Association-Informed Hierarchical Dependency and Bayesian Diagnostic Analysis of Urban Gas Pipeline Accidents in China

2.1 Accident cases and factor coding

A dataset of 150 urban gas pipeline accidents that occurred in China between 2016 and 2025 was compiled from publicly available accident investigation reports, government notices, professional or industry records, mainstream media reports, and other verifiable public materials. Based on the principal cited source for each case, 78 cases (52.0%) were supported primarily by government or other official sources, 45 (30.0%) by professional or industry sources, 19 (12.7%) by mainstream media, and 8 (5.3%) by other verifiable public materials. The study focused on municipal and yard gas pipelines, buried urban distribution networks, pipeline construction and rehabilitation, maintenance and emergency repair, excavation or drilling damage, corrosion and aging, pipeline-component defects, inadequate burial or separation distance, and relevant external disturbances. Cylinder-gas accidents, accidents confined to indoor end-use appliances, and cases outside the urban pipeline-system boundary were excluded. Because the cases were selected according to study relevance, documentation adequacy, and public availability rather than probability sampling, the dataset is not intended to be statistically representative of all urban gas pipeline accidents in China during 2016–2025.

Before coding, case records were standardized according to accident date, location or project, event description, and principal accident mechanism. Potential duplicates were screened using a normalized event identity combining accident date, location/project or organization, event title, and principal mechanism; high-similarity records were then checked manually against the original sources. Multiple reports referring to the same physical accident were treated as one event, whereas independently documented accidents within the same project or organization were retained as separate cases. Each retained accident was assigned a unique case identifier and linked to its principal source.

Accident-causation information was extracted from the case materials and coded using the 24Model framework. Semantically similar causal descriptions were consolidated into standardized factors. A binary coding scheme was applied: a factor was assigned a value of 1 when its occurrence was supported by the available accident evidence and 0 otherwise. In total, 1,065 original causation statements were consolidated into 24 factors, yielding a 150 × 24 binary accident-causation matrix for subsequent analysis.

To improve coding consistency and reliability, the coding results were independently cross-checked by safety-engineering researchers. Primary coding and any recoding identified during the case audit were verified against the cited source documents by a second researcher; disagreements were resolved through discussion and re-examination of the original evidence. After verification, the final 150 × 24 binary matrix was frozen and used as the single common input for all matrix-derived analyses reported in this study, including association mining, structural derivation, CPT estimation, cross-validation, and bootstrap analysis.

2.2 Accident-causation factor system

The accident-causation factor system was established based on the 24Model, which organizes accident causes across individual and organizational levels [14-16, 21-23]. The 24 factors were classified into five categories: unsafe actions (A), unsafe conditions (B), habitual unsafe behavior and individual safety capability (C), deficiencies in the safety management system (D), and deficiencies in safety culture (E). The factor definitions were adapted to the operational characteristics of urban gas pipeline systems while retaining the hierarchical logic of the 24Model. The resulting factor system is presented in Table 1.

Table 1. Accident-causation factor system for urban gas pipeline accidents

2.3 Apriori association mining and hierarchical structural modeling

Apriori association-rule mining was applied to identify recurrent co-occurrence relationships among the 24 coded factors [24, 25]. For a rule $X \rightarrow Y$, support, confidence, and lift were calculated as follows:

$\operatorname{Support}(X \rightarrow Y)=\frac{n(X \cap Y)}{N}$        (1)

$\operatorname{Confidence}(X \rightarrow Y)=\frac{n(X \cap Y)}{n(X)}$        (2)

$\operatorname{Lift}(X \rightarrow Y)=\frac{P(Y \mid X)}{P(Y)}$         (3)

where, N is the total number of accident cases, n(X) is the number of cases containing factor X, and n(X∩Y) is the number containing both factors. Association rules were retained when support, confidence, and lift were no lower than 0.04, 0.60, and 1.10, respectively. Reciprocal representations of the same factor association were consolidated at the factor-pair level for subsequent structural orientation, while both directional rules remained in the association-rule results.

Directional relationships used for hierarchical modeling were determined by combining the 24Model hierarchy with accident-process information and established pipeline-safety knowledge. Only relationships with a supported directional interpretation were included in the directed relation matrix. The matrix was transformed into a reachability matrix using Boolean operations, and ISM levels were identified iteratively from the reachability set R(i) and antecedent set A(i) [26]. A factor was assigned to the current upper level when

$R(i)=R(i) \cap A(i)$         (4)

After each level was removed, the procedure was repeated until all directionally connected factors had been classified. A transitive reduction was then applied to remove redundant direct links while preserving node reachability. The resulting direct relations were used as the structural basis of the BN.

2.4 Bayesian network modeling and diagnostic inference

A discrete BN was constructed from the directed dependency structure. Of the 24 coded accident-causation factors, the 20 factors with directionally supported relationships were represented as binary nodes with states Yes and No. B2, B6, B8, and E1 were retained in the factor system and association analysis but were not included in the directed BN because no sufficiently supported directional relationships were identified. For a BN containing nodes $X_1, \ldots, X_p$, the joint distribution was factorized as [19, 27, 28]

$P\left(X_1, \ldots, X_p\right)=\prod_{i=1}^p P\left(X_i \mid P a\left(X_i\right)\right)$         (5)

where, Pa(Xi) denotes the parent set of node Xi. Conditional probability tables (CPTs) were estimated directly from the binary accident matrix. For node Xi under parent-state configuration pa_j, a symmetric Beta(1,1) prior was adopted:

$\hat{P}\left(X_i=1 \mid p a_j, D\right)=\frac{N_{1 j}+1}{N_{1 j}+N_{0 j}+2}$        (6)

where, N_1j and N_0j are the numbers of cases in which Xi was coded as Yes and No, respectively, under pa_j. The same estimation procedure was applied to all parent-state configurations.

The BN was implemented and analyzed using GeNIe Modeler (BayesFusion, LLC), which was used for network visualization and probabilistic inference.

Diagnostic inference was conducted for direct-cause factors located at the upper level of the directed ISM and connected to at least one upstream node in the BN. Seven factors satisfied these criteria: A1, A2, A3, B1, B3, B4, and B7. For an upstream factor X and target factor T, the diagnostic probability change and conditional probability contrast were defined as

$\Delta_{\text {diag}}(X, T)=P(X=1 \mid T=1)-P(X=1)$         (7)

$\begin{gathered}\Delta_{\text {cond}}(X, T)=P(T=1 \mid X=1)-P(T=1 \mid X=0)\end{gathered}$         (8)

These two measures were used to characterize target-specific probabilistic dependencies among the accident-causation factors.

2.5 Robustness analysis

Robustness was evaluated at the association-rule, BN-parameter, and network-structure levels. Threshold sensitivity was first examined using 27 combinations of support (0.03, 0.04, and 0.05), confidence (0.55, 0.60, and 0.65), and lift (1.05, 1.10, and 1.15). Additional one-factor sensitivity tests extended the ranges to 0.02-0.06 for support, 0.50-0.70 for confidence, and 1.00-1.20 for lift. Similarity between each rule set and the central rule set was evaluated using the Jaccard index:

$J(A, B)=\frac{|A \cap B|}{|A \cup B|}$        (9)

The predictive stability of the BN parameters was assessed using 20 repetitions of five-fold cross-validation. CPTs were re-estimated within each training fold, and predictive performance on held-out cases was evaluated using mean negative log-likelihood per binary variable. Sensitivity to the Beta prior was examined using α = 0.5, 1.0, and 2.0.

Sampling uncertainty was further evaluated using 1,000 non-parametric bootstrap replicates, with 150 cases sampled with replacement in each replicate [20]. For structural robustness, Apriori mining and the predefined direction-assignment procedure were repeated and the retention frequencies of the central associations and directed edges were recorded. For probabilistic inference, the final BN structure was retained and its CPTs were re-estimated for each bootstrap sample. The resulting distributions of Δdiag and Δcond were summarized using percentile-based 95% intervals, together with the frequencies with which each upstream factor ranked among the leading diagnostic factors. The complete analytical workflow is summarized in Figure 1.

1.png

Figure 1. Analytical workflow of the association-informed interpretive structural modeling (ISM)-BN framework

4.1 Hierarchical organization of accident-causation factors

The directed ISM reveals a differentiated organization of accident-causation factors across the five levels. D6 and E2 occupy the deepest level, while D4, D3, and D8 connect broad organizational deficiencies with more specific management, behavioral, and physical factors. Most A- and B-category factors are concentrated toward the result side of the hierarchy. This configuration is broadly consistent with the 24Model, in which unsafe actions and unsafe conditions represent more immediate manifestations of accident causation, whereas organizational and safety-management deficiencies operate at deeper levels [14-16]. The resulting hierarchy is therefore best interpreted as a dependency structure rather than a deterministic causal chain.

The position of D3 is particularly informative. Inadequate third-party work control occupies an intermediate management level and is connected downstream with third-party damage, communication failure, and missing warning or marking conditions. Process-based third-party excavation models similarly represent pipeline damage through dependencies involving notification, facility records, locating, marking, and field control [9, 10]. The present structure therefore places D3 within a broader management-control process rather than treating third-party damage as an isolated event.

4.2 Target-specific diagnostic patterns

The Bayesian results show that dominant upstream relationships differ among the seven diagnostic targets. Third-party damage, communication failure, corrosion-related degradation, unsafe operation, and design/construction defects do not share a single universal antecedent. Instead, each accident manifestation is associated with a different combination of managerial, individual, and technical factors. This target-specific pattern suggests that prevention priorities should be organized around the dominant mechanisms of different accident modes rather than a single overall ranking of factor occurrence.

For A1, D3 exhibits a clear and highly stable diagnostic relationship, and the D3 → A1 edge is retained in almost all bootstrap samples. This result is consistent with natural-gas pipeline studies linking third-party damage to excavation-management and control processes [9-11]. For B1, D7 is the dominant diagnostic antecedent. Previous Bayesian research on externally corroded natural-gas pipelines has incorporated corrosion mechanisms, pipeline condition, and maintenance strategies within the same probabilistic framework [12]. The D7-B1 result therefore highlights maintenance and integrity management as an important dimension of corrosion-related accident cases.

A2 shows a different pattern: C1, D2, and D5 form a closely ranked antecedent group, and their internal ordering varies across bootstrap samples. This indicates that unsafe operation is associated with a combination of individual competence, hazard-control practice, and safety training rather than a single management deficiency. Recent oil and gas pipeline accident research similarly emphasizes the simultaneous involvement of human and organizational factors in accident development [13].

D6 has comparatively broad structural reach in the revised network and is connected directly or indirectly with several management-control nodes and multiple direct-cause targets. Its relationship with B7 is also bootstrap-stable. Rather than indicating that D6 is universally dominant, these results suggest that poor rule and responsibility implementation may function as a cross-cutting management condition influencing several more specific control processes, consistent with the multilevel organizational logic of the 24Model [14-16].

4.3 Methodological implications and robustness

A key feature of the framework is the separation of association discovery from structural orientation. Apriori identifies recurrent statistical relationships, whereas direction is constrained subsequently using accident-causation theory, process information, and engineering knowledge. This separation reduces the risk of interpreting conditional co-occurrence as causal precedence, a distinction that is fundamental in observational causal analysis [17].

The robustness analyses show that different components of the model have different levels of empirical stability. Confidence has the largest effect on the detailed rule set, while a subset of associations remains recurrent across parameter settings. Bootstrap analysis similarly shows that some directed relationships are highly stable whereas others are sensitive to sample composition. Greater evidential weight should therefore be assigned to relationships supported simultaneously by the full-sample structure, high bootstrap retention, and stable diagnostic updating. Bootstrap-based assessment of Bayesian-network features is particularly useful under limited samples [20].

Because the dataset contains accident cases only, the marginal node probabilities characterize factor activation within documented accidents rather than the probability that an operating pipeline will experience an accident. The principal probabilistic output is therefore target-specific evidence updating. This diagnostic use of BN is consistent with their general probabilistic formulation and with safety applications based on posterior or reverse inference [10, 18, 28].

4.4 Limitations and future research

Several limitations should be considered. First, the 150 cases constitute a purposively assembled accident dataset based on publicly available documentation rather than a probability sample of all urban gas pipeline operations in China. Differences in investigation depth, disclosure quality, and source availability may influence factor coding. A factor coded as 0 indicates that sufficient supporting evidence was not identified in the available material and does not necessarily demonstrate its objective absence from the accident process.

Second, the dataset contains accident cases but no matched non-accident operating observations. The model is therefore suitable for examining dependencies and diagnostic updating within accident cases but cannot estimate population-level accident incidence or absolute failure probability. Future studies could combine accident records with exposure data, normal-operation observations, and pipeline-segment operating histories to extend the framework toward predictive risk estimation.

Third, the retained directions are evidence-constrained structural relationships rather than experimentally identified causal effects. Residual uncertainty remains for some factor pairs, and several edges are sensitive to sample composition. Independent expert elicitation, temporally resolved accident sequences, and external datasets could provide further evaluation of structural orientation and generalizability. Sparse parent-state combinations also remain for several CPTs, particularly A2. Expanding the accident database and incorporating additional operational data would improve parameter estimation. For mechanisms with strong temporal characteristics, dynamic BN provide a natural extension and have already been applied to gas-pipeline risk evolution [11, 29].