A collision risk assessment method for unmanned ships based on self-connected graph neural network

Abstract

The present invention relates to the technical field of intelligent ship collision risk assessment, and discloses an unmanned ship collision risk assessment method based on a self-connected graph neural network, including: constructing a risk relationship graph of multiple ships at sea, constructing ship nodes, encoding the navigation status information of the ship as the attribute of the ship node; constructing a graph neural network, sampling the neighborhood ship nodes of each ship node, aggregating the navigation status features, and embedding and updating the spatiotemporal state; calculating the risk index between ships based on the support vector regression method and the one-dimensional feature vector of each ship node; using an activation function to convert the risk index between ships to obtain a collision risk probability distribution. The present invention uses a graph neural network to extract and quantify the navigation status information of multiple ships, and can directly obtain the probability distribution of the possibility of different collision risk levels between adjacent ships in the graph data, which provides strong support for the autonomous and safe navigation of ships in complex multi-ship scenarios in a more objective and efficient manner.

Description

Technical Field

[0001] The present invention relates to the technical field of intelligent ship collision risk assessment, and in particular to an unmanned ship collision risk assessment method based on a self-connected graph neural network. Background Art

[0002] With the rapid development of artificial intelligence technology, deep learning has been widely used in the maritime field, but there are still few cases of applying deep learning technology to ship collision risk assessment.

[0003] Ship collision accidents are one of the most serious safety accidents in maritime transportation, which may cause casualties, property losses and serious damage to the marine environment. Therefore, accurate assessment of ship collision risks is crucial to ensure maritime navigation safety. Traditional ship collision risk assessment methods mainly rely on the empirical knowledge of experts in the field of ships, such as the use of the nearest encounter time, ship domain, Bayesian network combined with expert knowledge base, and fuzzy logic. These methods can provide estimates of collision risks to a certain extent, but they are usually limited by the subjectivity of expert knowledge and may not be able to quantify the complex nonlinear relationships between multiple ships and the dynamically changing navigation environment. There are many challenges in exploring the evolution of multi-ship risks under the influence of collision avoidance operations.

[0004] Therefore, in order to ensure the navigation safety of multiple ships at sea under spatiotemporal evolution, it is urgent to design a ship collision risk assessment method that can learn from knowledge in real time. Summary of the invention

[0005] In order to solve the above technical problems, the present invention provides an unmanned ship collision risk assessment method based on a self-connected graph neural network; the present invention mainly realizes the dynamic construction of a risk relationship diagram of multiple ships at sea by extracting navigation status information, and uses the extracted ship navigation status information vector to form a node attribute matrix and a weighted adjacency matrix as the input of the model, and uses multiple graph neural network layers to extract high-dimensional hidden features of multiple ship nodes, and uses a normalization method to quantify the potential collision risks of multiple ships, so as to provide strong judgment support for autonomous and safe navigation of ships in complex multi-ship scenarios.

[0006] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0007] A method for assessing the collision risk of unmanned ships based on a self-connected graph neural network is proposed. By constructing a multi-ship collision risk model at sea, the collision risk probability between ships is estimated. The method specifically includes the following steps:

[0008] Step S1: Construct a risk relationship diagram for multiple ships at sea: Construct ship nodes based on the geographical locations of each ship in the multi-ship collision avoidance scenario , , Indicates the total number of ships in the multi-ship collision avoidance scenario, encodes the navigation status information of the ships as the attribute of the ship nodes; and uses the risk index between ships as the attribute of the edges between the corresponding ship nodes;

[0009] Step S2: construct Graph Neural Network Layer Graph neural network, which analyzes each ship node in the risk relationship graph of multiple ships at sea The sampling of neighboring ship nodes is carried out through the The graph neural network layer The results obtained by sampling the order neighborhood ship nodes are used to aggregate the navigation status features and embed the spatiotemporal status. The graph neural network finally outputs a one-dimensional feature vector for each ship node; ;

[0010] Step S3, calculating the risk index between ships based on the support vector regression method and the one-dimensional feature vector of each ship node;

[0011] Step S4: Use The activation function transforms the risk index between ships to obtain the collision risk probability distribution between ships.

[0012] Furthermore, step S1 specifically includes the following steps:

[0013] S11. Obtain the navigation status information of each ship. The navigation status information of the i-th ship includes the geographical location , Speed , heading angle , the distance between the current ship and the adjacent ship and vessel type ; are the horizontal and vertical coordinates of the geographical location of the ith ship respectively;

[0014] S12. Constructing ship nodes based on the geographical locations of each ship in the multi-ship collision avoidance scenario ; Encode the navigation status information of the i-th ship and obtain the navigation status information vector As a ship node Attributes, Represents the navigation status information vector corresponding to the i-th ship The dth component of The attributes of the ship nodes constitute the node attribute matrix ;

[0015] S13. The set of edges used to connect ship nodes is recorded as , for The mth edge in the graph, the risk index between ships is used as the attribute of the edge, and the set of edge attributes is , for The mth edge attribute in ; the ship nodes, and the edges connecting the ship nodes, constitute the risk relationship graph of multiple ships at sea;

[0016] Setting up the weighted adjacency matrix , the jth ship node in the risk relationship graph of multiple ships at sea and the i-th ship node When connected, Elements in ; and When not connected, hour.

[0017] Further, in step S2, each ship node in the risk relationship diagram of multiple ships at sea is The sampling of neighboring ship nodes is carried out through the The graph neural network layer The results obtained by sampling the order neighborhood ship nodes are used to aggregate the navigation status features and embed the spatiotemporal status. The graph neural network finally outputs a one-dimensional feature vector for each ship node, which specifically includes the following steps:

[0018] S21. For each ship node , randomly The sampling of neighboring ship nodes of order; ;

[0019] S22, navigation status feature aggregation: each ship node The neighborhood information and feature information of the neighborhood ship node are aggregated to the ship node The neighborhood ship aggregation feature vector superior:

[0020] ;

[0021] In the formula, Represents a ship node The index set of the neighborhood ship nodes, is the weighted adjacency matrix corresponding to the risk relationship graph of multiple ships at sea The elements in Ship Node The index of the neighboring ship node; Indicates that the jth neighboring ship node is in Aggregate feature vector in the graph neural network layer; initial aggregate feature vector of the jth neighborhood ship node , is the attribute of the j-th ship node; is the aggregator function;

[0022] S23, spatiotemporal state embedding update: through ship nodes In the Aggregate feature vectors in graph neural network layers as well as , for ship nodes In the Aggregate feature vectors in graph neural network layers To update:

[0023] ;

[0024] in For the The weight matrix of the graph neural network layer, is a nonlinear activation function, It is the CONCAT function;

[0025] S24, The graph neural network finally outputs a one-dimensional feature vector of each ship node, and the one-dimensional feature vector is used to represent the convolution features of the attributes of each ship node.

[0026] Furthermore, a residual connection layer and a nonlinearity are added after each graph neural network layer. Function layer, residual connection layer is used to help the gradient of the current graph neural network layer flow directly to the previous graph neural network layer; the nonlinear The function layer is used to maintain Internal stability of graph neural networks.

[0027] Furthermore, step S3 specifically includes:

[0028] Inter-vessel risk index Used to predict the collision risk between the i-th ship and the j-th ship, Connect the i-th ship node in the risk relationship graph of multiple ships at sea and Ship nodes The index of the edge; for Neighboring ship nodes;

[0029] The risk index between ships is calculated by using the support vector regression method: the i-th ship node The one-dimensional feature vector of and the jth ship node The one-dimensional feature vector of Perform feature splicing to obtain the spliced ​​feature vector :

[0030] ;

[0031] Represents feature concatenation operation;

[0032] The kernel function of the support vector regression method chooses the Gaussian kernel function :

[0033] ;

[0034] in The support vector regression method support vectors, is a nonlinear activation function;

[0035] The prediction function of the inter-vessel risk index is:

[0036] ;

[0037] in, is the element in the weighted adjacency matrix corresponding to the risk relationship graph of multiple ships at sea; It is with The Lagrange multipliers associated with the support vectors are used to calculate and similarities between; It is the bias term of the marine multi-ship collision risk model.

[0038] Furthermore, step S4 specifically includes:

[0039] exist Graph neural network after adding Probability layer, through The activation function transforms the risk index between ships to obtain the collision risk probability distribution between ships. :

[0040] ;

[0041] In the formula, is the risk index between ships, for Activation function.

[0042] Compared with the prior art, the beneficial technical effects of the present invention are:

[0043] 1. The unmanned ship collision risk assessment method provided by the present invention uses a self-connected topological structure to integrate the complex global encounter situation of multiple ships and construct a risk relationship graph structure of multiple ships at sea, so that the unmanned ship can not only understand the status of the ships directly adjacent to it, but also consider the potential impact of ships at a longer distance on it according to the order of the neighboring ships. By using a graph neural network to extract and quantify the navigation status information of multiple ships, the probability distribution of the possibility of different collision risk levels between adjacent ships can be directly obtained in the graph data, providing strong judgment support for the autonomous and safe navigation of ships in complex multi-ship scenarios in a more objective and efficient manner.

[0044] 2. The unmanned ship collision risk assessment method provided by the present invention quantifies the hidden navigation state characteristics between ships by constructing a complex graph network structure, focusing on the risk and collision probability between neighboring ships. It conforms to the attention habits and collision avoidance operation sequence of ship drivers in actual navigation environments, and is more conducive to the adaptation of scenarios where intelligent ships and manned ships are mixed.

[0045] 3. The unmanned ship collision risk assessment method provided by the present invention constructs a risk relationship graph structure of multiple ships at sea under complex scenarios. By using graph neural networks, it is possible to analyze the collision avoidance risks of multiple ships at different positions as they evolve over time, and can achieve faster convergence, thus solving the problem that traditional ship field theory cannot quantify multiple ships and their evolution.

[0046] 4. In complex multi-ship navigation collision avoidance scenarios, the collision avoidance operations between ships will continuously affect multiple ships in space over time. This can be understood as an operation to solve the original collision avoidance risk will introduce a new collision avoidance risk. The unmanned ship collision risk assessment method provided by the present invention can be used to The embedding update of each ship node in the graph neural network changes according to the changes in the neighboring ship relationship of the ship node. That is to say, even if it is the original selected ship, if a new ship collision avoidance connection relationship is suddenly introduced, then its corresponding embedding update will also change, and it can be convenient for network learning without iterating the entire network. This solves the problem of multi-order neighboring ship influence caused by multi-ship collision avoidance operations in complex multi-ship navigation collision avoidance scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a flow chart of the unmanned ship collision risk assessment method of the present invention.

[0048] Figure 2 A risk relationship diagram of multiple ships at sea with navigation status factors added provided in an embodiment of the present invention.

[0049] Figure 3 The embodiment of the present invention provides Forward output flow chart of a graph neural network.

[0050] Figure 4 The embodiment of the present invention provides Schematic diagram of the multi-layer structure of a neural network. DETAILED DESCRIPTION

[0051] A preferred embodiment of the present invention is described in detail below with reference to the accompanying drawings.

[0052] like Figure 1 As shown, the present invention constructs a risk relationship diagram of multiple ships at sea based on the geographical location and navigation status information of ships at sea, and uses Graph neural networks can effectively capture the complex relationships of geospatial data and effectively handle the spatiotemporal risk evolution scenarios of multiple ships due to collision avoidance or other operations, build a multi-ship collision risk model at sea, and estimate the probability of collision risk between ships.

[0053] This embodiment provides an unmanned ship collision risk assessment method based on a self-connected graph neural network, including steps S1 to S4.

[0054] Step S1: Construct a risk relationship diagram for multiple ships at sea: Construct ship nodes based on the geographical locations of each ship in the multi-ship collision avoidance scenario , , It represents the total number of ships in the multi-ship collision avoidance scenario, encodes the navigation status information of the ships as the attribute of the ship nodes, and uses the risk index between ships as the attribute of the edges between the corresponding ship nodes.

[0055] Step S1 specifically includes the following steps:

[0056] S11. Obtain the navigation status information of each ship. The navigation status information of the i-th ship includes the geographical location , Speed , heading angle , the distance between the current ship and the adjacent ship and vessel type ; are the horizontal and vertical coordinates of the geographical location of the ith ship respectively;

[0057] S12. Constructing ship nodes based on the geographical locations of each ship in the multi-ship collision avoidance scenario ; Encode the navigation status information of the i-th ship and obtain the navigation status information vector As a ship node Attributes, Represents the navigation status information vector corresponding to the i-th ship The dth component of The attributes of the ship nodes constitute the node attribute matrix .

[0058] S13. The set of edges used to connect ship nodes is recorded as , for The mth edge in the graph, the risk index between ships is used as the attribute of the edge, and the set of edge attributes is , for The mth edge attribute in the graph; the ship nodes, and the edges connecting the ship nodes, constitute the maritime multi-ship risk relationship graph.

[0059] S14. To represent the connectivity between ship nodes, a weighted adjacency matrix is ​​set , the jth ship node in the risk relationship graph of multiple ships at sea and the i-th ship node When connected, Elements in ; and When not connected, hour.

[0060] See also Figure 2 , Figure 2 The left side shows the randomly generated ship nodes that need to perform collision avoidance operations in the multi-ship collision avoidance scenario. There are 7 ships in total, namely The connection between ship nodes is an edge, and the risk index between ships is the attribute of the edge. Through the relationship between ship nodes and edges in the maritime multi-ship risk relationship graph, the node attribute matrix containing the multi-ship navigation status information vector and the weighted adjacency matrix representing the connectivity and the influence of neighboring ships can be extracted as Input of the graph neural network, the navigation status information vectors of the seven ships constitute the node attribute matrix , ; The weighted adjacency matrix is ​​recorded as , used to store connectivity information between ships.

[0061] Step S2: construct Graph Neural Network Layer Graph neural network, which analyzes each ship node in the risk relationship graph of multiple ships at sea The sampling of neighboring ship nodes is carried out through the The graph neural network layer The results obtained by sampling the order neighborhood ship nodes are used to aggregate the navigation status features and embed the spatiotemporal status. The graph neural network finally outputs a one-dimensional feature vector for each ship node; ;

[0062] Step S2 specifically includes the following steps:

[0063] S21. During sea voyage, the collision avoidance of a ship is mainly related to the surrounding ships. Therefore, a neighborhood ship sampling step is designed to sample the neighboring ships for each ship, that is, for each ship node , randomly The sampling of neighborhood ship nodes of order.

[0064] S22, navigation status feature aggregation: each ship node The neighborhood information and feature information of the neighborhood ship node are aggregated to the ship node The neighborhood ship aggregation feature vector superior:

[0065] ;

[0066] In the formula, Represents a ship node The index set of the neighborhood ship nodes, is the weighted adjacency matrix corresponding to the risk relationship graph of multiple ships at sea The elements in reflect the influence of the jth neighboring ship on the current ship, i.e., the ith ship; Ship Node The index of the neighboring ship node; Indicates that the jth neighboring ship node is in Aggregate feature vector in the graph neural network layer; initial aggregate feature vector of the jth neighborhood ship node , is the attribute of the jth ship node; is an aggregator function used to aggregate neighborhood ship information.

[0067] S23, spatiotemporal state embedding update: through The ship node is in Aggregate feature vectors in graph neural network layers as well as , for The ship node is in Aggregate feature vectors in graph neural network layers Updated to take into account both the historical information of the current ship and the information of neighboring ships:

[0068] ;

[0069] in For the The weight matrix of the graph neural network layer, is a nonlinear activation function, It is the CONCAT function.

[0070] S24, executing steps S21 to S23 for each ship node in the risk relationship diagram of multiple ships at sea, and executing a total of The navigation state feature aggregation and spatiotemporal state embedding update of the ship.

[0071] S25. After each graph neural network layer, a residual connection layer is added to help the gradient flow directly to the previous layer and a nonlinear SELU function layer is added to ensure the internal stability of the network. The graph neural network layer is trained to process the node attribute matrix and the weighted adjacency matrix , the output is a one-dimensional convolution feature matrix , the elements of the one-dimensional convolution feature matrix are one-dimensional feature vectors representing the convolution features of the attributes of the ship node.

[0072] Figure 4 Shown The multi-layer structure of the graph neural network adds a residual connection layer and a nonlinear SELU function layer after each graph neural network layer that performs navigation state feature aggregation and spatiotemporal state embedding update operations. The number of graph neural network layers is equal to the sampling order of the neighborhood ship nodes.

[0073] Figure 3 Shown The forward output process of the graph neural network includes sampling of neighboring ship nodes, aggregation of navigation status features, and embedding and updating of spatiotemporal states. By sampling the subgraph of the risk relationship graph of multiple ships at sea, the current ship node , set the sampling order of the neighborhood ship nodes to 2, that is , the subgraph obtained by sampling the first-order neighborhood ship nodes is The subgraph obtained by sampling the ship nodes in the second-order neighborhood is ; Multiple samples consisting of each target ship node and its neighboring ship nodes are formed, and then two rounds of navigation state feature aggregation and spatiotemporal state embedding update process are performed on the sampled samples to realize the update of the aggregated feature vector of the selected ship node.

[0074] Step S3: Calculate the risk index between ships based on the support vector regression method and the one-dimensional feature vector of each ship node.

[0075] S31. In the constructed risk relationship diagram of multiple ships at sea, the risk index between ships Used to predict the collision risk between the i-th ship and the j-th ship. Connect the i-th ship node in the risk relationship graph of multiple ships at sea and Ship nodes The index of the edge; for The neighboring ship nodes.

[0076] S32, using support vector regression method to calculate the risk index between ships: the i-th ship node The one-dimensional feature vector of and the jth ship node The one-dimensional feature vector of Perform feature splicing to obtain the spliced ​​feature vector :

[0077] ;

[0078] Represents feature concatenation operation;

[0079] The kernel function of the support vector regression method chooses the Gaussian kernel function :

[0080] ;

[0081] in The support vector regression method support vectors, is a nonlinear activation function;

[0082] The prediction function of the inter-vessel risk index is:

[0083] ;

[0084] in, is the element in the weighted adjacency matrix corresponding to the risk relationship graph of multiple ships at sea; It is with The Lagrange multipliers associated with the support vectors are used to calculate and similarities between; It is the bias term of the marine multi-ship collision risk model.

[0085] Step S4: Use The activation function transforms the risk index between ships to obtain the collision risk probability distribution between ships.

[0086] Step S4 specifically includes:

[0087] exist Figure nerve after increase Probability layer, through The activation function transforms the risk index between ships to obtain the collision risk probability distribution between ships:

[0088] ;

[0089] In the formula, is the risk index between ships.

[0090] like Figure 4 As shown in FIG. 1 , a softmax probability layer is set after the support vector regression layer to realize the conversion of the risk index between ships to the collision risk probability distribution between ships.

[0091] It is obvious to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the present invention can be implemented in other specific forms without departing from the spirit or essential features of the present invention. Therefore, from any point of view, the embodiments should be regarded as exemplary and non-limiting, and the scope of the present invention is defined by the appended claims rather than the above description, and it is intended that all changes falling within the meaning and scope of the equivalent elements of the claims are included in the present invention, and any reference numerals in the claims should not be regarded as limiting the claims involved.

[0092] In addition, it should be understood that although this specification is described in terms of implementation methods, not every implementation method contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

Claims

1. A method for assessing the collision risk of unmanned ships based on a self-connected graph neural network, characterized in that: By building a multi-ship collision risk model at sea, the collision risk probability between ships is estimated, which specifically includes the following steps: Step S1: Construct a risk relationship diagram for multiple ships at sea: Construct ship nodes based on the geographical locations of each ship in the multi-ship collision avoidance scenario , , Indicates the total number of ships in the multi-ship collision avoidance scenario, encodes the navigation status information of the ships as the attribute of the ship nodes; and uses the risk index between ships as the attribute of the edges between the corresponding ship nodes; Step S2: construct Graph Neural Network Layer Graph neural network, which analyzes each ship node in the risk relationship graph of multiple ships at sea The sampling of neighboring ship nodes is carried out through the The graph neural network layer The results obtained by sampling the order neighborhood ship nodes are used to aggregate the navigation status features and embed the spatiotemporal status. The graph neural network finally outputs a one-dimensional feature vector for each ship node; ; Step S3, calculating the risk index between ships based on the support vector regression method and the one-dimensional feature vector of each ship node; specifically comprising: Inter-vessel risk index Used to predict the collision risk between the i-th ship and the j-th ship, Connect the i-th ship node in the risk relationship graph of multiple ships at sea and Ship nodes The index of the edge; for Neighboring ship nodes; The risk index between ships is calculated by using the support vector regression method: the i-th ship node The one-dimensional feature vector of and the jth ship node The one-dimensional feature vector of Perform feature splicing to obtain the spliced ​​feature vector : ； Represents feature concatenation operation; The kernel function of the support vector regression method chooses the Gaussian kernel function : ； in The support vector regression method support vectors, is a nonlinear activation function; The prediction function of the inter-vessel risk index is: ； in, is the element in the weighted adjacency matrix corresponding to the risk relationship graph of multiple ships at sea; It is with The Lagrange multipliers associated with the support vectors are used to calculate and similarities between; It is the bias term of the marine multi-ship collision risk model; Step S4: Use The activation function transforms the risk index between ships to obtain the collision risk probability distribution between ships.

2. The unmanned ship collision risk assessment method based on self-connected graph neural network according to claim 1 is characterized in that: Step S1 specifically includes the following steps: S11. Obtain the navigation status information of each ship. The navigation status information of the i-th ship includes the geographical location , Speed , heading angle , the distance between the current ship and the adjacent ship and vessel type ; are the horizontal and vertical coordinates of the geographical location of the ith ship respectively; S12. Constructing ship nodes based on the geographical locations of each ship in the multi-ship collision avoidance scenario ; Encode the navigation status information of the i-th ship and obtain the navigation status information vector As a ship node Attributes, Represents the navigation status information vector corresponding to the i-th ship The dth component of The attributes of the ship nodes constitute the node attribute matrix ; S13. The set of edges used to connect ship nodes is recorded as , for The mth edge in the graph, the risk index between ships is used as the attribute of the edge, and the set of edge attributes is , for The mth edge attribute in ; the ship nodes, and the edges connecting the ship nodes, constitute the risk relationship graph of multiple ships at sea; Setting up the weighted adjacency matrix , the jth ship node in the risk relationship graph of multiple ships at sea and the i-th ship node When connected, Elements in ; and When not connected, hour.

3. The unmanned ship collision risk assessment method based on self-connected graph neural network according to claim 1 is characterized in that: In step S2, each ship node in the risk relationship diagram of multiple ships at sea is The sampling of neighboring ship nodes is carried out through the The graph neural network layer The results obtained by sampling the order neighborhood ship nodes are used to aggregate the navigation status features and embed the spatiotemporal status. The graph neural network finally outputs a one-dimensional feature vector for each ship node, which specifically includes the following steps: S21. For each ship node , randomly The sampling of neighboring ship nodes of order; ; S22, navigation status feature aggregation: each ship node The neighborhood information and feature information of the neighborhood ship node are aggregated to the ship node The neighborhood ship aggregation feature vector superior: ； In the formula, Represents a ship node The index set of the neighborhood ship nodes, is the weighted adjacency matrix corresponding to the risk relationship graph of multiple ships at sea The elements in Ship Node The index of the neighboring ship node; Indicates that the jth neighboring ship node is in Aggregate feature vector in the graph neural network layer; initial aggregate feature vector of the jth neighborhood ship node , is the attribute of the j-th ship node; is the aggregator function; S23, spatiotemporal state embedding update: through ship nodes In the Aggregate feature vectors in graph neural network layers as well as , for ship nodes In the Aggregate feature vectors in graph neural network layers To update: ； in For the The weight matrix of the graph neural network layer, is a nonlinear activation function, It is the CONCAT function; S24, The graph neural network finally outputs a one-dimensional feature vector of each ship node, and the one-dimensional feature vector is used to represent the convolution features of the attributes of each ship node.

4. The unmanned ship collision risk assessment method based on self-connected graph neural network according to claim 3 is characterized in that: Add a residual connection layer and a nonlinearity after each graph neural network layer. Function layer, residual connection layer is used to help the gradient of the current graph neural network layer flow directly to the previous graph neural network layer; the nonlinear The function layer is used to maintain Internal stability of graph neural networks.

5. The unmanned ship collision risk assessment method based on self-connected graph neural network according to claim 1 is characterized in that: Step S4 specifically includes: exist Graph neural network after adding Probability layer, through The activation function transforms the risk index between ships to obtain the collision risk probability distribution between ships. : ； In the formula, is the risk index between ships, for Activation function.

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