A Bayesian Model Based on the Bow-Tie Causal Framework (BT-BN) for Maritime Accident Risk Analysis: A Case Study of the Bohai Sea

Abstract

Maritime accidents are low-probability, high-consequence events, making mechanism analysis crucial for risk mitigation. Existing studies often focus on single scenarios or factors and frequently mix pre-incident observational data with subjective unsafe behavior labels, limiting causal-chain construction for proactive risk prediction. To address these issues, this study proposes a Bow-Tie-based causal-chain Bayesian network, establishing a hierarchical inference chain of “observed parameters–unsafe causes–accident types” to capture causal interactions among multiple factor categories and enable inference from pre-incident data to potential unsafe causes and accident types. Applied to the Bohai Sea region, sensitivity analysis quantified the effects of risk factors under varying conditions on collision, sinking, and grounding probabilities. The results show that the method can infer accident types and unsafe causes using only pre-incident data, achieving over 70% accuracy and closely matching accident investigation findings. Moreover, it reveals layer-by-layer mechanisms of key contributing factors and provides targeted management interventions, supporting quantitative decision-making for maritime regulators and shipping companies, with significant practical applicability.

1. Introduction

Maritime transport serves as the principal mode of global trade, accounting for nearly 90% of international cargo movement [1]. Nevertheless, it is among the most hazardous forms of transport, as major maritime accidents often inflict severe economic and environmental damage [2] and result in substantial loss of life [3]. Characterized as low-probability yet high-consequence events, maritime accidents have drawn considerable attention from both the public and governmental authorities worldwide [4]. Statistics from the European Maritime Safety Agency (EMSA) indicate that between 2014 and 2023, a total of 26,595 marine casualties and incidents were reported, resulting in 7604 injuries and 650 fatalities. In 2023 alone, 2676 incidents were recorded, slightly above the long-term annual average [5]. Maritime safety, therefore, continues to confront formidable challenges [6], and contemporary research increasingly emphasizes safety and risk assessment as critical avenues for accident prevention [7].

To facilitate the systematic summarization of accident patterns and the development of risk models, numerous scholars have examined maritime traffic risks through the lens of accident case studies [8], aiming to elucidate the significance and influence of vessel characteristics [9], environmental conditions [10], and organizational behaviors on the likelihood and severity of accidents [11]. As a statutory procedure conducted by maritime authorities worldwide, maritime accident investigations are governed by the Accident Investigation Code [12], which mandates the identification and assessment of “causal factors”, namely the actions, omissions, events, or conditions that contribute to the occurrence or severity of an accident [13]. The findings of such investigations provide a robust and reliable foundation for subsequent case analyses [14].

The causation of maritime accidents is typically multifaceted [15], often arising from a combination of technical failures, human errors, organizational deficiencies, or a chain of interrelated events [16]. The establishment of accident reports and databases has enabled extensive statistical analyses of these contributing factors [17]. Ref. [18] utilized global maritime accident datasets to examine the determinants influencing both accident types and severity levels, as well as the underlying mechanisms at play. Through the application of the Most Probable Explanation (MPE) approach, researchers have analyzed potential scenarios under varying conditions to identify latent accident risks. Ref. [19] based on the analysis of 594 maritime accidents from 2014 to 2023, a data-driven BN model was established to examine the individual and joint contributions of human factors and operational conditions to different types of maritime accidents. Ref. [20] developed a dynamic Human Factors Analysis and Classification System for Maritime Accidents (HFACS-MA) to assess human error in complex maritime operations, integrating five hierarchical levels of human factors and a Bayesian Network to capture dependencies among risk-influencing factors.

With the increasing complexity of maritime transportation systems and the advancement of vessel information technologies toward digitalization and intelligence [21], maritime accidents often exhibit characteristics of diversity, ambiguity [22], and specificity, rendering the investigation of their root causes particularly challenging [23]. To capture the intrinsic relationships among causal factors, a variety of analytical approaches have been proposed, including Fault Tree Analysis (FTA) [24], and the Human Factors Analysis and Classification System (HFACS) [25]. While these methods have proven effective in identifying critical risk factors, their reliance on static causal chains limits their capacity to accommodate the dynamic nature of risk evolution in complex operational environments [26].

Researchers have observed that maritime accidents are frequently triggered by the coupled interaction of multiple factors, such as human, mechanical, material, procedural, and environmental [27], which make it difficult for single-dimensional analyses to fully capture the complexity of causal chains [28]. Against this backdrop, Bayesian Network models, which simultaneously characterize causal relationships and probabilistic dependencies [29], have emerged as one of the most widely adopted and effective tools for causal-chain analysis in maritime accidents [30]. For instance, Ref. [9] integrated the NK model with Bayesian Networks to quantitatively assess the coupling risks in Chinese ship collision accidents, using accident reports to establish dependencies among human, vessel, environment, and management factors, and applying sensitivity analysis to reveal the dominant contributors and coupled causal pathways. Ref. [31] employed complex network theory to construct ship collision risk networks from accident reports, enabling the identification and quantitative assessment of key causal factors, though its capacity to capture the causal directionality remains limited.

Bayesian Networks and related methods have shown strong potential for analyzing maritime accident causality, but key limitations remain. First, studies often focus on specific accidents or isolated factors, overlooking systematic interactions among human, vessel, environmental, and managerial elements [32]. Second, at the micro level, objective data such as timing and weather are commonly combined with subjective post-accident labels like “inadequate lookout” or “crew unseaworthiness”, without clarifying their causal roles. In practice, risk-warning systems rely only on pre-accident data; post-event causes are unavailable in real time [33]. Thus, models depending on such retrospective labels cannot support proactive risk prediction. There is a clear need for causal frameworks that distinguish between different levels of causation and connect macro-level structures with micro-level observations to improve maritime risk assessment.

To address the aforementioned limitations, this study integrates the causal-chain concept of Bow-Tie theory into the construction of Bayesian Networks, establishing a hierarchical inference pathway from observational parameters through unsafe causes to accident types and thus providing a systematic link between the causes and consequences of adverse events. Moreover, the proposed method accounts for human, vessel, environmental, and managerial factors within a unified modeling framework, capturing the interactions among multi-level factors and overcoming the limitations of prior research, which largely focused on individual factors or specific scenarios. On the other hand, through progressive inference, the method connects objective pre-accident observational data with latent unsafe causes, thus remedying the deficiency of traditional approaches where observational factors and behavioral labels were conflated without causal-chain interpretation.

Building upon this rationale, the approach enables the identification of potential unsafe causes before accidents occur, supports early warning of maritime traffic risks, and reveals how different combinations of unsafe causes trigger specific accident types [34]. In practical applications, the method offers decision-making support for Vessel Traffic Services (VTS), maritime supervision. For instance, when risk analysis indicates “crew lookout negligence under adverse weather”, timely measures like enhanced monitoring or speed restrictions can be taken to reduce collision risks [35].

The paper is organized as follows. Section 2 introduces the accident dataset. Section 3 describes the methodology and its interpretative framework. Section 4 applies the method to the Bohai Sea region to examine three common maritime accident types and build corresponding network models. Section 5 discusses the causal-chain analysis results and provides recommendations for maritime stakeholders. The conclusion summarizes the study.

2. Study Area and Data

This study uses data compiled from maritime accident reports publicly released by the Maritime Safety Administration (MSA) of China (http://en.msa.gov.cn/). These reports provide detailed accounts of significant incidents that impact the maritime traffic system.

It should be noted, however, these reports primarily aim to determine accident causes and assign responsibility, so some causal descriptions may reflect subjective judgments or post hoc reasoning. In this study, only objective and quantifiable data such as environmental parameters, vessel characteristics, and accident types were used, while narrative variables related to causality were treated as intermediate explanatory factors to reduce subjectivity in statistical inference.

The study focuses on the Bohai Sea, a northern coastal region connecting inland waters to the Yellow Sea. Due to its complex navigation environment and high vessel density, it is a critical area for maritime safety research. Accordingly, accident reports published between January 2013 and January 2025 by the MSA bureaus of Tianjin, Liaoning, Hebei, Shandong, and Heilongjiang were selected and reviewed.

2.1. Distribution Characteristics of Accident Types

According to the accident classification standard established by the International Maritime Organization (IMO), maritime accidents are categorized into eight major types: collision, grounding, sinking, contact, fire, storm damage, foundering, fatality, and others [36]. A total of 122 maritime accidents were recorded in the Bohai Sea from 2013 to 2025. Figure 1 illustrates the spatial distribution of these accidents, among which collision, sinking, grounding, fatality, and fire constitute the five most hazardous scenarios.

However, as fatality and fire-related accidents are largely attributable to onboard operations or cargo management rather than navigational factors, their relevance to the maritime traffic environment and vessel maneuvering behavior is limited. Consequently, this study focuses exclusively on three representative navigation-related accident types: collision, sinking, and grounding. In total, 90 accident investigation reports were selected as the research sample.

2.2. Distribution Characteristics of Accident Timing

To investigate the temporal characteristics of maritime accidents, accident frequency and severity were analyzed on a monthly basis. As shown in Figure 2, collisions occurred more frequently from May to July and from October to December. Seasonality is a prominent characteristic of the maritime transport market [37]. Given the intrinsic link between maritime safety and shipping activity, the observed seasonal pattern in collision accidents aligns closely with trade cycles. In contrast, other accident types exhibit substantial month-to-month variability. Establishing the influence of seasonal factors on maritime accident incidence is, therefore, essential for effective risk management and prevention strategies.

2.3. Distribution Characteristics of Accident Locations

The spatial distribution of maritime accidents was examined to inform geographical strategy development [38]. Figure 3 illustrates the accident severity and positioning from 2013 to 2025. To further identify regions with dense accident occurrences, a DBSCAN clustering analysis was applied to the accident coordinates ($eps$ = 10 nautical miles, $minPts$ = 5). The resulting spatial clusters are visualized in Figure 4, which highlights seven distinct concentration zones primarily distributed along major waterways and port approaches, especially near the Bohai Bay coastline and estuarine areas. In this experiment, 68 accidents were identified as noise points that did not belong to any cluster. The cluster centers and the number of accidents within each cluster are summarized in

Table 1. Quantitative results of DBSCAN clustering on maritime accident locations (eps = 10 nautical miles, minPts = 5). The table lists the geographic centers of the identified clusters and the number of accident cases in each cluster. These results confirm the spatial aggregation pattern observed in Figure 3.

Cluster	Cluster Size	Center Latitude	Center Longitude	Position Description
1	8	38.958	121.770	Dalian port outer fairway
2	6	38.596	120.879	Western Bohai strait shipping lane
3	10	38.341	118.128	Southern Bohai bay coastal route
4	10	38.922	117.994	Approaches to Tianjin port
5	6	39.858	119.635	Qinhuangdao-Tangshan coastal route
6	9	39.069	119.188	Central Bohai bay shipping lane
7	5	39.354	119.401	Qinhuangdao port anchorage/channel

, indicating that regions in high-traffic waterways and near ports, with higher density along the Bohai Bay coastline and estuarine zones, exhibit the highest accident concentrations, reflecting the combined impact of vessel traffic and complex hydrographic conditions. In contrast, accidents in open waters are more scattered, with a few smaller clusters likely associated with specific routes or adverse weather conditions. Collision and sinking incidents dominate busy corridors, while fires and fatalities are more widespread. Severity varies accordingly: major incidents occur at ports and junctions, minor ones are more evenly distributed.

3. Method

To address the challenges of complex causal relationships and limited pre-incident observations in maritime accident risk analysis, this study develops a hierarchical Bayesian network model based on Bow-Tie theory (BT-BN). The model construction and inference are implemented in three sequential stages.

First, the Bow-Tie causal-chain concept is incorporated into the network structure design. A “precursor–cause–consequence” framework guides the establishment of conditional dependencies among observational parameters, causal factors, and accident types, progressively revealing their interrelations. Second, accident data are employed for parameter learning and model validation, ensuring that the network accurately reflects observed probabilistic patterns. Finally, Bayesian inference is performed on specific accident cases using the learned network, enabling probabilistic reasoning of accident causes and associated factors. The overall workflow of the proposed BT-BN method is illustrated in Figure 5.

3.1. Identification of Risk Factors

To analyze the influence of various risk factors on different types of maritime traffic accidents, it is essential to identify and filter risk influencing factors (RIFs) from accident investigation reports. In this study, the generation of RIFs involves four stages: (1) online database retrieval; (2) review and screening of accident reports; (3) extraction and analysis of accident content; and (4) synthesis and selection of risk factors. In practice, multiple historical maritime accident reports were manually examined, from which two categories of factors were extracted:

• Observational factors (e.g., wind force, wave height, visibility), directly obtained from recorded environmental and operational parameters, subsequently discretized into multiple states;
• Causal factors (e.g., crew incompetence, vessel unseaworthiness), standardized from the investigative conclusions and transformed into Boolean variables, recorded as “Yes” if present in the accident and “No” otherwise.

For example, one accident report noted: “The vessel ‘HY69’, originally designed for inland navigation, deliberately evaded maritime supervision and entered the sea under unsuitable conditions, thereby violating Article 35, Paragraph 1 of the Maritime Traffic Safety Law of the People’s Republic of China; furthermore, the vessel failed to be manned by the required number of certified crew members, contravening Article 13 and Article 33, Paragraph 2 of the same law”. From this description, two causal factors vessel unseaworthiness and crew lack of proficiency were identified. Similarly, another report stated: “According to the professional meteorological forecast released by Dalian Meteorological Station at 15:30 on 20 September 2021 for Changxing Island Port Area: from the afternoon to night, overcast with light showers turning partly cloudy, southwest winds force 7–8 with gusts up to force 9, weakening to force 6–7 with gusts up to force 8 in the morning, heavy to very heavy seas”. From this account, wind force and wave height parameters were directly extracted as observational factors for model input.

3.2. Construction of the Bow-Tie Bayesian Network (BT-BN)

Bow-Tie (BT) analysis is a widely used risk management and accident analysis tool that identifies and illustrates causal relationships in accidents, along with preventive and mitigative measures. The risk pathway is shown in Figure 6. The framework has been widely applied to manage occupational risks, leading to risk assessment models and software tools [39]. As a method combining proactive and reactive elements, BT analysis systematically addresses hazards within a hazard and effects management process. It has been used to evaluate safety management systems for marine facilities, especially in gap analyses [40].

In practice, BT analysis highlights the systematic links among precursors, causal factors, and consequences [41]. In maritime accident analysis, precursors include environmental conditions (e.g., wind force, sea state, visibility) and vessel status (e.g., size, type); causal factors are potential triggers (e.g., severe weather, unseaworthiness); and consequences represent accident types. For example, adverse conditions such as strong winds, high waves, and poor visibility, combined with an inland vessel navigating beyond its certified limits, may give rise to causal factors such as unseaworthiness and inadequate lookout, ultimately resulting in a collision. This framework organizes complex, multi-factorial influences into a structured “precursor–cause–consequence” chain, supporting both the identification of key risk factors and the design of preventive strategies.

Building on this, the study adapts this BT framework to build a hierarchical Bayesian model. Observational parameters serve as precursors, accident causes as intermediate factors, and accident types as outcomes. This structure supports inferring causes from observations and predicting outcomes from causes, forming a three-level system: observational factors, causal factors, and outcomes.

The Bayesian Network (BN) is the core model, using conditional probabilities to quantify causal links and uncertainty. By combining BT’s structure with BN reasoning, a multi-level BT-BN model is created. It defines 13 observational RIFs and 9 causal RIFs; details are in

Table 2. Hierarchical structure of BT-BN model for maritime accident risk analysis. The model comprises three levels: top-level accident outcomes, intermediate-level causal factors (environmental, vessel-related, and crew-related), and bottom-level observed factors (meteorological, vessel static, and vessel dynamic parameters). Each factor node is specified with its possible states, and quantitative division criteria are provided for measurable parameters.

Level	Category	Factor Node	State	Division Basis
Top level	Accident	Accident event	Sinking, collision, grounding	-
Intermediate level (Causal factor)	Environmental	Adverse weather	Yes, no	-
		Poor visibility	Yes, no	-
	Vessel cause	Unseaworthy	Yes, no	-
		Abnormal loading	Yes, no	-
		Abnormal draught	Yes, no	-
	Crew cause	Inadequate lookout	Yes, no	-
		Hazard underestimation	Yes, no	-
		Ineffective action	Yes, no	-
		Crew lack of proficiency	Yes, no	-
Bottom level (Observed factor)	Meteorological parameter	Wind scale	Low, medium, high, extreme	Force: (0,3], (3,6], (6,8], (8,10], (10, ∞)
		Wave scale	Low, medium, high, extreme	Wave height (m): (0,0.5], (0.5,1], (1,2], (2, ∞)
		Visibility level	Poor, fair, favorable	-
		Time	Early morning, morning, afternoon, evening	00:00–6:00, 6:00–12:00, 12:00–18:00, 18:00–24:00
	Vessel static parameter	Vessel size	Small, medium, large, ultra large	Gross tonnage: (0,500], (500,3000], (3000,10,000], (10,000, ∞)
		Seaworthiness area	Inland waterway, coastal, offshore, domestic water, international water	-
		Vessel type	Cargo ship, fishing boat, service ship, container ship	-
	Vessel dynamic parameter	Loading condition	Light load, half load, full load	Load ratio: (0,30%], (30%,70%], (70%, ∞)
		Draft condition	Safe, elevated, critical	Draft ratio: (0,50%], (50%,80%], (80%, ∞)
		Position	Traffic dense area, coastal area, coastal edge, offshore	Distance to shore (nm): (0,5], (5,20], (20,50], (50, ∞)
		Speed	Low, normal, high, overspeed, stationary	Speed (knot): (0,4], (4,8], (8,12], (12, ∞)
		Crew complement	Complete, incomplete	-
		Navigational status	Underway, working, anchor	-

.

3.3. Parameterization and Probability Estimation

BT analysis provides a causal framework by delineating the logical sequence from threats to top events and subsequently to consequences, thereby establishing a clear structural basis for accident risk assessment. Integrating the BT framework with a BN preserves this causal structure while introducing probabilistic modeling and inference, enabling a complete analysis of the probability of accidents from observational data through latent causes.

A BN, also known as a belief network, is an effective theoretical model for handling uncertainty and reasoning [42]. In a BN, variables are represented as nodes, and directed arcs from parent to child nodes encode the relationships among variables. Formally, a BN consists of a directed acyclic graph (DAG) defining the network structure, and a set of conditional probability tables (CPTs) capturing dependencies among variables [43]. Figure 7 illustrates a representative BN, providing a concise depiction of inter-variable relationships.

Conditional probabilities quantify the strength of association between parent and child nodes, forming the foundation for BN inference [44]. In this study, conditional probabilities for each node were determined using statistical methods and Bayes’ theorem. During the parameter learning phase, data were discretized, and the conditional probabilities were estimated via maximum likelihood estimation, thereby enabling probabilistic reasoning across the constructed BN.

After constructing the BN structure to define interactions among nodes, it is necessary to calculate each node’s marginal probability and CPT to quantify the influence among variables. Denoting each node as $X_i$, the set of parent nodes of $X_i$ as $V_i$, and the set of all n nodes as X, the joint probability of the network can be expressed as

$$p\left(X\right)=\prod _{i=1}^{n}p\left(X_i\right|V_i).$$

(1)

3.4. Validation Framework and Inference Mechanism

Based on the constructed BT-BN model for maritime ship accident risks in the Bohai Sea area, this study employed the GeNIe software (version 3.0.5703.0, BayesFusion LLC, Pittsburgh, Pennsylvania, USA) to perform model validation and inference analysis. During validation, historical accident data were input into the model to conduct probabilistic reasoning for scenarios such as collision, sinking, and grounding, thereby evaluating the model’s effectiveness in capturing the influence of actual risk factors and reflecting the patterns of accident occurrence.

Building on this, a sensitivity analysis was conducted to quantify the impact of each risk factor on accident probabilities, facilitating the identification of key common risk factors that significantly affect maritime traffic safety. Drawing from these results, an accident causal chain was constructed, elucidating the primary driving mechanisms underlying accident occurrence and providing a scientific basis for the management of vessel traffic safety.

4. BT-BN-Based Maritime Accident Risk Assessor for the Bohai Sea

4.1. Structure Learning

During the network structure learning phase, this study applies the causal-chain concept of BT analysis to guide the construction of the BN, following a hierarchical framework in which observational factors inform causal factors, which in turn determine accident types.

It is important to clarify that the causal chain model developed herein is intended to reveal conditional dependencies and potential mechanistic pathways among accident factors at the structural level, rather than to verify causal effects in an experimental sense. Given the retrospective nature of accident investigation reports, the definition of “causal factors” is often derived from outcome-based reasoning, making it difficult to establish a fully objective causal mapping with observational data. To address this issue, statistical tests were employed to identify significant associations among variables, thereby quantifying the coupling strength between observational and causal factors.

Specifically, Pearson’s chi-square tests were conducted to examine the relationships between 9 causal factors and 13 observational factors. Considering that post hoc attribution may artificially reinforce causal links and consequently yield smaller overall p-values, the p-value in this study was not used as evidence for causal inference but rather treated as an indicator of coupling strength. To mitigate attribution bias and multicollinearity effects, a stringent significance threshold ($p<1.0\times {10}^{-6}$) was applied, retaining only those dependency relationships that remained highly reliable under biased conditions. The resulting significant associations are presented in

Table 3. Pearson’s chi-square tests identified significant associations between causal and observational factors. Nine causal and 13 observational factors were analyzed, with a significance threshold of $p<1.0\times {10}^{-6}$. The table shows only observational factors with statistically significant dependencies on the corresponding causal factors and their p values. This analysis quantifies the coupling strength between observable parameters and underlying causes in maritime accident risk assessment.

Causal Factor	Observed Factor	p Value
Adverse weather	Wind scale	$2.30\times {10}^{-15}$
	Wave scale	$7.89\times {10}^{-9}$
	Loading condition	$3.87\times {10}^{-9}$
	Draft condition	$4.76\times {10}^{-7}$
Poor visibility	Vsibility level	$7.78\times {10}^{-20}$
Unseaworthy	Seaworthiness area	$6.32\times {10}^{-10}$
	Loading condition	$1.09\times {10}^{-7}$
	Draft condition	$1.92\times {10}^{-6}$
	Vessel size	$1.17\times {10}^{-6}$
Abnormal loading	Loading condition	$4.77\times {10}^{-17}$
	Draft condition	$9.30\times {10}^{-10}$
Abnormal draught	Draft condition	$7.78\times {10}^{-20}$
	Loading condition	$3.73\times {10}^{-6}$
Inadequate lookout	Time	$1.30\times {10}^{-11}$
	Navigational status	$3.45\times {10}^{-7}$
	Vsibility level	$6.27\times {10}^{-7}$
Hazard underestimation	Speed	$3.37\times {10}^{-11}$
	Seaworthiness area	$5.73\times {10}^{-9}$
	Crew complement	$1.68\times {10}^{-7}$
	Navigational status	$6.76\times {10}^{-8}$
Ineffective action	Navigational status	$1.98\times {10}^{-11}$
	Speed	$4.25\times {10}^{-10}$
	Position	$2.74\times {10}^{-8}$
	Vessel size	$9.00\times {10}^{-7}$
	Vessel type	$7.47\times {10}^{-7}$
	Wave scale	$6.89\times {10}^{-7}$
Crew incompetence	Crew complement	$5.09\times {10}^{-15}$
	Seaworthiness area	$7.65\times {10}^{-8}$
	Vessel size	$3.66\times {10}^{-7}$

.

Based on prior chi-square correlation analyses, dependency links between nodes were initially established to form the BT-BN network. To validate and refine causal relationships, an edge ablation test was performed: edges were sequentially removed, model parameters re-estimated, and the resulting change in network score measured using the K2 function. Formally, for an edge e:

$$\Delta \mathrm{Score}\left(e\right)=\mathrm{Score}(G\mid D)-\mathrm{Score}(G_{-e}\mid D),$$

(2)

where G is the original network, $G_{-e}$ the network with edge e removed, D the dataset, and $\mathrm{Score}(·)$ the K2 scoring function [45]. Edges with large positive $\Delta \mathrm{Score}\left(e\right)$ are considered important and retained; edges with non-positive $\Delta \mathrm{Score}\left(e\right)$ are treated as redundant.

The importance of individual edges was evaluated via edge ablation, with the results summarized in

Table 4. Top 15 edges in the BT-BN whose removal most affected model performance. The score drop after removal quantifies each edge’s contribution to risk propagation. Edges such as ”crew complement → crew lack of proficiency” caused substantial score decreases, indicating critical roles. In contrast, removing edges such as ”load factor → adverse weather”, ”draft → adverse weather”, and ”failure to actively avoid risk → wave height” increased performance scores, suggesting redundancy or spuriousness; these edges were removed in the study.

Edge	Score Drop ($\mathit{\Delta }\mathbf{K}2$)	Importance Ranking
Hazard underestimation → Accident	344.16	1
Adverse weather → Accident	262.69	2
Unseaworthy → Accident	259.30	3
Inadequate lookout → Accident	258.61	4
Abnormal loading → Accident	258.18	5
Poor visibility → Accident	257.23	6
Abnormal draught → Accident	254.65	7
Ineffective action → Accident	254.36	8
Crew lack of proficiency → Accident	252.87	9
Draft condition → Abnormal draught	30.69	10
Visibility level → Poor visibility	24.58	11
Wind scale → Adverse weather	24.55	12
Crew complement → Crew lack of proficiency	17.80	13
Time → Inadequate lookout	15.05	14
Wave scale → Adverse weather	13.02	15

.

The structural necessity analysis indicates that several key edges within the network closely align with the core propagation pathways of the accident risk chain. For instance, in conditions of poor visibility, the lack of a proper lookout can trigger an accident. This sequence not only contributes significantly to the model score but also aligns with expert judgment, demonstrating the causal plausibility of the network structure.

Collectively, the BT-BN model in this study effectively captures the global dependencies within accident chains while also exhibiting strong causal rationality in the evaluation of local edge importance. Ultimately, based on the causal relationships among node variables, the dependency links were finalized, and the topology of BT-BN model in this study was constructed using GeNIe Academic software, as illustrated in Figure 8.

4.2. Parameter Learning

Conditional probabilities quantify the strength of the relationship between parent and child nodes, and their determination forms the foundation for Bayesian network inference. In this study, the conditional probability tables for each node are established using mathematical statistics and Bayes’ theorem. Taking the “Adverse weather” node as an example, the observed nodes “Wind scale” and “Wave scale” are connected to it, with the corresponding conditional probabilities presented in the

Table 5. Conditional probability table of the ”Adverse weather” node with respect to its parent nodes ”Wind scale” and ”Wave scale.” The categories ”Small”, ”Medium”, ”High,” and ”Ultra” denote different levels of wind scale and wave scale, while ”Yes” and ”No” indicate whether the situation is recognized as adverse weather or not.

			Wave Scale
			Small	Medium	High	Ultra
Wind Scale	Small	Yes	0.0178	0.0833	0.0178	0.9166
		No	0.9821	0.9166	0.9821	0.0833
	Medium	Yes	0.1000	0.0750	0.1250	0.9466
		No	0.9000	0.9250	0.8750	0.0533
	High	Yes	0.8566	0.8566	0.9100	0.9666
		No	0.1433	0.1433	0.0900	0.0333
	Ultra	Yes	0.9500	0.9500	0.9500	0.9715
		No	0.0500	0.0500	0.0500	0.0284

. In the table, “No” denotes the absence of the “Adverse weather” node state, whereas “Yes” indicates its occurrence. For instance, when both medium waves and medium wind levels occur, the probability of being classified as adverse weather is 7.5%, while the probability of not being classified as such is 92.5%.

Upon defining the network structure and CPTs, a BT-BN model for maritime accident risk in the Bohai Sea was constructed using GeNIe software, as shown in Figure 9.

4.3. Global Sensitivity Analysis of Accident Risk

In the comprehensive risk assessment, the top-level accident event was designated as the target node, and sensitivity analysis was employed to evaluate the contribution of each variable to the overall risk level [46]. The essence of sensitivity analysis lies in examining how variations in input nodes affect the output risk, thereby identifying the factors that play pivotal roles in global risk.

The results, illustrated in Figure 10, depict the influence of each node on the integrated risk using different colors: red indicates a significant impact, pink denotes a moderate effect, white represents a weak influence, and gray signifies negligible impact. According to the RIF index, speed, navigational status, vsibility level, draft condition, loading condition were identified as the critical factors contributing most substantially to the overall accident risk.

Further observation reveals that adverse weather, abnormal loading, abnormal draught, inadequate lookout exert direct influence across all accident types, with relatively minor differences among them. In contrast, aside from a few high-impact factors, the individual effect of other risk factors on the overall risk remains limited. This indicates that during accident evolution, most risk factors indirectly affect the overall accident through coupling and cumulative effects, whereas a small number of key factors directly determine the type of accident that occurs.

4.4. Hierarchical Impact Analysis of Risk Factors

In Section 4.3, the top-level accident event was set as the target node, and sensitivity analysis identified the key factors with the greatest impact on overall risk, revealing the main drivers of accidents at a global level. However, these results apply only to overall risk assessment and offer limited insight into how risk factors at different levels contribute within the accident chain. To address this, this section analyzes second-level risk factors and third-level environmental and vessel characteristics, using conditional probability difference and distribution disparity methods to assess each node’s effect size and discriminatory power. This approach clarifies the contributions of critical nodes and the causal mechanisms behind differences in accident types. Specifically:

Second-level nodes (causal factor layer): The top-level ”Accident” node was further decomposed into three sub-events: collision, sinking, and grounding. Sensitivity analysis was first applied to the second-level risk factor nodes. The method employed, conditional probability difference, quantifies the change in accident probability when a risk factor shifts between ”yes” and ”no” states, thereby measuring its direct effect on specific accident types. Formally, the sensitivity of accident type $A_i$ to a given risk factor X can be expressed as

$$\Delta P_i\left(X\right)=P(A_i\mid X=\mathrm{yes})-P(A_i\mid X=\mathrm{no}),i\in \left\{\mathrm{collision},\mathrm{sinking},\mathrm{grounding}\right\}.$$

(3)

The results of the sensitivity analysis are summarized in

Table 6. Sensitivity analysis of causal factors with respect to different accident types, quantified by conditional probability differences ($\Delta P$). Positive values indicate that the presence of a factor increases the probability of an accident type, while negative values indicate a decreasing effect. The rightmost column highlights the accident type(s) most sensitive to each factor.

Causal Factor	Grounding ($\mathit{\Delta }\mathit{P}$)	Collision ($\mathit{\Delta }\mathit{P}$)	Sinking ($\mathit{\Delta }\mathit{P}$)	Main Sensitivity
Adverse weather	+0.032	−0.087	+0.055	Sinking, grounding
Poor visibility	+0.016	−0.027	+0.010	Grounding, sinking
Unseaworthy	+0.005	−0.006	+0.001	Negligible impact
Abnormal loading	+0.017	−0.049	+0.032	Sinking, grounding
Abnormal draught	+0.029	−0.053	+0.025	Sinking, grounding
Inadequate lookout	−0.018	+0.052	−0.034	Collision
Hazard underestimation	+0.019	−0.012	−0.007	Collision
Ineffective action	−0.012	+0.028	−0.015	Collision
Crew incompetence	−0.019	+0.027	−0.009	Collision

. Collision accidents are mainly sensitive to human factors such as ”inadequate lookout”, ” ineffective action”, and ”crew incompetence”, which greatly increase collision likelihood, showing that operational and behavioral errors drive most collision risk. Sinking accidents are more influenced by environmental and vessel conditions like ”adverse weather,” ”abnormal loading”, and ”abnormal draught”, with extreme weather and improper loading as key triggers. Grounding accidents are closely linked to ”hazardunder estimationt”, ”poor visibility”, and ”draft anomalies”, indicating that poor environmental awareness and limited maneuverability are major contributing factors.

Third-level nodes (observational variable layer): After identifying the direct effects of risk factor nodes, the analysis focused on multi-state variables in the environmental and vessel characteristic layer. While earlier results highlighted key risk factors driving accidents, they did not capture how varying environmental conditions and vessel attributes influence outcomes. To address this, lift analysis was applied to third-level nodes to better characterize the contextual dependencies behind differences in accident types.

The lift method compares the conditional probability of a target accident type under a specific state of a given factor with its baseline probability, thereby quantifying the extent to which that state either promotes or suppresses accident occurrence. Formally, the lift of accident type $A_i$ given that variable X is in state x is defined as

$$\mathrm{Lift}(A_i,X=x)={\displaystyle \frac{P(A_i\mid X=x)}{P\left(A_i\right)}},$$

(4)

where $P(A_i\mid X=x)$ is the conditional probability of accident type $A_i$ under state x of variable X, and $P\left(A_i\right)$ is the baseline probability of accident type $A_i$. A lift value greater than 1 indicates that the state promotes accident occurrence, whereas a value less than 1 indicates a suppressing effect. The higher the lift, the greater the influence of that state on the accident likelihood.

As shown in

Table 7. Lift analysis of environmental and vessel factors for grounding accidents. Each lift value represents the ratio of the conditional probability of a grounding event given the peak state of a factor to the baseline probability of grounding. Higher values indicate greater contribution of the factor to accident likelihood.

Event	Observed Factor	Peak State	Lift
Grounding	Wind scale	High	1.11
	Speed	High	1.11
	Draft condition	Critical	1.09
	Wave scale	High	1.09
	Position	Traffic dense area	1.07
	Time	Afternoon	1.07
	Crew complement	Complete	1.06
	Navigational status	Anchor	1.06
	Visibility level	Favorable	1.05
	Loading condition	Full load	1.05
	Seaworthiness area	Domestic water	1.04

,

Table 8. Lift analysis of environmental and vessel factors for collision accidents. Each lift value represents the ratio of the conditional probability of a collision event given the peak state of a factor to the baseline probability of collision. Higher values indicate stronger influence on accident occurrence.

Event	Observed Factor	Peak State	Lift
Collision	Seaworthiness area	Inland waterway	1.23
	Wind scale	Low	1.10
	Wave scale	Low	1.10
	Speed	Overspeed	1.09
	Time	Evening	1.07
	Loading condition	Light load	1.06
	Draft condition	Safe	1.05
	Crew complement	Incomplete	1.05
	Position	Offshore	1.04
	Navigational status	Underway	1.03
	Visibility level	Poor	1.02

and

Table 9. Lift analysis of environmental and vessel factors for sinking accidents. Each lift value represents the ratio of the conditional probability of a sinking event given the peak state of a factor to the baseline probability of sinking. Higher values indicate stronger influence on accident occurrence.

Event	Observed Factor	Peak State	Lift
Sinking	Wind scale	Extreme	1.18
	Wave scale	Extreme	1.16
	Loading condition	Full load	1.12
	Navigational status	Anchor	1.10
	Seaworthiness area	Inland waterway	1.09
	Position	Traffic dense area	1.08
	Draft condition	Critical	1.08
	Speed	Stationary	1.07
	Time	Afternoon	1.04
	Visibility level	Favorable	1.03
	Crew complement	Incomplete	1.01

, third-level environmental and vessel characteristics exhibit distinct sensitivity patterns across different accident types. Lift analysis was applied to quantify the influence of specific observed factors on accident likelihood, with higher lift values indicating greater promotion of accident occurrence.

For grounding accidents (Table 7), high wind, high waves, high speed, and critical draft conditions greatly increase risk, indicating that poor sea conditions and improper maneuvering are key drivers. Collision accidents (Table 8) in inland or coastal waters are most likely under conditions such as overspeeding, nighttime operation, and incomplete crew, underscoring the significant role of human factors in complex channels and low visibility. For sinking accidents (Table 9), extreme winds, extreme waves, and full load conditions produce the largest increases in accident probability, showing that severe weather and vessel loading are the primary drivers.

In summary, unlike the global sensitivity analysis in Section 4.3, which identifies key factors affecting overall risk, the hierarchical node effect analysis provides a more in-depth and multi-level perspective. The experimental results show that collision accidents are mainly driven by human errors, grounding accidents by environmental and maneuvering limitations, and sinking accidents by adverse weather and vessel loading. Third-level observations show how conditions like wind, wave height, visibility, vessel speed, and loading affect accident likelihood. This hierarchical approach clarifies causal mechanisms behind different accident types, offering deeper insight for targeted risk prevention.

5. Model Validation

5.1. Sinking Case Study

At 05:30 on 19 April 2017, the Chinese bulk carrier Fuhang 66, transporting approximately 1800 m³; of silt from Tianjin Port’s Nanjiang Port Area to the Dagang Port Area, sank while at anchor in the waters of Tianjin Port Dagang under heavy wind and waves, following flooding of its cargo hold. The accident report indicated that the weather conditions were clear, with winds shifting from the northwest to the southeast at Wind scale 7, reaching up to scale 8, and wave heights ranging between 3.5 and 4.0 m. The incident resulted in a direct economic loss of approximately 3.9 million CNY, with no casualties or marine pollution, and was classified as a general-level accident.

By configuring all observational nodes to reflect the environmental parameters, as well as the static and dynamic conditions of the vessel at the time of the incident, the BN model was executed. The model inferred the causes as adverse weather conditions, unseaworthiness, overloading, abnormal draft, and crew unfitness. These inferred causes were entirely consistent with those identified in the official accident report. The probability of the sinking incident was calculated to be 73%. For this case, the accident occurrence probability predicted by the model is illustrated in Figure 11.

5.2. Collision Case Study

At 05:46 on 30 May 2015, the Marshall Islands-flagged Rickmers Hamburg collided with the Chinese vessel Wanjiangshun 1318 in the main channel of Tianjin Port. As a result, Wanjiangshun 1318 sank, causing one fatality and one missing crew member. At the time of the accident, the prevailing conditions were an east-southeast wind at Wind scale 2, sea state 1, and heavy fog, with visibility reduced to approximately 100 m. The incident was classified as a general-level accident.

By configuring all observational nodes to represent the prevailing conditions, with environmental parameters as light wind, slight sea, and poor visibility; static vessel parameters as large-sized ship, seaworthy for international waters; and dynamic vessel parameters as medium load, safe draft, underway, early morning, fully crewed, excessive speed, and location along the coastal periphery.

The model inferred the causes as poor visibility, inadequate lookout, insufficient risk assessment, and failure to take effective evasive measures. These inferred causes were consistent with those identified in the official accident report. The probability of this collision was calculated to be 87%. For this case, the accident occurrence probability predicted by the model is illustrated in Figure 12.

5.3. Grounding Case Study

At approximately 09:30 on 3 April 2018, the Chinese dry bulk vessel B, laden with 28,244.88 tones of coal, departed Jinzhou Port bound for Zhuanghe Dalian Port Area. During berthing assistance by tugboats, the vessel grounded. At the time of the incident, northeasterly winds of wind 6–7 and heavy seas prevailed. There were no casualties or marine pollution; the direct economic loss was estimated at roughly CNY 2 million, and the incident was classified as a general-level accident.

All observation nodes were set to the vessel’s static and dynamic states and environmental conditions at the time of the accident. The model identified severe weather, unseaworthiness, abnormal loading, abnormal draft, inadequate hazard assessment, and insufficient evasive action as causes. The official report cited the captain’s underestimation of strong lateral currents and crosswinds during berthing, along with poor ship-handling skills, as key factors. Specifically, excessive speed reduction increased wind exposure, creating a large drift angle that caused the vessel to leave the channel and ground. Although “inadequate hazard assessment” and “insufficient evasive action” were not explicitly stated, the model’s inferences align with the report’s findings on underestimation and improper handling, showing the BN model’s ability to uncover behavioral and decision-making flaws from limited data. The model calculated a 69% grounding probability; results for this case are shown in Figure 13.

The predicted probability of grounding accidents is relatively low, primarily because they represent a smaller share of all accident types. Among the observational inputs, draft ratio is the most influential factor, while other environmental parameters, vessel dynamic states, and static characteristics largely overlap with those of self-sinking and collision accidents, limiting their discriminative power. In summary, using the constructed Bayesian Network model with accident probability as the output and 13 observational factors as inputs allows for the prediction of probability distributions across different accident types.

6. Results and Recommendations

6.1. Construction Results of Causal Chain

Based on the results of multiple experiments, including sensitivity analysis, lift index evaluation, and case study simulations, this study distilled the key causal chains underlying three representative accident types: collision, sinking, and grounding.

Table 10. Key causal chains for three representative maritime accident types—collision, sinking, and grounding—summarizing environmental, vessel, and crew causes at each hierarchical level and their transmission pathways.

Event	Causal Chain	Environmental	Vessel Cause	Crew Cause	Causal Chain Summary
Collision	Crew-dominated chain	Night navigation, poor visibility, complex waterways	—	Inadequate lookout, lack of evasive action, crew Incompetence	Complex environment or operational pressure → perception and judgment limitation → human error → collision
	Speed-Equipment coupling chain	—	Overspeed	Insufficient evasive capability, delayed response	Overspeed or insufficient crew → reduced evasive time and capability → collision
Sinking	Environment-load coupling chain	Extreme wind, extreme wave	Abnormal load, abnormal draft	—	Adverse weather and improper load → stability and structural degradation → control failure or flooding → sinking
	Load management chain	—	Abnormal load, abnormal draft	Improper ballast	Abnormal load → insufficient stability or ballast imbalance → higher sinking risk in adverse sea conditions
Grounding	Perception-control limitation chain	Poor visibility	Abnormal draft, high speed	Inadequate risk assessment	Poor visibility or abnormal draft → limited perception and reduced maneuverability → grounding
	Weather-sea state chain	High wind, high wave	—	Lateral drift, control difficulty	High waves or cross currents → increased lateral forces → navigation control difficulty → grounding

summarizes the main contributing factors at each hierarchical level and their transmission pathways.

The findings indicate that collision accidents are primarily driven by the interplay between complex navigational environments and human factors; self-sinking accidents are predominantly caused by the coupling of adverse meteorological conditions with vessel loading status; and grounding accidents reflect the combined effects of inadequate environmental perception and limited vessel maneuverability. Overall, the causal chains of maritime accidents consistently follow a hierarchical progression from environmental conditions to vessel status, then to human factors, and finally to the accident outcome.

This pattern not only clarifies the logical sequence of accident formation but also aligns with prior research, which indicates that collisions and groundings often stem from unsafe crew behaviors [47], while sinking accidents are more directly influenced by environmental and vessel-related factors [48]. It also reflects the narrative style of accident investigation reports, which frequently attribute causation to unsafe crew actions and their preconditions, thereby reinforcing the chain-like connection between environmental and human factors in the model results.

6.2. Recommendations for Maritime Safety Management

6.2.1. Collision Accidents

The experimental results demonstrate that collision accidents are primarily driven by the interaction between complex navigational environments and human factors, with unsafe crew behaviors serving as the critical triggering link.

Further data analysis reveals pronounced differences in crew qualifications and operational practices across vessels with varying navigational ranges. Inland vessels commonly exhibit deficiencies such as missing crew certifications and limited familiarity with collision avoidance regulations. A typical example is the collision between YOU & ISLAND and Liaosuiyu 35555 on 28 March 2020, in the central Liaodong Bay of the Bohai Sea, where the fishing vessel’s insufficient watchkeeping personnel and incomplete crew certification indirectly led to inadequate lookout and failure to take timely evasive action. For such vessels, rigorous enforcement of qualification reviews and mandatory training programs is essential to enhance compliance rates and improve regulatory proficiency [49]. By contrast, vessels operating in domestic or international waters generally maintain full certification, yet are more prone to overspeeding at night, highlighting the need for stricter speed control measures and enhanced risk awareness education [50].

Therefore, differentiated management strategies should be adopted for vessels with varying navigational ranges: inland vessels require stricter qualification verification and mandatory training to ensure compliance and rule familiarity, while domestic and international vessels necessitate reinforced speed control and risk awareness, particularly at night. At a general level, measures such as optimized shift scheduling, alcohol testing, and safety culture enhancement are essential to systematically mitigate collision risks.

6.2.2. Sinking Accidents

The causal-chain analysis indicates that sinking accidents are typically driven by the coupling of adverse meteorological conditions with vessel loading characteristics, wherein extreme wind and wave forces are compounded by inadequate stability or improper loading, ultimately causing stability degradation and leading to loss of control, and eventual sinking.

Accordingly, the enhancement of maritime safety management should be advanced along three dimensions: seaworthiness, cargo management, and environmental risk control. At the seaworthiness level, regulatory oversight of vessel stability and structural integrity should be strengthened [51]. Besides, particular attention should be devoted to structural deficiencies and the risks associated with aging vessels [52]. Previous studies have demonstrated that structural failures, metal fatigue, and inadequate watertightness are critical triggers of flooding and sinking incidents [53]. Establishing a systematic framework for stability monitoring and intelligent early warning would play a pivotal role in preventing sinking event. At the loading operation level, strict enforcement of load and draft control regulations is required, alongside clearer accountability mechanisms spanning ports and shipping companies [54]. At the environmental level, the dynamic integration of meteorological forecasting with voyage planning should be reinforced, together with the establishment of joint assessment mechanisms for extreme weather and loading-related risks [55]. Complementary training programs should also be provided to improve crew risk awareness and emergency response capabilities under adverse conditions [56].

Collectively, these measures can substantially reduce the probability of sinking accidents and enhance the overall safety performance of vessels navigating in complex maritime environments.

6.2.3. Grounding Accidents

The causal-chain analysis of grounding accidents reveals that they are primarily driven by limitations in crew perception and maneuverability. On the one hand, under poor visibility, abnormal draft, or excessive speed, inadequate risk perception often lead to misjudgments. On the other hand, high winds, high waves, and crosscurrents significantly increase lateral forces on vessels, complicating ship handling.

Accordingly, improving the prevention and control of grounding accidents requires efforts on several fronts. First, in terms of perception, crew training in situational awareness should be strengthened, coupled with the adoption of high precision navigation and collision avoidance support systems, to enhance environmental recognition and risk estimation under low visibility conditions [57]. Second, at the level of maneuverability, appropriate control of draft and speed should be enforced, while performance evaluation mechanisms for ship handling should be improved to ensure sufficient maneuvering margins in high risk waters [58]. Third, in relation to meteorological, decision support systems should be reinforced under conditions of strong winds, high waves, and crosscurrents. A dynamic assessment mechanism targeting lateral drift risk should be established, with measures such as speed reduction, rerouting, or voyage delay adopted where necessary to mitigate accident probability [59].

6.2.4. Overall Recommendations

In summary, although the major types of maritime accidents differ in their primary drivers, all are shaped by the interplay of environmental conditions, vessel status, and human factors, thereby emphasizing the need for a comprehensive and integrated approach to maritime safety.

Common measures include strengthening crew training and risk awareness programs, improving vessel operational monitoring and technical support systems [60]. At the same time, each accident type requires targeted interventions addressing its specific causal factors, such as speed control and fatigue management for collisions, stability and loading management for sinking, and navigation perception and maneuverability for grounding. By combining general and specific measures, maritime authorities and shipping companies can achieve a more robust safety management system, effectively reducing accident risks.

7. Conclusions

The existing studies on maritime accident causation have two main limitations: they insufficiently differentiate factor hierarchies and often conflate observational data with unsafe behaviors. To address these issues, this paper proposes a BT-BN causal modeling approach. The method constructs a hierarchical inference chain from observational parameters to unsafe causes to accident types. It integrates human, vessel, environmental, and managerial factors within a unified framework. This approach effectively captures interactions across different causation levels and enhances the model’s explanatory power.

The experimental results show that the proposed method can both predict accident risks and reveal differentiated sensitivity characteristics. Grounding accidents are mainly driven by strong winds, high waves, and excessive speed; collisions occur more often in complex waterways under nighttime over speeding and inadequate crewing; sinking accidents are significantly influenced by extreme weather combined with heavy loading. These findings indicate that the method quantitatively captures the triggering effects of unsafe cause combinations on accident outcomes. Case-based validation further demonstrates that using only objective observational data at the time of the accident, the model can infer accident types with over 70% accuracy and identify unsafe causes consistent with official investigation reports. This highlights its dual potential for proactive risk warning and retrospective explanation. Hierarchical causal-chain analysis distilled the strongest causative links for each accident type, identifying key factors and their transmission pathways.

Based on this analysis, targeted maritime safety recommendations such as enhanced monitoring of critical stages, optimized crew training, and refined operational protocols were proposed. These strategies provide quantitative evidence and actionable guidance to improve maritime traffic safety. Beyond immediate applications, the constructed causal network and extracted causal chains provide a foundation for optimizing shipping policies and improving marine and coastal governance.

The proposed methodology is generally applicable and can be extended to maritime accidents in other regions or to different types of incidents. Nevertheless, this study has several limitations: First, the analyzed accident reports were obtained solely from the Maritime Safety Administration (MSA) of the People’s Republic of China and pertain to incidents occurring within the Bohai Sea area. As these reports are post-incident investigations, the “causal factor” components may contain subjective attributions or responsibility assessments, preventing a fully objective causal mapping with the observational parameters. Second, the sample size is relatively limited (n = 90), and certain variables exhibit overlapping definitions or strong interdependencies, which may lead to an overestimation of statistical associations. Finally, the proposed causal chain model relies on statistical correlations and hierarchical reasoning without external experimental or interventional validation; thus, the findings primarily reflect conditional dependencies and potential mechanistic pathways rather than strict causal effects. Future research should, therefore, broaden the data sources to encompass other maritime regions and diverse accident types, integrating richer objective observational and real-time behavioral data to further validate and refine the model, thereby providing a more comprehensive and robust foundation for maritime safety management.