Analyzing the Causation of Collision Accidents Between Merchant and Fishing Vessels in China’s Coastal Waters by Integrating Association Rules and Complex Networks

Abstract

The frequent occurrence of collision accidents between merchant and fishing vessels in China’s offshore waters not only threatens human lives and property, but also disrupts shipping and fishing activities and may cause marine environmental pollution. To effectively reduce such accidents and increase maritime safety in Chinese coastal waters, this study integrates association rules with complex networks to develop a directed weighted network of causal factors. Grounded theory and the Human Factors Analysis and Classification System (HFACS) are applied to identify and categorize causal factors from 152 collision accident investigation reports. Potential causal relationships are mined using the association rule, which is then applied to construct the causal network. Finally, the topological characteristics of the network are analyzed. The results reveal that serious negligence in lookout, failure to assess collision risks properly, and failure to adopt a safe speed significantly impact collision accidents. These findings highlight the necessity of implementing targeted preventive measures to address critical factors. This study provides valuable insights for maritime stakeholders to develop effective strategies.

1. Introduction

The boom in the shipping market has driven the expansion of vessel inventory and shipping activities, significantly elevating the probability of maritime accidents [1,2]. Collisions constitute the predominant type of maritime accidents [3]. Based on the statistics of collision accident reports compiled by the China Maritime Safety Administration, collisions between commercial and fishing vessels account for approximately 50% of incidents. As a large shipping and fishing country, China’s merchant and fishing vessels frequently cross and operate in limited sea areas due to different routes and operation modes, resulting in occasional collision accidents. These accidents not only result in serious casualties and economic losses [4], but may also have non-negligible destructive effects on the marine environment [5]. To improve maritime safety in coastal waters, it is of great significance to study the causal factors of collision accidents between commercial and fishing vessels in coastal waters.

Existing research mainly focuses on the causes, risks, and prevention strategies of collision accidents between commercial and fishing vessels. Wang et al. [6] analyzed human and organizational factors in accidents and identified crucial causal elements and developmental pathways. Zhu et al. [7] assessed the collision risks in the nearshore waters of Fujian from AIS data and visualized risk concentration areas. Yang et al. [8] analyzed the characteristics and contributory factors of collision accidents, visualized the spatial distribution, and proposed corresponding prevention strategies. Oh et al. [9] researched collisions involving fishing vessels in Wando waters and analyzed the causal factors of collisions between fishing and other vessels. Zhang et al. [10] constructed an accidental risk evolution network based on collisions, which not only identified the crucial factors but also proposed prevention strategies. Gai et al. [11] presented a fuzzy fusion method to evaluate the collision risks to provide solutions for multiple vessel collision avoidance. Przywarty et al. [12] offered a simulation model to evaluate the navigational safety of fishing vessels concerning the causes of collision between fishing and merchant ships in the Polish Exclusive Economic Zone waters. Jung [13] proposed risk prevention and control strategies to decrease the risk of collision between fishing and non-fishing vessels by reviewing the operational characteristics of fishing vessels and all the regulations related to their operation. Wang et al. [14] investigated the optimal method for avoiding collisions due to the high incidence of collision accidents during the fishing season in Chinese coastal waters.

Scholars have analyzed the causes and risks of ship collisions using various methods. Yu et al. [15] developed a Bayesian spatiotemporal model to estimate collision risks based on the interaction between space and time and proposed preventive measures. Shinoda et al. [16] investigated the risks of collision between fishing vessels and large ships using Bayesian networks (BNs). Ugurlu et al. [17] constructed a BN to causally analyze fishing vessel collision and sinking accidents to reveal the mechanisms of accidents and provide guidance for policies. Liu et al. [18] systematically analyzed the causation of maritime accidents within China’s coastal zones using machine learning methods. Fan et al. [19] constructed a data-driven BN model to assess the impact of human factors according to the reports of maritime accidents. Sur and Kim [20] assessed and ranked the risks of fishing vessel accidents using a fuzzy synthetic evaluation method, taking South Korean waters as an example, to reduce maritime accident risks. Silveira et al. [21] assessed the ship collision risk in open waters using the ELECTRE Tri-nC multiple criteria outranking method. Ugurlu and Cicek [22] analyzed the causative factors of vessel collisions and their interrelations using fault tree analysis. They concluded that the human factor is the dominant cause. The HFACS is an essential tool for accident analysis and is mostly applied to classify the causative factors of maritime accidents [23]. Gil [24] analyzed vessel collision avoidance using the Systems-Theoretic Process Analysis method. Dong et al. [25] employed the N-K model to quantify interaction effects among causative elements in collisions between merchant and fishing vessels.

Existing studies have primarily relied on statistical analysis [20], accident cases [7], or simulation approaches [19], while lacking in-depth research on the interactions among multiple contributing factors. Complex network theory can reveal the interrelationships among multiple elements in a system [26], and association rules can uncover frequent patterns of association among causal factors [27]. Combining these two approaches offers a new perspective for the analysis of the causation of collisions between merchant and fishing vessels. The integration of these two approaches in accident causation analysis is seldom applied to the study of accidents between merchant and fishing vessels. International regulations and conventions serve a vital purpose in ensuring maritime safety. The Convention on the International Regulations for Preventing Collisions at Sea (COLREG) [28] outlines the fundamental rules for avoiding collisions, with rules 3, 18, and 26 defining the status of fishing vessels, right of way, and signaling requirements. The International Convention on Standards of Training, Certification and Watchkeeping for Seafarers (STCW) [29] clarifies the requirements for training and certification to ensure that they are competent for duty. The International Safety Management System Code (ISM Code) [30] provides a regulatory framework for the safe operation of ships. However, some accidents occur as a result of these conventions being ignored or violated, demonstrating the urgent need for a systematic analysis of the relationship between convention compliance and accident causation. Based on this, this study attempts to combine association rules and complex networks to establish an interaction network model for the causal factors of collisions through an in-depth analysis of accident data. This model can not only visualize the intricate relationships between causal factors but also provide suggestions for enhancing maritime safety along the Chinese coastline by identifying key causal factors.

The remaining sections of this paper are structured as follows. Section 2 describes the data collection and introduces the methods of grounded theory, the HFACS, association rules, and complex network techniques used in this study. In Section 3, the results obtained through association rule mining are mapped into a complex network, constructing a network of causal factors for collision accidents. This directed weighted network is then subjected to quantitative analysis, with the findings represented visually. Finally, the conclusions are summarized in Section 4.

2. Data and Methodology

The methodology is shown in Figure 1. It combines the HFACS, grounded theory, association rules, and complex networks. The methodology is divided into three main steps. In Step 1, a database containing information on collisions between merchant and fishing vessels is established. This study adopts grounded theory with three-stage coding to analyze accident data, aiming to extract the causes of the accidents. It then applies the HFACS framework to identify causal elements and to hierarchize the causal factors. In Step 2, the structured causal data derived from the HFACS classification are converted into transaction sets, where each accident serves as a transaction. Association rule mining is introduced to obtain association relationships (association rules) between causal factors using the Apriori algorithm. The validated association rules are mapped into a directed weighted network, with causal factors as nodes, association rules as edges, and confidence values as weights, to generate the causal network. Causation analysis is performed in Step 3. Topological parameters, including degree, clustering coefficient, node criticality, and robustness analyses, are calculated to analyze the mechanism of interaction of the causal factors.

2.1. Data Collection

Here, the scope of the study is limited to Chinese coastal waters, with a time frame covering the past ten years. Therefore, the data source is the reports of collision accidents between merchant and fishing vessels from 2014 to 2023, published on the official website of the China Maritime Safety Administration. A total of 152 accident reports were collected, and the information is displayed in Figure 2. The number of accidents has decreased, with collision accidents decreasing annually in recent years.

2.2. Methodology Overview

2.2.1. Grounded Theory and HFACS

Grounded theory is a qualitative approach used to build a theory based on raw data [31]. The goal of grounded theory is to build a theory from empirical data. In the early stages of a study, researchers typically have no theoretical assumptions, but rather begin with actual observations, conduct empirical inductions from raw data, and eventually form a systematic theory. The operational steps are shown in Figure 3 and include phenomenon definition, data collection, three-level coding, and saturation testing. Of these steps, open coding, axial coding, and selective coding are the core steps of grounded theory [32].

The HFACS was developed in 2001 [33] and was first used to analyze aviation accidents [34]. This model is now applied to the analysis of accident causations in various industries, including coal mining [35], construction [36], railroads [37], and maritime [38]. The model consists of four layers, with layer 1 being unsafe acts, including errors and violations. Layer 2 represents the preconditions for unsafe behaviors, mainly encompassing environmental elements, operator conditions, and individual factors. Layer 3 denotes unsafe supervision, including improper supervision, failure to rectify existing faults, and supervision violations. Layer 4 is associated with organizational impacts, including resource management, organizational culture, and organizational procedures. The different layers are linked by cause-and-effect relationships, where higher layers correspondingly affect lower layers [39]. After the coding process, the extracted causal factors are classified using the HFACS to establish a hierarchical structure. These results form the basis for subsequent analysis.

2.2.2. Association Rules

The association rule is utilized to uncover valuable interrelationships between data items (Xu et al., 2018) [40]. Association rules can be depicted as follows: set $I=\left\{\left.i_i,i_2,\dots ,i_n\right\}\right.$ is a collection of items, given a transaction database $T=\left\{\left.t_1,t_2,\dots ,t_n\right\}\right.$, where each t is a non-empty subset of itemset $I$. Association rule takes the form $X\to Y$, where $X\subset I,Y\subset I,X\cap Y=\varnothing$. $X$ and $Y$ are referred to as lefthand side (LHS) and righthand side (RHS). Association rules are defined by three key metrics—support, confidence, and lift. The formulas for these indicators are listed below [41]:

$$Support\left(X\to Y\right)=P\left(X\cup Y\right)$$

(1)

$$Confidence\left(X\to Y\right)=P\left(Y/X\right)$$

(2)

$$Lift\left(X\to Y\right)=conf.\left(X\to Y\right)/supp.\left(Y\right)$$

(3)

Support for the association rule $X\to Y$ measures the joint occurrence of $X$ and $Y$ in the dataset. Confidence evaluates the likelihood of $X$ occurring given that $Y$ is already present. An association rule that satisfies the minimum support and confidence criteria is regarded as strong [42]. Lift indicates how much the probability of $Y$ occurring changes in the case of $X$ occurring. A lift value higher than 1 means that the association rule is meaningful. These three thresholds are typically manually set based on the requirements [43].

The goal of association rule is to discover frequent itemsets and association rules [44]. The Apriori algorithm presented by Agrawal et al. [45] is a classic algorithm that is widely applied and easy to use. The flowchart of the Apriori algorithm is shown in Figure 4. First, candidate 1-itemsets are generated by scanning the database. Then, candidate 1-itemsets are pruned based on the minimum support threshold to obtain frequent 1-itemsets. Next, frequent 1-itemsets are utilized to obtain candidate 2-itemsets, from which frequent 2-itemsets are selected. This procedure is repeated until no more frequent itemsets are generated.

In this study, each accident is treated as a transaction, and the causal factors obtained from the HFACS classification are regarded as items. The Apriori algorithm is introduced to explore association rules between causal elements. The validated association rules are further constructed into a directed weighted network, serving as the basis for causation analysis.

2.2.3. Complex Network

A complex network is a specific type of network consisting of nodes and connected edges [26]. Complex networks have been widely applied to accident causation analysis in the fields of railroads [46] and roads [47]. In this study, the complex network is applied to analyze the causality of collisions between merchant ships and fishing vessels.

A complex network is denoted as $G=\left(V,E\right)$, where $V=\left\{\left.v_1,v_2,\dots ,v_n\right\}\right.$ is the set of all nodes and $E=\left\{\left.e_1,e_2,\dots ,e_n\right\}\right.$ represents the set of all edges. The complex networks can be expressed in terms of the adjacency matrix as follows:

$$A_{ij}=\left\{\begin{array}{l}{a}_{ij}\times w_{ij},i\to j\\ 0,else\end{array}\right\}$$

(4)

where $a_{ij}=1$ when factor $i$ triggers factor $j$, otherwise $a_{ij}=0$. $w_{ij}$ indicates the weights of the edges between neighboring nodes $i$ and $j$ in the complex network. For the purpose of causation analysis, an association rule is used to build a causal network. The results are mapped to the directed weighted network. The process is illustrated in Figure 5.

Each causal factor denotes a node. The LHS and RHS of the association rule stand for two neighboring nodes $i$ and $j$. Every association rule has a directed edge; the confidence value is defined as the weight of the edge.

The characteristics of the constructed complex network can be evaluated using these indicators.

(1)

Degree

For any node, its degree expresses the number of edges connected to it. In a directed network, the degree of node $i$ is categorized into total-degree, out-degree, and in-degree, where the total-degree of node $i$ represents the total number of edges connecting node $i$; the out-degree of node $i$ represents the quantity of edges from node $i$ to other nodes; and the in-degree of node $i$ represents the number of edges from other nodes to node $i$, which can be expressed as

$$d\left(i\right)={\displaystyle \sum _{j\in V}{a}_{ji}}+{\displaystyle \sum _{j\in V}{a}_{ij}}$$

(5)

$$d_{in}\left(i\right)={\displaystyle \sum _{j\in V}{a}_{ji}}$$

(6)

$$d_{out}\left(i\right)={\displaystyle \sum _{j\in V}{a}_{ij}}$$

(7)

(2)

Average path length

The average path length ($L$) represents the average of the shortest paths between all possible pairs of nodes. It is calculated as

$$L={\displaystyle \frac{{\displaystyle \sum d_{ij}}}{N(N-1)}},i\ne j$$

(8)

where $N$ represents the total number of nodes and $d_{ij}$ indicates the shortest distance between two nodes.

(3)

Clustering coefficient

It is an indicator used to measure the level to which a node’s neighboring nodes are tightly connected. It reflects the extent to which the neighboring nodes form closed triangles. The clustering coefficient $C_i$ of node $i$ can be obtained as

$$C_i={\displaystyle \frac{2E_i}{k_i(k_i-1)}}$$

(9)

where $E_i$ refers to the quantity of edges among neighboring nodes of node $i$ that are also connected to each other, $k_i$ refers to the number of edges of node $i$ that are connected to other nodes.

There is also a need to quantitatively portray the effect of edge weights on clustering coefficients in complex networks with directed weighted edges. The definition of the weighted form of the clustering coefficient can be written as follows:

$$C_i^w={\displaystyle \frac{1}{s_i(k_i-1)}}{\displaystyle \sum _{j,k}\frac{w_{ij}+w_{ik}}{2}}{a}_{ij}{a}_{ik}{a}_{jk}$$

(10)

where $s_i$ denotes the aggregate of the weights of all neighboring edges of node $i$; $w_{ij}$ represents the weights of all edges between neighboring nodes $i$ and $j$; and $w_{ik}$ represents the weights of all edges between neighboring nodes $i$ and $k$.

(4)

Betweenness centrality

The betweenness of a node is the quantity of shortest routes through the node in a network, and reflects the pivotability and transitivity of the node. The formula is as follows:

$$B_i={\displaystyle \sum _{j\ne i\ne k\in N}\frac{N_{jk}\left(i\right)}{N_{jk}}}$$

(11)

where $N_{jk}$ is the sum of all shortest paths from node $j$ to node $k$; $N_{jk}\left(i\right)$ denotes the number of paths passing through node $i$ in all shortest paths from node $j$ to node $k$; and $N$ stands for the total number of nodes in the complex network.

Betweenness centrality ($BC$) evaluates the level to which a node serves as a bridge in the network, revealing the node’s importance and influence within the network [48]. The betweenness centrality of a node is its normalized betweenness value. It is defined as follows:

$$B{C}_i={\displaystyle \frac{2B_i}{(N-1)(N-2)}}$$

(12)

(5)

Node criticality

In complex network analysis, assessing node importance is a central task in studying the structure and function of networks. The goal of this assessment is to identify the nodes that play a crucial role in the network, thereby revealing the network’s overall characteristics and key functions. Common algorithms for assessing node importance include classical centrality index algorithms, the PageRank algorithm, the K-Shell decomposition algorithm, and the node importance entropy algorithm.

Among them, the PageRank algorithm is a classic method for assessing node importance based on network structure and link relationships [49], particularly demonstrating significant advantages in node ranking within directed weighted networks. The core of this algorithm is to evaluate the importance or authority of each webpage by analyzing the link structure between pages on the internet. Unlike traditional algorithms that assess importance based on node degree or local structures, the PageRank algorithm estimates the significance of a node through the link relationship of the whole network, taking into account the relative influence of the node. Therefore, the algorithm not only reflects the direct connection of a node but also accounts for the influence of other nodes that point to it, providing a strong global perspective.

The advantages of the PageRank algorithm are primarily in these aspects: Firstly, the algorithm is highly adaptable and suitable for directed, weighted, and sparse networks, making it capable of handling complex and diverse network structures. Secondly, PageRank can effectively solve the problems of “dead loop” or “sink node” by introducing a damping factor, which enhances the robustness of the algorithm and ensures the stable convergence of iterative computation. In addition, the PageRank algorithm adopts an iterative calculation method, gradually updating the PageRank value of each node until it converges to a stable final result, allowing for the ranking of the significance of all nodes. The formula is given below:

$$P{R}_i=\gamma {\displaystyle \sum _{j\in V}\frac{a_{ji}}{d_{out}(j)}}P{R}_j+{\displaystyle \frac{1-\gamma }{N}}$$

(13)

where $\gamma$ is a damping factor, which in the PageRank algorithm typically takes a value between 0 and 1. The most commonly used value is 0.85, with the remaining $1-\gamma$ being used to prevent “dead-ends”. $N$ refers to the sum of nodes in the network.

In a directed weighted network, the PageRank algorithm is used to calculate the criticality of a node by considering the weights of the edges. The formula is given below:

$$P{R}_i=\gamma {\displaystyle \sum _{j\in V}\frac{w_{ji}}{s_{out}(j)}}P{R}_j+{\displaystyle \frac{1-\gamma }{N}}$$

(14)

where $w_{ji}$ represents the weight of the edge from node $j$ to node $i$; $s_{out}\left(j\right)$ is the total weight of all outgoing edges from node $j$.

(6)

Robustness analysis

The robustness of a complex network is the capacity of the network to retain overall connectivity and functionality when some nodes or edges fail due to faults or attacks [50]. This attribute reflects the network’s resistance to external disturbances and is an important indicator of network stability and continuity. In the causal network, network connections can be effectively disrupted by reducing the robustness of the network, thereby blocking the dynamic evolutionary chain of causal factors. Specifically, in the case of maritime accidents, weakening or destroying the network structure of accident-related causal interactions and cutting off propagation paths is crucial for preventing the spread of accidents, minimizing losses, and promoting prevention. In the process of research on robustness, the attacks can be categorized into two types based on their characteristics and objectives—random attacks and deliberate attacks. Random attacks refer to randomly selecting nodes or edges in the network for deletion or destruction, with no specific target and more sporadic destruction effects. Deliberate attacks, on the other hand, are targeted at nodes or edges of high importance in the network for purposeful deletion or destruction. These attacks are highly purposeful and often focus on hub nodes or critical paths within the network. Global efficiency is commonly employed to analyze network robustness. The global efficiency reflects the rate of development and propagation of causal factors in the network. By assessing the connections and interactions among different causal factors, global efficiency can reveal the propagation pathways of causal factors in commercial fishing vessel collisions and their potential impacts. In this study, global efficiency is applied to assess the robustness of the network. The formula is as follows:

$$E_{\mathrm{g}}={\displaystyle \frac{1}{N(N-1)}}{\displaystyle {\sum }_{i\ne j}\frac{1}{d_{ij}}}$$

(15)

where $N$ is the total number of nodes in the network and $d_{ij}$ indicates the minimum path length from node $i$ to node $j$.

3. Results and Discussion

3.1. Identification of Causal Factors by Combining HFACS and Grounded Theory

This study aims to conduct a causation analysis and explore the mechanism of interaction between causation by collecting and analyzing accident investigation reports. Causal factors are identified using grounded theory, with the assistance of the qualitative analysis software NVivo 15 for data management and coding. Additionally, the HFACS is used to categorize the identified causal elements.

Table 1. Results of grounded theory (example).

Original Content	Conceptualization	Category	Main Category	Core Category
Negligent lookout and failure to adequately assess the situation and the risk of collision.	Failure to maintain proper lookout	Failure to maintain proper lookout	Error	Unsafe acts

shows an example of the coding process for accident causation through grounded theory.

During the open coding phase, the text content related to accident causes is tagged, and relevant concepts are extracted to form initial categories. Subsequently, within the axial coding period, these initial categories are further organized and integrated to form main categories. In the selective coding phase, the logical relationships between the main categories are clarified, and core categories are extracted. Finally, to verify the saturation of the theory, the remaining 12 accident reports are chosen for saturation testing. The results show that no new notions or categories appeared, indicating that the coding process has reached theoretical saturation.

The factors identified through grounded theory coding are further mapped to the HFACS model to analyze causal factors that are eventually identified as contributing to collisions. As a result, the causal factors are identified based on 152 reports of accidents, which are divided into four tiers—unsafe acts, preconditions for unsafe acts, unsafe supervision, and organizational influences. Detailed information is provided in

Table 2. The causal factors identified by HFACS.

Variables	Causal Factors
O01	Inadequate security management of the company
O02	Inadequate education and training
O03	Inadequate content of safety management system documents
O04	Poor safety awareness
P01	Poor communication
P02	Failure to formulate relevant work plans before the vessel departs, or the work plan contains risks
P03	Failure to comply with regulations in certain ship structures
P04	Drinking/Alcoholism
P05	Illegal operations and unlawful business practices of fishing vessels
P06	Illegal installation of fisheries production facilities and fish rafts
P07	Complex navigation environment
P08	Poor visibility
P09	Inadequate caution in unfamiliar waters
P10	Failure to repair mechanical issues on the vessel in a timely manner, or mechanical equipment failure
P11	Overloaded vessel, or suspected overload
P12	Unqualified crew
P13	Crew fatigue
P14	Engine or electrical failure, or loss of power
S01	Failure to strictly implement daily management regulations by the captain
S02	Poor risk awareness in daily ship management by the captain
S03	Illegal or non-compliant operations of the ship, with issues in certificates or qualifications
S04	Failure to provide sufficient and qualified crew members
S05	Deliberate shutdown of AIS, use of false AIS, and AIS failures
S06	Failure to monitor the vessel’s navigation dynamics and technical status
A01	Serious negligence in lookout, failure to maintain suitable lookout
A02	Failure to assess collision risks properly
A03	Failure to comply with onboard navigation or related operational procedures
A04	Failure to adopt a safe speed
A05	Underestimation of environmental impacts, poor risk management decisions
A06	Failure of pilots to navigate with care
A07	Improper operation
A08	Inadequate estimation of environmental risks and risky voyages out of port
A09	Failure to exercise caution and maintain necessary vigilance during navigation
A10	Failure to maneuver the ship with good seamanship
A11	Violation of rules and regulations related to ship navigation
A12	Poor sense of responsibility of the crew on duty
A13	Violation of operational procedures, habitual violations
A14	Failure to take effective avoidance measures promptly
A15	Inadequate or erroneous use of navigational aids, or unavailability of navigational aids
A16	Failure of the crew on duty to grasp and strictly carry out the planned route.
A17	Improper selection of anchoring and docking positions
A18	Inadequate maintenance of a safe distance from navigational obstructions, shore, or other vessels.
A19	Violation of collision avoidance provisions
A20	Failure to verify the effectiveness of avoidance response measures
A21	Improper emergency response measures
A22	Failure to conduct shift handovers according to regulations
A23	Failure to report the emergency or accident to maritime authorities
A24	Insufficient or no staff on duty

. Figure 6 presents the frequency statistics of the causal factors. According to the statistical results, the three most common causal factors for collisions are A01 (serious negligence in lookout, failure to keep suitable lookout), A14 (failure to adopt valid avoidance measures promptly), and A02 (failure to assess collision risks properly). This indicates that unsafe behavioral factors are the key cause of accidents, reflecting deficiencies in crew training and risk awareness. The high frequency of these factors also suggests that accidents typically result from the interaction of multiple factors. To effectively reduce accident risks and heighten maritime safety, it is necessary to address multiple dimensions, such as personnel management and risk control, and comprehensively enhance the preventive capabilities against accidents.

Many of the causal factors in Table 2 reflect non-compliance with major international maritime conventions. For example, issues such as “unqualified crew” and “inadequate training” violate the requirements of the STCW. Similarly, “negligent lookout”, “failure to assess risk of collision”, and “failure to adopt a safe speed” violate COLREG provisions for lookout, safe speed, and risk assessment. In addition, factors such as “poor security management” and “insufficient safety documentation” indicate inadequate implementation of the ISM Code. These findings highlight regulatory shortcomings and emphasize the urgency for stricter enforcement and supervision.

3.2. Association Rules Results

To reveal potential links between causal factors, association rule analysis is conducted on the data. The setting of the threshold in association rules plays a decisive role in the quality of association rules. The trial-and-error approach is adopted to find a suitable set of thresholds for this study. Initially, two sets of thresholds are selected, with minimum support and confidence levels set to 0.01 and 0.1, and 0.1 and 0.8, respectively, to mine rules from the collision accidents. To control the complexity of the generated rules and enhance their interpretability, the maximum rule length is limited to 2. Using the first set of thresholds, 624 association rules are generated, while the second set results in only 19 rules. However, these outcomes are deemed unsuitable for further analysis.

After multiple adjustments, the minimum support threshold is finally set to 0.01, the minimum confidence threshold to 0.3, and the lift to higher than 1, with the maximum rule length limited to 2. The association rule is performed using the “arules” package in R 4.4.2. Finally, 199 association rules are created using the Apriori algorithm. The results are visualized using the “arulesViz” package in R. Figure 7 illustrates the distribution of obtained association rules, where every point denotes an association rule, and the color shades represent the magnitudes of the lift. Most of the rules exhibit confidence values ranging from 0.1 to 0.6, while the support values are mainly centered between 0.013 and 0.07. The top 10 association rules sorted by confidence values are shown in

Table 3. Top 10 association rules sorted by confidence.

No.	Rules	Support	Confidence	Lift
1	{A17} => {A01}	0.01	1.00	1.09
2	{P02} => {A01}	0.01	1.00	9.50
3	{A08} => {A01}	0.02	1.00	1.09
4	{P10} => {A01}	0.03	1.00	1.09
5	{A16} => {A01}	0.03	1.00	1.09
6	{S05} => {P12}	0.03	1.00	3.04
7	{O02} => {A01}	0.03	1.00	1.09
8	{P09} => {P08}	0.05	1.00	7.24
9	{A23} => {A01}	0.07	1.00	1.09
10	{S01} => {A01}	0.06	1.00	1.09

. The results show that most of the rules are associated with A01 (serious negligence in lookout, failure to retain suitable lookout), indicating that lookout negligence is a core causal factor and is closely linked with other causal factors. Strengthening lookout capabilities is a key direction for reducing accident risks.

3.3. Development of a Complex Network of Causal Factors

Based on the 199 association rules generated in Section 3.2, this study mapped causal factors as nodes, rules as directed edges, and rule confidence as weights to construct a causal network with 40 nodes and 199 directed edges. In Figure 8, gray nodes represent organizational influences, green nodes indicate unsafe supervision, yellow nodes signify preconditions for unsafe acts, and purple nodes correspond to unsafe acts, all categorized under HFACS.

3.4. Network Topological Characterization

(1)

Degree

In complex networks, the degree of a node evaluates the connectivity of a node in the network. In a causal network, the degree of a node reflects the interactions among causal factors. The in-degree of a node expresses the level to which it is influenced by other nodes, the out-degree reflects the degree to which it causes an impact on other nodes, and the total-degree represents the direct impact of the node within the network. The more connections a node has, the more impact it has. Figure 9 illustrates the in-degree, out-degree, and total-degree values for each node.

According to Figure 9, the nodes with the largest total-degree values are A01 (serious negligence in lookout, failure to retain suitable lookout) and A02 (failure to assess collision risks properly), followed by P07 (complex navigation environment) and A04 (failure to adopt a safe speed). Nodes with higher total-degree values are considered critical nodes, and targeted measures for such nodes can effectively reduce the connectivity of the network. The nodes with high in-degree values include A01 (serious negligence in lookout, failure to retain suitable lookout), A02 (failure to assess collision risks properly), P07 (complex navigation environment), and P12 (unqualified crew). These nodes are heavily influenced by other nodes and can result in serious consequences. Nodes with high out-degree values include S01 (failure to strictly implement daily management regulations by the captain), S02 (poor risk awareness in daily ship management by the captain), P08 (poor visibility), and A12 (poor sense of responsibility of the crew on duty). The direct impact of these nodes on other nodes is more significant.

(2)

Average path length

In the causal network, the average path length reflects the propagation efficiency of causal factors within the network. A shorter average path length means that causal factors can propagate more quickly through the network. The average path length of the interaction network is 1.2019, indicating that any change in a causal factor can, on average, influence other factors in just 1.2019 steps. This suggests that changes in key factors can quickly trigger chain reactions, significantly impacting the progression of accidents. It is essential to emphasize high-impact nodes and their connections to optimize accident prevention and management.

(3)

Clustering coefficient

The clustering coefficient is used to measure the likelihood of forming triangles among nodes in a network, which means the degree of closeness between a node and its neighboring nodes being interconnected. It is one of the most important metrics for analyzing the topology of a network. In this study, a weighted clustering coefficient is used to capture the concentration of causal elements in the network, and the results are shown in Figure 10.

The node with the highest clustering coefficient is O02 (inadequate education and training), with a value of 0.9. It is followed by A20 (failure to verify the effectiveness of avoidance response measures), P09 (inadequate caution in unfamiliar waters), and A05 (underestimation of environmental impacts, poor risk management decisions). The results show that these nodes are closely related to their neighboring nodes, and once changes occur, they may trigger a chain reaction in the adjacent nodes or even lead to larger-scale accidents. Thus, it is imperative to reinforce the proactive control of these nodes to effectively reduce accident hazards.

(4)

Betweenness centrality

Betweenness centrality evaluates the importance of a node’s role as a “bridge” or “intermediary” in a network. Specifically, if a node is located on multiple pairs of nodes, it is likely to play a key role in the transfer of information or the flow of resources, thus becoming an important hub in the network. Figure 11 shows the distribution of nodes’ betweenness centrality.

Fourteen nodes have a value of zero, suggesting that these 14 nodes do not play a mediating role. P12 (unqualified crew) has the largest betweenness centrality, indicating that unqualified crew plays a key bridging role in the accident causation network, connecting multiple causative factors. It not only directly affects safe operations but may also exacerbate the propagation of other causal factors. This issue is particularly prominent in the fishing industry, where many fishing vessel crew members lack professional training and suitable skills, leading to the common phenomenon of “putting down the hoe and going to the ship”. This affects operational safety and may increase accident risks; therefore, strengthening crew quality training and qualification is essential for enhancing maritime safety.

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Node Criticality Analysis

The PageRank algorithm is used to evaluate the criticality of the nodes in the network, and the results are shown in Figure 12. From these factors, A02 (failure to assess collision risks properly) exhibits the greatest PageRank value, followed by P07 (complex navigation environment), A01 (serious negligence in lookout, failure to retain suitable lookout), and A04 (failure to adopt a safe speed). High PageRank values indicate that these factors have a significant influence on the network and may serve as key nodes triggering interactions with other factors. In particular, failure to properly assess collision risks may exacerbate the impact of other factors, increasing the probability of accidents. Factors such as complex navigational environments, lookout negligence, and failure to adopt a safe speed also have high PageRank values, but their effects may be amplified by inaccurate risk assessments. To reduce the impact of these critical factors, collision risks should be thoroughly assessed, and advanced technologies should be utilized to ensure timely risk identification and response. Additionally, crew training and safety awareness should be strengthened, with regular drills and exercises conducted to improve the decision-making ability of crew members in complex environments, thereby reducing collision risks. It is noteworthy that 7 out of the top 10 nodes are classified as unsafe behaviors, which indicates that unsafe acts occupy a significant position in the causal network. These acts have become critical factors in collision accidents. Effectively controlling these causal factors of high importance will be useful in significantly reducing collision accidents.

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Robustness analysis

Network robustness is the capacity to preserve structural and functional integrity when subjected to various disruptions. In this study, network robustness is evaluated through three attack strategies, including random attack, deliberate attack on the basis of nodes’ PageRank ranking, and intentional attack grounded in nodes’ mediator centrality ranking. Figure 13 demonstrates the changes in network efficiency under different attack nodes.

In Figure 13, the initial efficiency of the network is 0.4770. With the rising number of attacked nodes, the rate of decline in network efficiency shows significant differences under different attack strategies. The comparison results indicate that deliberate attacks cause a much faster degradation of the network compared with the random attack. When 10 nodes are attacked, the random attack reduces the network efficiency by 23%, while the same number of targeted attacks results in approximately a 64% decrease in network efficiency. When the sum of attacked nodes is less than 18, the impact of targeted attacks on network efficiency is significantly greater than that of random attacks as the number of failed nodes increases. This highlights that targeted attacks on key nodes can trigger drastic changes in the network structure. In contrast, under random attacks, the likelihood of vital nodes being selected is relatively low, and thus the network structure does not change substantially until an extensive number of nodes are affected, eventually leading to a collapse. This emphasizes the importance of targeted interventions on key causal factors in accident prevention and control.

In conclusion, the robustness of the causal interaction network continues to decrease as the number of attacked nodes increases. Compared with random attacks, the rate of decline in network robustness is faster under intentional attacks. This suggests that implementing targeted prevention and control strategies for critical causal factors is more effective.

3.5. Practical and Statistical Implications of High-Ranking Factors

A01 (serious negligence in lookout), A02 (failure to assess collision risks properly), and P12 (unqualified crew) not only exhibit high centrality in the causal network but also reflect violations of international regulations such as COLREG and STCW. These factors occupy central positions connecting multiple causal chains and serve as crucial nodes driving risk propagation. From a practical point of view, these causal factors reflect weaknesses in the enforcement of navigational rules and crew management. Strengthening rule enforcement and qualification management can help cut off key risk chains and improve maritime safety.

4. Conclusions

In this study, an analysis of the causation of collisions between merchant and fishing vessels was conducted by integrating association rules with complex networks. The most critical causes of collisions were “unqualified crew”, “inadequate education and training”, “serious negligence in lookout”, “failure to assess collision risks properly”, and “complex navigation environment” from Figure 9, Figure 10, Figure 11 and Figure 12. These factors reflect common violations of international conventions such as COLREG [28] and STCW [30]. The following suggestions are made based on these results.

Firstly, to address the core risk factors of “unqualified crew” and “inadequate education and training”, there is a need to develop a competency assessment system for crew members. Simultaneously, policies related to the training, examination, and certification of fishing vessel crew members should be optimized in accordance with the STCW, appropriately incorporating content on collision avoidance knowledge and maritime emergency survival skills. Additionally, standardized bridge watchkeeping regulations for fishing vessels should be formulated and strictly implemented. Secondly, for the key causes such as “serious negligence in lookout” and “failure to assess collision risks properly”, it is urgent to develop an integrated intelligent early warning and decision-support informatization system for the risks and potential hazards in waters shared by merchant and fishing vessels. Regarding the factor of “complex navigation environment”, navigation management strategies in key waters should be improved, and the segregation of concentrated shipping lanes from fishing operation zones should be promoted to reduce intersection risks. Finally, in view of the importance of key nodes in the accident propagation network, a multi-node joint early warning mechanism should be developed to facilitate dynamic tracking and proactive prevention of critical causal factors to enhance risk resistance and improve maritime safety in the Chinese seacoast.

This study had several limitations. Firstly, the grounded theory coding process relies on the researcher’s understanding, which may be influenced by personal experience and background, leading to some subjectivity in the results. Secondly, analysis of the relatively small number of accidents may have caused some potentially important findings to be missed. Thirdly, new causal factors may emerge with the development of maritime activities. Therefore, future research should continuously update the dataset of causal factors to adapt to new situations. Finally, this study is based on data from China’s coastal waters; thus, the findings may be influenced by regional environmental conditions and regulatory differences and may not be directly generalizable to other countries or regions.