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Evaluating resilience in urban transportation systems for sustainability: A systems-based Bayesian network model
Junqing Tang, Hans Heinimann, Ke Han, Hanbin Luo, Botao Zhong
TL;DR
Long-term, multi-dimensional transportation resilience is difficult to assess, and its relationship with urban economic development remains underexplored. This paper applies a systems-based Bayesian network to four Chinese cities, finding moderate resilience overall and dynamic, non-linear resilience–economy patterns. Its analyses point decision-makers toward capabilities for rapid rebuilding and adaptation.
Problem
Long-term, multi-dimensional transportation resilience and its relationship with regional economic development remain insufficiently explored, limiting comprehensive evaluation of urban transportation systems.
Source: §1 · p. 3Method
The paper builds a systems-based hierarchical Bayesian network spanning transportation infrastructure stages and evaluates four Chinese cities using forward inference, sensitivity analysis, and backward reasoning.
Source: §1 · pp. 3–4, §6 · p. 22Results
Resilience levels were moderate at 50% to 60% across the four cities; Beijing and Tianjin showed a V-shaped long-term pattern, and resilience did not always correlate positively with economic growth.
Source: §6 · p. 22Takeaways & Limitations
Sensitivity analysis and backward reasoning suggest decision-makers should give more attention to quick rebuilding and making changes to cope with future disturbances.
Source: §6 · p. 22The observed association between transportation resilience and economic growth may not remain unchanged over time.
Source: §5 · p. 21
Abstract
from arXiv · showhide
This paper proposes a hierarchical Bayesian network model (BNM) to quantitatively evaluate the resilience of urban transportation infrastructure. Based on systemic thinkings and sustainability perspectives, we investigate the long-term resilience of the road transportation systems in four cities of China from 1998 to 2017, namely Beijing, Tianjin, Shanghai, and Chongqing, respectively. The model takes into account the factors involved in stages of design, construction, operation, management, and innovation of urban road transportation, which collected from multi-source data platforms. We test the model with the forward inference, sensitivity analysis, and backward inference. The result shows that the overall resilience of all four cities' transportation infrastructure is within a moderate range with values between 50% to 60%. Although they all have an ever-increasing economic level, Beijing and Tianjin demonstrate a clear "V" shape in the long-term transportation resilience, which indicates a strong multi-dimensional, dynamic, and non-linear characteristic in resilience-economic coupling effect. Additionally, the results obtained from the sensitivity analysis and backward inference suggest that urban decision-makers should pay more attention to the capabilities of quick rebuilding and making changes to cope with future disturbance. As an exploratory study, this study clarifies the concepts of long-term multi-dimensional resilience and specific hazard-related resilience and provides an effective decision-support tool for stakeholders when building sustainable infrastructure.
1 Introduction
Transportation resilience is difficult to assess comprehensively because prior work often emphasizes isolated network measures or event-specific settings, while long-term development and economic coupling remain less explored. The paper addresses these gaps with a systems-based Bayesian model spanning infrastructure stages and examines long-term resilience in four Chinese cities.
1 Introduction
- Resilience is difficult to measure consistently because it is multidimensional and interpreted differently across fields, despite the need to manage qualities beyond isolated measures such as reliability.Transportation systems face acute shocks and chronic stresses across design, construction, operation, and management.Source: §1 · p. 2
- Prior transportation studies often overlook long-term development and have explored the coupling between resilience and regional economic development relatively little.Many systems-based studies are also context-dependent and event-specific, while infrastructure-wide evaluation across design, construction, operation, management, and innovation has rarely been investigated.Source: §1 · p. 3
- The paper constructs a hierarchical Bayesian network model to evaluate multi-dimensional transportation resilience under uncertainty, using stage-related indicators from a sustainability perspective.Four Chinese cities serve as case studies for examining long-term resilience and economic development.Source: §1 · pp. 3–4
- The paper presents its systems-based framework as a decision-support contribution and suggests that its reasoning may transfer to other urban systems.It also identifies a pathway for understanding resilience and sustainable development in urban transportation.Source: §1 · p. 4
2 Methodology
The methodology uses a hierarchical Bayesian network to represent dependencies among transportation-resilience factors, then applies forward inference, sensitivity analysis, and backward reasoning to assess and diagnose resilience.
2.1 Bayesian networks
- A Bayesian network represents variables as nodes and conditional dependencies as directed links, with conditional probability tables supporting a factorized joint probability distribution.The proposed model uses expert knowledge, professional assessment, and logic reasoning on resilience frameworks to determine its structure and conditional probabilities.Source: §2.1 · pp. 4–6
2.2 Deductive reasoning
- Forward inference estimates the probability distribution of a target leaf node from evidence entered for the root-node variables.The analysis uses predefined conditional probability tables.Source: §2.2 · p. 6
2.3 Sensitivity analysis
- Sensitivity analysis uses the Sensitivity Index to rank variables by their influence on the probability of a target state.The index measures the difference between the maximum and minimum target-state probabilities across a variable's states.Source: §2.3 · pp. 6–7
2.4 Abductive reasoning
- Abductive reasoning infers posterior probabilities for root variables from evidence about a target resilience state, enabling a stepwise pathway diagnosis.A factor whose posterior probability approaches 100% may be treated as dominant; it can then be added as evidence in the next diagnostic step.Source: §2.4 · p. 7
3 Model construction
The model organizes urban transportation resilience evaluation into function, quality, and factor layers, linking general system capabilities to measurable transportation indicators. It represents resilience through four functions and ten system qualities, then establishes a Bayesian network baseline from selected factors.
3.1 Hierarchical layout of the BNM
- The proposed Bayesian network uses a macro-meso-micro hierarchy of Function, Quality, and Factor layers, with sustainability perspectives guiding variable selection and causal reasoning.Source: §3.1 · p. 7
3.2 Function layer
- The Function layer represents resilience through four transferable capabilities: resist degradation, re-stabilize critical functionality, rebuild it, and reconfigure after recovery.Reconfiguration updates the system after an event to support adaptation and greater resilience to future events.Source: §3.2 · pp. 7–9
3.3 Quality layer
- Ten system qualities form the Quality layer, with resilience modeled as a compound attribute of Availability and Changeability.Availability relates Reliability and Maintainability; Changeability reflects adaptation based on Maintainability and Adaptability.Source: §3.3 · p. 9
3.4 Factor layer
- Fourteen representative factors cover transportation design, construction, operation, maintenance, management, and innovation, with indicators assigned to qualities by their attributes.Annual traffic accidents indicate Safety, road density indicates Serviceability, and submitted and granted patents indicate Adaptability.Source: §3.4 · pp. 10–11
3.5 Baseline of the BN model
- The baseline BNM sets Resilience and other Function, Quality, and Factor variables as boolean, except congestion level, which has three categorical states.The Serviceability conditional probability table combines the three congestion states with three binary factors across 24 scenarios.Source: §3.5 · pp. 11–12, Figure 4 · p. 12
4 Case study
The case study evaluates long-term road-transport resilience in four Chinese cities using historical data and Bayesian inference. Resilience is moderate overall, varies in its relationship with economic growth, and is most sensitive to rebuilding and adaptation capabilities.
4.1 Data description
- Historical data for Beijing, Tianjin, Shanghai, and Chongqing span 1998–2017 and come from multiple sources; missing values were filled by medians or regression predictions.Source: §4.1 · p. 12
4.2 Probability data assessment
- Continuous S4 passenger-traffic priors use TNORM bounded by observed minima and maxima; across the four cities, µ=34596 and STD=40840.Source: §4.2 · p. 13, Figure 6 · p. 14
4.3.1 Forward inference
- 50%–58% overall resilience across four cities; Beijing is highest at 58%, Chongqing lowest at 50%, and 2015–2017 exceeds most earlier years.Source: §4.3.1 · p. 14, Figure 7 · p. 16
- Beijing and Tianjin show rough V-shaped resilience trends, while Shanghai and Chongqing rise more steadily; Beijing and Shanghai increase faster from 2005–2017.Source: §4.3.1 · pp. 14–15
- Resilience and GDP correlate positively for Beijing, Tianjin, and Shanghai after 2005, but not before; Tianjin’s R2 rises from around 0.4 overall to 0.7 for 2005–2017.Source: §4.3.1 · pp. 15–16, Figure 8 · p. 17
4.3.2 Sensitivity analysis
- X3 rebuilding, X6 changeability, and X4 reconfiguration rank as the three most influential resilience variables, highlighting rebuilding and adaptation capabilities.Source: §4.3.2 · pp. 17–18, Figure 10 · p. 19
4.3.3 Backward inference
- With 100% positive resilience as the target, backward inference identifies X3 (>60%), then X6, then X4 (~80%) as a stepwise pathway.Source: §4.3.3 · p. 19
5 Implications and limitations
The paper frames transportation resilience as a multidimensional, evolving property that requires system-wide assessment and coordinated attention across infrastructure life-cycle stages. The four-city results indicate moderate resilience, while causal explanations for some observed patterns remain uncertain and the study’s evidence has important methodological and geographic limits.
5 Implications and limitations
- All four cities’ transportation systems showed overall positive-resilience probabilities at a medium level, with increasing trends, while Beijing and Tianjin’s “V” shapes lacked precise explanations.The authors caution that events or political strategies might have triggered the shapes, but causal relationships are difficult to pinpoint.Source: §5 · p. 20
- Resilience should be addressed across design, construction, operation, maintenance, management, and innovation, with practitioners coordinating around rapid rebuilding and adaptation to future threats.The paper describes resilience-building as a progressive process in which the social system managing and maintaining infrastructure co-evolves with it.Source: §5 · p. 21
- Transportation resilience is associated with time and factors such as economic growth, but that association may change, making social-technical trade-offs difficult.The authors argue that systemic thinking should inform infrastructure management.Source: §5 · p. 21
- The BNM supports multidimensional assessment and backward diagnosis, unlike performance metrics tied to a key indicator and topology models requiring full system architecture.Figure 11 presents backward diagnosis conditioned on positive resilience and then on “Able” and “Changable” states.Source: Figure 11 · p. 20, §5 · p. 21
- Qualitative CPT determination draws on expert knowledge but may introduce individual bias, and the absence of an agreed resilience benchmark makes mathematical validation difficult.The authors identify both as limitations of the proposed BNM.Source: §5 · p. 21
- Because the study covers only Chinese cities and lacks comparisons, resilience patterns elsewhere and differences across Chinese administrative levels remain unexamined.The authors also note possible hidden relationships among transportation resilience, regional economic development, and geographic characteristics.Source: §5 · p. 22
6 Conclusions
The study uses a systems-based Bayesian network model to evaluate long-term transportation resilience in four Chinese cities. Resilience was moderate overall, did not consistently track economic growth, and the analyses highlighted capabilities decision-makers should prioritize.
6 Conclusions
- The proposed multi-dimensional, systems-based Bayesian network model evaluates urban transportation resilience and is illustrated through case studies in four Chinese cities.The study examines long-term resilience and its relation to urban economic development.Source: §6 · p. 22
- 50% to 60%: transportation resilience was moderate in Beijing, Tianjin, Shanghai, and Chongqing from 1998 to 2017, with recent increases and V-shaped trajectories in Beijing and Tianjin.The V shapes indicate dynamic long-term performance.Source: §6 · p. 22
- Transportation resilience did not always correlate positively with economic growth over the 20-year observation, indicating a nonlinear relationship.The authors describe resilience as multi-dimensional.Source: §6 · p. 22
- Sensitivity analysis and abductive reasoning point to quick rebuilding and making changes as capabilities for decision-makers to prioritize across infrastructure stages.The authors identify these capabilities as potential driving forces for resilient mobility systems.Source: §6 · p. 22
- The approach is exploratory and does not offer a one-size-fits-all solution; the authors invite further studies from alternative perspectives.They describe it as a new attempt to study transportation resilience from a long-term sustainability perspective.Source: §6 · p. 22