A method for measuring the resilience of a maritime network

Abstract

The application provides a shipping network resilience measurement method, comprising the following steps: S1, constructing a directed weighted network based on ship position data; S2, establishing a network node service capability level evaluation model by using an improved K-shell algorithm; S3, establishing a network resilience evaluation model based on the service capability values of various nodes and the flow values of the nodes; S4, attacking the network resilience evaluation model by using different attack strategies, simulating the resilience level changes of the network under different attack scenarios, and the resilience level changes are first test results; S5, inputting the resilience level changes and the network node speed changes into a network resilience dynamic simulation evaluation model, and outputting second test results; and the final results of the shipping network resilience measurement are the first test results and the second test results. The application can analyze the network resilience level under different disturbance propagation intensity and recovery intensity parameter combinations, and provides an important guarantee for the security and reliability of the network.

Description

Technical Field

[0001] This invention relates to the field of complex network technology, and more particularly to a method for measuring the resilience of maritime networks. Background Technology

[0002] As a major mode of international trade, shipping handles approximately 90% of the world's freight volume. This has led to a continuous increase in the size and complexity of shipping networks, placing higher demands on their reliability and stability. Resilience assessment has become crucial for ensuring the efficient operation of transportation systems.

[0003] Existing methods for assessing the resilience of maritime networks primarily analyze the resilience level of these networks by examining changes in complex network-related indicators such as network efficiency, network connectivity, node centrality, network density, clustering coefficient, and average shortest path. However, these network structure-based indicators remain insufficiently intuitive in reflecting network resilience levels and have limitations. Summary of the Invention

[0004] In view of this, the purpose of this invention is to propose a method for measuring the resilience of maritime networks, in order to address the technical problem that existing resilience measurement methods are not intuitive enough in reflecting network resilience and resilience levels. Based on AIS data, this invention constructs a maritime network covering ports and key maritime hub nodes, fully considering the traffic characteristics and service capabilities of network nodes, and proposes an innovative method for evaluating the resilience of maritime networks. This method expands the applicability of resilience evaluation models.

[0005] The technical means employed in this invention are as follows:

[0006] A method for measuring the resilience of maritime networks includes the following steps:

[0007] S1. Construct a directed weighted network based on ship position data;

[0008] S2. An improved K-shell algorithm is used to establish a network node service capability level evaluation model; the network node service capability level evaluation model is used to calculate the service capability values ​​of various types of nodes in the directed weighted network, and the traffic values ​​of each node in the directed weighted network are statistically analyzed.

[0009] S3. Establish a network resilience evaluation model based on the service capability values ​​and traffic values ​​of various types of nodes; input the service capability values ​​and traffic values ​​of various types of nodes into the network resilience evaluation model to calculate the network resilience level.

[0010] S4. Attack the network resilience evaluation model using different attack strategies, and statically simulate the changes in the network resilience level under different attack scenarios. The changes in resilience level are the first test results.

[0011] S5. Embed the resilience level value obtained in S4 into the SIRS model, set different disturbance propagation intensity and recovery intensity, establish a network resilience dynamic simulation evaluation model, input the resilience level change into the SIRS model to obtain the network node velocity change, input the resilience level change and the network node velocity change into the network resilience dynamic simulation evaluation model, and output the second test result; the final result of the maritime network resilience measurement is the first test result and the second test result.

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

[0013] S11. Based on the collected maritime vessel transportation location data, extract the nodes and edges of the transport vessels;

[0014] S12. Establish an adjacency matrix based on nodes and edges, and present the interaction relationships between nodes based on the adjacency matrix.

[0015] Furthermore, S2 specifically includes the following steps:

[0016] S21. Based on the network topology characteristics, extract the node traffic of each node in the directed weighted network, including supply nodes, demand nodes, and key hub nodes.

[0017] S22. By considering the connection strength of node edges, node weights, and node positions, an improved K-shell algorithm is used to calculate the service capacity value of network nodes. The improved K-shell algorithm calculation formula is as follows:

[0018]

[0019] In the formula, k s (j) represents the level of j after K-shell decomposition, N i Let W represent the set of neighboring nodes of node i. ij This represents the weight of the edge between nodes, where δ represents the weight coefficient.

[0020] e ij e represents the influence coefficient of the edges between nodes. ij The calculation formula is as follows:

[0021]

[0022] In the formula, N i N represents the neighboring nodes of node i. j N represents the neighboring nodes of node j. i ∩N j N represents the common neighbor nodes of node i and node j. i ∪N j This represents the sum of the neighboring nodes of node i and node j.

[0023] Furthermore, in S3:

[0024] The network resilience evaluation model is as follows:

[0025]

[0026] In the formula, q l Let F(l) represent the traffic of the demand node, and let F(l) represent the service capacity value of the demand node. min Q represents the minimum service capacity of the demand node. s Let F(s) represent the flow of the supply node, and C represent the service capacity value of the supply node. m F(m) represents the traffic of the critical hub node, and F(m) represents the service capacity value of the critical hub node.

[0027] Furthermore, S4 specifically includes the following steps:

[0028] S41. Network attack strategies are divided into random attack / recovery strategies and deliberate attack / recovery strategies;

[0029] S42. Under the random removal / restore policy, nodes are randomly removed / restored, using 50 Monte Carlo simulations as the basis for random removal / restore. For the deliberate attack / restore policy based on node service capabilities, nodes are deleted / restored in descending order of their values.

[0030] S421. The network resilience level is analyzed using random removal and removal methods based on the importance of node service capabilities. The calculation formula is as follows:

[0031]

[0032] In the formula, y0 represents the initial flow of the node, NF s NF represents the set of supply node failures. m NF represents the set of failures of critical hub nodes. l y represents the set of failed demand nodes. i This represents the traffic that occurs when a network node fails after being attacked; Q s '、C m '、q l ' represents the remaining traffic of the supply node, critical hub node, and demand node after a node has been attacked; F'(l), F'(l) min F'(s) and F'(m) represent the service capability values ​​of a node after it has been attacked; RI α This represents the network resilience value of a node after it has been disturbed;

[0033] S422. The network resilience level is analyzed using random recovery and node service capability-based recovery methods. The calculation formula is as follows:

[0034]

[0035] In the formula, NR s Represents the supply node recovery set, NR m Represents the critical hub node recovery set, NR l Indicates the set of nodes to be restored, y i 'Indicates the traffic restored by the network node; Q s '、C m '、q l ' represents the total recovery flow of supply nodes, critical hub nodes, and demand nodes, respectively; F(l), F(l) min F(s) and F(m) represent the service capacity values ​​of a node after it recovers; RI β This represents the network resilience value of a node in a recovery scenario.

[0036] Furthermore, S5 specifically includes the following steps:

[0037] S51. Input the directed weighted network into SIRS to generate network node change values;

[0038] S52. Apply the SIRS model to statistically analyze the failure and recovery of network nodes under different propagation rates and recovery rates at different times, calculate the failure and recovery ratios of network nodes, and use them as input parameters for the network resilience dynamic evolution model; the network resilience dynamic evolution model includes a network resilience loss quantification model and a network resilience recovery quantification model.

[0039] S53. Based on the SIRS model, analyze the changes in node state and establish a quantitative model of network resilience loss under different disturbance rates and recovery rates. The formula is as follows:

[0040]

[0041] In the formula, L(t) represents the network resilience loss, α represents the disturbance propagation strength, and RI(t) represents the network resilience loss. α λ represents the network resilience of nodes when they are disturbed, β represents the recovery strength, and λ represents the network resilience value. I The failure rate of network node states is represented by γ, which is used to ensure function convergence.

[0042] S54. Based on the SIRS model, analyze node state changes and establish a quantitative model for network resilience recovery under different disturbance rates and recovery rates. The formula is as follows:

[0043]

[0044] In the formula, R(t) represents the network resilience recovery amount, RI(t) β λ represents the network resilience value of a node under recovery scenarios, β represents the recovery strength, and λ represents the network resilience value of a node under recovery scenarios. R γ represents the recovery ratio of the network node state, and is used to ensure function convergence.

[0045] The present invention also provides a storage medium comprising a stored program, wherein, when the program is executed, any of the above-described maritime network resilience measurement methods are performed.

[0046] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes any of the above-described maritime network resilience measurement methods through the computer program.

[0047] Compared with the prior art, the present invention has the following advantages:

[0048] This invention targets maritime networks, establishing a complex network model that presents the interactions between network nodes, acquiring node traffic, establishing a node service capability evaluation model, and then proposing a network resilience evaluation model to analyze the network resilience level and analyze network resilience changes from a static simulation perspective. Furthermore, based on the SIRS model, a dynamic evolution model of network resilience is established. The advantage of the maritime network resilience measurement method proposed in this invention lies in its full consideration of network node characteristics, quantification of network resilience level, analysis of network resilience under different attack / recovery strategies from a static simulation perspective, and analysis of the dynamic evolution process of network resilience under different combinations of disturbance and recovery strength parameters from a dynamic simulation perspective.

[0049] The maritime network resilience measurement method provided by this invention enables quantitative assessment of network resilience, reflecting the network's transport capacity and efficiency during operation. The dynamic evolution model of network resilience provided in this invention's embodiments can analyze the network resilience level under different combinations of disturbance propagation and recovery strength parameters, providing crucial assurance for network security and reliability. Attached Figure Description

[0050] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0051] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0052] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0053] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0054] like Figure 1 As shown, the present invention provides a method for measuring the resilience of maritime networks, comprising the following steps:

[0055] S1. Construct a directed weighted network based on ship position data (AIS);

[0056] Specifically, a directed weighted complex network was constructed using AIS data on the operational positions of 399 liquefied natural gas vessels during 1,345 voyages collected between September 4, 2023 and September 21, 2024.

[0057] S11. Based on the collected maritime vessel transportation location data, extract the nodes and edges of the transport vessels;

[0058] S12. Establish an adjacency matrix based on nodes and edges, and present the interaction relationships between nodes based on the adjacency matrix. Preferably, the uCinet software is used to present the interaction relationships between nodes.

[0059] S2. An improved K-shell algorithm is used to establish a network node service capability level evaluation model. This model is then used to calculate the service capability values ​​of various types of nodes in the directed weighted network, thereby determining the importance of key nodes. The traffic values ​​of each node in the directed weighted network are also statistically analyzed.

[0060] S21. Based on the network topology characteristics, extract the node traffic of each node in the directed weighted network, including supply nodes, demand nodes, and key hub nodes.

[0061] S22. By considering the connection strength of node edges, node weights, and node positions, an improved K-shell algorithm is used to calculate the service capacity value of network nodes. The improved K-shell algorithm calculation formula is as follows:

[0062]

[0063] In the formula, k s (j) represents the level of j after K-shell decomposition, N i Let W represent the set of neighboring nodes of node i. ij This represents the weight of the edge between nodes, where δ represents the weight coefficient.

[0064] e ij e represents the influence coefficient of the edges between nodes. ij The calculation formula is as follows:

[0065]

[0066] In the formula, N i N represents the neighboring nodes of node i. j N represents the neighboring nodes of node j. i ∩N j N represents the common neighbor nodes of node i and node j. i ∪N j This represents the sum of the neighboring nodes of node i and node j.

[0067] S3. Establish a network resilience evaluation model based on the service capability values ​​and traffic values ​​of various types of nodes; input the service capability values ​​and traffic values ​​of various types of nodes into the network resilience evaluation model to calculate the network resilience level.

[0068] The network resilience evaluation model is as follows:

[0069]

[0070] In the formula, q l Let F(l) represent the traffic of the demand node, and let F(l) represent the service capacity value of the demand node. min Q represents the minimum service capacity of the demand node. s Let F(s) represent the flow of the supply node, and C represent the service capacity value of the supply node. m F(m) represents the traffic of the critical hub node, and F(m) represents the service capacity value of the critical hub node.

[0071] S4. Attack the network resilience evaluation model using different attack strategies, and statically simulate the changes in the network resilience level under different attack scenarios. The changes in resilience level are the first test results.

[0072] S4 specifically includes the following steps:

[0073] S41. Network attack strategies are divided into random attack / recovery strategies and deliberate attack / recovery strategies;

[0074] S42. Under the random removal / restore policy, nodes are randomly removed / restored, using 50 Monte Carlo simulations as the basis for random removal / restore. For the deliberate attack / restore policy based on node service capabilities, nodes are deleted / restored in descending order of their values.

[0075] S421. The network resilience level is analyzed using random removal and removal methods based on the importance of node service capabilities. The calculation formula is as follows:

[0076]

[0077] In the formula, y0 represents the initial flow of the node, NF s NF represents the set of supply node failures. m NF represents the set of failures of critical hub nodes. l y represents the set of failed demand nodes. i This represents the traffic that occurs when a network node fails after being attacked; Q s '、C m '、q l ' represents the remaining traffic of the supply node, critical hub node, and demand node after a node has been attacked; F'(l), F'(l) min F'(s) and F'(m) represent the service capability values ​​of a node after it has been attacked; RI α This represents the network resilience value of a node after it has been disturbed;

[0078] S422. The network resilience level is analyzed using random recovery and node service capability-based recovery methods. The calculation formula is as follows:

[0079]

[0080] In the formula, NR s Represents the supply node recovery set, NR m Represents the critical hub node recovery set, NR l Indicates the set of nodes to be restored, y i 'Indicates the traffic restored by the network node; Q s '、C m '、q l' represents the total recovery flow of supply nodes, critical hub nodes, and demand nodes, respectively; F(l), F(l) min F(s) and F(m) represent the service capacity values ​​of a node after it recovers; RI β This represents the network resilience value of a node in a recovery scenario.

[0081] S5. Input the resilience level value obtained in S4 into the Susceptible-Infected-Recovered-Susceptible (SIRS) model, set different disturbance propagation and recovery intensities, establish a dynamic simulation evaluation model for network resilience, input the resilience level change into the SIRS model to obtain the network node velocity change, input the resilience level change and the network node velocity change into the dynamic simulation evaluation model for network resilience, and output the second test result; the final result of the maritime network resilience measurement is the first test result and the second test result.

[0082] S51. Input the directed weighted network into SIRS to generate network node change values;

[0083] S52. Apply the SIRS model to statistically analyze the failure and recovery of network nodes under different propagation rates and recovery rates at different times, calculate the failure and recovery ratios of network nodes, and use them as input parameters for the network resilience dynamic evolution model; the network resilience dynamic evolution model includes a network resilience loss quantification model and a network resilience recovery quantification model.

[0084] S53. Based on the SIRS model, analyze the changes in node state and establish a quantitative model of network resilience loss under different disturbance rates and recovery rates. The formula is as follows:

[0085]

[0086] In the formula, L(t) represents the network resilience loss, α represents the disturbance propagation strength, and RI(t) represents the network resilience loss. α λ represents the network resilience of nodes when they are disturbed, β represents the recovery strength, and λ represents the network resilience value. I The failure rate of network node states is represented by γ, which is used to ensure function convergence.

[0087] S54. Based on the SIRS model, analyze node state changes and establish a quantitative model for network resilience recovery under different disturbance rates and recovery rates. The formula is as follows:

[0088]

[0089] In the formula, R(t) represents the network resilience recovery amount, RI(t) β λ represents the network resilience value of a node under recovery scenarios, β represents the recovery strength, and λ represents the network resilience value of a node under recovery scenarios.R γ represents the recovery ratio of the network node state, and is used to ensure function convergence.

[0090] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for measuring the resilience of maritime networks, characterized in that, Includes the following steps: S1. Construct a directed weighted network based on ship position data; S2. An improved K-shell algorithm is used to establish a network node service capability level evaluation model; the network node service capability level evaluation model is used to calculate the service capability values ​​of various types of nodes in the directed weighted network, and the traffic values ​​of each node in the directed weighted network are statistically analyzed. S3. Establish a network resilience evaluation model based on the service capability values ​​and traffic values ​​of various types of nodes; input the service capability values ​​and traffic values ​​of various types of nodes into the network resilience evaluation model to calculate the network resilience level. The network resilience evaluation model is as follows: In the formula, This represents the traffic at the demand node. This represents the service capacity value of the demand node. This represents the minimum service capacity of the demand node. This represents the flow of the supply node. This represents the service capacity value of the supply node. This represents the traffic flow at key hub nodes. This represents the service capacity value of a critical hub node; S4. Attack the network resilience evaluation model using different attack strategies, and statically simulate the changes in the network resilience level under different attack scenarios. The changes in resilience level are the first test results. S5. Embed the resilience level change obtained in S4 into the SIRS model, set different disturbance propagation intensity and recovery intensity, establish a network resilience dynamic simulation evaluation model, input the resilience level change into the SIRS model to obtain the network node velocity change, input the resilience level change and the network node velocity change into the network resilience dynamic simulation evaluation model, and output the second test result. The final results of the maritime network resilience measurement are the first test result and the second test result.

2. The method for measuring the resilience of maritime networks according to claim 1, characterized in that, S1 specifically includes the following steps: S11. Based on the collected maritime vessel transportation location data, extract the nodes and edges of the transport vessels; S12. Establish an adjacency matrix based on nodes and edges, and present the interaction relationships between nodes based on the adjacency matrix.

3. The method for measuring the resilience of maritime networks according to claim 1, characterized in that, S2 specifically includes the following steps: S21. Based on the network topology characteristics, extract the node traffic of each node in the directed weighted network, including supply nodes, demand nodes, and key hub nodes. S22. By considering the connection strength of node edges, node weights, and node positions, an improved K-shell algorithm is used to calculate the service capacity value of network nodes. The improved K-shell algorithm calculation formula is as follows: In the formula, Indicates the decomposition of the K-shell The level at which they are located Represents a node The set of neighboring nodes, This represents the weight of the edges between nodes. Indicates the weighting coefficient; This represents the influence coefficient of the edges between nodes. The calculation formula is as follows: In the formula, Represents a node The neighboring nodes, Represents a node The neighboring nodes, Represents a node and nodes Common neighbor nodes, Represents a node and nodes The sum of neighboring nodes.

4. The method for measuring the resilience of maritime networks according to claim 1, characterized in that, S4 specifically includes the following steps: S41. Network attack strategies are divided into random attack / recovery strategies and deliberate attack / recovery strategies; S42. Under the random removal / restore policy, nodes are randomly removed / restored, using 50 Monte Carlo simulations as the basis for random removal / restore. For the deliberate attack / restore policy based on node service capabilities, nodes are deleted / restored in descending order of their values. S421. The network resilience level is analyzed using random removal and removal methods based on the importance of node service capabilities. The calculation formula is as follows: In the formula, This represents the initial flow of the node. Represents the set of supply node failures. This represents the set of failed critical hub nodes. This represents the set of failed demand nodes. This represents the traffic that occurs when a network node becomes unusable after being attacked. , , This indicates the remaining traffic of supply nodes, critical hub nodes, and demand nodes after a node has been attacked. , , , This represents the service capability value of a node after it has been attacked. This represents the network resilience value of a node after it has been disturbed; S422. The network resilience level is analyzed using random recovery and node service capability-based recovery methods. The calculation formula is as follows: In the formula, Indicates the supply node recovery set, This represents the recovery set of key hub nodes. This indicates the set of nodes to be restored. This indicates the traffic recovered by the network node; , , These represent the total recovery flow of supply nodes, key hub nodes, and demand nodes, respectively. , , , This represents the node's service capacity value after the node recovers. This represents the network resilience value of a node in a recovery scenario.

5. The method for measuring the resilience of maritime networks according to claim 1, characterized in that, S5 specifically includes the following steps: S51. Input the directed weighted network into the SIRS model to generate network node change values; S52. Apply the SIRS model to statistically analyze the failure and recovery of network nodes under different propagation rates and recovery rates at different times, calculate the failure and recovery ratios of network nodes, and use them as input parameters for the dynamic simulation and evaluation model of network resilience; the dynamic simulation and evaluation model of network resilience includes a network resilience loss quantification model and a network resilience recovery quantification model. S53. Based on the SIRS model, analyze the changes in node state and establish a quantitative model of network resilience loss under different disturbance rates and recovery rates. The formula is as follows: In the formula, This indicates the amount of network resilience loss. Indicates the intensity of disturbance propagation. This represents the network resilience value of a node when it is disturbed. Indicates the strength of recovery. This indicates the failure rate of network nodes. Used to ensure function convergence; S54. Based on the SIRS model, analyze node state changes and establish a quantitative model for network resilience recovery under different disturbance rates and recovery rates. The formula is as follows: In the formula, This indicates the amount of network resilience recovery. This represents the network resilience value of a node under recovery scenarios. Indicates the strength of recovery. This indicates the recovery rate of the network node's state. Used to ensure function convergence.

6. A storage medium, characterized in that, The storage medium includes a stored program, wherein when the program is executed, it performs the maritime network resilience measurement method according to any one of claims 1 to 5.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, The processor executes the maritime network resilience measurement method according to any one of claims 1 to 5 through the computer program.

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