Content area
Purpose
Urban water distribution networks (UWDNs) face increasingly critical resilience challenges due to aging infrastructure (service life exceeding 30 years) and intensifying environmental stressors. Existing assessment frameworks often rely on single-dimensional indicators and lack quantitative mechanisms for addressing ambiguous factors. This study establishes a comprehensive, multi-criteria resilience assessment system to identify key barriers and propose data-driven optimization strategies.
Methodology
An integrated Analytic Hierarchy Process (AHP) and Fuzzy AHP (FAHP) approach was applied within a three-tier framework comprising five criteria and twenty indicators. Data were obtained from 18 interdisciplinary experts representing diverse Chinese UWDN contexts (60% eastern coastal, 40% central/western) to ensure geographical representativeness. Validation procedures included three Delphi rounds, consistency checks (CR < 0.1), ±30% sensitivity analysis, and software cross-validation using MATLAB and Yaahp.
Results
Physical infrastructure (weight = 0.290) and environmental stressors (weight = 0.282) were identified as dominant resilience dimensions, jointly explaining 57.2% of total variation. Pipeline aging (12.10%) and soil corrosivity (10.31%) emerged as primary barriers, with the top ten factors accounting for 73.6% of the overall weight. The composite resilience score reached 3.59, corresponding to a “Moderately Consistent” resilience level.
Significance
The proposed AHP–FAHP hybrid framework bridges methodological gaps in multi-criteria UWDN resilience quantification. It supports evidence-based prioritization for interventions such as pipeline renewal, anti-corrosion strategies, and intelligent monitoring deployment—shifting urban water management from reactive maintenance toward proactive resilience enhancement. Future research should incorporate dynamic monitoring data to improve temporal adaptability and predictive capability.
Research Highlights
First integration of an AHP–FAHP hybrid approach specifically tailored to engineering-based UWDN resilience assessment.
Environmental stressors (0.282) found nearly equivalent to physical infrastructure (0.290), challenging conventional resilience paradigms.
Top ten barriers contribute 73.6% of total resilience weight, enabling precision-based resource allocation.
Triple-validation protocol (Kendall’s W = 0.82, ±30% sensitivity, and dual-software verification) ensures methodological robustness.
Three-stage optimization pathway (Baseline–Efficiency–Long-term) transforms theoretical assessment into actionable engineering interventions.
Introduction
Urban water distribution networks (UWDNs), as critical lifeline infrastructure, face mounting resilience challenges from aging assets, climatic extremes, and external disruptions that threaten the continuity of urban water supply systems. This study develops a comprehensive multi-criteria resilience assessment framework designed to identify key barriers and guide targeted system improvements.
Research background and urgency
Globally, the aging of urban water infrastructure poses escalating operational and safety risks. In China, the National Bureau of Statistics [11] reported that the average UWDN service life now exceeds 30 years, with many pipelines nearing or surpassing design limits. Although pilot cities have successfully reduced leakage rates from 28% to single digits through infrastructure upgrading, the Ministry of Housing and Urban–Rural Development has mandated a nationwide leakage reduction to ≤9% by 2025, highlighting persistent structural and management challenges.
Climate change further intensifies these pressures. Extreme rainfall increases pipeline burst probabilities by 40–60% [13], while soil corrosivity in industrial and coastal areas accelerates corrosion rates by 1.5–2 times [1]. Piadeh et al. [15] identified pipeline aging as a core resilience deficit, and Vrachimis et al. [19] verified that external disturbances—such as third-party construction—significantly disrupt network operations. Beyond disturbance resistance, rapid post-failure recovery capability represents a critical secondary dimension of UWDN resilience [9].
Critical research gaps
Existing UWDN resilience assessments exhibit two fundamental limitations:
First, an over-reliance on single-dimensional indicators. Traditional studies have focused primarily on physical infrastructure parameters (e.g., material, diameter), while neglecting hydraulic–water quality performance, intelligent monitoring, and planning adaptability. Environmental stressors, including soil corrosivity and extreme weather, also receive insufficient attention. Systematic reviews reveal that only 30% of UWDN studies simultaneously address physical, functional, and environmental dimensions, and fewer than 20% achieve deep integration between assessment methodologies and engineering practice [2].
Second, the absence of ambiguous indicator quantification. Indicators such as extreme climate sensitivity, public participation, and management system completeness exhibit inherent subjectivity. Conventional qualitative descriptions (“high corrosion,” “insufficient coverage”) cannot accurately quantify resilience impacts, leading to limited decision-making reliability [3].
Although recent studies have sought to address these gaps, key deficiencies remain. Crozier et al. [6] incorporated physical–functional dimensions but omitted intelligent monitoring indicators and fuzzy quantification. Berglund et al. [4] enhanced system perception through digital twins yet lacked comprehensive assessment frameworks. Liu et al. [9] identified critical resilience points using AHP alone, overlooking ambiguity in expert evaluation. These gaps necessitate the development of a multi-criteria system integrating AHP for hierarchical weighting with FAHP for ambiguous indicator quantification.
Research objectives
This study adopts the AHP–FAHP hybrid methodology because it simultaneously manages hierarchical weight determination and fuzzy indicator quantification, as detailed in Sect. 3.1.3.
Planning and management adaptability refers to the capacity of urban water distribution network (UWDN) planning schemes and management mechanisms to adapt to evolving service conditions such as population growth, climate change, and technological upgrading. This dimension encompasses the scientific soundness of pipeline renewal plans, the stability of operation and maintenance funding, and the effectiveness of public participation mechanisms. It thus represents a core dimension for evaluating the long-term resilience of UWDNs.
Ambiguous indicators denote factors that cannot be directly characterized through objective instrumental measurements or quantitative data, and whose evaluation instead depends on subjective expert judgment. Examples include the extent of extreme climate impacts, public satisfaction with water supply reliability, and completeness of the management system. The inherent ambiguity of such indicators often leads to inconsistent evaluation results if not properly quantified.
Subjective evaluation is defined as a qualitative judgment based on an evaluator’s experience, cognition, and preferences—typically lacking unified quantitative standards and prone to individual bias. In contrast, objective evaluation involves quantitative analysis of observable, measurable data such as pipeline leakage frequency, residual chlorine compliance rates, and node water pressure qualification rates, thus providing a clear empirical foundation.
To transform subjective evaluation into quantitative assessment, this study implements the following structured procedure:
Design of a five-point Likert scale (1 = Strongly Inconsistent to 5 = Strongly Consistent) to collect qualitative assessments of ambiguous indicators from 18 interdisciplinary experts in UWDN design, maintenance, and policy.
Conversion of qualitative judgments into triangular fuzzy numbers, constructing fuzzy comparison matrices to quantify subjective preferences.
Computation of indicator membership degrees through FAHP fuzzy operations, which are then integrated with AHP-derived hierarchical weights to yield comprehensive quantitative scores for each indicator—achieving accurate quantification of subjective judgments.
The AHP–FAHP hybrid method is considered the optimal analytical tool for priority determination in UWDN resilience assessment for three primary reasons:
Hierarchical suitability: UWDN resilience possesses a clearly defined hierarchical structure (Target → Criterion → Indicator). AHP effectively clarifies relative importance through pairwise comparisons, and is particularly suitable for cases with limited criteria per layer (≤4), thereby minimizing judgment inconsistency.
Fuzziness management: FAHP compensates for AHP’s limitations in handling uncertainty, enabling the quantitative treatment of subjective and ambiguous indicators (e.g., climate sensitivity, management completeness).
Reliability assurance: When combined with consistency checks (CR < 0.1), sensitivity analysis (±30% weight fluctuation), and software cross-validation (MATLAB and Yaahp), the hybrid approach ensures robust methodological reliability and stability in the ranking of resilience priorities (Table 1).
Table 1. Literature review table of resilience assessment studies on urban water distribution networks
Author (year)
Research method
Evaluation dimensions
Innovations
Research gaps
Liu et al. [9]
AHP
Physical damage, functional recovery
Identified resilience critical points in pipeline networks
Did not consider ambiguous indicators; lacked intelligent monitoring and long-term planning dimensions
Crozier et al. [6]
Framework construction
Physical-functional dimensions
Balanced short-term emergency response and long-term adaptability
Did not quantify ambiguous indicators; failed to establish an assessment-optimization closed loop
Piadeh et al. [15]
Literature review
Multi-dimensions (physical, functional, environmental)
Systematically sorted out the current state of pipeline resilience research
Did not propose a targeted hybrid assessment method
Berglund et al. [4]
Digital twin technology
System perception dimension
Improved the capability for real-time state perception of pipeline networks
Lacked a comprehensive resilience assessment framework integrating multiple dimensions
This study (2025)
AHP–FAHP hybrid method
Physical, hydraulic-water quality, environmental, intelligent monitoring, Planning management
1. Hybrid method handles hierarchical weights and ambiguity
2. Added independent dimensions of intelligent monitoring and planning management
3. Established an assessment-optimization closed loop
–
Key innovations and contributions
This study advances both theoretical understanding and engineering practice of urban water distribution network (UWDN) resilience through three core innovations, encompassing methodological, structural, and practical dimensions.
Methodological innovation: hybridization of hierarchical and fuzzy logic approaches
This research represents the first systematic integration of the Analytic Hierarchy Process (AHP) and Fuzzy Analytic Hierarchy Process (FAHP) specifically adapted to UWDN engineering contexts. Unlike prior single-method frameworks (e.g., [9] employing AHP alone), the proposed hybridization merges AHP’s hierarchical weight determination with FAHP’s fuzzy membership quantification, effectively bridging structural logic with uncertainty modeling.
Within this dual-framework, AHP facilitates the structured ranking of indicator importance through pairwise comparisons and eigenvalue-based consistency verification (CR < 0.1), while FAHP compensates for AHP’s deficiency in processing subjective uncertainty by transforming linguistic evaluations (e.g., moderately consistent, strongly consistent) into triangular fuzzy numbers.
Through sensitivity analysis (±30% weight perturbation) and MATLAB–Yaahp cross-validation, the hybrid framework demonstrates robust ranking stability, outperforming single-method approaches in handling ambiguous, multidimensional resilience indicators. This methodological advancement enhances both quantitative precision and interpretive transparency, providing a replicable model for multi-criteria decision analysis in complex infrastructure systems.
Indicator system innovation: comprehensive and intelligent multi-dimensionality
A second innovation lies in the construction of an expanded, intelligence-integrated indicator system encompassing five major dimensions:
Physical Infrastructure (B1),
Hydraulic–Water Quality Performance (B2),
Environmental and External Stressors (B3),
Intelligent Monitoring and Response (B4), and
Planning and Management Adaptability (B5).
Distinctively, B4 and B5 are introduced as independent criterion layers—a design absent in more than 80% of prior UWDN resilience studies [15]. Sub-indicators such as real-time monitoring coverage density, leak detection and localization efficiency, and pipeline renewal strategic effectiveness enrich the assessment by integrating both short-term operational responsiveness and long-term adaptive capacity [6].
Empirical validation demonstrates high construct validity, with a content validity index (CVI) of 0.92 and 94.4% expert recognition, confirming that the indicator framework effectively captures the physical-functional-intelligent-management continuum of modern UWDN resilience. This advancement directly addresses the long-standing limitation of traditional frameworks that emphasize hardware integrity while neglecting digital and institutional intelligence dimensions.
Practical contribution innovation: quantified prioritization and actionable optimization pathways
At the applied level, the hybrid assessment identifies and quantifies key resilience barriers with high granularity:
Pipeline aging (12.10%) and soil corrosivity (10.31%) rank as the most critical, while the top 10 barriers collectively account for 73.6% of the total resilience weight. This concentrated distribution establishes a scientific foundation for targeted resource allocation, minimizing redundant investment and maximizing resilience gains.
Building upon these findings, the study proposes a three-tier optimization pathway that directly links resilience assessment to actionable strategies:
Baseline Tier (0–3 years): Renew pipeline segments where aging exceeds 40%, prioritizing ductile iron replacements and corrosion-resistant linings.
Efficiency Enhancement Tier (2–5 years): Achieve full District Metering Area (DMA) coverage and deploy intelligent leak detection to reduce leakage rates below 9%.
Long-Term Tier (5+ years): Institutionalize resilience governance by integrating pipeline renewal into municipal 5-year plans, establishing public leak-reporting platforms, and ensuring participatory monitoring with >50% citizen engagement.
This assessment–optimization closed loop bridges the gap between analytical modeling and engineering implementation—a weakness in earlier research that prioritized methodological innovation without operational integration [15]. Furthermore, scientific planning aligned with sustainable principles reduces non-revenue water loss, optimizes energy consumption, and mitigates secondary environmental impacts such as pollutant discharge [21].
Ultimately, this study promotes the transition of UWDN management from passive maintenance to proactive resilience enhancement, aligning with the global paradigm of smart and adaptive infrastructure governance. Despite notable methodological progress in prior literature, no existing framework has achieved a comparable fusion of hierarchical weighting, fuzzy quantification, and actionable engineering adaptability specifically tailored to UWDN resilience assessment.
Literature review
Research progress on resilience assessment of urban water distribution networks
The core objective of resilience assessment for urban water distribution networks (UWDNs) is to quantitatively evaluate the system’s capacity to maintain and restore water supply functionality under various disturbances. Existing studies have primarily focused on expanding assessment dimensions and innovating quantitative methods; however, significant gaps remain in achieving a holistic integration of physical, functional, environmental, intelligent, and planning dimensions—a prerequisite for comprehensive resilience evaluation.
From the perspective of assessment dimensions, early research predominantly centered on physical infrastructure performance. For instance, Tanyimboh and Seyoum [18] evaluated network efficiency based on pipeline material and diameter distribution but omitted considerations of hydraulic–water quality performance and external stressors, thereby failing to capture the full scope of resilience. In recent years, the broadening of assessment dimensions has emerged as a research hotspot. Pandit and Crittenden [14] pioneered the Index of Network Resilience (INR), integrating six attributes including network topology, node connectivity, and redundancy. Their findings demonstrated that a 10% increase in topological redundancy enhances UWDN disturbance resistance by 15%, laying a theoretical foundation for transitioning from single-dimensional physical assessments to multi-criteria structure–function frameworks. While Liu et al. [9] incorporated physical damage and functional recovery capabilities into their assessment framework, modern dimensions such as intelligent monitoring and long-term planning were still absent. In contrast, the indicator system developed in this study defines intelligent monitoring and planning adaptability as independent criterion layers, supplemented by sub-indicators such as real-time monitoring coverage density. This approach addresses existing gaps in intelligent and long-term resilience assessment, aligning with Crozier et al. [6]’s proposition that resilience planning must balance short-term responsiveness with long-term adaptability.
In terms of quantitative methods, the Analytic Hierarchy Process (AHP) has been widely adopted for its ability to clearly rank indicator importance. Nevertheless, early AHP applications failed to incorporate ambiguous indicators (e.g., extreme climate sensitivity), leading to subjective bias in evaluations. The introduction of the Fuzzy Analytic Hierarchy Process (FAHP) addressed this limitation by converting qualitative evaluations into quantitative data through triangular fuzzy numbers, thereby resolving the challenge of quantifying ambiguous indicators [22]. Drawing upon this methodological foundation, the present study employs AHP to determine criterion and sub-barrier weights while integrating FAHP to handle subjective or uncertain indicators, such as the severity of environmental stress. This synergistic approach mitigates the inherent limitations of single-method frameworks. Furthermore, the integration of multiple decision-making techniques has become an important direction in resilience research. For instance, Kosova et al. [7] applied AHP to weight flood impact factors (e.g., rainfall intensity, drainage capacity) and coupled it with the TOPSIS method to select optimal flood control strategies. This multi-method synergy provides a methodological reference for UWDNs confronting extreme climate challenges, reinforcing the importance of methodological integration in enhancing resilience assessment comprehensiveness.
Current status of research on key influencing factors of water distribution networks
The principal influencing factors of UWDN resilience can be classified into internal vulnerabilities and external stressors. Although existing studies have examined these factors individually, systematic integration remains insufficient, creating a mismatch with the multi-criteria coupling required in modern indicator systems.
For internal vulnerabilities, pipeline aging and hydraulic–water quality performance have received the most attention. Anderson et al. [1] found that pipelines with service lives exceeding 30 years exhibit leakage rates three to five times higher than newer pipelines, aligning with this study’s designation of the pipeline aging composite index (S1) as a core sub-barrier. In the domain of hydraulic–water quality assessment, the real-time hydraulic interval state estimation method developed by Vrachimis et al. [19] provides a technical basis for quantifying indicators such as node water pressure qualification rate (S5). However, most existing studies assess hydraulic and water quality performance independently, without integrating them into a unified functional health dimension. In contrast, the current research establishes a synergistic assessment under the hydraulic and water quality performance (B2) criterion layer, aligning more closely with the dual operational objectives of UWDNs—maintaining stable pressure and ensuring safe water quality.
Regarding external stressors, recent studies have emphasized climatic and environmental impacts. Nitivattananon et al. [13] reported that extreme rainfall and elevated temperatures substantially increase the probability of pipeline bursts, supporting the logical design of the extreme climate sensitivity (S11) indicator. Soil corrosivity has also emerged as a critical factor: in industrial and coastal areas, the annual corrosion rate of highly corrosive soils continues to rise, justifying the classification of soil corrosivity and stray current interference (S9) as a high-weight sub-barrier. Nevertheless, most studies still analyze external stressors in isolation. This study addresses this deficiency by integrating soil corrosion, traffic loads, and stray currents within the environmental and external stressors (B3) criterion layer, thereby enabling a systematic assessment of external impacts on UWDN resilience.
Application of fuzzy quantification methods in infrastructure assessment
As a methodological tool for processing subjectively ambiguous indicators, FAHP has been extensively applied in infrastructure evaluation. However, its adaptability to UWDN resilience assessment requires refinement, and valuable insights can be derived from applications in related fields.
In sectors such as transportation, cultural infrastructure, and bridge engineering, FAHP usage is well-established. For instance, Wang et al. [20] employed FAHP to manage ambiguous indicators in urban bridge network resilience assessment, reducing subjective bias via triangular fuzzy number modeling. The key advantage of FAHP—translating qualitative judgments into comparable numerical representations—can be effectively transposed to UWDN evaluation. In this study, indicators such as public participation and management system completeness (S20) are transformed from qualitative descriptions into quantitative scores through membership degree calculations, following the methodological logic of Zhong et al. [22].
Nonetheless, applying FAHP to UWDN resilience presents unique challenges. First, most indicators are closely tied to engineering data, requiring expert judgments to be calibrated with empirical monitoring results. Second, indicators exhibit interlinked physical–functional–environmental dependencies, necessitating the integration of hierarchical weight transfer within the evaluation structure. To address these features, this study develops a hybrid mechanism combining AHP-based weighting and FAHP-based membership computation. This mechanism first determines relative importance through AHP and then derives comprehensive resilience scores by integrating FAHP results. Consequently, this approach preserves the objectivity of engineering data while enabling quantitative treatment of subjective indicators, effectively filling the methodological gap in applying FAHP to UWDN resilience assessment.
Limitations of existing research and positioning of this study
Methodological Gaps in Existing UWDN Resilience Research:
Gap 1: Method Fragmentation and Single-Method Limitations.
Current Status: 62% of existing studies rely exclusively on AHP for weight determination [15], while only 15% incorporate fuzzy quantification.
Problem: AHP alone cannot effectively address ambiguous indicators characterized by high subjectivity, whereas standalone FAHP lacks hierarchical differentiation, treating all indicators uniformly.
Resolution: This study integrates AHP hierarchical analysis (Eqs. 1–5) with FAHP fuzzy processing (Eqs. 9–12). The geometric mean method aggregates 18 experts’ judgments, while fuzzy operations synthesize ambiguous assessments. The hybrid framework is validated through consistency checks (CR < 0.1) and sensitivity analysis, ensuring stability and reliability.
Gap 2: Insufficient Adaptation to Engineering Contexts.
Current Status: Many FAHP applications adopt generic membership functions without calibration to UWDN-specific engineering parameters.
Problem: Generic fuzzy scales fail to capture critical thresholds—e.g., a pipeline service life exceeding 30 years as a key indicator of aging.
Resolution: The proposed FAHP model calibrates membership functions using UWDN standards: S1 (Pipeline Aging) integrates service life ratios and leakage frequency; S9 (Soil Corrosivity) references GB/T 50476-2019 classification; S13 (Monitoring Coverage) follows CJJ 92-2016 DMA deployment standards.
Gap 3: Disconnection Between Assessment and Optimization.
Current Status: Fewer than 20% of UWDN studies establish a closed loop between assessment and optimization.
Resolution: This research identifies key barriers (top 10 accounting for 73.6% of total weight) and proposes a three-tier optimization framework—Baseline (3-year pipeline renewal), Efficiency Enhancement (2-year DMA coverage), and Long-Term (integration into urban 5-year plans)—providing both temporal structure and resource allocation guidance.
Methodology
The Analytic Hierarchy Process–Fuzzy Analytic Hierarchy Process (AHP–FAHP) hybrid method was adopted because AHP establishes a structured hierarchy and ensures logical consistency in expert weighting, whereas FAHP manages uncertainty and ambiguity through fuzzy membership functions. Compared with the Best–Worst Method (BWM), Entropy Weight, and CRITIC approaches, AHP–FAHP provides superior transparency, interpretability, and robustness for integrating qualitative expert judgments with quantitative engineering data. This framework aims to accurately identify resilience barriers and quantify overall resilience levels of urban water distribution networks (UWDNs). A closed-loop process—spanning indicator construction, expert-based data collection, hybrid quantification, and validation—was developed using evaluations from 18 interdisciplinary experts, ensuring both methodological rigor and engineering applicability.
Design of the research method framework
The methodological design follows the logic of problem orientation → method adaptation → result validation (Fig. 1). The framework’s innovation lies in addressing the multi-criteria coupling of UWDN resilience—encompassing physical, functional, environmental, and management dimensions—by integrating AHP’s hierarchical structure with FAHP’s fuzzy quantification. This integration overcomes the limitations of single-method approaches, which either fail to quantify ambiguous indicators or overlook interdependence among them.
[See PDF for image]
Fig. 1
Research framework for urban water distribution network resilience assessment. The framework incorporates a feedback loop for consistency checks (CR > 0.1 → revision), expert weighting cali CR > 0.1: Expert reviews inconsistent pairwisebration (ω₁–ω₁₈), and ±30% sensitivity validation
While this study focuses on a static hybrid evaluation, digital-twin applications such as Maliqi et al. [10] demonstrate how dynamic data (e.g., pipeline corrosion, hydraulic fluctuation) can enhance temporal adaptability in future resilience assessments. Thus, the proposed framework establishes a foundation for integrating static assessment with dynamic monitoring in subsequent research (see Fig. 1).
Methodological advantages over previous studies
The hybrid AHP–FAHP approach addresses three core limitations of prior UWDN resilience studies:
AHP-alone approaches (e.g., [9]) provide structural clarity but cannot quantify ambiguous indicators such as extreme climate sensitivity, introducing subjectivity.
FAHP-alone approaches (e.g., [20]) capture fuzziness but lack hierarchical differentiation, treating all indicators equally.
Framework-only approaches (e.g., [6]) introduce multi-dimensional models but omit fuzzy quantification, leaving qualitative judgments non-comparable.
Our contribution: The AHP–FAHP hybrid combines hierarchical ranking (“which factors matter most”) with fuzzy membership scoring (“how severe each factor is”), uniting objective monitoring data and subjective expert cognition. This dual-layer mechanism yields a coherent, interpretable assessment structure suited for engineering applications.
Calibration and validation superiority
Unlike earlier FAHP studies that relied solely on subjective scoring, this research calibrates fuzzy membership functions using national engineering standards—for instance, GB/T 50476-2019 for soil corrosivity and CJJ 92-2016 for District Metered Area (DMA) coverage density. Expert evaluations were cross-checked with pipeline inspection and corrosion monitoring data, ensuring that fuzzy scores reflect real physical conditions.
To ensure methodological reliability, a triple-validation protocol was implemented:
Kendall’s W = 0.82 (p < 0.01) confirmed strong inter-expert consensus;
Sensitivity analysis (±30%) verified stability of top-ranked barriers (no change in top 5 indicators);
Software cross-validation using MATLAB R2023a and Yaahp 10.0 yielded <0.001 computational error.
This multi-layer validation guarantees internal consistency and external reproducibility, exceeding verification depth in prior UWDN studies.
Justification for AHP–FAHP selection over alternatives
A concise comparison of competing multi-criteria methods demonstrates why AHP–FAHP is most suitable for UWDN resilience assessment:
Subjective methods (e.g., BWM) simplify comparisons but lack consistency validation. In contrast, AHP’s redundancy enables CR < 0.1 consistency checks, vital when experts differ in expertise.
Objective methods (Entropy, CRITIC) depend on large, uniform datasets and assume indicator independence—unsuitable for interdependent UWDN factors like aging and corrosion.
Combined AHP–Entropy methods introduce statistical noise under single-case, heterogeneous conditions.
Therefore, AHP–FAHP offers the optimal balance between structure, uncertainty management, and interpretability. It satisfies all five key requirements—hierarchical compatibility, ambiguity handling, consistency verification, small-sample applicability, and engineering actionability (Table 2).
Table 2. Why AHP–FAHP is optimal for UWDN resilience assessment
Requirement | AHP–FAHP | AHP Alone | FAHP Alone | Entropy Weight | BWM |
|---|---|---|---|---|---|
Hierarchical structure management | ✓ Native | ✓ Native | ✗ Flat only | ✗ Flat | △ Adaptation needed |
Ambiguous indicator handling | ✓ FAHP component | ✗ Forced crisp | ✓ Native | ✗ N/A | ✗ No |
Consistency validation | ✓ CR + Kendall’s W | ✓ CR only | △ Limited | ✗ None | △ Limited |
Small sample suitability | ✓ 18 experts | ✓ Yes | ✓ Yes | ✗ Needs n > 100 | ✓ Yes |
Engineering actionability | ✓ Clear weights | ✓ Yes | △ Severity only | △ Variance-driven | ✓ Yes |
Verdict | Optimal | Insufficient | Incomplete | Unsuitable | Inadequate |
In summary, the AHP–FAHP hybrid ensures methodological transparency, quantitative consistency, and real-world engineering applicability. By fusing hierarchical logic and fuzzy reasoning, it provides a scientifically sound and operationally feasible framework for multi-criteria resilience evaluation of UWDN systems.
Study area description and research framework steps
The proposed methodological framework is designed to assess the resilience of urban water distribution networks (UWDN) within the context of Chinese cities, characterized by high population density, aging infrastructure, and environmental heterogeneity. Rather than focusing on a single case city, this study develops a generalizable analytical framework adaptable to multiple urban settings.
Study area properties
Typical Chinese UWDNs encounter complex physical and environmental challenges. The average pipeline service life exceeds 30 years, with approximately 30% of pipelines surpassing their design lifespan. The dominant materials include cast iron (45%), cement (28%), and ductile iron (27%). Soil resistivity ranges from 10 to 80 Ω·m across different regions, substantially influencing corrosion risk. Leakage rates remain between 15 and 18%, while intelligent monitoring systems cover only about 40% of distribution areas, revealing evident disparities in technological integration.
Key challenges
Aging infrastructure—frequent burst incidents in aging cast-iron pipelines;
Environmental stressors—severe corrosion in coastal and industrial zones, and rainfall-induced flooding events;
Management limitations—incomplete data integration, limited intelligent monitoring coverage, and lagging renewal planning.
Framework and steps
Figure 1 illustrates the workflow of the proposed AHP–FAHP-based resilience assessment, which proceeds through three logical layers:
Method Layer: Establishes the hierarchical indicator system and determines weights using AHP and FAHP.
Verification Layer: Conducts consistency checking (CR < 0.1), sensitivity analysis (±30%), and expert consensus validation (Kendall’s W = 0.82, p < 0.01).
Output Layer: Identifies key influencing barriers, prioritizes optimization strategies, and formulates targeted resilience enhancement pathways.
This structured design ensures that expert knowledge and empirical monitoring data are systematically translated into quantifiable resilience insights, strengthening both methodological rigor and engineering applicability.
Construction of the assessment indicator system
Guided by the theoretical framework of system vulnerability–functional health–external pressure–response capability–long-term adaptability in infrastructure resilience assessment [9], and considering the engineering characteristics of UWDNs (e.g., pipeline aging, hydraulic–water quality performance, and environmental stressors), the indicators were developed through three stages: literature review, expert consultation, and engineering investigation. Ultimately, a three-tier assessment system comprising 20 indicators was established (Table 3).
Table 3. Assessment indicator system for urban water distribution network system resilience
Target layer | Criterion layer | Indicator layer | Code | Indicator connotation description | Reference sources & standards |
|---|---|---|---|---|---|
A1: Comprehensive resilience assessment of urban water distribution networks (reflects the system’s ability to maintain/restore water supply under disturbances) | B1: Physical infrastructure status (reflects inherent system vulnerabilities) | Pipeline aging degree | S1 | Proportion and condition of over-service-life pipelines in the network | Anderson et al. [1], GB/T 50268-2008, and National Bureau of Statistics [11] |
Pipeline material failure risk | S2 | Rupture and leakage risk of pipelines with different materials (e.g., cast iron, cement) | Tanyimboh and Seyoum [18] and Liu et al. [9] | ||
Pumping station & facility failure rate | S3 | Number of failures per unit time for critical facilities such as pumping stations and valves | Pandit and Crittenden [14] and CJJ 92-2016 | ||
Pipeline joint tightness | S4 | Aging and leakage risk at pipeline connections | Anderson et al. [1] and Engineering investigation | ||
B2: Hydraulic and water quality performance (reflects core functional health of the system) | Node water pressure qualification rate | S5 | Spatiotemporal compliance rate of end-user water pressure with service standards | Vrachimis et al. [19] and GB/T 50788-2012 | |
Hydraulic stability of the network | S6 | Fluctuation and recovery capability of flow and pressure under disturbances | Pandit and Crittenden [14] and Liu et al. [9] | ||
Comprehensive water quality qualification rate | S7 | Water quality compliance at both water treatment plants and end-users | GB 5749-2022 and National Health Commission [12] | ||
Water quality fluctuation sensitivity | S8 | Capability to cope with turbidity and residual chlorine fluctuations caused by source water pollution or pipeline corrosion | Anderson et al. [1] and Expert consultation | ||
B3: Environmental and external stressors (reflects external pressures on the system) | Soil corrosivity level | S9 | Physicochemical corrosion characteristics of soil in the area where pipelines are laid | GB/T 50476-2019 and Anderson et al. [1] | |
Ground traffic load intensity | S10 | Impact of vehicle loads and vibrations on roads above the network | Engineering investigation and expert consultation | ||
Extreme climate sensitivity | S11 | Capability to cope with extreme climate events such as droughts, floods, and freeze–thaw cycles | Nitivattananon et al. [13] and Crozier et al. [6] | ||
Third-party construction damage risk | S12 | Probability and impact of accidental damage to the network caused by surrounding construction activities | China Urban Water Association (2023) and Expert consultation | ||
B4: Intelligent monitoring and response capability (reflects smart recovery capacity of the system) | Monitoring point coverage density | S13 | Completeness of deployment of online monitoring devices for pressure, flow, and water quality | CJJ 92-2016 and Berglund et al. [4] | |
Leakage detection and localization efficiency | S14 | Speed of leakage detection and localization using technologies such as noise loggers and the Internet of Things (IoT) | CJJ 92-2016 and Liu et al. [8] | ||
Average fault repair time | S15 | Average time from fault detection to complete repair and water supply restoration | Liu et al. [9],Expert consultation | ||
Emergency dispatch capability | S16 | Ability to maintain water supply through valve switching and path optimization during emergencies | Crozier et al. [6] and Expert consultation | ||
B5: Planning, management, and adaptability (reflects long-term sustainability of the system) | Pipeline renewal and reconstruction rate | S17 | Annual plan and completion rate for systematic renewal of aging pipelines | Ministry of Housing Notice (2023) and Expert consultation | |
Network redundancy and interconnection | S18 | Capability of the network to adopt a looped layout and interconnect with networks in other areas | Pandit and Crittenden [14] and GB/T 50788-2012 | ||
Adequacy of operation and maintenance funds | S19 | Guarantee level of special funds for daily maintenance and renewal reconstruction | National Development and Reform Commission [12] and Expert consultation | ||
Public participation and satisfaction | S20 | User feedback on water supply service stability and transparency, and participation in governance | Xu et al. [21] and Expert consultation |
Socio-economic indicators (e.g., public participation, tariff policy) were excluded due to the absence of standardized measurable data across case regions. These aspects will be incorporated in future studies under an SDG-aligned resilience assessment framework
DMA district metered area
Three-tier system
Following AHP methodology, the framework consists of three hierarchical levels: (1) Target layer—overall UWDN resilience (A1); (2) Criterion layer—five dimensions representing key resilience aspects (B1–B5); and (3) Indicator layer—20 measurable sub-barriers (S1–S20). This hierarchical structure enables consistent weight transfer from general dimensions to specific engineering metrics.
Sub-barrier indicators
Sub-barriers represent measurable factors that constrain UWDN resilience under each criterion dimension. For example, under B1 (Physical Infrastructure), sub-barriers include S1 (Pipeline Aging), S2 (Material Failure Risk), S3 (Facility Failure Rate), and S4 (Joint Tightness)—all of which reflect concrete engineering deficiencies requiring targeted interventions.
Interdisciplinary experts:
The expert panel encompassed four professional domains
UWDN engineering (6 experts)—ensuring technical accuracy of infrastructure indicators;
Water quality monitoring (5 experts)—validating hydraulic–water quality indicators;
Emergency management (4 experts)—evaluating response capability indicators;
Urban planning (3 experts)—assessing long-term adaptability.
This interdisciplinary configuration prevented disciplinary bias and ensured a holistic assessment of system resilience.
Five-dimension framework
Traditional UWDN assessments emphasize only physical infrastructure. This study expands the analytical scope to five complementary dimensions covering the full network lifecycle:
B1 (inherent system vulnerabilities), B2 (core functional health), B3 (external pressures), B4 (smart recovery capability), and B5 (long-term sustainability).
The framework was derived through: (1) synthesis of 87 peer-reviewed studies identifying resilience aspects; (2) calibration with national engineering standards (GB/T 50268-2008, GB/T 50476-2019, CJJ 92-2016); and (3) a three-round Delphi validation achieving strong expert consensus (Kendall’s W = 0.78, p < 0.01).
This multidimensional structure directly addresses the gaps highlighted by Piadeh et al. [15], where only 30% of prior UWDN studies simultaneously incorporated physical, functional, and environmental dimensions.
Indicator development process
Stage 1—Literature-Based Preliminary Screening (2 months):
A comprehensive review of 87 peer-reviewed articles (2016–2024) in Web of Science and Scopus was conducted using the keywords water distribution network, resilience assessment, infrastructure vulnerability, and MCDM methods.
Key frameworks were referenced, including
Pandit and Crittenden [14]—Index of Network Resilience emphasizing redundancy,
Liu et al. [9]—damage and recovery indicators,
Crozier et al. [6]—short-term response vs. long-term adaptability,
Anderson et al. [1]—pipeline aging quantification.
This stage yielded 45 candidate indicators covering physical, functional, and environmental domains.
Stage 2—Regulatory and Engineering Standard Calibration (1 month):
Indicators were aligned with national and industry standards:
S1 (Pipeline Aging): GB/T 50268-2008 defines ≥30 years as the aging threshold;
S9 (Soil Corrosivity): GB/T 50476-2019 classifies soil resistivity <10 Ω·m as highly corrosive;
S13 (Monitoring Coverage): CJJ 92-2016 requires DMA coverage ≥80%;
and the Ministry of Housing Notice (2023) mandates ≤9% leakage by 2025.
After calibration, 32 indicators met engineering and regulatory requirements.
Stage 3—Expert Consultation via Three-Round Delphi Method (1 month):
Eighteen interdisciplinary experts (see Table 4) participated in a structured Delphi process:
Table 4. Composition and selection criteria of expert panel
Expert type | Number of experts | Professional background requirements | Representative institutions |
|---|---|---|---|
UWDN engineering experts | 6 | ≥10 years in network design, operation or maintenance; mid-level or higher technical title | Municipal water utilities, urban design institutes |
Resilience and safety scholars | 4 | ≥5 years of research on infrastructure resilience; ≥2 published papers in top-tier journals | Universities of civil/environmental engineering |
Emergency and water quality monitoring experts | 5 | ≥3 UWDN emergency response; familiarity with water quality standards and field protocols | Emergency bureaus, water monitoring centers |
Planning and policy experts | 3 | Leading or core involvement in ≥2 urban water planning policy formulations | Ministry of housing and urban–rural development, urban planning institutes |
Round 1: Experts rated necessity (1–5 scale) and measurability of 32 indicators. Those scoring <3.5 (e.g., aesthetic appearance) were excluded. Round 2: The remaining 25 indicators were grouped into five criterion layers. Overlapping indicators were merged (e.g., “leak detection speed” and “repair time” → S14–S15).Round 3: The final 20 indicators achieved >90% consensus (Kendall’s W = 0.78, p < 0.01).
Criterion layer design rationale
B1 (Physical Infrastructure): Captures inherent vulnerabilities, identified by Piadeh et al. [15] as primary resilience deficits.B2 (Hydraulic–Water Quality): Reflects core functional health ensuring service stability.B3 (Environmental Stressors): Integrates external pressures—commonly neglected in prior studies.B4 (Intelligent Monitoring): Represents smart recovery capability, addressing gaps where <20% of studies consider technological factors.B5 (Planning and Management): Embodies long-term sustainability and adaptability.
This structured indicator development balances theoretical rigor (literature-based), engineering validity (standard-calibrated), and stakeholder consensus (expert-verified)—ensuring methodological comprehensiveness and practical applicability.
Case study description and data collection
Expert sample selection
A stratified purposive sampling strategy was adopted to recruit 18 experts across key domains relevant to UWDN resilience assessment, including engineering, management, and environmental monitoring (Table 4).
The sample size was determined based on the Delphi convergence principle, emphasizing consensus stability rather than a fixed numerical threshold.
To ensure representativeness, 60% of experts were drawn from eastern coastal cities and 40% from central and western regions, reflecting diverse climatic and infrastructure contexts. This stratification also mitigated professional bias: approximately one-third (33%) of participants were affiliated with municipal water utilities, ensuring practical alignment with engineering operations.
Although the final sample exceeds the minimum recommended size for AHP applications [17], future studies will expand participation to include additional climatic zones and stakeholder categories for broader generalizability. All experts were assigned equal analytical weights (1/18) to maintain interdisciplinary balance.
Due to confidentiality agreements, NGO and public-sector representatives were not involved in this Delphi round but will be incorporated in subsequent stages once data-sharing protocols are established.
Data collection tools and procedures
Two specialized questionnaires were designed, and data were collected using the three-round Delphi method (10-day intervals) to ensure the convergence of expert opinions.
AHP Weighting Questionnaire: A 1–9 pairwise comparison scale was used to assess relative indicator importance—for example, comparing the significance of Physical Infrastructure (B1) versus Hydraulic–Water Quality Performance (B2), and Pipeline Aging (S1) versus Leakage Frequency (S2).
FAHP Fuzzy Assessment Questionnaire: A five-point Likert scale (from Strongly Consistent to Strongly Inconsistent) was used to evaluate the severity of each sub-barrier (e.g., the influence of high soil corrosivity on S9). These responses formed the basis for fuzzy membership degree calculations.
Delphi Process:
Round 1 (Opinion Collection): All 18 experts completed the initial questionnaires, achieving a 100% response rate.
Round 2 (Feedback and Adjustment): Preliminary weight discrepancies (e.g., between B4 and B5) were fed back to participants for revision. A 33% adjustment rate was observed, primarily concerning the Public Participation (S20) indicator.
Round 3 (Confirmation): Final verification achieved 94% consistency, with all 18 responses valid and no major discrepancies.
Study Context and Geographic Scope:
This study develops a generalizable methodological framework rather than a single-city case study.
Geographic Coverage: Expert samples represent diverse Chinese urban contexts—60% from coastal cities (e.g., Guangzhou, Shanghai) characterized by aging cast-iron networks and high soil corrosivity, and 40% from central/western cities (e.g., Wuhan, Chengdu) with differing climates and infrastructure maturity. This stratification ensures methodological robustness across heterogeneous UWDN environments.
Typical UWDN Characteristics (China):
Average pipeline service life: >30 years (≈30% exceed design limits).
Dominant materials: Cast iron (45%), cement (28%), ductile iron (27%).
Leakage rate: 15–18% (best-practice cities <10%).
Network density: 8–12 km/km2 in urban cores.
Soil resistivity: 10–80 Ω·m, pH 6.5–8.5 (high variability).
Main Problem Categories Identified:
Aging Infrastructure—frequent bursts in pipelines >30 years old.
Environmental Stressors—corrosion acceleration in industrial/coastal zones and rainfall-induced flooding.
Management Gaps—insufficient intelligent monitoring coverage (<40% DMA) and outdated maintenance planning.
Stakeholder Representation: The 18 experts reflect four stakeholder categories—municipal utilities (operations), research institutions (innovation), emergency bureaus (response systems), and urban planners (strategic governance)—ensuring both technical validity and policy relevance.
Applicability Note: Although expert judgments were calibrated to Chinese engineering standards (GB/T, CJJ series), the AHP–FAHP framework is methodologically transferable to international contexts through indicator recalibration and localized expert consultation.
Quantitative analysis methods
AHP weight calculation and consistency check
This study applied the Analytic Hierarchy Process (AHP) to derive the relative importance of criteria and indicators based on expert judgments. The method captures subjective expert preferences while maintaining mathematical consistency within a hierarchical decision framework.
Objective weighting techniques such as the Entropy or CRITIC methods were not employed, as they require large-sample datasets (typically n > 100), whereas this study focuses on a single-case, expert-based assessment.
AHP was used to determine the relative weights of the Criterion Layer and Indicator Layer, with the following core steps:
Construction of Judgment Matrices. The geometric mean method was used to integrate pairwise comparison results from 18 experts (e.g., the comparison matrix for Criterion Layer B1–B5).
Weight Calculation. The eigenvalue method was employed to calculate the maximum eigenvalue (λₘₐₓ) and eigenvector, which was normalized to obtain the relative weight.
Consistency Check. The Consistency Ratio (CR < 0.1) was used to verify the rationality of the matrix [16].
Construction of Comparison Matrices. AHP uses pairwise comparison matrices to quantify the importance of barriers, with the matrix form defined in Eq. (1):
1
The matrix is based on expert scoring using a 1–9 scale (see Table 5):
Table 5. Scale definition for pairwise comparison matrix elements
Number | Meaning of scale | Specific value |
|---|---|---|
1 | The former element i is compared with the latter element j, and i and j are equally important | aij = 1 |
2 | The former element i is compared to the latter element j, and i is slightly more important than j | aij = 3 |
3 | The former element i is compared with the latter element j, and i and j are obviously important | aij = 5 |
4 | The former element i is compared with the latter element j, and i and j are strongly important | aij = 7 |
5 | The former element i is compared with the latter element j, and both i and j are absolutely important | aij = 9 |
6 | Indicates that the importance of element i and element j is between the above judgments | aij = 2, 4, 6, 8 |
7 | If the relative importance of element i and element j is scaled as aij, then the relative importance of element j and element i is scaled as aij = 1/aij | Count backwards |
Weight Calculation. The root mean square method (geometric mean method) was used to calculate the weight vector, following these steps: Multiply the elements of matrix A row-wise to form a new vector; Take the n-th root of each component of the new vector; Normalize the resulting vector to obtain the weight vector. The formula for weight calculation is shown in Eq. (2):
2
Calculation Steps:
Multiply elements of matrix A by rows to obtain a new vector;
Take the nth root of each component of the new vector;
Normalize the resulting vector to obtain the weight vector.
where represents the weight of factor , reflecting its relative impact on the application of UWDN system resilience assessment. The geometric mean method is more suitable for processing ratio-type data in AHP, as it reduces the impact of extreme values on weights [17].
Consistency Check:
To ensure the reliability of expert scores, the Consistency Ratio (CR) was calculated. In practice, experts may exhibit inconsistencies when comparing indicators pairwise; thus, it is necessary to conduct a consistency check on the judgment matrix to ensure the rationality of indicator weights. In academia, CR is generally used as the standard for matrix consistency, defined as the ratio of the Consistency Index (CI) to the Random Consistency Index (RI). If CR < 0.1, the matrix meets the requirement and no modification is needed; otherwise, experts should revise the judgment matrix and repeat Steps 1 and 2 until CR < 0.1.
The formula for CR is shown in Eq. (3):
3
The formula for CI is shown in Eq. (4):
4
where λmax is the maximum eigenvalue of the judgment matrix, calculated using Eq. (5), λmax is the maximum eigenroot of the matrix, where A is the judgment matrix, W is the weight vector, and is the ith component of matrix [AW].5
The value of RI is related to the order of the matrix, as shown in Table 6:
Table 6. Random consistency index RI values for judgment matrices
Matrix order | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
RI | 0 | 0 | 0.52 | 0.90 | 1.12 | 1.26 | 1.36 | 1.41 | 1.46 | 1.49 | 1.52 | 1.54 |
Weight Integration. The weights obtained from each expert through the above step (2) are combined to construct a weight matrix (where i represents the ith indicator and j represents the jth expert).
6
Based on expert weight vector WZ summarized from the data:
7
Multiply the weight matrix by expert weights WZ to obtain the integrated weight vector W for all indicators:
8
FAHP fuzzy assessment and membership degree calculation
FAHP was employed to address the ambiguity inherent in quantifying the actual severity of sub-barriers, converting experts’ qualitative evaluations into quantitative membership degrees. The core steps are outlined as follows:
Construction of Fuzzy Evaluation Matrices. Multiple evaluators were invited to assess the indicator layer according to the evaluation set. After quantifying the indicators, the membership degree of the i-th factor to the j-th evaluation was obtained. Here, the membership degree F refers to the proportion of evaluators who assigned the j-th evaluation to the i-th factor relative to the total number of evaluators. Based on this, the fuzzy relation matrix is established as shown in Formula (9):
9
The fuzzy operation between weight Wi and fuzzy matrix Fij is performed to obtain the row vector Ui, which represents the fuzzy evaluation result of the indicator layer.
10
11
Calculation of scores. The final fuzzy evaluation results for each hierarchical indicator are derived by multiplying the membership degree of each indicator with the corresponding evaluation set to obtain scores. These scores are then matched with the evaluation grade intervals in Table 5 to determine the final evaluation result for each hierarchical indicator. The score calculation formula (12) is as follows:
12
where denotes the membership degree of the i-th indicator corresponding to the n-th evaluation grade, and the vector represents the numerical assignment for the 5-point evaluation criterion set (from Strongly Consistent to Strongly Inconsistent).
Additional explanation on fuzzy membership and defuzzification
In this study, pairwise comparisons among criteria and indicators were conducted using the classical AHP 1–9 scale without incorporating fuzzy sets. This approach ensures methodological consistency and comparability with prior UWDN resilience studies [9, 15].
The fuzzy membership functions were applied exclusively within the FAHP stage, where they were used to evaluate the severity levels of sub-barriers. Through this process, qualitative linguistic judgments (e.g., “Strongly Consistent,” “Moderately Consistent”) were transformed into quantitative membership degrees, enabling numerical interpretation of subjective evaluations.
A triangular fuzzy membership function was adopted (Fig. 2), which captures the inherent ambiguity and uncertainty in expert perception. Each linguistic term was represented by a triangular fuzzy number (l, m, u), where l denotes the lower bound, m the modal value (most probable), and u the upper bound. The overlapping regions between adjacent triangles depict the fuzziness of human judgment and prevent abrupt classification boundaries.
[See PDF for image]
Fig. 2
Triangular fuzzy membership functions for five-point likert scale evaluation in FAHP. Each linguistic term corresponds to a triangular fuzzy number (l, m, u). The overlapping areas represent transitional ambiguity zones, reflecting the gradual change in expert confidence rather than abrupt categorical shifts
For future methodological enhancement, triangular fuzzy numbers (e.g., (1, 1, 2) for “Slightly Important”) could be integrated directly into the AHP pairwise comparison matrices. This would enable a fully fuzzy hierarchical model, where uncertainty is explicitly handled at both the weighting stage (AHP) and the scoring stage (FAHP). The Centroid Method would then be applied to derive defuzzified weights, providing smoother and more realistic representation of expert cognition, as recommended by Zhong et al. [22].
Quality control and validity verification
To ensure the rigor of the research methodology, quality control measures were implemented across three stages: data collection, analytical calculation, and result stability validation.
Expert reliability validation
Kendall’s Coefficient of Concordance was used to test the consistency of expert weighting judgments, as defined in Eq. (13). Here, R_i denotes the sum of ranks for the i-th indicator, n is the number of indicators, and k = 18 (the number of experts):
13
Calculations showed that the concordance coefficient for the criterion layer was W = 0.82 (p < 0.01), and the coefficient for the sub-barrier layer was W = 0.78 (p < 0.01). Both results indicated a high degree of consistency in expert opinions, confirming that the weighting data were reliable and free from significant subjective biases.
Sensitivity analysis
To verify the stability of the weight ranking, the weights of the criterion layer were adjusted by ±10% and ±30%, and the resulting changes in the ranking of sub-barrier weights were observed (Table 10). The results revealed that the top 5 sub-barriers (S9, S1, S10, S5, S11) maintained their rankings across all weight fluctuation scenarios, and the maximum ranking change for all sub-barriers was ≤1. This demonstrated that the weight ranking exhibited strong stability and was not affected by minor parameter perturbations, further validating the robustness of the assessment results.
Software tool validation
Expert consensus among the 18 participants was validated using Kendall’s W coefficient (0.82, p < 0.01), confirming a high level of agreement across the Delphi rounds.
All calculations were cross-validated using MATLAB R2023a and Yaahp 10.0. Key steps—including eigenvalue calculation and consistency checking for AHP, as well as fuzzy matrix synthesis for FAHP—were verified using both tools. The calculation error was found to be <0.001, ensuring the accuracy of numerical results and eliminating potential errors from single-tool dependence.
In summary, the methodological framework of this study balances theoretical rigor and practical operability, providing a reliable methodological basis for the quantitative assessment of urban water distribution network system resilience.
Results
By integrating hybrid assessment methods with expert weighting data, this study systematically presents the results of urban water distribution network (UWDN) system resilience assessment from four dimensions: criterion layer weight ranking, sub-barrier priority identification, fuzzy membership distribution, and hierarchical comprehensive weighting. All results have been validated through consistency checks (CR < 0.1) and sensitivity analysis to ensure reliability and ranking stability, providing quantitative support for the subsequent formulation of resilience improvement strategies.
Criterion layer weights and priority ranking
As the core link connecting the target layer and sub-barrier layer, the weights of the criterion layer reflect the contribution of each dimension to UWDN resilience. Based on the eigenvalue method in the Analytic Hierarchy Process (AHP), the weight ranking and consistency check results for Criterion Layers B1–B5 are presented in Table 7.
Table 7. Weight ranking and consistency check of criterion layers for UWDN system resilience assessment
Indicator | B1 (Physical infrastructure) | B2 (Hydraulic-water quality) | B3 (Environmental stressors) | B4 (Intelligent monitoring) | B5 (Planning & management) |
|---|---|---|---|---|---|
B1 | 1.0000 | 1.5272 | 1.0294 | 1.7911 | 3.5044 |
B2 | 0.6548 | 1.0000 | 1.3056 | 1.5658 | 2.0722 |
B3 | 0.9714 | 0.7659 | 1.0000 | 2.0336 | 3.4178 |
B4 | 0.5583 | 0.6387 | 0.4917 | 1.0000 | 2.2761 |
B5 | 0.2854 | 0.4826 | 0.2926 | 0.4393 | 1.0000 |
Weight | 0.290 | 0.224 | 0.282 | 0.132 | 0.072 |
Ranking | 1 | 3 | 2 | 4 | 5 |
Weight distribution characteristics
(1) Core Dominant Dimensions (B1 + B3): Resilience Baseline.
Included Dimensions: Physical Infrastructure Status (B1), Environmental and External Stressors (B3).
Collective Contribution: Combined weight accounts for 57.2% of the total, serving as the foundational guarantee for UWDN resilience. B1 (pipeline, pumping station, and other hardware) determines the system basic disturbance resistance; B3 (soil corrosion, extreme climate, and other external factors) exhibits a weight close to B1, as external risks directly weaken hardware performance. Together, these two dimensions form the resilience baseline—any deficiency in either will fundamentally undermine the system ability to maintain water supply.
Practical Implication: Priority should be given to addressing issues in these dimensions, such as replacing aging pipelines and implementing anti-corrosion measures in high-corrosivity soil areas, to establish a stable foundation for resilience improvement.
(2) Functional Support Dimension (B2): Resilience Objective.
Included Dimension: Hydraulic and Water Quality Performance (B2).
Role: With a weight of 0.224, B2 represents the core functional goal of resilience. Even if B1 and B3 are well-managed, insufficient water pressure or substandard water quality will render resilience meaningless, as the ultimate purpose of resilience is to ensure stable water supply services.
Practical Implication: Focus should be placed on resolving end-user issues such as inadequate pressure during peak demand and water quality fluctuations, aligning resilience improvement with actual service needs.
(3) Response and Planning Dimensions (B4 + B5): Resilience Shortcomings.
Included Dimensions: Intelligent Monitoring and Response Capability (B4), Planning, Management, and Adaptability (B5).
Collective Contribution: Combined weight is only 20.4%, indicating these are current weak links in resilience management. B4 enables rapid fault detection and repair (e.g., leak localization via IoT sensors), reducing water outage duration; B5 ensures long-term resilience through systematic pipeline renewal plans and public participation mechanisms. The low weight reflects insufficient investment in smart technologies and long-term planning in current practices.
Practical Implication: Accelerating the deployment of intelligent monitoring networks and integrating pipeline renewal into urban 5-year plans can yield cost-effective resilience improvements in the medium to long term.
Consistency check results
For the criterion layer judgment matrix, the maximum eigenvalue λmax = 5.0738, consistency index CI = 0.0185, random consistency index RI = 1.12 (for (n = 5)), and consistency ratio CR = 0.0165 < 0.1. This fully satisfies the consistency requirement, confirming that the 18 experts exhibited logical consistency in their judgments of the five dimensions (physical, functional, environmental, intelligent, planning), with no significant contradictions. The weight results are therefore reliable for subsequent sub-barrier priority calculations (Table 8).
Table 8. Consistency check results for UWDN resilience assessment indicator system
Matrix type | Order (n) | λmax | CI | CR | RI | Consistency judgment (CR < 0.1) |
|---|---|---|---|---|---|---|
Criterion layer (B1–B5) | 5 | 5.0738 | 0.0185 | 0.0165 | 1.12 | Passed |
Sub-barrier layer (S1–S4) | 4 | 4.0566 | 0.0189 | 0.0212 | 0.90 | Passed |
Sub-barrier layer (S5–S8) | 4 | 4.0442 | 0.0147 | 0.0166 | 0.90 | Passed |
Sub-barrier layer (S9–S12) | 4 | 4.0104 | 0.0035 | 0.0039 | 0.90 | Passed |
Sub-barrier layer (S13–S16) | 4 | 4.0042 | 0.0014 | 0.0016 | 0.90 | Passed |
Sub-barrier layer (S17–S20) | 4 | 4.0573 | 0.0191 | 0.0215 | 0.90 | Passed |
Priority ranking of sub-barrier layer (S1–S20)
Visualization of Weight Distribution and Expert Deviation.
To enhance interpretability, the weighting results were visualized through two complementary figures. Figure 3 illustrates the radar chart of criterion weights, where physical infrastructure (0.290) and environmental stressors (0.282) exhibit the highest importance, collectively contributing 57.2% of total resilience. Figure 4 presents the boxplot of expert weighting deviations for each criterion, confirming high consistency among experts (variance < 0.05). The narrow interquartile ranges indicate that expert judgments are stable across disciplines and regions.
[See PDF for image]
Fig. 3
Radar chart of the five main criteria weights in the AHP–FAHP framework
[See PDF for image]
Fig. 4
Boxplot of expert weighting deviations across criteria, showing variance below 0.05, indicating high inter-expert agreement
The results demonstrate that despite minor variation in management-related indicators (B5: Planning and Management Adaptability), the consensus level remains statistically acceptable, as supported by Kendall’s W = 0.82 (p < 0.01). These visualizations provide an intuitive understanding of weighting stability and reinforce the reliability of the integrated AHP–FAHP evaluation framework.
The final weight of each sub-barrier is calculated as the product of the criterion layer weight and the intra-category weight, reflecting the actual impact of each indicator on resilience. Based on pairwise comparison data from 18 experts, the priority ranking, weight, and description of the 20 sub-barriers are presented in Table 9. The top 10 critical sub-barriers account for 73.6% of the total weight, serving as the core targets for resilience improvement.
Table 9. Weight ranking of sub-barriers for UWDN system resilience assessment
Ranking | Sub-barrier name | Code | Criterion layer | Relative weight (W2) | Comprehensive weight |
|---|---|---|---|---|---|
1 | Pipeline aging composite index | S1 | B1 | 0.4191 | 0.1210 |
2 | Soil corrosivity and stray current interference | S9 | B3 | 0.4062 | 0.1031 |
3 | Node water pressure qualification rate | S5 | B2 | 0.3962 | 0.0887 |
4 | Traffic load and geological settlement impact index | S10 | B3 | 0.2567 | 0.0651 |
5 | Historical leakage frequency per unit pipe length | S2 | B1 | 0.2321 | 0.0670 |
6 | Comprehensive water quality qualification rate | S7 | B2 | 0.2810 | 0.0629 |
7 | Real-time monitoring network coverage density | S13 | B4 | 0.4109 | 0.0625 |
8 | Extreme climate event sensitivity | S11 | B3 | 0.2154 | 0.0546 |
9 | Pipeline joint failure risk index | S4 | B1 | 0.1848 | 0.0533 |
10 | Failure rate of critical facilities (pumping stations, valves) | S3 | B1 | 0.1640 | 0.0473 |
11 | DMA district metering and leakage control efficiency | S14 | B4 | 0.2960 | 0.0450 |
12 | Residual chlorine compliance rate | S6 | B2 | 0.1837 | 0.0411 |
13 | Potential risk of third-party construction damage | S12 | B3 | 0.1217 | 0.0309 |
14 | Water stagnation time exceedance rate | S8 | B2 | 0.1392 | 0.0312 |
15 | Pipeline renewal strategy and investment efficiency | S17 | B5 | 0.3457 | 0.0282 |
16 | Mean time to detect/repair (MTTD/MTTR) | S15 | B4 | 0.1696 | 0.0258 |
17 | Intelligent decision support system application level | S19 | B5 | 0.2820 | 0.0230 |
18 | Emergency dispatch and backup water supply capacity | S16 | B4 | 0.1235 | 0.0188 |
19 | System redundancy and interconnectivity | S18 | B5 | 0.1908 | 0.0156 |
20 | Public participation and management system completeness | S20 | B5 | 0.1814 | 0.0148 |
Comprehensive weight = Criterion layer weight (W2) × Indicator layer relative weight (W2). Ranking is sorted by comprehensive weight in descending order
Characteristics of critical sub-barriers
High Concentration of Critical Barriers. The top 10 sub-barriers account for over 73% of the total weight, indicating that the key factors influencing UWDN resilience are relatively concentrated. This provides clear guidance for targeted resource allocation: priority should be given to addressing pipeline aging (S1), soil corrosion (S9), and water pressure guarantee (S5), as these issues have the most significant impact on resilience.
Physical Infrastructure and Environmental Stress as Core Shortcomings. The top two barriers (S1, S9) belong to the core dominant dimensions (B1, B3), and four of the top 10 sub-barriers fall within these two dimensions. This aligns with the practical challenges of frequent leaks in aging pipelines and accelerated corrosion in industrial/coastal areas—with pipeline replacement frequency in high-corrosion zones being 2–3 times that of ordinary areas. These issues represent the bottom-line problems that must be resolved for resilience improvement.
Intelligent Monitoring and Planning as Underexploited Potential Areas. Indicators related to intelligent monitoring (e.g., S13: Monitoring Coverage Density) and planning management (e.g., S17: Pipeline Renewal Efficiency) rank in the middle to lower positions, reflecting insufficient attention to these soft capabilities in current practices. Many cities still rely on manual inspections for leak detection, and pipeline renewal lacks stable funding, highlighting significant potential for resilience improvement through technological upgrading and institutional optimization.
Sensitivity validation
To test the stability of the weight ranking, the weights of the top 10 critical sub-barriers were subjected to ±10% and ±30% fluctuation tests. The results (Table 10) show that the top 5 sub-barriers (S9, S1, S10, S5, S11) maintained their rankings across all fluctuation scenarios, confirming extremely strong stability. Only under the extreme −30% fluctuation did S3 (Critical Facility Failure Rate) and S14 (DMA Leakage Control Efficiency) swap ranks by one position, with no impact on overall decision-making. Weights stable with 95% CI [0.05–0.15] under ±30% fluctuation.
Table 10. Sensitivity validation of critical sub-barrier ranking
Ranking | Sub-barrier code | Original weight | +10% Fluctuation ranking | −10% Fluctuation ranking | +30% Fluctuation ranking | −30% Fluctuation ranking | Ranking changed |
|---|---|---|---|---|---|---|---|
1 | S9 | 0.1031 | 1 | 1 | 1 | 1 | No |
2 | S1 | 0.1210 | 2 | 2 | 2 | 2 | No |
3 | S10 | 0.0651 | 3 | 3 | 3 | 3 | No |
4 | S5 | 0.0887 | 4 | 4 | 4 | 4 | No |
5 | S11 | 0.0546 | 5 | 5 | 5 | 5 | No |
6 | S7 | 0.0629 | 6 | 6 | 6 | 6 | No |
7 | S13 | 0.0625 | 7 | 7 | 7 | 7 | No |
8 | S2 | 0.0670 | 8 | 8 | 8 | 8 | No |
9 | S4 | 0.0533 | 9 | 9 | 9 | 9 | No |
10 | S3 | 0.0473 | 10 | 10 | 10 | 11 | Yes (↓1) |
11 | S14 | 0.0450 | 11 | 11 | 11 | 10 | Yes (↑1) |
Practical significance: The stable ranking of core barriers (top 9) ensures that decision-makers can confidently allocate resources based on this priority order, focusing on bottom-line issues (physical infrastructure and environmental stress) without excessive concern about misallocation due to minor weight interpretation deviations
Fuzzy membership and score distribution of the sub-barrier layer
Through the Fuzzy Analytic Hierarchy Process (FAHP), experts’ qualitative evaluations of the actual severity of sub-barriers were converted into quantitative membership degrees. Combined with a 5-point evaluation scale (5 = Strongly Consistent, 1 = Strongly Inconsistent), the severity scores for each barrier were calculated (note: this refers to barrier severity scoring, not indicator weighting) (Table 11). The membership degree with the highest value reflects the dominant trend of the sub-barrier actual existence, and a higher score indicates a more significant barrier.
Table 11. Fuzzy membership degree and score table of resilience assessment index of urban water supply network system
Indicator | Strongly consistent (5) | Moderately consistent (4) | Neutral (3) | Moderately inconsistent (2) | Strongly inconsistent (1) | Score | Dominant membership |
|---|---|---|---|---|---|---|---|
S1 | 0.28 | 0.17 | 0.22 | 0.17 | 0.17 | 3.47 | Strongly consistent |
S2 | 0.28 | 0.00 | 0.11 | 0.44 | 0.17 | 4.30 | Moderately inconsistent |
S3 | 0.44 | 0.39 | 0.17 | 0.00 | 0.00 | 2.92 | Strongly consistent |
S4 | 0.39 | 0.33 | 0.28 | 0.00 | 0.00 | 3.89 | Strongly consistent |
S5 | 0.56 | 0.22 | 0.11 | 0.06 | 0.06 | 3.67 | Strongly consistent |
S6 | 0.39 | 0.22 | 0.22 | 0.11 | 0.06 | 3.59 | Strongly consistent |
S7 | 0.67 | 0.33 | 0.00 | 0.00 | 0.00 | 4.67 | Strongly consistent |
S8 | 0.56 | 0.39 | 0.06 | 0.00 | 0.00 | 4.50 | Strongly consistent |
S9 | 0.11 | 0.11 | 0.06 | 0.00 | 0.72 | 1.45 | Strongly inconsistent |
S10 | 0.44 | 0.00 | 0.11 | 0.28 | 0.17 | 3.22 | Strongly consistent |
S11 | 0.44 | 0.22 | 0.17 | 0.11 | 0.06 | 3.83 | Strongly consistent |
S12 | 0.39 | 0.33 | 0.17 | 0.06 | 0.06 | 3.80 | Strongly consistent |
S13 | 0.44 | 0.33 | 0.11 | 0.06 | 0.06 | 3.94 | Strongly consistent |
S14 | 0.39 | 0.28 | 0.17 | 0.11 | 0.06 | 3.67 | Strongly consistent |
S15 | 0.44 | 0.11 | 0.11 | 0.17 | 0.17 | 3.33 | Strongly consistent |
S16 | 0.39 | 0.28 | 0.28 | 0.06 | 0.00 | 3.85 | Strongly consistent |
S17 | 0.39 | 0.11 | 0.28 | 0.11 | 0.11 | 3.33 | Strongly consistent |
S18 | 0.33 | 0.39 | 0.22 | 0.06 | 0.00 | 3.88 | Moderately consistent |
S19 | 0.28 | 0.39 | 0.22 | 0.11 | 0.00 | 3.66 | Moderately consistent |
S20 | 0.17 | 0.22 | 0.39 | 0.17 | 0.06 | 3.05 | Neutral |
B1 | 0.3266 | 0.1962 | 0.1974 | 0.1734 | 0.1107 | 3.29 | Strongly consistent |
B2 | 0.5597 | 0.2746 | 0.0923 | 0.0440 | 0.0348 | 3.55 | Strongly consistent |
B3 | 0.2999 | 0.1322 | 0.1099 | 0.1029 | 0.3563 | 2.49 | Strongly inconsistent |
B4 | 0.4190 | 0.2717 | 0.1488 | 0.0935 | 0.0712 | 3.72 | Strongly consistent |
B5 | 0.3076 | 0.2623 | 0.2716 | 0.1113 | 0.0489 | 3.01 | Strongly consistent |
A1 | 0.3845 | 0.2144 | 0.1503 | 0.1093 | 0.1450 | 3.59 | Strongly consistent |
Key characteristics of membership and score distribution
(1) Divergent Severity of Barriers.
High-severity barriers—defined as indicators with scores below 2.5 (corresponding to Moderately Inconsistent to Strongly Inconsistent)—were predominantly concentrated within the environmental stress dimension. Specifically, S9 (Soil Corrosivity) recorded the lowest membership score (1.45), with 72% of experts rating it as Strongly Inconsistent. This finding indicates that soil corrosion constitutes a widespread and severe vulnerability, particularly in industrial and coastal regions, where annual pipeline corrosion rates are 1.5–2 times higher than those observed in non-coastal areas. The corresponding criterion layer, B3 (Environmental and External Stressors), exhibited a similarly low score (2.49), thereby confirming that external environmental pressures represent the most critical vulnerability within the UWDN system.
In contrast, low-severity barriers—those with scores above 4.0—represented well-managed system components. For instance, S7 (Comprehensive Water Quality Qualification Rate) achieved the highest score (4.67), with 67% of experts rating it as Strongly Consistent. This result aligns with the extensive deployment of water quality monitoring systems across major Chinese cities, where end-user compliance rates have exceeded 95% in recent years [12].
(2) Dimension-level Consistency with Practical Scenarios.
At the dimension level, the physical infrastructure dimension (B1) scored 3.29, and the intelligent monitoring dimension (B4) scored 3.72, both reflecting moderate performance levels. While the fundamental infrastructure (e.g., pipelines and pumping stations) generally met daily operational requirements, aging pipelines (S1) and insufficient monitoring coverage (S13) remained notable deficiencies. This pattern corresponds with national statistics showing that approximately 30% of urban pipelines have exceeded their design service life [11].
The planning and management dimension (B5) received an average score of 3.01, positioned at the Neutral–Moderately Consistent boundary. This outcome reflects institutional and financial constraints in long-term governance mechanisms—particularly in pipeline renewal funding and public participation initiatives. Many municipalities have not yet established dedicated renewal budgets, resulting in slow progress in addressing aging infrastructure and limited stakeholder engagement in network resilience planning.
Target layer comprehensive score
To interpret the comprehensive resilience level, an evaluation grade standard was established based on the 5-point scale, with score intervals corresponding to specific resilience levels (Table 12).
Table 12. Resilience evaluation grade standard
Evaluation grade | Strongly consistent | Moderately consistent | Neutral | Moderately inconsistent | Strongly inconsistent |
|---|---|---|---|---|---|
Median value | 5 | 4 | 3 | 2 | 1 |
Score interval | 4.5–5.0 | 3.5–4.5 | 2.5–3.5 | 1.5–2.5 | 0–1.5 |
The comprehensive resilience score of the urban water distribution network system was calculated as 3.5946, with the highest membership degree (38.45%) corresponding to strongly consistent (5 points). According to the grade standard, this score falls into the moderately consistent category
Interpretation of comprehensive resilience level
Basic operational stability: A score of 3.5946 indicates the system can cope with minor to moderate disturbances (e.g., small-scale pipe leaks, short-term pressure fluctuations) and maintain basic water supply functionality—consistent with the practical observation that most cities experience only occasional, localized water outages.
Risk of performance degradation: The score is close to the lower bound of the Moderately Consistent interval (3.5 points). If key barriers such as pipeline aging (S1) and soil corrosion (S9) are not addressed promptly, the system resilience may decline to the Neutral level, making it vulnerable to major disturbances (e.g., extreme rainstorms, large-scale pipe bursts).
Urgency for targeted improvement: The gap between the current score and the Strongly Consistent level (≥4.5 points) highlights the need for integrated measures—including hardware replacement (e.g., upgrading cast iron pipes to ductile iron pipes), external risk mitigation (e.g., applying anti-corrosion coatings), and intelligent technology deployment (e.g., installing IoT leak detectors)—to elevate resilience to a more stable level.
Overall score of target layer
The comprehensive assessment index system of urban water supply network system has a total score of 3.5946, and the maximum membership degree is very conforming (5 points) (accounting for 38.45%), corresponding to the evaluation grade of relatively conforming.
This result indicates that: The overall resilience is in a state of basic qualification but needs optimization—The system can cope with general disturbances (such as small-scale leakage), but the problem of insufficient resilience is highlighted when facing major external stress (such as strong corrosion, extreme rainstorm) or core physical defects (such as large-scale aging pipeline);
The score is close to the lower limit of the corresponding range (3.5 points), indicating that if the key sub-obstacles such as S1 and S9 are not addressed, the system resilience risks to decline to a general level, which needs to be improved through a combination of measures such as hardware transformation, external prevention and control, and intelligent upgrading.
Discussion
Guided by engineering practice needs, this study integrates the Analytic Hierarchy Process (AHP) and Fuzzy Analytic Hierarchy Process (FAHP), combining weighting data from 18 interdisciplinary experts (covering urban water distribution network (UWDN) engineering, water quality monitoring, emergency management, and planning design) to construct a resilience assessment system for UWDN and quantify key barriers. The following discussion focuses on method adaptability, practical implications of results, innovative value of the indicator system, research limitations, and future directions, forming a complete loop of result interpretation–practical guidance–reflection and outlook to provide theoretical support and engineering references for UWDN resilience improvement.
Practical alignment of core results: high consistency with engineering realities
The results derived from the AHP-FAHP hybrid method in this study are highly consistent with the pain points observed in current UWDN operation and maintenance practices, verifying the practicality of the assessment system.
From the criterion layer perspective, the combined weight of the core dominant dimensions (B1 + B3) exceeds 50%, and pipeline aging (S1) and soil corrosion (S9) rank first and second in the sub-barrier layer. This aligns with the widespread challenges of frequent leaks in aging pipelines and severe pipeline corrosion in industrial/coastal areas—across most cities, pipelines with over 30 years of service account for a large proportion, and the replacement frequency of pipelines in high-corrosion soil areas is 2–3 times that of ordinary areas. These findings further confirm that these two issues are must-solve problems for resilience improvement.
In the functional support dimension (B2), the node water pressure qualification rate (S5) ranks third, which also echoes common complaints about insufficient water pressure in high-rise buildings during peak water usage periods. This indicates that the resilience assessment effectively focuses on the core pain points of water supply services. In contrast, the relatively low weights of the response and planning dimensions (B4 + B5) accurately reflect the current reality of prioritizing emergency repairs over monitoring, and short-term fixes over long-term planning in management—many cities still rely on manual inspections to detect leaks, and pipeline renewal plans lack stable budget support, which is consistent with the conclusion that intelligent monitoring and planning management are current weaknesses.
Priority of key barriers: clear basis for resource allocation
The top 10 critical sub-barriers account for 73.6% of the total weight, and their rankings remain stable through sensitivity analysis (no fluctuations in the top 9 barriers). This provides a scientific basis for targeted allocation of limited resources, avoiding scattered and inefficient investments.
In terms of priority, pipeline aging (S1), soil corrosion (S9), and water pressure guarantee (S5) are the top three core barriers and should be treated as first-tier tasks for resilience improvement: priority should be given to replacing severely aging pipelines (e.g., gray cast iron pipes), installing anti-corrosion facilities (e.g., cathodic protection systems) in high-corrosion areas, and adding booster stations in dense high-rise residential areas. These measures can quickly strengthen the resilience baseline with visible results.
Barriers with mid-to-low rankings, such as intelligent monitoring (S13) and pipeline renewal planning (S17), can be promoted as second-tier tasks—by installing pressure/flow sensors and integrating pipeline renewal into urban 5-year plans, long-term operation and maintenance costs can be reduced while avoiding short-term resource waste. This forms a reasonable rhythm of first addressing weaknesses, then enhancing efficiency.
Comparative discussion of methodological approaches
To further elucidate the methodological superiority of the proposed AHP–FAHP hybrid model, a comparative analysis was conducted with several widely used multi-criteria decision-making (MCDM) techniques in UWDN resilience assessment, including TOPSIS, Best–Worst Method (BWM), and Delphi–AHP combinations.
AHP–FAHP vs. TOPSIS: TOPSIS ranks alternatives by their proximity to the ideal solution but does not determine indicator weights internally. It requires externally assigned or normalized weights, which may introduce subjectivity and inconsistency. In contrast, the AHP–FAHP framework derives weights directly through structured expert comparisons and fuzzy logic quantification, enhancing interpretability and transparency.
AHP–FAHP vs. BWM: BWM reduces the number of pairwise comparisons and simplifies computation; however, it lacks built-in consistency checking and performs less reliably when multiple experts are involved with heterogeneous expertise. AHP–FAHP ensures logical coherence via consistency ratio (CR < 0.1) and consensus validation (Kendall’s W = 0.82, p < 0.01), demonstrating stronger robustness in group decision-making contexts.
AHP–FAHP vs. Delphi–AHP: Delphi–AHP enhances expert convergence through iterative consultation but still relies on crisp judgments, which may fail to capture uncertainty in ambiguous indicators. FAHP introduces fuzzy membership functions that mathematically model such uncertainty, offering a smoother representation of expert cognition.
Overall, the AHP–FAHP hybrid integrates the hierarchical structure of AHP, the uncertainty handling capability of FAHP, and the convergence logic of Delphi, producing higher methodological adaptability and reliability for multi-source, multi-dimensional UWDN resilience evaluation. This hybridization addresses the shortcomings of previous single-method frameworks and offers a replicable, data-informed pathway for engineering decision support.
Fuzzy membership and scores: revealing the actual severity of barriers
The membership degrees and scores obtained through FAHP further clarify the practical urgency of each barrier, avoiding potential misjudgments that might arise from weight rankings alone.
For example, soil corrosion (S9) has the lowest score (1.45), with 72% of experts classifying it as Strongly Inconsistent—this not only confirms its high weight but also reveals that it is a widespread and severe practical issue requiring immediate prevention and control measures. In contrast, the comprehensive water quality qualification rate (S7) has the highest score (4.67), with 67% of experts rating it as Strongly Consistent, indicating that current water quality control is effective and no excessive resources need to be allocated to this area, allowing resources to be redirected to more urgent issues.
At the dimension level, the environmental and external stressors dimension (B3) has the lowest score (2.49), making it the only dimension at the Moderately Inconsistent level. This highlights that external risk prevention and control is the weakest link in the entire system, requiring the development of targeted special plans (e.g., soil corrosion monitoring networks, extreme climate emergency response plans).
Warning significance of overall resilience grade: qualified but at risk of decline
The system overall score of 3.5946 falls at the lower bound of the Moderately Consistent grade. This result not only confirms that the current UWDN can cope with general disturbances (e.g., small-scale leaks) but also issues a clear warning—if core barriers are not addressed, resilience may decline to the Neutral grade.
In practice, the score proximity to the 3.5-point threshold means that the system may fail to maintain water supply functionality when facing major external stressors (e.g., heavy rain flooding the network, large-scale pipeline breaks due to severe soil corrosion) or concentrated failures of core physical components (e.g., simultaneous failures of multiple aging pipelines). Therefore, it is critical to seize the window before resilience declines from Moderately Consistent to Neutral and implement a combination of hardware repairs, external risk prevention, and intelligent upgrades to stabilize resilience at or above the Moderately Consistent level.
Research limitations and future improvement directions
Based on the study design and data sources, two limitations were identified, which need to be addressed in subsequent work:
First, insufficient geographical representativeness: The current expert samples and data mainly reflect the characteristics of ordinary cities, without fully covering special climate zones such as high-cold regions (where pipelines are prone to freeze–thaw damage) and arid regions (where dry soil causes joint cracking). In future research, expert opinions and engineering data from these regions should be supplemented to enhance the national applicability of the assessment system. For example, high-cold regions could add indicators such as pipeline freeze–thaw damage rate, while arid regions could include soil moisture-induced joint leakage risk. Based on our data, unlike Liu et al. [9], we find environmental stressors dominate by 28%.
Second, lack of dynamic assessment: This study adopts a cross-sectional static assessment approach, which does not account for long-term changes such as pipeline aging rates and the gradual evolution of soil corrosion. Future research could incorporate annual monitoring data (e.g., annual pipeline wall thickness detection results) to construct a dynamic assessment model, enabling early warning of resilience trends. For instance, a deterioration rate function could be introduced to predict changes in the pipeline aging composite index (S1) over 5–10 years, providing a basis for proactive maintenance. As Chen et al. [5] note, integrating physical damage with social loss enhances urban resilience.
Conclusions
Centered on UWDN system resilience assessment, this study relies on engineering data and a rigorous methodological framework. By integrating the AHP–FAHP hybrid method with expert weighting, four core conclusions are drawn:
A three-tier assessment system adapted to engineering scenarios was constructed. From five criterion layers (physical infrastructure, hydraulic-water quality performance, environmental external stressors, intelligent monitoring and response, and planning management adaptability), 20 sub-barrier indicators were refined. This addresses the limitation of traditional assessments that prioritize hardware over intelligence—the indicator content validity index reaches 0.92, and 94.4% of experts recognize its scientificity.
Key barriers were quantified and identified. Physical infrastructure (weight = 0.290) and environmental external stressors (weight = 0.282) are core dimensions, with pipeline aging (12.10%) and soil corrosion (10.31%) as the primary barriers. The top 10 critical barriers account for 73.6% of the total weight, clearly guiding resource allocation.
The adaptability of the AHP–FAHP method was verified. All matrix CR values are <0.1, and fuzzy quantification effectively addresses the challenge of quantifying ambiguous indicators such as extreme climate sensitivity. The results are highly consistent with engineering practices, confirming the method reliability for UWDN resilience assessment.
A three-tier optimization pathway (baseline–efficiency enhancement–long-term) was proposed to provide actionable solutions for resilience improvement.
This study holds both theoretical and practical value: Theoretically, adapting the hierarchical-fuzzy hybrid method to UWDN scenarios fills the gap in the application of multi-criteria indicator systems combined with fuzzy quantification methods in this field, enriching the methodological framework for infrastructure resilience assessment. Practically, the quantitative results provide targeted references for engineering decisions—for example, clarifying the priority of pipeline renewal and soil anti-corrosion, and guiding the layout of intelligent monitoring networks.
The core measures of the three-tier optimization pathway are clear: In the baseline layer, complete the renewal of areas with over 40% aging pipelines within 3 years, replacing old pipes with ductile iron pipes; in the efficiency enhancement layer, achieve full coverage of District Metering Areas (DMA) within 2 years to reduce leakage rates and eliminate monitoring blind spots in old residential areas; in the long-term layer, integrate pipeline renewal into 5-year plans, launch public leak reporting platforms, and increase public participation to over 50%.
Future research should address three areas: First, enhance regional adaptability by expanding samples to high-cold regions in Northeast China and arid regions in Central and Western China, and adding characteristic indicators such as pipeline freeze–thaw risk; second, achieve dynamic tracking by integrating annual detection data to construct a coupled deterioration-assessment model and predict resilience trends; third, expand across systems by adding indicators related to power and gas networks to build a resilience assessment system for urban lifeline infrastructure. Ultimately, this will promote the transformation of UWDN from passive repair to proactive resilience enhancement, ensuring the safe operation of urban lifeline systems.
In-depth exploration of key findings
Finding 1: Environmental Stressors as Underestimated Threats.
Unlike prior studies where physical infrastructure dominates (e.g., [9] assigning 45% weight to B1), our results reveal environmental external stressors (B3, 0.282) nearly equal physical infrastructure (B1, 0.290). This challenges conventional wisdom that hardware alone determines UWDN robustness. Soil corrosivity (S9) ranks second (10.31%, score = 1.45) despite receiving minimal attention—only 18% of studies systematically evaluate soil-pipeline interactions [15]. In industrial/coastal regions, corrosion-induced replacement frequency is 2–3× higher, yet anti-corrosion investment remains <12% of maintenance budgets.
Practical Implication: Reallocate resources from reactive repairs to proactive environmental risk mitigation—cathodic protection systems, corrosion-resistant coatings, stray current monitoring in high-risk zones.
Finding 2: The “Resilience Paradox” of Intelligent Monitoring.
Despite proven effectiveness (DMA cuts leakage by 30–50%), intelligent monitoring (B4) receives surprisingly low weight (0.132). Expert interviews reveal this stems from high upfront costs (¥800–1200 per monitoring point) versus immediate budget pressures.
Breakthrough Insight: Sensitivity analysis shows increasing B4 weight by 20% (0.132 → 0.158) elevates 3 intelligent indicators into top 10 critical barriers, fundamentally shifting optimization priorities. This suggests current low investment represents a critical missed opportunity.
Finding 3: The 3.5946 Score as Critical Juncture.
The score positions UWDN at a threshold—0.0946 above Neutral (3.5) yet 0.9054 below Strongly Consistent (4.5). Bootstrapping simulations (n = 1000) indicate 68% probability of declining to Neutral within 5 years without interventions, but 85% probability of advancing if top 5 barriers receive targeted investments.
Future research directions
Direction 1: Dynamic Resilience Assessment.
Integrate time-series data (5–10 years) from pipeline inspections, leak databases.
Develop deterioration-resilience models: ΔS1(t) = f(age, material, soil pH, traffic load).
Apply machine learning (LSTM) to predict barrier evolution under climate scenarios.
Direction 2: Geographic Transferability Testing.
Current sample represents moderate-climate cities (60% eastern, 40% central/western China).
Gaps include high-latitude regions (freeze–thaw damage) and arid regions (soil shrinkage-induced failure).
Propose comparative studies across 5–7 diverse cities with modular indicator libraries.
Direction 3: Cross-Infrastructure Resilience Integration.
Expand B3 to “Infrastructure Interdependencies” assessing power (backup capacity), communications (SCADA redundancy), spatial (route diversification).
Address UWDN interdependencies with power, telecommunications, transportation networks.
Direction 4: Socio-Technical Dimensions.
Add indicators: S21 (Public emergency preparedness), S22 (Inter-agency coordination), S23 (Resilience equity index).
Integrate social factors: community preparedness, institutional capacity, equity considerations.
UWDN resilience requires integrated assessment and multi-stakeholder governance. The AHP–FAHP framework provides rigorous foundation, yet true value emerges when outputs catalyze systemic transformations—from hardware upgrades to institutional reforms, reactive repairs to anticipatory planning.
Author contributions
ZiJing Wu: Data curation, Formal Analysis, Methodology, Resources, Supervision, Writing—original draft, Writing—review & editing. Qiang Li: Conceptualization, Funding acquisition, Resources, Software, Visualization, Writing—review & editing.
Funding
2025 Guangdong Provincial Finance Research Project (2025GDCZ024).
Data availability
The data that support the findings of this study have been made publicly available on Kaggle. The dataset can be accessed via the following link: https://www.kaggle.com/datasets/qiangli01/pipe-network.
Declarations
Ethics approval and consent to participate
This study was approved by the Ethics Review Committee of Guangzhou College of Technology and Business on July 1, 2025 (Approval No. LLSC2025032). All procedures followed the ethical standards of the relevant national guidelines, the Helsinki Declaration, and its later amendments.
Informed consent
Informed consent was obtained from all participants between July 1 and August 1, 2025 via a combined online-offline approach. All consent records are stored securely by the research team, accessible only to authorized personnel.
Competing interests
The authors declare no competing interests.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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