Evaluation of Ship Importance in Offshore Wind Farm Area Based on Fusion Gravity Model in Complex Network

Abstract

With the rapid expansion of offshore wind farms (OWFs), ensuring maritime safety in adjacent waters has become an increasingly critical challenge. This study proposes an innovative dynamic risk assessment method that integrates a fusion gravity model into a complex network framework to comprehensively evaluate ship importance in OWF areas. By treating ships and wind farms as network nodes and modeling their interactions using AIS data, the method effectively captures spatiotemporal traffic dynamics and precisely quantifies ship importance. Multiple network indicators, including centrality, clustering coefficient, and vertex strength, are fused to comprehensively assess node criticality. A case study in the Yangtze River Estuary empirically demonstrates that ship importance is not static but dynamically and significantly changes with trajectories, interactions with other vessels, and proximity to OWFs, successfully identifying high-risk ships and sensitive OWF areas. The contribution of this research lies in providing a data-driven, quantifiable, novel framework capable of real-time identification of potential threats in maritime traffic. This approach offers direct and practical insights for traffic control, early warning system development, and optimizing maritime traffic management policies, facilitating a shift from reactive response to proactive prevention. Ultimately, it enhances safety supervision efficiency and decision-making support in complex maritime environments, safeguarding the sustainable development of the offshore wind industry.

1. Introduction

The rapid development of offshore wind farms (OWFs) has become a critical component of the global transition to renewable energy [1,2]. According to the International Energy Agency (IEA), OWFs are one of the most promising sectors in terms of growth potential [3,4,5]. Numerous countries and regions, including Europe, North America, and Asia, have significantly increased their investments in offshore wind energy, driving advancements in offshore wind technology to achieve carbon neutrality targets [6]. With the increasing demand for clean, sustainable energy, OWFs are being deployed in increasingly congested maritime areas. These offshore facilities have made significant contributions to energy production, but they also introduce new navigational challenges, especially regarding ship safety and traffic management in these areas [7,8]. The complexity and dynamic nature of these challenges, particularly their potential threats to the sustainability of marine resource development, highlight the shortcomings of traditional risk assessment methods.

As critical energy infrastructure, OWFs are typically located in wind-rich areas that are often frequented by maritime traffic. After the construction of OWFs, ships must navigate through areas with wind turbines and other related infrastructure, which can obstruct traditional shipping routes and introduce new risks [9,10]. The proximity of ships to wind farm structures, as well as their speed, course, and other factors, can significantly affect ship safety [11,12,13]. Navigating through these areas becomes even more challenging, particularly in adverse weather conditions or complex marine environments, where ships have limited maneuvering space, and collision risks are heightened [14,15]. Therefore, effective management of these dynamic and evolving risks is essential for ensuring the sustainable safety of both maritime traffic and offshore wind infrastructure.

In recent years, advancements in complex network theory have provided new opportunities for analyzing maritime traffic dynamics [16,17,18]. Complex networks are powerful tools that help understand the complex relationships and interactions between multiple entities [19]. In maritime traffic, interactions between ships, OWFs, and the surrounding environment can be represented as a complex network, where each ship or OWF is a node, and the interactions between ships or between ships and OWFs form the edges that connect these nodes [20]. This approach provides a scientific basis for risk assessment and management, aiding in the analysis of ship behaviors, traffic complexities, and potential risks within a maritime system. Notably, several existing studies have successfully applied complex network theory to analyze maritime traffic dynamics and assess ship importance, often using centrality measures to identify critical vessels [16,17,18].

However, despite the great potential of complex network theory in maritime traffic, existing research on the dynamic risk assessment of vessels in offshore wind farm areas still exhibits significant gaps, especially in supporting their sustainable operation and management. Specifically, traditional risk assessment methods and most complex network-based studies tend to focus on static risk analysis or single-indicator assessments of vessel importance, failing to adequately capture the complex dynamic evolution of vessel traffic flows and the comprehensive risks they pose in real-time. These approaches also rarely consider the multi-dimensional, non-linear complex interactions between vessels and wind farm structures and generally lack a data-driven tool capable of integrating multi-source information, comprehensively quantifying vessel importance, and supporting proactive risk warnings. This limitation means that existing risk assessments cannot effectively support the long-term, stable, sustainable development goals of OWFs, as they fail to provide refined perception and early warning mechanisms for dynamic risk sources. This paper aims to fill this critical gap by developing a robust framework for dynamic risk assessment that directly contributes to the sustainability of OWF operations.

To address these gaps, this paper proposes a novel method for identifying high-risk ships in OWF areas by treating ships and OWFs as nodes within a complex network. Specifically, we construct a dual-layer dynamic complex network where nodes represent ships and OWFs, and edges represent interactions between ships and between ships and OWFs. Building upon this, we innovatively introduce a fusion gravity model. This model integrates multiple core network metrics (including but not limited to vertex strength, weighted clustering coefficient, degree centrality, betweenness centrality, and closeness centrality) to calculate a comprehensive “mass” value for ships, thereby assessing their “gravitational pull” and dynamic importance within the network. By analyzing the network structure and the risk values of individual ship nodes, high-risk ships can be identified based on this fusion gravity model, enabling the implementation of targeted risk mitigation strategies. This approach not only considers the behavior of individual ships but also fully accounts for the complex interactions between ships and OWFs, as well as between ships and other ships, allowing for more precise identification of potential high-risk ships. By using real-time ship trajectories to construct a dynamic complex network and quantifying the risk of each ship based on its movement patterns and its surrounding wind farm environment, this method offers a comprehensive risk assessment that is particularly suited for the complex navigational environment of OWF areas. The main contributions of this study can be summarized as follows:

(1)

Theoretical innovation. For the first time, a gravity model that integrates multi-dimensional network metrics is proposed and constructed, overcoming the limitations of traditional single-indicator evaluations and providing a new theoretical framework for assessing dynamic node importance in complex systems.

(2)

Methodological practicality. A dual-layer dynamic complex network is constructed, capable of real-time and detailed characterization of the intricate interaction mechanisms of maritime traffic in OWF areas (including ship-to-ship and ship-to-OWF interactions), providing a solid methodological foundation for dynamic risk perception and early warning.

(3)

Practical guidance. This study provides a data-driven, quantifiable dynamic decision support tool that assists regulatory authorities in more accurately identifying potential risk sources and optimizing traffic management strategies, thereby enhancing the safety and operational efficiency of OWFs and promoting the sustainability of marine resource development.

The remainder of this paper is organized as follows: Section 2 reviews the relevant literature on OWF risk assessment, complex network theory, and gravity models. Section 3 elaborates on the proposed fusion gravity model and the dual-layer dynamic network construction methodology. Section 4 presents the case study area and data, and showcases the empirical results. Section 5 discusses the findings and their practical implications. Finally, Section 6 concludes this study and outlines future work.

2. Literature Review

This section aims to review the challenges of vessel traffic in Offshore Wind Farm (OWF) areas, the development of risk assessment methodologies, the application of complex network theory in maritime traffic, and the advancements of gravity models in related studies. Through a critical analysis of existing research, we will identify current shortcomings, thereby laying the foundation for the methodology proposed in this study and highlighting its innovation and contribution to the sustainable development of OWFs.

2.1. Vessel Traffic Challenges and Risks in OWF Areas

OWFs are typically located in areas with abundant wind resources, which often overlap with busy maritime shipping routes. Regions like the North Sea in Europe, the East China Sea, and the South China Sea in Asia, where both OWFs and shipping lanes are highly concentrated [21,22]. The layout of OWFs may conflict with existing shipping lanes, requiring adjustments to the routes or operational methods of ships. Shipping companies may need to reroute their ships around OWF areas, leading to longer voyages, extended transit times, and increased operational costs. In some cases, when OWFs are located near shipping lanes, adjustments to navigation operations may be necessary, causing a slowdown in shipping traffic [23,24]. The potential impact of OWFs on shipping safety primarily lies in the safety risks ships may face, especially when navigating near OWF equipment [25]. OWFs are often designated as no-entry or restricted areas, where ships are not allowed to enter [26]. However, under adverse weather conditions, such as fog, storms, or high winds, the reduced visibility or lack of navigational aids increases the risk of collisions or navigation errors [27]. Crews need to undergo enhanced training and be equipped with more advanced equipment to navigate safely near OWF areas. Furthermore, the presence of OWFs could also negatively impact emergency response operations, particularly in the event of maritime accidents, where obstacles around ships may affect the efficiency of emergency responses [28,29]. The construction of OWFs impacts shipping efficiency primarily through the diversion of shipping lanes, speed restrictions for ships, and longer voyages. One critical factor is the adjustment of shipping routes, where ships may need to bypass OWF areas, resulting in longer travel distances. In regions with dense OWFs, ships may need to travel further, which increases travel time, fuel consumption, and operational costs [30]. A study on shipping efficiency highlights that route diversions could lead to shipping delays, especially in high-traffic areas. The decline in shipping efficiency could have a greater economic impact, particularly for countries that rely on maritime trade [31].

In response to the challenges between OWF construction and maritime traffic, many countries and regions have started developing relevant policies and technical solutions. Research in the UK and Denmark has shown that by reasonably planning the layout of OWFs and establishing buffer areas around shipping lanes, the interference of OWFs on shipping can be effectively reduced [32,33]. In addition, advanced navigation technologies, such as automated ship tracking systems and collision warning technologies, are also being developed to improve shipping safety [13]. Collaboration between OWF developers, shipping companies, and maritime authorities during the planning phase can ensure the coordinated development of OWFs and shipping activities [34].

2.2. Risk Assessment Methodologies in OWF Areas and Their Limitations

Traditional shipping risk evaluation methods are mostly based on historical data, combining information such as ship speed, course, and distance to other ships to estimate the probability of accidents [35,36,37]. These methods have some application value in general maritime risk management, but their effectiveness is limited when dealing with complex marine environments, particularly in areas with OWFs. Specifically, traditional static risk assessment models fail to fully consider the complex, dynamic interactions between ships and OWFs, and between ships themselves. They typically cannot reflect in real-time how the importance or risk level of individual vessels changes at specific times and locations due to interactions with other entities.

In recent years, with the development of Automatic Identification Systems (AIS) and satellite monitoring technologies, real-time data has become an essential part of shipping risk assessment [38,39]. AISs can track real-time ship dynamics, providing data such as position, speed, and course. This data not only helps to assess a ship’s movement trajectory in OWF areas but also provides precise information on ship proximity [40]. Therefore, dynamic risk assessment methods based on AIS have become a research hotspot in recent years. These methods can monitor ship behavior in real time and dynamically adjust risks based on real-time data [41,42]. However, existing dynamic risk assessment models often overlook the dynamic impact of OWFs themselves and their potential influences on shipping lanes and ship courses. Changes in OWFs are not limited to their fixed locations but also include the potential disruption to shipping caused by their operational activities. More importantly, current dynamic assessment models generally lack a framework capable of integrating multi-source information to comprehensively quantify the multi-dimensional importance of vessels within a complex network, which is essential for refined and proactive risk management. Therefore, a critical challenge in current research is how to comprehensively consider the dynamic interactions between ships, OWFs, and other environmental factors to construct more accurate risk assessment models.

2.3. Application of Complex Network Theory in Maritime Traffic Safety

The application of complex network theory in shipping risk management has gradually become an important research method [16,43]. This theory treats maritime facilities such as ships, OWFs, and ports as nodes in a network, with the connections between the nodes representing the interactions between ships, OWFs, and the environment. Complex network models can effectively reveal the complex interactions between ships and OWFs, as well as other facilities, providing a new perspective for shipping risk assessment [16,17,18]. Centrality measures in complex networks, such as degree centrality and betweenness centrality, can be used to identify ships that occupy key positions in the maritime traffic network, which are often exposed to higher collision risks. By modeling ship behavior in a networked structure, researchers can analyze the interactions between ships and OWFs to identify potential high-risk ships.

In recent years, dynamic complex network models based on AIS data have made significant progress in shipping risk analysis [44,45]. By establishing dynamic complex networks and combining real-time ship trajectory data with OWF operational information, it is possible to assess ship navigation risks more accurately. This method not only helps identify high-risk ships but also predicts potential risks in densely trafficked maritime areas, providing more precise decision support for shipping management [20]. Furthermore, complex network theory offers new insights into OWF risk management [46,47]. By modeling the distance, speed, and interaction frequency between ships and OWFs, it becomes possible to predict ship traffic density and potential collision risks near OWFs, providing effective preventive measures for navigational safety, particularly in regions with high concentrations of OWFs. However, existing complex network applications for vessel risk assessment in OWF areas still exhibit limitations: most studies tend to construct single-layer networks (e.g., focusing solely on ship-to-ship interactions), failing to adequately capture the more detailed and direct interactions between vessels and wind farm structures. Simultaneously, despite the introduction of centrality metrics, how to effectively fuse these multi-dimensional network topological features to obtain a comprehensive, dynamic, and physically meaningful quantitative assessment of individual vessel importance remains an underexplored issue.

2.4. Research Gaps and Contributions of This Study

Despite the growing body of research addressing the shipping risk management issues brought about by OWFs, several key gaps remain. Current studies primarily focus on traditional static risk assessments or simple models based on spatial relationships, failing to fully account for the complex dynamic environments and ship behavior. In summary, despite the growing body of research addressing the shipping risk management issues brought about by OWFs, several key gaps remain:

(1)

Lack of a dynamic, multi-dimensional framework for ship importance assessment: Existing methods struggle to capture the dynamic changes in vessel importance over time and mostly rely on single indicators or macroscopic statistics, failing to comprehensively integrate various topological features of vessels within a complex traffic network, leading to insufficient precision in identifying high-risk vessels.

(2)

Insufficient characterization of complex interaction mechanisms: Few existing complex network applications simultaneously consider and effectively integrate both “ship-to-ship” and “ship-to-OWF” interaction types. This limits a comprehensive understanding of the overall risk landscape in OWF areas, especially when emphasizing dynamic and localized high-risk interactions.

(3)

Absence of a proactive warning tool combining network structure and gravity concepts: There is currently a lack of a practical, data-driven tool that integrates complex network analysis (particularly multi-dimensional node importance) with gravity model concepts, by quantifying vessel “gravitational” importance to support proactive risk warnings and sustainable management in OWF areas.

To address this challenge, this study proposes a method for evaluating the importance of ships in offshore wind farm areas based on a fusion gravity model within a complex network framework. In this approach, maritime traffic in OWF waters is modeled as a complex network system, where ship navigation behaviors are represented as interactions between nodes and edges. A fusion gravity model is introduced, and multiple network metrics are employed to identify critical ships, enabling a dynamic and quantitative analysis of navigational risks within OWF regions. The key innovations of this method are as follows: (1) The introduction of a multi-factor coupled gravity model, which overcomes the limitations of previous methods that relied solely on single indicators such as degree or k-shell values. (2) The integration of dynamic and structural characteristics through complex network analysis provides more comprehensive and real-time decision support for maritime safety in wind farm areas. (3) The ability to apply this approach to real AIS data, making it both practical and highly applicable for broader implementation.

3. Method

3.1. Traffic Situation Complex Network in OWF Area

To describe the maritime traffic situation in the waters of OWFs, a dual-layer complex network approach is adopted to measure the relationship between ships and OWFs [48]. In the first layer, ships serve as nodes, and connections between ships are established to reflect their interaction characteristics. In the second layer, both ships and OWFs act as nodes, and connections are formed based on indicators such as the proximity between ships and OWFs, highlighting the impact of ships on OWFs. By constructing and analyzing this dual-layer complex network, the importance distribution of ships in the OWF waters and their potential threats and impacts on the OWFs can be comprehensively revealed.

In the first layer, define the set of ships as $V_s=\left\{s_1,s_2,\dots ,s_n\right\}$, where each ship node $s_i$ is represented by its geographic coordinates $s_i=\left(x_i,y_i\right)$. In the second layer, define the set of wind farms as $V_w=\left\{w_1,w_2,\dots ,w_m\right\}$, where each wind farm node $w_j$ is represented by its center point $w_j=\left(x_j,y_j\right)$. The total set of nodes is $V=V_s\cup V_w$.

An edge $e_{ij}$ is created between two nodes $v_i,v_j\in V$ if the approaching rate of nodes $r(v_i,v_j)$ is less than 0. The approaching rate is expressed by the projection of the relative speed of two nodes at relative distances.

$$r(v_i,v_j)={\displaystyle \frac{\overrightarrow{D_{ij}}·\overrightarrow{V_{ij}}}{‖\overrightarrow{D_{ij}}‖}}=‖\overrightarrow{V_{ij}}‖·\cos (\overrightarrow{D_{ij}},\overrightarrow{V_{ij}})$$

(1)

where $\overrightarrow{D_{ij}},\overrightarrow{V_{ij}}$ are the relative distance and speed between $v_i$ and $v_j$, respectively.

The set of ship-to-ship edges ($E_{ss}$) and ship-to-wind farm edges ($E_{sw}$) are as follows:

$$E_{ss}=\left\{e_{s_i,s_j}\left|s_i,s_j\in V_s,\hspace{0.17em}r(s_i,s_j)<0\right.\right\}$$

(2)

$$E_{sw}=\left\{e_{s_i,w_j}\left|s_i\in V_s,w_j\in V_w,\hspace{0.17em}r(s_i,w_j)<0\right.\right\}$$

(3)

The total edge set is:

$$E=E_{ss}\cup E_{sw}$$

(4)

Figure 1 is a schematic diagram of the traffic situation complex network in the OWF area. In Figure 1, ships $s_2$ and $s_3$ are in close proximity to each other, forming an edge $e_{s_2,s_3}$. Meanwhile, the ship $s_2$ and OWF $w_3$ also shows a tendency to approach each other, thus forming another edge $e_{s_2,w_3}$. Similarly, ship $s_4$ shows a tendency to approach OWFs $w_1$ and $w_2$, resulting in the generation of corresponding edges. Ship $s_1$ and OWF $w_4$ do not have any close proximity interactions with other ships or the OWFs, so no edges are generated between them and any other nodes. In this case, $s_1$ and $w_4$ can be ignored when evaluating the maritime traffic situation and identifying key ships.

In this research, we introduced the maritime traffic situation complexity model to establish a weighted complex network. The complexity between ships and the complexity between ships and OWFs are set as the edge weights. The specific calculation method can be referred to in our previous research [20]. In the first layer, the weight calculation for ship-to-ship edges is as follows:

$$W(s_i,s_j,t)=\left\{\begin{array}{l}{({\displaystyle \frac{1}{ed(s_i,s_j,t)}})}^{1+k(s_i,s_j,t)},ed(s_i,s_j,t)\ge 1\\ {({\displaystyle \frac{1}{ed(s_i,s_j,t)}})}^{1-k(s_i,s_{j}t,)},ed(s_i,s_j,t)<1\end{array}\right.$$

(5)

$$ed(s_i,s_j,t)=\sqrt{{\displaystyle \frac{{(x_i-x_j)}^2}{a_i^2}}+{\displaystyle \frac{{(y_i-y_j)}^2}{b_i^2}}}$$

(6)

$$k(s_i,s_j,t)={\displaystyle \frac{ed(s_i,s_j,t)-ed(s_i,s_j,t-1)}{ed(s_i,s_j,t-1)}}$$

(7)

where $W(s_i,s_j,t)$ is the weight of the edge between the ship $s_i$ and ship $s_j$ at time $t$. $ed(s_i,s_j,t)$ is the elliptical distance between the ship $s_i$ and ship $s_j$ at time $t$. $k(s_i,s_j,t)$ is the rate of change in positional proximity between the ship $s_i$ and ship $s_j$ at time $t$.

In the second layer, the weight calculation for ship-to-wind farm edges is as follows:

$$W(s_i,w_j,t)=D{(s_i,w_j,t)}^{1-V(s_i,w_j,t)}$$

(8)

$$D(s_i,w_j,t)=\left\{\begin{array}{cc}{e}^{-\left|d(s_i,w_j,t)-D_s\right|/D_s}& d(s_i,w_j,t)>D_s\\ 1& d(s_i,w_j,t)\le D_s\end{array}\right.$$

(9)

$$V(s_i,w_j,t)={\displaystyle \frac{d(s_i,w_j,t)-d(s_i,w_j,t-1)}{d(s_i,w_j,t-1)}}$$

(10)

where $W(s_i,w_j,t)$ is the weight of the edge between $s_i$ and $w_j$ at time $t$. $V(s_i,w_j,t)$ is the changing rate as the ship $s_i$ approaches the OWF $w_j$’s boundary at time $t$. $D(s_i,w_j,t)$ is the space proximity between the ship $s_i$ and the OWF $w_j$’s boundary at time $t$. $d(s_i,w_j,t)$ is the distance between the ship $s_i$ and the OWF $w_j$’s boundary at time $t$. $D_s$ as the safety distance from the OWF $w_j$’s boundary.

3.2. Ship Importance Calculation Based on Fusion Gravity Model

Node importance evaluation based on the gravity model is a quantitative approach that combines node interactions and network structural features [49]. It measures the relative importance of nodes in a network by considering their inherent properties, the properties of neighboring nodes, and the relationships between nodes. This approach is commonly applied in complex networks to identify central nodes, key influencers, or critical components. The core idea is that a node’s importance is determined not only by its own characteristics but also by the “attraction” exerted by other nodes in the network. This attraction is modeled using the gravity formula.

$$I_i={\displaystyle \sum _{j\in N(i)}\frac{m_i{m}_j}{d_{ij}}}$$

(11)

where $I_i$ is the importance of the node $i$. $N(i)$ is the set of neighbors of node $i$. $m_i$ and $m_j$ are the “mass” of nodes $i$ and $j$, representing their attributes (e.g., degree, vertex strength, centrality, etc.). $d_{ij}$ is the distance between nodes $i$ and $j$ (e.g., topological distance (physical distance).

In the complex network constructed in this study, ships and OWFs are regarded as nodes of the network. In such a network, the interactions between nodes and the overall network structure are crucial for evaluating the importance of nodes. Existing gravity model-based approaches typically consider only a single attribute of a node, such as degree or k-shell value, as the mass in the gravity model. Moreover, these methods do not fully account for the varying influence of each node in a real-world maritime traffic complex network. To address these two issues, this study first integrates multiple node attributes—including vertex strength, weighted clustering coefficient, degree centrality, betweenness centrality, and closeness centrality—as the mass of a node. A new fusion gravity model is then proposed to comprehensively evaluate the importance of nodes by incorporating their multi-attribute characteristics. The definition of the node importance indicators is as follows.

(1)

Vertex strength

In complex network analysis, node attributes are crucial for evaluating a node’s role within the network. In weighted networks in particular, it is important to consider not only the number of connections a node has but also the strength of those connections. Therefore, vertex strength is introduced as a key metric to measure the total interaction intensity between a node and its neighboring nodes. This helps to more accurately reflect the node’s influence and activity within the network. Vertex strength is a measure in complex networks that represents the sum of the weights of edges connected to a given node, indicating the total intensity of its interactions with other nodes. For a node $S_i$ in a weighted network, the vertex strength $S_i$ is defined as the sum of the weights of all edges linked to it [48].

$$S_i={\displaystyle \sum _{j\in N(i)}{W}_{ij}}$$

(12)

where $S_i$ is the vertex strength of node $i$. $W_{ij}$ is the weight of the edge between nodes $i$ and $j$. $N(i)$ is the set of adjacent to node $i$.

(2)

Weighted clustering coefficient

In complex networks, the clustering coefficient is an important metric used to measure the local connectivity of a node, reflecting the tendency of nodes to form tightly connected groups or “triadic relationships”. In weighted networks, it is not sufficient to consider only the presence of connections; the strength of those connections must also be taken into account to more accurately represent the real-world intensity of interactions between nodes [50].

For a node $i$ in a weighted undirected network, the weighted clustering coefficient $C_i^w$ measures the average strength of connections among its neighbors, weighted by the importance of the links involving the node $i$. The calculation formula is as follows:

$$C_i^w={\displaystyle \frac{1}{S_i(k_i-1)}}{\displaystyle \sum _{j,h}\frac{W_{ij}+W_{ih}}{2}}·a_{ij}{a}_{ih}{a}_{jh}$$

(13)

where $C_i^w$ is the weighted clustering coefficient of the node $i$. $S_i$ is the strength of node $i$, i.e., the sum of the weights of its connection edges. $k_i$ is the degree of node $i$. $W_{ij}$ is the weight of the edge between node $i$ and node $j$. $a_{ij}$ equals 1 if there is an edge between $i$ and $j$, and 0 otherwise. $j$ and $h$ are neighboring nodes of $i$.

(3)

Degree centrality

Degree centrality is a fundamental metric used to measure the importance of a node within a network [51]. It is based on the number of connections a node has, with the assumption that nodes connected to more nodes are more important within the network. Nodes with high degree centrality typically have greater influence in information flow, resource distribution, and other aspects. Degree centrality is the number of connections a node has, and it is commonly used to reflect the relative importance of that node in the network. For a node $i$ in an undirected network, its degree centrality $C_{D_i}$ is defined as the number of nodes directly connected to it.

$$C_{D_i}={\displaystyle \frac{d_i}{N-1}}$$

(14)

where $C_{D_i}$ is the degree centrality of node $i$. $d_i$ is the degree of node $i$. $N$ is node number of the network.

(4)

Betweenness centrality

Betweenness centrality is a metric in complex networks that measures the importance or intermediary role of a node in the transmission of information across the network [51]. It reflects how often a node acts as a bridge or intermediary between other nodes, especially when information is transmitted from one node to another. The higher a node’s betweenness centrality, the more central its role in controlling the flow of information within the network. The betweenness centrality $C_{B_i}$ of node $i$ is defined as the proportion of the shortest paths between any two nodes that pass through node $i$. The calculation formula is as follow:

$$C_{B_i}={\displaystyle \sum _{p\ne i\ne q}\frac{\sigma (p,i,q)}{\sigma (p,q)}}$$

(15)

where $C_{B_i}$ is the betweenness centrality of node $i$. $\sigma (p,i,q)$ represents the number of shortest paths between node $p$ and node $q$ pass through node $i$. $\sigma (p,q)$ represents the number of shortest paths between node $p$ and node $q$.

(5)

Closeness centrality

Closeness centrality is a measure in complex networks used to assess the average shortest path length from a node to all other nodes. Nodes with higher closeness centrality are often positioned at key points in the network, as they can quickly interact with other nodes [52]. For a node $i$, closeness centrality is defined as the inverse of the average shortest path length from the node to all other nodes in the network. The calculation formula is as follows:

$$C_{C_i}={\displaystyle \frac{N-1}{{\displaystyle \sum _{\begin{array}{l}j=1\\ i\ne j\end{array}}^N{d}_{ij}}}}$$

(16)

where $C_{C_i}$ represents the closeness centrality of the node $i$. $d_{ij}$ represents the distance between the nodes $i$ and node $j$.

After calculating the node importance indicators, the fusion value of the node is computed to integrate the node’s local information in order to evaluate its importance. Generally speaking, the influence of a node on the network is reflected in its own value. We believe that in a local network, the greater the node’s importance indicator value, the greater its influence. In this research, the fusion value of a node is defined as follows:

$$f_i=w_1{\displaystyle \frac{S_i}{S_{\max }}}+w_2{\displaystyle \frac{C_i^w}{C_{\max }^w}}+w_3{\displaystyle \frac{C_{D_i}}{C_{D_{\max }}}}+w_4{\displaystyle \frac{C_{B_i}}{C_{B_{\max }}}}+w_5{\displaystyle \frac{C_{C_i}}{C_{C_{\max }}}}$$

(17)

where $S_{\max }$, $C_{\max }^w$, $C_{D_{\max }}$, $C_{B_{\max }}$ and $C_{C_{\max }}$ represent the maximum vertex strength, maximum weighted clustering coefficient, maximum degree centrality, maximum betweenness centrality, and maximum closeness centrality of the nodes in the network, respectively. $w$ is the weight of the indicator. In this study, the entropy weight method is used to determine the weights of the indicators, and the calculation method is as follows:

(1)

Data standardization. The max-min standardization method is adopted.

$$x_{il}^{\prime }={\displaystyle \frac{x_{il}-\min (x_l)}{\max (x_l)-\min (x_l)}}$$

(18)

where $x_{il}^{\prime }$ is the normalized value. $x_{il}$ is the $l$th indicator value of node $i$. max($x_l$) is the maximum value of the lth indictor and min(x_l) is the minimum value of the lth indictor.

(2)

Entropy of each indicator. The entropy of each indicator can be calculated as follows:

$$e_l=-\ln {(n)}^{-1}{\displaystyle \sum _{i=1}^n{p}_{il}\ln p_{il}}$$

(19)

where $n$ is the number of nodes, $p_{il}$ can be calculated as follows:

$$p_{il}={\displaystyle \frac{x_{il}^{\prime }}{{\displaystyle \sum _{i=1}^n{x}_{il}^{\prime }}}}$$

(20)

(3)

Weight calculation. According to the entropy e_l of each indicator, the weight w_l of the indicator can be determined as follows:

$$w_l={\displaystyle \frac{1-e_l}{{\displaystyle \sum _{l=1}^m(1-e_l)}}}$$

(21)

where m is the number of the indicator.

Inspired by the law of gravity, the interaction between two objects in the real world is directly proportional to their masses and inversely proportional to the square of the distance between them. Based on this principle, in the model, the fusion values $m_i$ and $m_j$ of nodes i and j are considered as the “masses” of the respective nodes, while the shortest path distance $d_{ij}$ between the nodes represents the relative distance between them. Therefore, the importance of a node $i$ based on the fusion gravity model is defined as follows:

$$I_i={\displaystyle \sum _{\begin{array}{l}j=1\\ i\ne j\end{array}}^N\frac{f_i{f}_j}{d_{ij}^2}}$$

(22)

where $f_i$ and $f_j$ are the fusion values of the node $i$ and node $j$, respectively, $d_{ij}$ is the shortest path distance between the node $i$ and node $j$.

4. Case Study

4.1. Research Area

Located in eastern China, the Yangtze River Estuary is one of the busiest shipping hubs in the world, handling a significant volume of both domestic and international maritime traffic. The estuary serves as a crucial intersection between the Yangtze River Basin and the East China Sea, as well as a key point where inland waterways and international shipping routes converge, making its traffic network highly complex and dynamic. The estuary sees a wide variety of ships, including cargo ships, container ships, fishing boats, and passenger ships, all of which add to the complexity of maritime traffic. Additionally, the region is characterized by numerous shipping lanes, docking areas, and frequent fishing activities, all of which further complicate the management of maritime traffic.

In recent years, the construction of an offshore wind farm in the Yangtze River Estuary has been integrated into China’s green energy development strategy, as the area possesses abundant wind resources, making it highly suitable for wind energy development. According to the Shanghai 2024 offshore wind power project competitive allocation work plan, the proposed offshore wind farm location is shown in Figure 2. However, the construction of offshore wind facilities and the subsequent adjustments to shipping lanes are expected to have a significant impact on the traffic dynamics of the estuary, particularly in terms of ship navigation, route planning, and traffic safety.

Therefore, selecting the Yangtze River Estuary as the research area is of significant importance and necessity. Analyzing this complex maritime environment and evaluating the impact of the OWF area on ship importance will provide a scientific basis for both maritime management and wind energy project planning. As a representative high-complexity maritime area, the findings of this study will not only be crucial for optimizing local traffic patterns but also offer valuable insights and references for OWF projects in similar areas.

AIS data from ships in the proposed OWF area in the Yangtze River Estuary were selected in this research to validate the effectiveness of the proposed method. AIS is a widely used monitoring technology in maritime traffic, providing real-time ship position, course, speed, and ship type, among other key parameters, which help to accurately describe the ship’s trajectory and navigation status. The extensive use of AIS data allows for detailed tracking of ship behavior in both space and time, making it the core data source for traffic situation analysis in this research.

However, some errors and outliers may be present in AIS data during the actual collection process. These outliers may be caused by various factors, such as signal interference, equipment malfunctions, and data transmission errors. Therefore, to ensure the accuracy and reliability of the data, the raw data must first undergo rigorous preprocessing. The preprocessing steps include the removal of obvious outlier data, such as unreasonable ship positions (e.g., coordinates significantly deviating from normal routes), unrealistic speeds (e.g., abnormally fast or slow values), and unreasonable course data. Additionally, as missing values may occur during the transmission of AIS data, interpolation is applied to handle the missing data. To ensure smoothness and continuity, a linear interpolation algorithm was used to fill in the gaps between data points, ensuring that the analysis results are not impacted by missing data.

The AIS data of ships in the research area on 31 July 2023 was used as the primary dataset for analysis. AIS data provides critical information regarding the ship’s position, speed, and heading. After data cleaning and interpolation, the processed data can be used for subsequent traffic situation analysis and ship importance evaluation. Using the processed AIS data, a traffic situation complexity network model was developed, abstracting the ships and OWFs in the research area as complex network nodes. This model is used to quantitatively analyze the dynamic behavior of ships and evaluate their importance in the research area. The abstraction process of the OWF nodes is shown in Figure 3. This will provide data support and a theoretical basis for optimizing maritime traffic management, helping relevant departments take targeted navigational safety measures during the OWF construction process to ensure safe maritime traffic.

4.2. Analysis of Ship Node Importance

The traffic situation complex network in the OWF area is developed to evaluate the traffic conditions on a minute-by-minute basis. Figure 4 illustrates the structure of the traffic situation complex network in the OWF area at four selected time slices. Subsequently, topological indicators for each ship node in the network were calculated, as shown in

Table 1. Topology indicators for ship nodes in research area at 31 July 2023 15:35:41.

MMSI	Ship ID	$\mathit{S}$	${\mathit{C}}^{\mathit{w}}$	${\mathit{C}}_{\mathit{D}}$	${\mathit{C}}_{\mathit{B}}$	${\mathit{C}}_{\mathit{C}}$
412379370	1	2.486343	0.184524	0.157173	0.003974	0.072894
412425920	2	8.043003	0.410881	0.280242	0.007782	0.159355
412755110	3	2.896846	0.206146	0.207248	0.006054	0.106989
413256860	4	8.105879	0.487733	0.352169	0.009452	0.204628
413268160	5	4.852541	0.249966	0.249183	0.006355	0.107127
413275370	6	9.355564	0.672561	0.418837	0.017496	0.239287
413298320	7	6.976006	0.346955	0.258628	0.007586	0.144157
413299580	8	2.186755	0.111385	0.082872	0.002493	0.047255
413341670	9	8.976986	0.595743	0.393441	0.014444	0.221274
413342350	10	9.761805	0.722143	0.419612	0.017738	0.273972
413356720	11	8.893421	0.577034	0.358794	0.013348	0.220745
413361840	12	10.08527	0.723422	0.440584	0.017766	0.287257
413382470	13	8.228493	0.505509	0.356426	0.009642	0.215852
413454640	14	6.753432	0.331398	0.251209	0.006858	0.114731

,

Table 2. Topology indicators for ship nodes in the research area at 31 July 2023 15:45:53.

MMSI	Ship ID	$\mathit{S}$	${\mathit{C}}^{\mathit{w}}$	${\mathit{C}}_{\mathit{D}}$	${\mathit{C}}_{\mathit{B}}$	${\mathit{C}}_{\mathit{C}}$
412379370	1	2.997004	0.140371	0.125492	0.002191	0.0686
412425920	2	5.941097	0.183229	0.246108	0.007162	0.164224
412755110	3	3.643833	0.141821	0.157204	0.003948	0.075621
413256860	4	7.21582	0.256299	0.267055	0.007496	0.240209
413268160	5	5.519993	0.165281	0.211663	0.006508	0.145915
413275370	6	7.991964	0.414854	0.330579	0.012455	0.337736
413298320	7	6.496467	0.193467	0.247828	0.007484	0.199698
413299580	8	2.257485	0.094454	0.088687	0.002023	0.039812
413341670	9	7.875341	0.398141	0.322694	0.011526	0.330895
413342350	10	8.373655	0.428375	0.341772	0.014126	0.387017
413356720	11	4.038069	0.146716	0.191361	0.006067	0.086822
413361840	12	8.993864	0.522103	0.347851	0.015088	0.396555
413382470	13	7.543431	0.299189	0.282808	0.007996	0.259705
413454640	14	7.857139	0.303386	0.317015	0.010398	0.280610

,

Table 3. Topology indicators for ship nodes in the research area at 31 July 2023 15:55:23.

MMSI	Ship ID	$\mathit{S}$	${\mathit{C}}^{\mathit{w}}$	${\mathit{C}}_{\mathit{D}}$	${\mathit{C}}_{\mathit{B}}$	${\mathit{C}}_{\mathit{C}}$
412379370	1	4.150514	0.192793	0.195335	0.005783	0.071116
412425920	2	8.361463	0.269239	0.241587	0.012853	0.121343
412755110	3	5.220449	0.210545	0.210188	0.008135	0.088678
413256860	4	4.817104	0.200421	0.210069	0.006269	0.087217
413268160	5	9.280613	0.383789	0.335931	0.014399	0.153450
413275370	6	0	0	0	0	0
413298320	7	1.551086	0.108261	0.092547	0.001983	0.054347
413299580	8	8.745402	0.325802	0.263409	0.012873	0.143619
413341670	9	1.740959	0.119982	0.100483	0.002137	0.057736
413342350	10	2.747228	0.143648	0.191011	0.004402	0.070618
413356720	11	1.806881	0.142597	0.161544	0.003974	0.063290
413361840	12	7.691775	0.241067	0.233862	0.011102	0.104597
413382470	13	8.817261	0.368533	0.287734	0.013219	0.152479
413454640	14	9.463648	0.411099	0.336131	0.015795	0.173963

and

Table 4. Topology indicators for ship nodes in the research area at 31 July 2023 16:05:33.

MMSI	Ship ID	$\mathit{S}$	${\mathit{C}}^{\mathit{w}}$	${\mathit{C}}_{\mathit{D}}$	${\mathit{C}}_{\mathit{B}}$	${\mathit{C}}_{\mathit{C}}$
412379370	1	4.876935	0.157008	0.165062	0.005759	0.103417
412425920	2	8.683687	0.310825	0.245051	0.016846	0.212225
412755110	3	5.834837	0.185814	0.239407	0.010769	0.187009
413256860	4	5.253732	0.174547	0.222853	0.009777	0.157623
413268160	5	2.220272	0.09657	0.127985	0.003401	0.053986
413275370	6	0	0	0	0	0
413298320	7	6.839134	0.273176	0.239416	0.012438	0.191218
413299580	8	2.720185	0.114122	0.135044	0.003447	0.059466
413341670	9	3.765748	0.134197	0.161249	0.005552	0.084152
413342350	10	3.261097	0.118732	0.156313	0.004605	0.075513
413356720	11	5.236339	0.173128	0.208859	0.008959	0.151864
413361840	12	8.134527	0.294065	0.241503	0.015034	0.195085
413382470	13	5.206963	0.163956	0.191254	0.007713	0.117098
413454640	14	8.206139	0.297173	0.242917	0.016366	0.199131

. These indicators provide valuable insights into the relative importance and position of each ship within the network, aiding in a better understanding of the traffic dynamics and associated risks within the designated study area. The importance of ship nodes in the research area at four time slices is shown in Figure 5.

Figure 4a and Figure 5a reveal that the top five ships in terms of importance are $s_{12}$, $s_{10}$, $s_6$, $s_9$, and $s_{11}$. At this moment, $s_{12}$’s trajectory intersects with those of ships $s_{11}$, $s_{13}$, $s_6$, and others, while it also remains in close proximity to wind farms $w_6$, $w_7$ and $w_8$, resulting in an increased risk. Similarly, $s_{10}$’s course intersects with those of $s_9$ and $s_{14}$, and its proximity to wind farm $w_5$ further exacerbates the risk, placing $s_{10}$ in the second position in terms of importance. On the other hand, $s_8$ exhibits the lowest level of importance at this moment, as its path does not intersect with any other ship’s course, nor does it converge with any wind farm. Consequently, $s_8$ represents a relatively low-risk ship in this scenario, with minimal influence on the network. From Figure 4b and Figure 5b, it is evident that the traffic situation remains similar to the previous moment. The trajectory of $s_{14}$ intersects with those of $s_9$ and $s_{10}$, thereby increasing the risk of convergence with these ships. Additionally, its proximity to wind farm $w_5$ further raises the risk level, causing the importance of $s_{14}$ to rise to the fifth position. Compared to the previous moment, the importance of $s_{14}$ has significantly increased, potentially affecting the safety of other ships. Figure 4c and Figure 5c show a more significant shift in the ranking of ship importance, with the top five ships now being $s_{13}$, $s_4$, $s_{12}$, $s_7$, and $s_2$. In this moment, $s_{13}$ is ranked first in terms of importance due to the convergence with $s_4$ and $s_5$, forming a three-ship crossing scenario. This complex intersection of trajectories drastically increases the associated risk. As a result, the importance of $s_{13}$ is significantly elevated. In contrast, $s_6$ now holds the lowest importance, as the prior risk of convergence dissipates, and $s_6$ no longer interacts with other ships or wind farms. This isolates $s_6$ as a node with zero importance in the network. Figure 4d and Figure 5d show that the top-ranked ship has shifted to $s_2$. As other ships have resolved their conflicts and exited the wind farm areas, $s_2$’s course brings it closer to wind farm $w_4$, with a very short distance between them. This proximity to the wind farm results in an increased risk, propelling $s_2$ to the highest importance rank at this moment.

The number of occurrences of the highest-ranked ship is shown in Figure 6. By ranking the importance of ships within wind farm waters at different times, it is possible to identify those posing the greatest impact on navigational safety. Counting how often a ship ranks first further helps determine the primary sources of risk. If a particular ship frequently occupies the top position, it indicates that this ship plays a central role in navigation risk and should be prioritized for monitoring and management. Conversely, if multiple ships alternately rank first, the risk is more dispersed, requiring broader and more dynamic surveillance. Overall, this statistic highlights risk concentration and supports the optimization of early warning and control strategies, though it should be complemented by analysis of other high-risk ships and comprehensive indicators for a more complete assessment.

The importance of each ship fluctuates over time, driven by changes in its navigation patterns and the spatial relationships with other ships and wind farms. The interactions between ships, as well as their convergence with wind farms, significantly influence the ranking of ship importance. This dynamic analysis provides a more accurate risk assessment and helps to implement more effective measures to ensure navigational safety.

To validate the effectiveness of the node importance evaluation method proposed in this paper, network efficiency was used. The network efficiency can be described as follows:

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

(23)

where $EF$ is the network robustness. N is the number of node in a complex network. $d_{ij}$ is the distance between node i and node j.

Two attack strategies are selected in this study: random attack and targeted attack. In the random attack, a node i is randomly selected, and the edges adjacent to this node are removed. In the targeted attack, four target attack strategies are employed to delete nodes based on $C_D$, $C_B$, $C_C$, and the method proposed in this paper. As shown in Figure 7, with the increasing number of deleted nodes, the network efficiency steadily declines. It can be observed that removing nodes using the method proposed in this paper causes the network efficiency to decline at the fastest rate. This demonstrates that the node importance evaluation strategy introduced here is not only theoretically sound but also effective in pinpointing critical ship nodes in practical applications.

4.3. The Impact of Ships on OWFs

Based on the analysis in the previous section, the importance ranking of ships navigating through the OWF area can be determined, allowing for greater attention to be paid to ships of higher importance. Meanwhile, the method proposed in this paper enables the ranking of OWF nodes, thereby identifying areas within the wind farm that pose higher risks in relation to ship activity. The importance of OWF nodes in the research area at four different time slices is shown in Figure 8. Topological indicators for each OWF node in the network were calculated, as presented in

Table 5. Topology indicators for OWF nodes in the research area on 31 July 2023, 15:35:41.

OWF ID	$\mathit{S}$	${\mathit{C}}^{\mathit{w}}$	${\mathit{C}}_{\mathit{D}}$	${\mathit{C}}_{\mathit{B}}$	${\mathit{C}}_{\mathit{C}}$
1	1.375561	0.106836	0.141704	0.007858	0.093964
2	1.303999	0.090856	0.117218	0.006473	0.056254
3	1.295477	0.083991	0.116933	0.004179	0.037828
4	2.224817	0.221832	0.223036	0.013195	0.175448
5	2.332542	0.241419	0.249369	0.016651	0.188725
6	1.919487	0.170932	0.158017	0.012065	0.117181
7	2.185694	0.173473	0.159599	0.012943	0.121353
8	1.671291	0.143437	0.147667	0.008659	0.101047

,

Table 6. Topology indicators for OWF nodes in the research area on 31 July 2023, 15:45:53.

OWF ID	$\mathit{S}$	${\mathit{C}}^{\mathit{w}}$	${\mathit{C}}_{\mathit{D}}$	${\mathit{C}}_{\mathit{B}}$	${\mathit{C}}_{\mathit{C}}$
1	2.269526	0.121851	0.119015	0.004521	0.049595
2	2.058773	0.114668	0.088484	0.002503	0.038932
3	1.064518	0.086962	0.084455	0.001446	0.035821
4	2.874515	0.194887	0.241877	0.007619	0.185692
5	2.986389	0.208514	0.246556	0.016364	0.196294
6	2.311298	0.143568	0.148526	0.004711	0.118865
7	2.435608	0.174218	0.208561	0.006977	0.178664
8	2.338684	0.157345	0.152562	0.006845	0.132927

,

Table 7. Topology indicators for OWF nodes in the research area on 31 July 2023, 15:55:23.

OWF ID	$\mathit{S}$	${\mathit{C}}^{\mathit{w}}$	${\mathit{C}}_{\mathit{D}}$	${\mathit{C}}_{\mathit{B}}$	${\mathit{C}}_{\mathit{C}}$
1	2.455677	0.207247	0.195165	0.009134	0.136733
2	2.271563	0.173871	0.174691	0.006003	0.098175
3	2.376027	0.186717	0.182501	0.007599	0.110588
4	2.956459	0.241242	0.248994	0.016514	0.213574
5	1.013661	0.093156	0.149999	0.003984	0.035931
6	1.753227	0.126158	0.161761	0.005739	0.080639
7	2.798557	0.232979	0.244818	0.016007	0.200973
8	2.580476	0.214254	0.202487	0.015467	0.144863

and

Table 8. Topology indicators for OWF nodes in the research area at 31 July 2023 16:05:33.

OWF ID	$\mathit{S}$	${\mathit{C}}^{\mathit{w}}$	${\mathit{C}}_{\mathit{D}}$	${\mathit{C}}_{\mathit{B}}$	${\mathit{C}}_{\mathit{C}}$
1	2.637381	0.212984	0.174804	0.00957	0.130385
2	1.368309	0.135108	0.123207	0.002945	0.032272
3	0.956095	0.111253	0.102501	0.002063	0.030691
4	2.773069	0.240316	0.228537	0.011601	0.170846
5	1.383832	0.138535	0.157483	0.003988	0.037665
6	2.751752	0.220835	0.198294	0.010388	0.133788
7	2.424841	0.174383	0.160946	0.008981	0.091119
8	2.192117	0.170154	0.157744	0.008609	0.047819

.

As shown in Figure 8a,b, $w_5$ exhibits significantly higher importance compared to other nodes. At this stage, $s_{10}$ and $s_{14}$ are located in close proximity to $w_5$, and their trajectories demonstrate a clear converging pattern, indicating a potential risk of intersection or interference. As a result, the local area surrounding $w_5$ becomes a high-risk hotspot for the wind farm, with its importance index reaching a peak within the overall risk network. However, as time progresses, the maritime traffic situation evolves. Figure 8c,d reveals that $s_{10}$ and $s_{14}$ have already moved away from the vicinity of $w_5$, leading to a rapid reduction in the direct risk facing this node. Consequently, the importance of $w_5$ declines significantly, and the corresponding risk level for this wind farm area decreases accordingly. Meanwhile, the importance of node $w_4$ rises sharply and becomes the most critical point. This is primarily due to the rapid convergence of $s_2$ and $s_{14}$ toward the region surrounding $w_4$, with their headings and trajectories indicating a high-speed approach. This pattern of potential ship concentration poses an elevated risk of collision or disruption. Therefore, at this stage, risk management efforts should shift focus to the monitoring and protection of $w_4$, and implement appropriate early-warning and avoidance measures to ensure the operational safety of the wind farm.

Based on the method proposed in this study, it is possible to quantitatively evaluate the contribution of each individual ship to the risk levels associated with different OWF areas. This method takes into account not only dynamic behavioral features such as ship position, speed, and heading, but also integrates the spatial distribution of OWF nodes and the evolving trajectories of ships, enabling accurate modeling and analysis of potential ship-OWF interactions. By thoroughly characterizing the risk relationships between the ship and each OWF node, the approach facilitates dynamic situational awareness and real-time risk forecasting in the vicinity of OWFs. Furthermore, it provides a robust decision-support tool for OWF operators, allowing them to formulate targeted traffic guidance measures, collision avoidance strategies, and priority monitoring plans based on the temporal and spatial distribution of ship-specific risk contributions. Ultimately, this enhances the overall operational safety of offshore wind power facilities and strengthens the capability to manage and mitigate maritime traffic risks. For example, the contribution of different ships to the importance of OWFs at 31 July 2023 15:35:41 is shown in Figure 9.

5. Discussion

5.1. Theoretical Innovation and Practical Application

The fusion gravity model-based complex network approach proposed in this study establishes a dynamic risk evaluation framework for maritime traffic in OWF areas. By modeling ships and OWF units as network nodes and their dynamic interactions as edges, the method not only identifies critical high-risk ships but also captures the spatiotemporal evolution of risk within the maritime environment, offering a distinct advantage over traditional static or macroscopic assessment methods. This provides significant theoretical support and data-driven insight for maritime traffic safety regulation in wind power waters. This study, through qualitative comparison with existing methods, further highlights the advantages of the proposed framework in terms of theoretical innovation and practical application.

Firstly, this method significantly enhances the proactivity and foresight of maritime supervision. Unlike traditional ship traffic management, which often relies on fixed navigational rules or historical routes and lacks real-time hazard awareness [36,37,38], the complex network structure developed in this study dynamically evolves with AIS data. This allows risk indicators and network topology to update in real time. By continuously identifying ship nodes with high connectivity or centrality, authorities can deploy preemptive alerts and shift from reactive management to anticipatory control. Functionally, this surpasses conventional risk identification methods that rely solely on ship density or static traffic volume analysis, offering a more refined and real-time tool for dynamic risk management.

Secondly, this method facilitates refined spatial governance strategies. The fusion gravity model innovatively integrates multiple node-level indicators, such as vertex strength, clustering coefficient, and various centrality measures. This enables more accurate assessments of individual ships’ risk contributions to specific OWF nodes. This multi-dimensional importance assessment method compensates for the limitations of single centrality metrics in existing complex system risk evaluations, significantly enhancing the comprehensiveness and accuracy of vessel importance determination. It provides feasibility for formulating quantitative criteria for setting graded exclusion areas or dynamic buffer zones. For example, OWF nodes that frequently experience strong interaction from nearby ships may warrant expanded avoidance areas or targeted deployment of intelligent navigation aids.

Thirdly, the method supports emergency response coordination and cross-sector collaboration. In scenarios involving ship congestion, trajectory intersection, or proximity to multiple critical OWF nodes, the model can promptly evaluate risk “hotspots.” This assists traffic command centers in resource allocation, such as guiding specific vessels or dispatching patrol ships. Compared to existing emergency response mechanisms that primarily focus on post-incident analysis or are experience-based, this framework, through real-time risk identification, enables more efficient and proactive emergency management. Combined with the operational needs of wind farm operators, this framework facilitates a triadic coordination model among maritime authorities, ship operators, and OWF stakeholders, thereby strengthening systemic resilience.

Furthermore, the proposed method demonstrates high scalability and adaptability. While this research uses the Yangtze River Estuary as a case study, its modeling structure and computational procedures are universally applicable across OWF areas of different scales, densities, and geographic conditions. This universality stems from its reliance on widely available AIS data and fundamental network topological principles, allowing it to be flexibly applied in various complex marine environments without extensive area-specific calibration, making it more advantageous in practical deployment. In the increasingly developed deep-sea and remote region OWFs, where navigational uncertainties are even more pronounced, this fusion gravity network model offers greater analytical and practical value.

5.2. Pathway to Software Application and Decision Support

To translate this theoretical model into a practical, operational software system for real-time maritime traffic safety management, a dedicated platform could be developed. The pathway involves defining clear inputs, processing mechanisms, and actionable outputs directed to relevant stakeholders:

(1)

Inputs: The core inputs for such a software system would include real-time AIS data streams (providing vessel positions, speeds, courses, and static information like ship type and dimensions), comprehensive spatial data of OWFs (including precise locations of wind turbines, cables, and exclusion zones), and pre-defined risk parameters and thresholds for the fusion gravity model. Future enhancements would incorporate real-time environmental data (e.g., wind speed, wave height, sea currents, visibility) to dynamically adjust risk assessments.

(2)

Outputs: The software would generate several critical outputs in real-time. These include dynamic risk assessments for individual ships and OWF units, identification of critical high-risk ships (e.g., those with high centrality or risk scores), pinpointing of risk “hotspots” (areas of aggregated high risk), and visual representations of the evolving complex network topology. Crucially, it would issue proactive alerts and warnings for impending high-risk situations (e.g., potential collisions, unauthorized entry into exclusion zones, or critical proximity to OWF assets).

Output destination and actionable insights: The generated outputs would be directed to relevant maritime safety stakeholders for immediate action.

Maritime authorities (e.g., Vessel Traffic Service—VTS): Would receive real-time alerts regarding critical ships and high-risk areas. Actions would include issuing navigational warnings to vessels, providing direct guidance or instructions to specific ships at risk, or deploying patrol boats for intervention and enforcement.

OWF operators: Would receive localized risk assessments impacting their assets. Actions could involve adjusting wind turbine operations (e.g., curtailing specific turbines in high-risk areas), initiating internal safety protocols, or coordinating with maritime authorities for joint incident management.

Ship operators/Captains: While not direct recipients of the full system output, future integration could allow for proactive guidance on safe routes or speed adjustments to their own vessels, enhancing autonomous safety measures.

This operational framework would enable a shift from reactive incident response to proactive risk management, fostering a more resilient and coordinated maritime safety ecosystem.

5.3. Potential Improvements of the Research

Nevertheless, several limitations remain. The current model does not yet incorporate important environmental variables such as weather conditions (wind speed, wave height, sea currents), tides, or visibility, all of which have a significant impact on ship navigation and may, in certain cases, alter the risk assessments and edge weights of the network. Weather and environmental conditions can drastically change ship movement patterns and, therefore, influence the dynamic interactions between ships and OWF units, especially in adverse weather scenarios. Moreover, the model does not account for non-AIS ships (e.g., small fishing boats), whose movements are not captured by the primary data source and, thus, introduce unquantified risks to maritime safety. Additionally, the current framework treats all ship types uniformly in its risk assessment, overlooking the vastly different safety and environmental consequences associated with various vessel categories. For instance, an incident involving a passenger ship or a gas carrier carries potentially catastrophic safety risks, while an oil tanker accident poses severe environmental hazards. The lack of differentiation in importance or risk weighting among these diverse ship types represents a significant simplification. Furthermore, in this study, each OWF is represented as a single node located at its geometric center. While this approach simplifies the network construction and provides a macroscopic view of interactions, for OWFs with asymmetric forms or vast geographical spreads, the geometric center may not fully capture all localized high-risk areas. Specifically, certain corners or individual wind turbine locations far from the center might present unique navigational hazards for vessels, potentially leading to an underestimation of risk in specific, high-exposure parts of an OWF. Lastly, the analysis is currently limited to a single-day snapshot and does not model multi-day risk trends, which might restrict the capture of long-term risk evolution and periodic patterns.

Future work could consider integrating multi-source data (including radar, satellite, and video surveillance) to enrich node attributes and potentially identify and track non-AIS vessels, thereby providing a more comprehensive understanding of traffic. To address the issue of ship type differentiation, future research will focus on incorporating distinct risk weightings or importance factors based on vessel type, acknowledging their unique safety and environmental risk profiles. This involves developing a nuanced approach within the fusion gravity model to assign higher importance to vessels like passenger ships, gas carriers, or oil tankers, reflecting their potential for more severe consequences in case of an accident. Regarding the representation of OWFs, future research will explore more refined approaches, such as modeling critical areas (e.g., entrance points, specific high-density turbine zones, or outer boundaries) as multiple sub-nodes, or employing a more detailed spatial grid to account for the internal complexity and varying risk profiles across the entire OWF area. This would allow for a more precise assessment of interaction risks that are spatially distributed within the wind farm. Additionally, incorporating real-time weather and oceanographic data into the edge weight calculations, adjusting for dynamic environmental conditions, would significantly improve the model’s ability to capture the changing nature of maritime risks. Furthermore, applying machine learning techniques to recognize ship behavioral patterns and construct predictive maritime risk models could further improve the model’s accuracy, generalizability, and adaptability to more complex scenarios.

In conclusion, the method proposed in this study offers both theoretical innovation, by integrating complex network analysis with a multi-factor gravity model to provide a “new paradigm” for dynamic node importance assessment in complex systems that differs from previous approaches, and high practical applicability. It provides a scalable, data-driven solution that can significantly enhance maritime traffic safety management in OWF regions and contribute to the development of more resilient, sustainable, and intelligent marine governance systems.

6. Conclusions

This study successfully developed a novel dynamic risk assessment framework, deeply integrating a fusion gravity model within a complex network, to precisely evaluate ship importance and maritime risk in offshore wind farm (OWF) areas. By abstracting ships and OWFs as network nodes and modeling their interactions using real-time AIS data, this method effectively captures and quantifies spatiotemporal traffic dynamics and the relative importance of vessels in complex maritime environments. Empirical results from a case study clearly demonstrated that ship importance dynamically fluctuates with navigation trajectories, proximity to OWFs, and interactions with other vessels, enabling the accurate identification of high-risk ships and sensitive OWF zones.

This dynamic, scalable, and data-driven solution provides critical support for decision-makers: it enables maritime authorities to implement more targeted monitoring and optimize navigational strategies; assists wind farm operators in establishing intelligent early warning systems and enhancing operational efficiency; and simultaneously opens new avenues for academic research into complex dynamic maritime traffic systems.

Future research will aim to incorporate environmental factors, non-AIS ship data, and predictive analytics to further improve model accuracy and broaden its applicability across diverse maritime scenarios.