious threats to personnel safety and operational stability. Based on the WSR methodology and 4M theory, this study identifies fire-related factors from the physical, operational, and human dimensions. And refine indicators at the four levels of personnel, equipment and facilities, environment, and management to establish a resilience assessment system for urban underground rail transit fires. The results detailed display the application of Cross-Influence Analysis (CIA) and analytic network process (ANP) methods in fire resilience evaluation, including theoretical framework construction, computational procedures, and result analysis. A comprehensive assessment system is developed, comprising 14 secondary indicators under four primary criteria: resistance capacity, adaptation capacity, absorption capacity, and resilience capacity. And then, the CIA and ANP methods were employed to quantify inter-indicator relationships and weights through 15 expert evaluations and 52 judgment matrices, facilitating disaster-adaptive strategy formulation. Finally, an empirical analysis of Xi’an Metro Line 1 reveals that resistance capacity and resilience capacity are critical to fire resilience, with fire cause investigation and post-incident review exhibiting the highest weights. Meanwhile, resilience enhancement strategies are proposed, including optimized monitoring equipment deployment, strengthened emergency drills, and improved personnel training. The paper innovatively integrates WSR methodology and 4M theory to establish a comprehensive, representative metro fire resilience assessment system with CIA-ANP quantification. This study provides novel methodological support for fire safety assessment in urban underground rail transit systems, offering significant theoretical and practical value.

1. Introduction

With the acceleration of urbanization, rail transit has become a core component of modern urban transportation systems. By the end of 2024, 562 cities across 79 countries and regions had operational urban rail transit systems worldwide, with a total length of 44,730.14 km. Underground rail transit, as the dominant mode, accounted for 89.14% of newly added mileage, reaching 22,918 km across 203 cities globally. China, as one of the fastest-growing countries, has 58 cities operating 362 lines totaling 12,168.77 km, with underground sections comprising 76.27%. However, this enclosed and high-density system also poses significant fire risks. Statistics show that by 2020, underground rail transit fires accounted for 118 incidents globally, representing 51% of all accidents. In China, the post-2000 period saw a surge in accidents, with a 70% increase from 2005 to 2010, and accident frequency in 2015–2020 remaining comparable to peak levels [1]. These data indicate that as rail networks expand, fire prevention has become a critical challenge for operational safety.

Fire resilience theory provides a new paradigm for system safety assessment. Fire resilience refers to the ability of cities, communities, or buildings to quickly recover adapt and continue developing in the face of fire disasters, emphasizing prevention, response, and recovery throughout the entire disaster cycle [2]. Scholars worldwide have conducted extensive research in this field: Gao J [3] introduced a fuzzy consistency matrix to address the ambiguity of fire risk assessment indicators and the complexity of structurally consistent pairwise comparison matrices, effectively reducing subjective bias. Tang Y [4] proposed the concept of fire resilience based on system resilience theory, integrating identification, assessment and optimization methods to embed resilience evaluation flexibly into infrastructure management. Xu X [5] analyzed high-tech electronics factories’ system composition and its impact on fire resilience, filling the gap in sustainability-oriented fire prevention strategies in operational environments. Wen X [6] conducted a comprehensive literature review on urban rail transit resilience assessment, introducing resilience concepts, quantitative measurement methods, and improvement strategies. Hu J [7] analyzed urban rail transit network characteristics and modeling approaches from a resilience perspective, defining network resilience while classifying and summarizing existing resilience metrics. Chen J [8] developed a timetable-based resilience assessment model, addressing the overlooked influence of train schedules on resilience evaluation. Li M [9] proposed a resilience assessment method for the Beijing subway network based on graph theory, and quantitatively evaluated the subway performance and fault recovery speed with a unified measurement standard and model. Zhang H [10] identified fire resilience factors and investigated their correlations and hierarchical dependencies. Himoto K [11] proposed a conceptual framework for quantifying fire resilience, offering a new perspective on fire safety performance. Thacker F E N [12] propose to define a fire resilient landscape as ‘a socio-ecological system that accepts the presence of fire, whilst preventing significant losses through landscape management, community engagement and effective recovery’. Himoto K [13] defined fire resilience as a function of internal space recovery time. Cutter’s team [14] focused on social dimensions, constructing a disaster resilience evaluation system. Saadat Y [15] proposed that the capacity of urban rail networks to withstand such disaster disturbances requires robustness and vulnerability assessment. Dell’Isola M [16] introduced a resilience assessment method for gas distribution networks, improving resilience through structural enhancements. Borghetti F [17] developed a two-step approach to evaluate road network resilience, aiding resilience planning in organizational capacity-building programs. Koc E [18] proposed Comprehensive Resilience Assessment Framework for transportation systems, enabling holistic analysis of transport system failures by addressing research gaps. Current fire risk assessments for underground rail transit predominantly rely on traditional single-method approaches, while capable of identifying risks, exhibit three key limitations: (1) lack of systematic consideration of the entire fire prevention-control-recovery process; (2) static data hardly to reflect changes in the operational environment in a timely manner; (3) the unidimensional evaluation that fails to comprehensively cover resilience characteristics.

Summarizing the above, to address the problem of information silos and improve evaluation effectiveness, it is necessary to establish a dynamic response mechanism and break through data fusion technology. Infrastructure resilience assessment typically employs quantifiable metrics to evaluate system performance under disruptions. Within transportation networks, these encompass functional recovery speed metrics such as Caliendo C [19] 2024 application of post-accident tunnel vehicle speed restoration as a proxy for traffic flow resilience, service availability indices exemplified by passenger throughput recovery rates in rail systems, and structural robustness thresholds including load-bearing capacity retention following seismic events. Tong J [20] 2024 synthesis of highway tunnel resilience frameworks further identifies prevalent indicators like evacuation efficiency, equipment redundancy rates, and incident response times. While effectively capturing physical–functional resilience dimensions, such conventional metrics frequently overlook critical nonlinear interdependencies among human, operational, and environmental factors—particularly in complex enclosed systems like underground rail transit where organizational adaptability through mechanisms like staff emergency coordination and dynamic risk cascades significantly influence outcomes. This methodological gap motivates our integrated WSR-4M-CIA-ANP framework, which advances beyond static metrics by systematically quantifying cross-dimensional interactions, thereby enabling comprehensive resilience optimization.

Firstly, systematic analysis across physical–operational–human dimensions and refined indicators covering personnel, equipment and facilities environment, and management, establish a comprehensive evaluation framework encompassing four core capabilities, namely, resistance, adaptation, absorption, and resilience. Then the fire resilience indicators examined in this study are not mutually independent but exhibit complex interrelationships and feedback mechanisms. These interactions form a networked structure. Through supermatrices and other tools, CIA and ANP quantitatively captures these complex correlations, better aligning with the actual characteristics of fire resilience systems. Finally, an empirical analysis of Xi’an Metro Line 1 validates the system’s effectiveness and proposed targeted strategies to enhance security capabilities. The results will tremendous provide novel theoretical foundations and practical guidance for fire safety management in urban rail transit systems.

2. Fire Resilience Assessment Analysis for Urban Underground Rail Transit

2.1. Fire Analysis of Urban Underground Rail Transit

2.1.1. Hazard-Inducing Factors in Underground Rail Systems

Fire accidents in urban underground rail transit exhibit multi-source hazard characteristics, with causation mechanisms systematically categorized into human factors, equipment factors and environmental factors. Statistical analysis of accident data reveals that mechanical/electrical equipment failures account for the highest proportion of fire incidents. Although less frequent, human factors typically lead to more severe consequences, while environmental factors demonstrate stronger unpredictability and uncontrollability. Within this tripartite framework, specific subcategories include: (1) Reliability deficiencies in equipment subsystems. (2) Insufficient operational compliance and emergency response capabilities of personnel. (3) Limitations in spatial configuration and fire-resistant material performance. By establishing an ‘equipment-personnel-environment’ hazard identification matrix, this classification provides scientific basis for weight allocation in fire resilience assessment systems, enabling effective translation from hazard mechanisms to resilience enhancement strategies.

2.1.2. Fire Characteristic Analysis

Underground rail transit fires exhibit distinctive characteristics including spatial confinement, high occupant density, and difficult rescue conditions, forming a unique fire risk system that differs significantly from above-ground structures [21]. The underground space is completely enclosed by concrete structures and lacks natural ventilation conditions. The high-temperature smoke generated by a fire is difficult to effectively discharge through thermal pressure, which can easily form a ‘chimney effect’. It only takes 3–5 min for the smoke temperature of a fire in a closed space to reach ultra-high temperature, and the thermal radiation intensity significantly increases [22]. Furthermore, the longitudinal spatial configuration connecting station halls and tunnels accelerates fire spread, with measured data showing smoke can reach adjacent railcars within 60 s horizontally, while vertical spread rates are even higher [23].

In terms of personnel evacuation, the evacuation of subway transfer stations in case of fire is mainly affected by the evacuation capacity of stairs/escalators from the platform to the lobby. The width, quantity, and evacuation capacity of stairs/escalators, as well as the flow of people and evacuation rate, will affect the evacuation capacity of the entire subway transfer station [24]. Compared with no fire evacuation, limited ventilation conditions may cause visibility to drop below 1 m in the early stages of a fire, and the concentration of toxic gases can reach the lethal threshold within 10 min, resulting in the underutilization of safety exits and prolonging evacuation time.

From an emergency response perspective, underground rail transit systems face significant challenges due to their limited entry/exit configurations and the unpredictable nature of fire incidents [25]. The electrical systems comprising power supply, signaling, communications, and over ten other subsystems are particularly vulnerable to domino effects during fires. For instance, HCl gas generated from burning cables can corrode sensitive equipment, thereby exacerbating accident consequences [26]. These interdependent characteristics dynamically evolve, creating unique fire risk propagation mechanisms in underground transit environments. Comprehensive understanding requires multi-physics coupling simulations to inform targeted prevention and mitigation strategies [27].

2.2. Fire Resilience

The concept of resilience was originally proposed by Western scholars to describe the capacity of objects or materials to recover after deformation under external forces. Fire resilience assessment refers to the scientific process of evaluating the vulnerability and recovery capacity of cities, communities or buildings when exposed to fire hazards. By systematically assessing various aspects of underground rail transit systems, low-resilience zones or structures can be identified, enabling targeted improvement measures to enhance future fire response capabilities from multiple dimensions. Given the intersection between urban underground rail transit fire resilience and urban characteristic indicators, such systems should demonstrate robustness, redundancy, rapidity, resourcefulness, adaptability, and recoverability, as summarized in

Table 1. Fire resilience analysis.

Characteristic Indicators	Definition	Key Role
Robustness	The basic resilience of the system in the event of a fire.	Improve the fire resistance of buildings.
Redundancy	Enhance system reliability through backup facilities or resources.	Reducing the impact of accidents.
Rapidity	Respond quickly after a disaster, allocate resources, and restore functionality.	Reduce functional downtime, minimize secondary disasters.
Resourcefulness	Enhance fire response strategies.	Improve fire prevention efficiency and reduce the risk of human error.
Adaptability	After a fire through design and management adjustments.	Enhance system flexibility.
Recoverability	The comprehensive ability to maintain basic functions and quickly repair after a disaster.	Accelerate operational recovery and reduce long-term downtime losses.

.

3. Fire Resilience Assessment System

3.1. Selection of Evaluation Methods

3.1.1. WSR Methodology

The WSR (Wuli-Shili-Renli) methodology was proposed by Professor Gu Jifa and Dr. Zhu Zhichang in 1994 as a systematic integration framework for complex system governance. Its theoretical core lies in deconstructing and reconstructing organizational contexts through the tripartite coupling perspective of ‘physical−operational−human’ dimensions [28]. WSR has been widely applied in various domains including enterprise strategic management due to characterized by systematicity, comprehensiveness, and adaptability. However, its effective implementation depends on an organization’s capacity for deep environmental complexity analysis and high-level collaborative governance mechanisms. Insufficient professional knowledge or systems management capabilities may lead to diminished practical efficacy.

3.1.2. Cross-Influence Analysis

CIA is a future scenario modeling technique for complex systems, designed to quantify nonlinear and interdependent interactions among multiple events and variables, thereby dynamically adjusting conditional probability distributions of event occurrences [29]. By constructing cross-impact matrices, this method overcomes the strong independence assumption inherent in conventional predictive models. CIA enables the integration of qualitative judgments with quantitative data, finding extensive applications in technology assessment, policy foresight, and risk governance. Despite its inherent uncertainties, CIA remains an indispensable tool for anticipatory governance of complex adaptive systems by revealing systemic interconnections and evolutionary pathways, thus providing multidimensional perspectives for strategic decision-making under uncertainty.

3.1.3. Analytic Hierarchy Process

The Analytic Hierarchy Process (AHP) is a simple, flexible, and practical multi criteria decision-making method proposed by Professor T.L. Saaty in the United States, which can provide reference for some complex and fuzzy problems [30]. Particularly suitable for issues difficult to quantify completely, AHP offers a novel, concise, and practical modeling approach. Its fundamental concept involves hierarchically structuring problems by dividing decision-making events into three levels: goal level, criterion level, and alternative level. The decision problem is systematically decomposed into a hierarchical structure, followed by solving judgment matrices to determine the weight of each element relative to elements in the higher level. Ultimately, the final weights of alternatives relative to the goal level are calculated, which can then inform subsequent strategy formulation.

3.1.4. Analytic Network Process

The ANP was developed by Saaty as an extension of the AHP, represents a multi-criteria decision-making framework for complex systems designed to overcome the linear constraints of hierarchical structures on element interdependencies and feedback relationships [31,32]. The implementation procedure involves: (1) defining decision objectives and evaluation criteria while decomposing the problem into control and network layers; (2) constructing pairwise comparison matrices based on expert judgment or empirical data, employing the 1–9 scale to quantify dominance relationships; (3) formulating supermatrices to integrate local weights, followed by weighted and limit operations to derive steady-state global weights. ANP combines qualitative and quantitative advantages, effectively addressing fuzzy, uncertain, and nonlinear interaction scenarios. However, its validity critically depends on data accuracy and expert consistency. Meanwhile computational complexity grows exponentially with network scale, necessitating specialized algorithms and software support.

3.1.5. The Systematic Integration of WSR, 4M, CIA, and ANP

The systematic integration of WSR methodology, 4M theory, CIA, and ANP is essential to overcome the limitations of standalone applications. The WSR methodology provides a holistic framework for identifying fire risk factors across physical, operational, and human dimensions but may yield overlapping indicators. The 4M theory resolves this redundancy by restructuring factors into actionable categories (personnel, equipment/facilities, environment, management), enabling quantifiable indicator refinement. CIA then quantifies nonlinear interdependencies among these refined indicators, addressing dynamic interactions ignored by static models. Finally, ANP incorporates these interdependencies into a networked weight-calculation structure, overcoming the linear constraints of traditional hierarchical methods. This complementary approach ensures a comprehensive, dynamic assessment of fire resilience, where WSR and 4M establish the indicator framework, CIA maps interactions, and ANP translates them into scientifically validated weights.

3.2. Establishment of Fire Resilience Assessment Process for Urban Underground Rail Transit

3.2.1. Framework Development for Fire Resilience Assessment System

The construction of an urban underground rail transit fire resilience assessment system is a systematic, multi-stage process requiring scientific methodology, and rigorous logical framework [33]. Initially, comprehensive identification of potential fire-inducing factors (personnel, equipment, and environmental) is conducted through historical accident analysis, literature review, and expert consultation. Subsequently, the WSR methodology was used to preliminarily screen and classify these factors from the physical, operational, and human dimensions, ensuring coverage of the three major levels of technology, management, and personnel. To further refine the above classification results, the 4M theory is introduced to integrate the classification results and classify factors into four categories: personnel, equipment and facilities, environment, and management. Its purpose is to eliminate duplicate or intersecting content and form more specific indicators. Next, according to the principle of fire resilience, the refined indicators are matched to ensure that each indicator is directly related to resilience. And combined with the CIA method for indicator screening and quantitative evaluation, the ANP super matrix is then used to calculate the weights of each indicator, thus constructing and obtaining a complete evaluation indicator system. Finally, dynamic adjustment mechanisms ensure practical applicability for disaster-adaptive strategy formulation, as illustrated in Figure 1.

3.2.2. Principles of Fire Resilience Assessment System

The fire resilience assessment system for urban underground rail transit must adhere to principles of scientific rigor, systematicity, applicability, dynamism, and comprehensiveness. The system fully utilize reliable data and methods to ensure the objectivity of indicators. It covers the assessment framework for fire prevention, emergency response, and post disaster recovery, achieving systematic analysis. It can also be dynamically adjusted to meet the needs of technological updates and other requirements [34,35]. The principle-based design integrates multiple dimensions including firefighting facilities, emergency plans, personnel training, and social support, with dynamic adjustment mechanisms accommodating technological updates. Combining quantitative and qualitative approaches, the assessment delivers accurate results to guide resilience enhancement and inform fire prevention decision-making.

3.2.3. Fire Resilience Assessment Indicators

Statistical analysis of recent urban underground fire incidents worldwide identified critical risk factors, which were systematically modeled using fault tree analysis. This approach quantitatively and qualitatively evaluated factor relationships and their relative impacts through ‘quality–quantity–form’ dimensional analysis. Integrating WSR methodology with 4M theory, the study transformed identified risk factors into measurable resilience indicators, including resistance, adaptation, absorption, and resilience capacities, as described in Figure 2.

The resistance capacity evaluates system robustness by assessing disturbance resistance and functional maintenance during fire initiation. Adaptation capacity focuses on resourcefulness, redundancy, and adaptability to measure flexible response capabilities. Absorption capacity examines impact mitigation through redundancy and resourceful resource allocation. It enables intervention before the fire’s destructive force peaks, reducing secondary losses caused by fire spread. Resilience capacity emphasizes rapidity and recoverability to evaluate post-disaster functionality restoration. The established correlations between primary and secondary indicators are systematically presented in

Table 2. Fire resilience and assessment indicator matching analysis.

Primary Indicators	Fire Resilience	Secondary Indicators Analysis
Resistance capacity	Robustness	Temperature and smoke detection equipment
		Ventilation and smoke extraction equipment
		Automatic sprinkler systems
		Surveillance equipment
Adaptability capacity	Redundancy Resourcefulness Adaptability	Internal material fire resistance rating
		Fire protection in buildings
		Off-site firefighting facilities
		The setting of fire partitions
Absorptive capacity	Redundancy Resourcefulness	Fire safety training and awareness
		Staff emergency command capabilities
		Emergency response plan development
Resilience capacity	Rapidity Recoverability	Emergency repair and restoration
		Fire cause investigation and assessment
		Reflection on the accident and summary

, demonstrating the quantitative relationships across resilience dimensions through comprehensive assessment.

Based on the design principles of the urban underground rail transit fire resilience assessment system, the asymmetric distribution of indicator quantities fundamentally derives from divergent functional dimensions and evaluation logic. Resistance capacity and adaptation capacity each incorporate four secondary indicators to comprehensively address the complexities of physical prevention systems and structural redundancy requirements. Conversely, absorption capacity and resilience capacity achieve methodological efficiency through consolidated three-indicator frameworks, intentionally accommodating critical social resilience dimensions within their streamlined structures: absorption capacity focuses on organizational-behavioral adaptability during fire incidents, where its triad of training, command capabilities, and emergency planning (C3)—inherently encompassing media coordination through crisis communication protocols—forms a synergistic operational whole; resilience capacity establishes a closed-loop recovery cycle wherein D1 executes immediate restoration, D2 analyzes root causes, and D3 refines lessons learned while encapsulating psychosocial recovery through passenger trauma support programs and post-event satisfaction surveys, with all three indicators exhibiting essential interdependencies that validate their consolidated quantification. This integrated approach maintains assessment rigor while holistically addressing both technical and human-centric resilience factors through strategically asymmetric yet functionally complete indicator allocation.

3.3. Fire Factor Identification in Urban Underground Rail Transit

3.3.1. Identification of Fire Factor from Method WSR

Based on the composition of urban underground rail transit systems and surrounding fire-influencing environments, the WSR methodology identifies fire resilience factors through physical–operational–human dimensions [36]. It can be divided into the following three parts, as shown in Figure 3:

(1)

The physical dimension examines material mechanisms during operation, covering facility equipment and built environments.

(2)

The operational dimension addresses organizational management and operational processes, focusing on coordinated firefighting technologies and equipment deployment.

(3)

The human dimension analyzes behavioral, psychological, and interactive aspects of personnel that directly influence fire progression, assessed through competency and behavioral factors.

Figure 3. Initial identification by WSR method.

Figure 3. Initial identification by WSR method.

3.3.2. 4M Theoretical Classification and Recognition

The 4M theory classifies fire factors into four categories: personnel, equipment and facilities, environment, and management [37]. Based on the contents of the six factors obtained by the WSR method and further integration in combination with the 4M theory, the fire factor indicators of urban underground rail transit are specifically sorted out from the four levels of personnel, equipment and facilities, environment and management, as shown in Table 3.

(1)

The personnel aspect encompasses personnel competency and behavior, where competency affects response speed and handling capability while behavior determines fire prevention and evacuation efficiency.

(2)

The equipment and facilities dimension covers equipment, tools, and technical conditions, including firefighting facilities, ventilation systems, escape devices, electromechanical equipment and fire compartmentation. These hardware directly determine the fire prevention and control capabilities and escape conditions.

(3)

The environment involves station architectural structures, decoration materials, spatial characteristics, and surrounding fire facilities, which collectively influence smoke diffusion, fire load, and external rescue conditions.

(4)

The management element comprises organizational administration and technical measures that enhance overall fire response capability through institutional frameworks and technological applications.

Table 3. Analysis of fire factors in urban subway systems.

4M	Indicators	Specific Details
Personnel	Emergency awareness	Staff/passenger safety awareness affects reaction speed
	Emergency skills	Skills such as using fire extinguishers and guiding people
	Psychological quality	Affects decision-making ability
	Evacuation behavior	Whether passengers follow instructions and maintain order
	Emergency decision	Staff assessment of fire conditions and response measures
	Collaborative	Internal collaboration and external rescue
	Fire assessment	Computer simulation
	Firefighting techniques	Advanced firefighting equipment
Equipment and Facilities	Firefighting equipment	The completeness and reliability of fire extinguishers, fire hydrants, and automatic sprinkler systems
	Ventilation systems	Effectively reduce smoke concentration, improve visibility
	Escape facilities	The width, number, and accessibility of passageways, the rationality of exit settings, and the integrity
	Electromechanical equipment	Equipment aging or improper maintenance
	Fire compartmentation facilities	Fire doors/walls and other facilities
	Monitoring and alarm systems	Timely fire warning to gain time for response.
Environment	Building structure	Platform/station hall layout and space height
	Material characteristics	The combustion performance and smoke
	Ventilation conditions	The design and operating status of the ventilation system
	Fire load	The amount and distribution of combustible materials
	Surrounding fire protection	Other civil firefighting facilities/fire stations
Management	Emergency plan	Clarify the responsibilities and action processes
	Emergency drill	Test the feasibility of the contingency plan
	Staff training	Improve staff fire emergency response capabilities.
	Information transmission	Ensure that fire information is communicated

Table 3. Analysis of fire factors in urban subway systems.

4M	Indicators	Specific Details
Personnel	Emergency awareness	Staff/passenger safety awareness affects reaction speed
	Emergency skills	Skills such as using fire extinguishers and guiding people
	Psychological quality	Affects decision-making ability
	Evacuation behavior	Whether passengers follow instructions and maintain order
	Emergency decision	Staff assessment of fire conditions and response measures
	Collaborative	Internal collaboration and external rescue
	Fire assessment	Computer simulation
	Firefighting techniques	Advanced firefighting equipment
Equipment and Facilities	Firefighting equipment	The completeness and reliability of fire extinguishers, fire hydrants, and automatic sprinkler systems
	Ventilation systems	Effectively reduce smoke concentration, improve visibility
	Escape facilities	The width, number, and accessibility of passageways, the rationality of exit settings, and the integrity
	Electromechanical equipment	Equipment aging or improper maintenance
	Fire compartmentation facilities	Fire doors/walls and other facilities
	Monitoring and alarm systems	Timely fire warning to gain time for response.
Environment	Building structure	Platform/station hall layout and space height
	Material characteristics	The combustion performance and smoke
	Ventilation conditions	The design and operating status of the ventilation system
	Fire load	The amount and distribution of combustible materials
	Surrounding fire protection	Other civil firefighting facilities/fire stations
Management	Emergency plan	Clarify the responsibilities and action processes
	Emergency drill	Test the feasibility of the contingency plan
	Staff training	Improve staff fire emergency response capabilities.
	Information transmission	Ensure that fire information is communicated

3.3.3. Establish of Assessment Index System

The WSR-4M model transforms identified fire risk factors into four core resilience indicators: resistance capacity (A), absorption capacity (B), adaptation capacity (C), and resilience capacity (D). Through systematic analysis, these primary indicators are further decomposed into 14 secondary indicators (A1–A3…D1–D3) to establish a comprehensive evaluation system, as presented in

Table 4. Fire resilience assessment indicators for urban underground rail transit systems.

Goal Level	Primary Indicators	Explanation of Primary Indicators	Secondary Indicators
Fire resilience Safety assessment system for urban underground rail transit	Resistance Capacity A	Ability to prevent the spread of fire and reduce damage to system functionality.	Temperature and smoke detection equipment A1
			Ventilation and smoke extraction equipment A2
			Automatic sprinkler systems A3
			Surveillance equipment A4
	Adaptability capacity B	The ability to mitigate the impact of a fire on system functionality through backup facilities	Internal material fire resistance rating B1
			Fire protection in Buildings B2
			Off-site firefighting facilities B3
			Setting of fire partitions B4
	Absorptive capacity C	Ability to flexibly adjust operational strategies, based on the characteristics and progression of a fire.	Fire safety training and awareness C1
			Staff emergency command capabilities C2
			Emergency response plan development, drills, and refinement C3
	Resilience capacity D	Ability to quickly resume operations, repair damaged facilities and equipment.	Emergency repair and restoration of professional capabilities D1
			Fire cause investigation and assessment D2
			Reflection on the accident and summary of lessons learned D3

[38]. Using the ANP framework, the assessment system is structured hierarchically with three layers: goal level (urban underground rail transit fire resilience assessment), criterion level (A–D primary indicators), and alternative level (14 coded secondary indicators). This standardized coding system facilitates clear identification and documentation throughout the assessment process while maintaining methodological rigor in quantifying interdimensional relationships.

4. Calculation and Analysis of Fire Resilience Assessment Model

Building upon the four primary resilience indicators resistance capacity, adaption capacity, absorption capacity, and resilience capacity in this work, synthesizes global research on metro station fire safety resilience to establish 14 secondary indicators encompassing critical economic and social dimensions. These secondary indicators may include but are not limited to the effectiveness of fire prevention facilities, the speed and efficiency of fire emergency response, the ability to control the spread of fire, the smoothness of personnel evacuation, the minimization of fire losses, the speed and quality of post disaster recovery, etc. The CIA method is adapted for logical sorting and establishment of interrelationships, and a standardized relationship matrix is established. Subsequently, the ANP was employed to construct judgment matrices, determining relative weights while modeling the interdependent network structure of mutually influencing indicators according to ANP principles.

4.1. Construction of ANP Network Structure

This study employs the ANP to construct a fire resilience assessment model for urban underground rail transit, featuring a core architecture comprising control and network layers. The control layer establishes ‘enhancing urban underground rail transit fire resilience’ as the overarching goal, supported by four interdependent evaluation criteria: resistance, adaptation, absorption, and resilience capacities, forming a complete decision-making framework. The network layer adopts a ‘cluster-element’ hierarchical structure, transforming these criteria into corresponding element clusters, each containing 3 or 4 specific indicators. At this point, the main focus should be on analyzing and judging whether there are any relevant relationships such as influence and feedback between all elements, which can be quantified and scored through expert surveys and other forms. And consistency verification is essential because the judgment matrix relies on experts’ subjective assessments, which may introduce logical inconsistencies due to cognitive biases or information gaps. Calculating the consistency ratio (CR) measures the severity of contradictions. In network architecture, the connections between element groups are determined by the elements within each group. If there is a pair of elements that have correlation between two groups of elements, then these two groups of elements are considered to have a connection.

4.2. Construction of Judgment Matrices

Following the CIA which quantified indicators and established inter-element relationships, pairwise comparisons are conducted to construct judgment matrices. Practically, domain experts evaluate relative influence between elements based on the predefined ANP network structure, with specific scoring criteria illustrated in

Table 5. Judgment matrices scale definition.

Scale	Meaning
1	The two elements are equally affected by the secondary criterion.
3	When comparing the two elements, the former is slightly larger than the latter due to the influence of the secondary criterion.
5	When comparing the two elements, the former is greater than the latter due to the influence of the secondary criterion.
7	When comparing the two elements, the former is significantly larger than the latter due to the influence of the secondary criterion.
9	When comparing the two elements, the former is greatly affected by the secondary criterion compared to the latter.
2, 4, 6, 8	The median value of the above adjacency judgment
The reciprocal of the above value	If the ratio of the degree to which elements i and j are affected by the sub-criterion is a, then the ratio of the degree to which element j and element i are affected by the sub-criterion is 1/a.

. Within the ANP framework, each judgment matrix is developed by comparing two elements’ relative dominance under a given criterion, where numerical ratings reflect their comparative influence on subordinate criteria. This systematic approach transforms qualitative expert judgments into quantitative matrices while preserving the network’s interdependent characteristics.

4.3. Solving Judgment Matrices

After obtaining the judgment matrices, the normalized eigenvector for each matrix must be calculated and subjected to consistency verification. This study adopts the AHP algorithm for eigenvector computation through the following procedure [39,40]:

First, let a_ij represent the original judgment matrix data and b_ij denote the standardized matrix elements. Column-wise normalization of the judgment matrix yields the standardized matrix, where each element b_ij is derived by dividing a_ij by the sum of its respective column elements. This transformation process ensures comparability across all matrix components while preserving relative weighting relationships.

$$b_{ij}={\displaystyle \frac{a_{ij}}{{{\displaystyle \sum }}_{k=1}^n{a}_{kj}}}$$

(1)

The second step is to sum the standard judgment matrix row by row:

$$W_i={\displaystyle \sum }_{j=1}^n{b}_{ij}$$

(2)

The third step is to normalize it to obtain the weights:

$$W_i={\displaystyle \frac{W_i}{{{\displaystyle \sum }}_{j=1}^n{W}_i}}$$

(3)

Then, conduct a consistency check on the judgment matrix to determine whether it is reasonable.

The first step is to calculate the deviation consistency index CI:

$$CI={\displaystyle \frac{{\lambda }_{max}-n}{n-1}}$$

(4)

Among them, ${\lambda }_{\mathrm{m}\mathrm{a}\mathrm{x}}$ represents the maximum eigenvalue of the judgment matrix, and n is the order of the judgment matrix.

The second step is to search for the random consistency index RI and are summarized in

Table 6. Random consistency index RI standard values.

m	1	2	3	4	5	6	7	8	9
RI	0	0	0.52	0.89	1.12	1.26	1.36	1.41	1.46

:

Step three, calculate the consistency ratio coefficient CR:

$$CR={\displaystyle \frac{CI}{RI}}$$

(5)

A CR value below 0.1 indicates successful consistency verification, confirming logical coherence in the judgment matrix. Conversely, CR values exceeding 0.1 reveal internal inconsistencies within the expert evaluations, necessitating reconstruction of the judgment matrix to eliminate contradictory pairwise comparisons. This threshold ensures the reliability of derived weights while maintaining methodological rigor throughout the ANP process.

4.4. Construction of ANP Supermatrix and Final Weight Calculation

The unweighted supermatrix, weighted supermatrix, and limit supermatrix are successively obtained employ supermatrix operations. The relative weights and overall weights of each index are calculated. The specific process is as follows.

First, Construct an unweighted super matrix. After solving the normalized eigenvectors of all judgment matrices and conducting consistency checks, the normalized eigenvectors of all judgment matrices are integrated into a large matrix, namely an unweighted super matrix. Assuming network layer element groups C₁, C₂, …, C_n where group C_i contains elements d_i1, d_i2, …, d_in, pairwise comparisons are conducted using element d_jn from group C_j as the secondary criterion to generate judgment matrices. The normalized eigenvector (W_i1(jn), W_i2(jn), …, W_in(jn))^T from each consistent matrix forms a local weight vector, collectively constituting block matrix W_ij through analogous procedures for other elements.

$$W_{ij}=\left[\begin{array}{cccc}{W}_{i1}^{\left(j1\right)}& W_{i1}^{\left(j2\right)}& \cdots & W_{i1}^{\left(jn\right)}\\ W_{i2}^{\left(j1\right)}& W_{i2}^{\left(j2\right)}& \cdots & W_{i2}^{\left(jn\right)}\\ ⋮& ⋮& \ddots & ⋮\\ W_{in}^{\left(j1\right)}& W_{in}^{\left(j2\right)}& \cdots & W_{in}^{\left(jn\right)}\end{array}\right]$$

(6)

Among them, if there is no influence relationship between element group C_j and element group C_i, then W_ij = 0. Finally, combining all the local weight vector matrices W_ij results in an unweighted supermatrix.

$$W=\left[\begin{array}{cccc}{W}_{11}& W_{12}& \cdots & W_{1n}\\ W_{21}& W_{22}& \cdots & W_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ W_{n1}& W_{n2}& \cdots & W_{nn}\end{array}\right]$$

(7)

Step two, calculate the weighted super matrix. Comparing the degree of influence of each element group C_j as a secondary criterion to form a judgment matrix, the normalized eigenvectors (i.e., weight vectors) are (v_1j, v_2j, …, v_Nj) T, thus obtaining the weighted matrix V.

$$V=\left[\begin{array}{cccc}{v}_{11}& v_{12}& \cdots & v_{1N}\\ v_{21}& v_{22}& \cdots & v_{2N}\\ ⋮& ⋮& \ddots & ⋮\\ v_{N1}& v_{N2}& \cdots & v_{NN}\end{array}\right]$$

(8)

Multiply the weighted matrix by the elements in the unweighted supermatrix W to obtain the weighted matrix (W_i). The supermatrix (W) composed of (W_ij) is the weighted supermatrix.

The third step is to obtain the limit supermatrix. When the weighted supermatrix is multiplied by itself an infinite number of times, it will converge to a fixed limit value that remains unchanged, resulting in the limit supermatrix. By calculating the extreme super matrix, the extreme ranking weights of each element can be obtained, which is the overall weight.

4.5. Determination of Model Weights for Assessment Indicators

By considering indicators at the criterion level, sub-criterion level, etc., and analyzing the relationships between criterion-layer indicators, an expert survey questionnaire was designed. It intended that each expert independently complete a form assessing pairwise influences among the 14 indicators, marking “1” for confirmed impacts and omitting or entering “0” for non-existent relationships. The aggregated assessments from all 15 experts were consolidated into the comprehensive results presented in

Table 7. The influence relationship of network structure indicators in the fire resilience evaluation system.

Indicators	A1	A2	A3	A4	B1	B2	B3	B4	C1	C2	C3	D1	D2	D3
Temperature and smoke detection equipment A1	0	1	0	0	0	1	0	1	0	0	1	0	1	0
Ventilation and smoke extraction equipment A2	1	0	1	1	0	0	0	1	0	0	1	0	1	0
Automatic sprinkler systems A3	0	0	0	1	0	1	0	1	0	0	0	0	1	0
Surveillance equipment A4	0	0	1	0	0	0	0	1	0	0	1	0	1	0
Internal material fire resistance rating B1	0	0	1	0	0	1	0	0	1	0	0	0	1	0
Fire protection in buildings B2	1	1	1	1	1	0	1	1	1	0	1	0	1	1
Off-site firefighting facilities B3	0	0	0	0	0	1	0	0	0	0	1	0	1	0
The setting of fire partitions B4	1	1	1	1	0	1	0	0	1	0	1	0	1	0
Fire safety training and awareness C1	0	0	0	0	1	0	1	0	0	1	1	0	0	1
Staff emergency command capabilities C2	0	0	0	1	0	0	0	0	1	0	1	1	1	1
Emergency response plan C3	1	1	1	1	0	1	1	0	1	1	0	1	1	1
Emergency repair and restoration D1	0	0	0	0	0	0	1	0	1	1	1	0	1	0
Fire cause investigation and assessment D2	0	1	1	0	1	0	0	1	1	1	1	0	0	1
Reflection on the accident and summary D3	0	0	0	1	0	0	1	1	1	1	1	0	0	0

. Expert opinions are collected as the comprehensive result. The sample size of 15 experts was determined to be sufficient based on their extensive experience in metro safety management, fire emergency planning, and fire inspection. A validation mechanism was implemented, where influence relationships were considered valid only if approved by over half of the experts. This approach aligns with standard practices in expert evaluation studies for similar resilience assessments, ensuring result reliability and minimizing subjective bias.

Through a systematic analysis of the impact relationship matrix within the assessment framework, the key interdependencies were identified and plotted in this study. The relationships among the various element groups, the relationships among the individual elements, and the relationships between the elements in one element group and those in other element groups. And based on the relationship, the network structure of the fire resilience safety evaluation system for urban underground rail transit was drawn and established, as shown in Figure 4. This figure illustrates the ANP model structure for fire resilience assessment, explicitly mapping interdependencies among 14 secondary indicators across four capacities: the Resistance Capacity cluster (A1–A4) represents physical prevention systems; the Adaptation Capacity cluster (B1–B4) shows structural redundancy factors such as fire compartmentalization (B4) interacting with external fire facilities (B3); and crucially, cross-capacity dependencies are visualized through inter-cluster links, such as emergency planning (C3) in Absorption Capacity modulating emergency restoration (D1) in Resilience Capacity—thereby transforming theoretical resilience dimensions into computable variables.

Based on the established indicator influence relationships, multiple judgment matrices are constructed for interacting criteria. Following data collection from industry experts and practitioners, the matrix results are aggregated to determine inter-indicator importance levels. Given the substantial number of matrices generated, representative examples are special selected for demonstration, while the detailed results are available in Appendix A.

These tables demonstrate weight relationships among indicators under different sub-criteria. Taking

Table A4. Decision matrix based on fire cause investigation and assessment D2 as a secondary criterion.

Indicators	B1	B2	B3	B4
Internal material fire resistance rating B1	1	0.5	3	8
Fire protection in buildings B2	2	1	7	6
Off-site firefighting facilities B3	0.333333333	0.142857143	1	3
The setting of fire partitions B4	0.125	0.166666667	0.333333333	1

in Appendix A as an example, it presents the judgment matrix constructed with fire cause investigation and assessment D2 as the sub-criterion, evaluating elements B1–B4 of interior material fire rating, building fire protection, external fire facilities, and fire compartmentalization that influence D2. Following the 1–9 scale method, fire protection in buildings B2 shows lesser influence on internal material fire resistance rating B1 compared to off-site firefighting facilities B3, thus receiving a weight of 2. All matrices undergo normalization and satisfy consistency requirements with CI < 0.1.

After processing all matrices to obtain normalized eigenvectors and verifying consistency, representative calculation results for the four selected datasets are provided. The normalized eigenvectors are subsequently integrated into an unweighted supermatrix, while the detailed results are available in Appendix B. Repeat the above steps for all groups of n elements, where i = 1, 2, …, n; j = 1, 2, …, n, and the hypermatrix W can be obtained.

$$W=\left[\begin{array}{cccc}{W}_{11}& W_{12}& \cdots & W_{1n}\\ W_{21}& W_{22}& \cdots & W_{2n}\\ ⋮& ⋮& ⋮& ⋮\\ W_{n1}& W_{n1}& \cdots & W_{nn}\end{array}\right]$$

(9)

The weighted matrix A is obtained through the following procedure: For each element group c_i (i = 1, 2, …, n) serving as a criterion, pairwise comparisons of cluster importance are performed. Judgment matrices are constructed and their normalized eigenvectors are calculated. When no relationship exists between element groups and c_i, zero values are assigned to the corresponding components of the weighting vector. This systematic approach ensures proper normalization throughout the matrix construction process.

$$A=\left[\begin{array}{cccc}{a}_{11}& a_{12}& \cdots & a_{1n}\\ a_{21}& a_{22}& \cdots & a_{2n}\\ ⋮& ⋮& ⋮& ⋮\\ a_{n1}& a_{n2}& \cdots & a_{nn}\end{array}\right]$$

(10)

Weight the supermatrix W with the matrix A to obtain the weighted supermatrix $\bar{W}$.

$$\stackrel{-}{W}=\left[\begin{array}{cccc}{a}_{11}{W}_{11}& a_{12}{W}_{12}& \cdots & a_{1n}{W}_{1n}\\ a_{21}{W}_{21}& a_{22}{W}_{22}& \cdots & a_{2n}{W}_{2n}\\ ⋮& ⋮& ⋮& ⋮\\ a_{n1}{W}_{n1}& a_{n2}{W}_{n2}& \cdots & a_{nn}{W}_{nn}\end{array}\right]$$

(11)

Then normalize the weighted hypermatrix $\bar{W}$ by columns to ensure that the sum of each column is 1.

If the elements of the weighted hypermatrix $\bar{W}$ are w_ij, then the size of w_ij reflects the one-step advantage of element i over element j. The advantage of i over j can also be obtained by $\sum _{k=1}^n{w}_{ik} w_{kj}$, which is called the two-step advantage, i.e., ${\bar{W}}^2$.

When ${\bar{W}}^{\infty }=\underset{t\to \infty }{lim}{\bar{W}}^t$, the limit super matrix can be obtained. Simply put, it is $\bar{W}$ infinite self-multiplication until the matrix results no longer changes, at which point the column vectors of the matrix are the global weights of the elements.

The urban underground rail transit fire resilience assessment model was established through systematic identification of fire-related factors and determination of four primary indicators of resistance capacity, adaptation capacity, absorption capacity, and resilience capacity, along with 14 secondary indicators. Inter-indicator relationships were carefully defined to construct the assessment framework. The ANP was then employed to assess mutual influences among indicators, resulting in the development of corresponding judgment matrices. Through matrix calculations, indicator weights were derived, with particular attention given to factors demonstrating higher weight proportions. Based on these findings, targeted disaster-adaptive strategies were formulated as illustrated in Figure 5. This diagram presents a hierarchically structured evaluation framework integrating four core capacities essential for fire resilience in underground rail systems. At the top level, the model divides resilience into resistance (A)—covering physical prevention systems like temperature/smoke detection (A1) and ventilation/smoke extraction (A2); Adaptability (B)—addressing structural safeguards such as Off-site Firefighting Support (B3) and fire partitions (B4); Absorptive capacity (C)—focusing on human factors like staff emergency command (C2); and resilience (D)—encompassing post-incident actions including Lessons Learned (D3).

5. Application of Resilience Safety Assessment Model for Urban Underground Rail Transit Fire

5.1. Introduction to Example Scenarios

The proposed fire resilience assessment model was rigorously validated through empirical application to Xi’an Metro Line 1. Xi’an Metro Line 1 is the second metro line to be put into operation in Xi’an. The entire line, which is 42.1 km long and underground with a total of 30 underground stations. The system operates six-carriage Type B trains and has recorded a maximum daily passenger flow of 933,400. This station on Line 1 is designed with standardized three-level island platforms, consisting of a concourse level containing service facilities, an equipment level, and an island-style platform level. The comprehensive fire protection system incorporates temperature and smoke detectors installed at all station entrances, concourses, platforms, and equipment rooms. Hydrants are positioned at 30-m intervals, equipped with water guns, hoses, and fire reels. Powder and CO₂ fire extinguishers are deployed beneath seats and at mini fire stations, while critical equipment rooms are protected by heptafluoropropane gas suppression systems. Emergency lighting, directional evacuation signs, and exit indicators are systematically installed throughout stations. Each station is designed with four entrances, two ventilation towers, and two barrier-free elevators to ensure efficient and safe emergency evacuation.

Xi’an Metro Line 1 was chosen for its representative characteristics of underground rail transit systems, including enclosed environments and high passenger volumes, which effectively validate the applicability of the assessment framework. While single-case studies have inherent limitations, the proposed research framework and methodology can serve as a valuable reference for other metro lines, demonstrating reasonable generalizability.

5.2. Construct a Judgment Matrix by Applying the Fire Resilience Assessment Indicators of Urban Underground Rail Transit

5.2.1. Establish an Influence Relationship Matrix

Based on the established urban underground rail transit fire resilience safety assessment system, an influence relation matrix was developed. For this assessment, the comprehensive results were derived from the opinions of 15 experts with extensive experience in subway safety management, fire emergency planning, and fire inspections. In cases of divergent opinions, an influence relation was considered valid if more than half of the experts acknowledged it. The collected data were used to construct

Table A3. Decision matrix based on staff emergency command capabilities C2 as a secondary criterion.

Indicators	D1	D2	D3
Emergency repair and restoration D1	1	2	0.125
Fire cause investigation and assessment D2	0.5	1	0.142857143
Reflection on the accident and summary D3	8	7	1

in Appendix A, the influence relation matrix for urban underground rail transit fire resilience safety evaluation indicators. In this matrix, the influence relation is directed from the row to the column, where ‘1’ indicates the presence of an influence relation between two elements, and ‘0’ indicates its absence, as shown in

Table 8. Influence relationship matrix of fire resilience assessment indicators for urban underground rail transit systems.

Indicators	A1	A2	A3	A4	B1	B2	B3	B4	C1	C2	C3	D1	D2	D3
Temperature and smoke detection equipment A1	0	1	1	1	0	1	0	1	0	0	1	0	1	0
Ventilation and smoke extraction equipment A2	1	0	1	1	0	1	0	1	0	0	1	0	1	0
Automatic sprinkler systems A3	0	0	0	1	0	1	0	1	0	0	1	0	1	0
Surveillance equipment A4	1	1	1	0	0	0	0	1	0	0	1	0	1	0
Internal material fire resistance rating B1	0	0	1	0	0	1	0	0	1	0	1	0	1	0
Fire protection in buildings B2	1	1	1	1	1	0	1	1	1	0	1	0	1	1
Off-site firefighting facilities B3	0	0	0	0	0	1	0	0	0	0	1	0	1	0
The setting of fire partitions B4	1	1	1	1	0	1	0	0	1	0	1	0	1	0
Fire safety training and awareness C1	0	0	0	0	1	0	1	0	0	1	1	1	1	1
Staff emergency command capabilities C2	0	0	0	1	0	0	0	0	1	0	1	1	1	1
Emergency response plan C3	1	1	1	1	0	1	1	1	1	1	0	1	1	1
Emergency repair and restoration D1	0	0	0	0	0	0	1	0	1	1	1	0	1	0
Fire cause investigation and assessment D2	1	1	1	1	1	1	0	1	1	1	1	0	0	1
Reflection on the accident and summary D3	1	1	1	1	1	0	1	1	1	1	1	1	1	0

.

5.2.2. Construction of Judgment Matrix and Calculation

Following the scoring of fire resilience assessment influence relations, further comparisons of the elements were conducted to derive judgment matrices after clarifying the influence and feedback relationships among them. Based on the established network hierarchy structure, the same 15 experts were invited to compare and score the elements. In the ANP, the judgment matrices were constructed by comparing the influence degree of two elements under a given criterion relative to a sub-criterion. A 1–9 scale method was applied for scoring all judgment matrices. After normalization, the CI was verified to be less than 0.1, meeting the consistency requirement.

According to the influence relation matrix of urban underground rail transit fire resilience assessment indicators in Appendix B, a total of 52 judgment matrices were established. For clarity, five randomly selected judgment matrices are presented, while the detailed results are available in Appendix C. After obtaining all judgment matrices, the normalized eigenvectors were calculated, and consistency tests were performed. The computational results of the judgment matrices were then derived. Selected data are presented, while the detailed results are available in Appendix D.

5.3. Weight Calculation of Fire Resilience Safety Assessment Indicators

After solving all normalized eigenvectors of the judgment matrices and conducting consistency tests, these normalized eigenvectors were integrated into a large matrix, referred to as the unweighted supermatrix. For any given element group C_j as the sub-criterion, pairwise comparisons were conducted to assess the influence of different element groups, forming a judgment matrix. The normalized eigenvector (i.e., the weight vector) (v_1j, v_2j, …, v_Nj)T(v_1j, v_2j, …, v_Nj)T was derived, resulting in the weighted matrix. The weighted supermatrix was then raised to an infinite power until it converged to a stable limit matrix, where the values remained constant. Through this computation, the final weight distribution of the indicator system was obtained, as presented in

Table 9. Weighting of indicators in the fire resilience safety evaluation system for urban underground rail transit.

Primary Indicators	Weighting	Secondary Indicators	Local Weighting	Global Weighting	Sorting
Resistance capacity A	0.41855	Temperature and smoke detection equipment A1	0.36978	0.15477	4
		Ventilation and smoke extraction equipment A2	0.37931	0.15876	3
		Automatic sprinkler systems A3	0.08289	0.03469	8
		Surveillance equipment A4	0.16803	0.07033	5
Adaptability capacity B	0.1133	Internal material fire resistance rating B1	0.13839	0.01568	13
		Fire protection in buildings B2	0.61942	0.07018	6
		Off-site firefighting facilities B3	0.04095	0.00464	14
		The setting of fire partitions B4	0.20124	0.0228	10
Absorptive capacity C	0.10115	Fire safety training and awareness C1	0.18269	0.01848	12
		Staff emergency command capabilities C2	0.28908	0.02924	9
		Emergency response plan C3	0.52823	0.05343	7
Resilience capacity D	0.367	Emergency repair and restoration D1	0.05880	0.02158	11
		Fire cause investigation and assessment D2	0.48401	0.17763	1
		Reflection on the accident and summary D3	0.45719	0.16779	2

.

5.4. Analysis of Assessment Results

The weight calculation results indicate that resistance capacity (A) holds a weight of 0.41855, ranking as the second most critical factor after resilience capacity. Among its sub-indicators, ‘ventilation and smoke extraction equipment (A2)’ ranks third in global weight, highlighting its essential role in early-stage fire control. ‘Temperature and smoke detection equipment (A1)’ and ‘Surveillance equipment (A4)’ also exhibit relatively high weights, demonstrating that advanced monitoring technologies form the foundation of subway fire safety. Resilience capacity (D) carries the highest weight (0.367) among the four first-level indicators, emphasizing the significance of post-disaster recovery measures in urban underground rail transit fire resilience evaluation. This is due to operational disruptions would severely impact urban traffic order and commuter mobility, making efficient post-fire restoration crucial for mitigating direct economic losses and reducing prolonged urban functional disruptions. Specifically, ‘fire cause investigation and assessment (D2)’ and ‘reflection on the accident and summary of lessons learned (D3)’ rank first and second in global weight, indicating their decisive role in enhancing the overall resilience of subway systems. The higher weighting of ‘reflection on the accident and summary (D3)’ compared to ‘emergency repair and restoration (D1)’ is justified by (D3) is critical role in long-term resilience improvement through systematic lesson-learning and accident prevention. In contrast, (D1) is classified as a short-term recovery measure, emphasizing (D3) is strategic importance for sustainable enhancement of metro system resilience.

Although adaptation capacity (B) and absorption capacity (C) have comparatively lower weights, they remain non-negligible. ‘Fire protection in buildings (B2)’ ranks sixth globally, underscoring the long-term importance of architectural design in fire prevention. ‘Emergency response plan development, drills, and refinement (C3)’ ranks seventh, highlighting the necessity of preparedness measures. The low weighting of ‘off-site firefighting facilities (B3)’ (0.00464) in adaptation capacity is due to the enclosed nature of underground rail transit systems, where fire prevention primarily relies on internal facilities.

The model was only tested on Line 1 of the Xi’an Metro, and the results show that: While single-case studies have inherent limitations in generalizability—such as man-related aspects (e.g., variations in passenger emergency response capabilities, staff operational proficiency, and workforce allocation like staffing levels during peak hours); machine-related factors (e.g., differences in equipment specifications such as signal system types, asset aging rates including component wear in high-frequency lines, and technical redundancy like backup power configurations); environment-related conditions (e.g., ambient temperature ranges such as extreme cold in northern regions, natural hazard exposures including landslide risks in mountainous areas, and spatial constraints like tunnel width limitations); and management-related elements (e.g., divergent emergency protocol designs such as evacuation procedure standardization, operational regulation stringency including crowd control measures, and maintenance scheduling like preventive check frequencies)—the proposed resilience assessment methodology and framework can serve as a valuable reference for other metro lines, demonstrating reasonable applicability through adaptable indicators and computational procedures.

In conclusion, the urban underground rail transit system should adopt disaster-adaptive strategies based on these scientific assessment results for future operation management and fire prevention deployment [41,42]:

(1)

Fire safety teams should analyze fire cases from various locations, strengthen safety management in alignment with local conditions, and conduct regular risk assessments with corrective reports. Key equipment such as ventilation, smoke detection, and surveillance systems must be maintained to ensure operational reliability during fires.

(2)

Station managers should institutionalize fire emergency training for staff, passengers, and responders, promoting scientific self-rescue and mutual aid knowledge to achieve widespread awareness.

(3)

Fire-resistant design must be integrated throughout the rail transit planning and construction phases, with strict quality control to enhance building fire resistance and overall disaster resilience.

6. Conclusions

A comprehensive fire resilience assessment framework was developed to address the high fire risks and severe consequences in urban underground rail transit systems. The WSR methodology and 4M theory were integrated to establish a CIA-ANP based assessment system, with quantitative weight determination and disaster-adaptive strategies formulated through systematic network analysis. The key conclusions are presented as follows:

(1)

An urban underground rail transit fire resilience safety assessment indicator system was established through systematic research. The WSR methodology was integrated with the 4M theory to initially identify fire risk factors from three broad dimensions: human, organizational, and material aspects. The identified factors were further refined and categorized using the 4M theory to derive more specific indicators. Through resilience characteristics analysis, corresponding resilience capacities were determined. The identified fire risk indicators were then matched with these resilience capacities, resulting in the development of a comprehensive framework. The final system comprises 14 secondary indicators organized under four primary indicators: resistance capacity, adaptation capacity, absorption capacity, and resilience capacity. This study first proposed the integration of WSR methodology and 4M theory for urban rail transit fire resilience. This dual-lens approach resolves indicator redundancy in traditional models.

(2)

Developed a novel CIA-ANP computational architecture that quantifies nonlinear interdependencies among 14 resilience indicators. This model overcomes static evaluation limitations, establishing the first network-based weighting system validated through Xi’an Metro Line 1’s operational data.

The model initially employed the CIA approach to evaluate systematic relation-ships among core indicators. Through rigorous expert surveys using the 1–9 scale, CR < 0.1 and matrix operations, mutual influence relationships between indicators were precisely quantified, forming a logically structured assessment framework. Subsequently, the ANP method was introduced to construct a dual-layer network structure consisting of control and network layers. This enabled in-depth analysis of interdependencies among the 14 secondary indicators. A total of 52 judgment matrices were developed, and the weights of each indicator were determined through limit supermatrix calculations. The approach ensured the objectivity of the assessment process, with the resulting weight distribution providing scientific basis for formulating targeted resilience enhancement strategies.

(3)

The assessment system and model were validated through a case study of Xi’an Metro Line 1. Expert scoring was conducted to apply the established ANP network analysis model for urban underground rail transit fire resilience assessment in practical scenarios. The results demonstrated that resistance capacity (A) obtained the highest weight of 0.41855 among the four primary indicators. At the secondary indicator level, ‘fire cause investigation and assessment (D2)’ and ‘reflection on the accident and summary of lessons learned (D3)’ ranked first and second with global weights of 0.17763 and 0.16779 respectively, confirming their decisive role in enhancing the metro system’s overall resilience. Based on the weight distribution results, corresponding disaster-adaptive countermeasures were proposed. This practical application effectively verified the significant practical value of both the evaluation system and the analytical model.

(4)

The empirical validation was only carried out on Xi’an Metro Line 1, which leads to inherent limitations in the general applicability of the research conclusions. Specifically, the quantitative weight distribution of the model is affected by subway environmental factors, personnel management factors, and equipment operation factors in different scenarios. Therefore, such quantitative weight distribution should be regarded as a product of specific scenarios rather than a fixed rule with universal guiding significance. However, the adopted methodological framework (WSR-4M indicator integration and CIA-ANP quantification) still has general applicability, as it can customize resilience assessments according to the specific conditions of the local subway, such as environment, personnel management, and equipment operation. To advance this research, future work will focus on: ① Algorithmic optimization of the ANP model through machine learning integration to enable real-time resilience monitoring; ② Multi-system validation extending the framework to above-ground rail networks, airport terminals, and bus hubs to identify universal resilience principles; ③ Dynamic resilience management via IoT-enabled data fusion for predictive interventions. Methodologically, we will hybridize ANP with entropy weighting to reduce expert dependency and establish open-access incident datasets for benchmarking.