Method and system for defining initial load of double-layer dependent command and control network node
By introducing the interlayer coupling strength and intralayer node degree of node betweenness centrality, and combining the characteristics of the lower-layer network hierarchy, the initial load of nodes in the two-layer dependent command and control network is defined. This solves the problem that existing methods cannot take into account both intralayer node interaction and interlayer coupling, and improves the network's resilience and robustness.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- LINGNAN NORMAL UNIV
- Filing Date
- 2025-12-29
- Publication Date
- 2026-05-01
AI Technical Summary
Existing methods for defining the initial load of nodes cannot simultaneously reflect the importance of nodes in intra-layer interactions and inter-layer coupling relationships. In particular, in multi-network interdependent two-layer command and control networks, existing methods cannot take into account both the local importance of nodes in their own layer and their ability to transmit information across layers.
By introducing interlayer coupling strength based on node betweenness centrality and combining intralayer node degree and interlayer coupling strength, an initial load calculation model for upper-layer network nodes is constructed. In combination with the hierarchical characteristics of lower-layer networks, an initial load allocation strategy suitable for lower-layer nodes is designed to ensure that load allocation conforms to their organizational position in the command system and cross-layer dependency characteristics.
It significantly improves the resilience of the two-layer interdependent command and control network, effectively suppresses the propagation of cascading failures, and enhances the network's robustness and stability.
Smart Images
Figure CN121967201A_ABST
Abstract
Description
A method and system for defining the initial load of nodes in a two-layer interdependent command and control network Technical Field
[0001] This invention relates to the field of complex networks and information technology, and in particular to a method and system for defining the initial load of nodes in a two-layer interdependent command and control network, especially a method and system for defining the initial load of nodes in a two-layer interdependent command and control network that takes into account both intra-layer degree and inter-layer coupling strength. Background Technology
[0002] Command and control networks consist of various battlefield command and control entities at different levels with command, control, and coordination relationships, and their interrelationships. They are responsible for integrating, transmitting, and processing information, providing decision-makers with real-time and accurate intelligence support and command issuance capabilities. However, as network hierarchies become increasingly complex and the interdependence between different types of networks continues to strengthen, command and control networks are highly susceptible to cascading failures across levels and networks when attacked or experiencing localized malfunctions, seriously threatening the stability and reliability of the entire operational system.
[0003] While existing methods for defining initial node load can characterize node importance to some extent, they typically only consider local topological features within their own layer (such as node degree), making it difficult to accurately reflect their actual role in cross-layer information interaction. Furthermore, they lack comprehensive consideration of the structural characteristics of different network layers, resulting in insufficient balance between intra-layer interaction characteristics and inter-layer coupling relationships in two- or multi-layer dependent networks. To address these issues, this invention proposes a method for defining initial node load in two-layer dependent command and control networks that considers both intra-layer node degree and inter-layer coupling strength.
[0004] This method first introduces a metric for inter-layer coupling strength based on node betweenness centrality, drawing upon the definition of inter-layer coupling strength based on node degree, to more accurately characterize the tightness of information exchange between dependent nodes and their criticality in cross-layer dependencies. Second, it constructs an initial load calculation model for upper-layer network nodes by combining intra-layer node degree and inter-layer coupling strength, reflecting both the structural importance of nodes within their current layer and their functional importance in cross-layer coupling. Third, it defines the average coupling strength between a node and all its dependent nodes to quantify its overall cross-layer dependency level. Finally, considering the hierarchical organizational characteristics, intra-layer degree, and average inter-layer coupling strength of the lower-layer network, it designs an initial load allocation strategy suitable for lower-layer nodes, ensuring that load allocation aligns with their organizational position within the command structure and fully reflects their cross-layer dependency characteristics.
[0005] Based on this, simulation experiments were conducted to systematically evaluate the impact of different attack strategies, capacity adjustment parameters, overload tolerance parameters, and various initial load definition methods on the network's resilience. Experimental results show that the proposed method can significantly improve the resilience of two-layer dependent command and control networks, effectively suppress the propagation of cascading failures, and provide a practical and feasible technical path for enhancing the robustness of command and control networks.
[0006] Furthermore, on the one hand, there are differences in understanding among those skilled in the art; on the other hand, the applicant studied a large number of documents and patents when making this invention, but due to space limitations, not all details and contents were listed in detail. However, this does not mean that the present invention does not possess the features of these prior art. On the contrary, the present invention already possesses all the features of the prior art, and the applicant reserves the right to add relevant prior art to the background art. Summary of the Invention
[0007] The purpose of this invention is to provide a method and system for defining the initial load of nodes in a two-layer interdependent command and control network. This addresses the problem that existing methods for defining initial load of nodes struggle to simultaneously reflect the importance of nodes in intra-layer interactions and inter-layer coupling relationships, especially in multi-network interdependent two-layer command and control networks. Existing methods cannot balance the local importance of a node within its own layer with its cross-layer information transmission capabilities. The definition method proposed in this invention considers both the intra-layer degree of a node and the inter-layer coupling strength based on node betweenness centrality, and combines the hierarchical characteristics of the lower-layer network with the average coupling strength of nodes. This achieves an accurate characterization of the initial load of nodes, thereby reducing the risk of cascading failures when the network is attacked and improving the network's resilience and robustness.
[0008] To address the shortcomings of existing technologies, this invention provides a method for defining the initial load of nodes in a two-layer interdependent command and control network from a first aspect. The method includes: defining the interlayer coupling strength based on node betweenness centrality; defining the initial load of upper-layer network nodes based on a nonlinear weighted sum of interlayer coupling strength and intra-layer node degree; defining the initial load of lower-layer network nodes based on the characteristics of the lower-layer network hierarchy and the definition method of the initial load of upper-layer network nodes; and integrating the above steps to construct a complete algorithm flow for defining the initial load of nodes in a two-layer interdependent command and control network.
[0009] The initial load of a node consists of the node’s intra-layer importance and inter-layer coupling strength. While reflecting the importance of nodes, it also takes into account the hierarchical characteristics of the command and control network and the significant feature of cross-layer information interaction. This not only improves the accuracy and robustness of the model, but also more comprehensively reflects the complexity and diversity of real networks.
[0010] According to a preferred embodiment, the step of defining the initial load of upper-layer network nodes based on a nonlinear weighted sum of interlayer coupling strength and intralayer node degree includes: defining interlayer coupling strength based on node betweenness centrality, and determining the initial load of each node in the upper-layer network based on the interlayer coupling strength based on node betweenness centrality.
[0011] This technical approach, by defining inter-layer coupling strength based on node betweenness centrality and combining it with intra-layer node degree to determine the initial load on upper-layer network nodes, more accurately reflects the key role of nodes in the network structure. Betweenness centrality measures a node's mediating ability in information transmission, while intra-layer node degree reflects the density of connections within the node's current layer. By combining these two, not only can nodes playing a crucial role in cross-layer information interaction be identified, but their influence within the current layer can also be considered during initial load allocation, thus achieving a reasonable assessment of node load. This method helps improve the adaptability of command and control networks to complex tasks and dynamic environments, while providing a more reliable basis for subsequent load allocation and state determination, enhancing the stability and efficiency of the entire system.
[0012] According to a preferred embodiment, the formula for calculating the interlayer coupling strength based on node betweenness centrality is as follows: ; ;in, For upper-layer network nodes, For lower-level network nodes; For nodes betweenness, For nodes betweenness; For nodes and The number of shortest paths between them. For nodes With nodes The nodes passed through in the shortest path between The quantity.
[0013] This technical step, by introducing a formula for calculating inter-layer coupling strength based on node betweenness centrality, enables a more scientific quantification of the interaction relationships between upper-layer and lower-layer network nodes. Betweenness centrality reflects the criticality of a node in the information transmission process; this formula, by multiplying the betweenness values of node i and node j, further emphasizes their synergistic role in cross-layer information flow. This calculation method considers not only the importance of a node within its own layer (intra-layer degree) but also its influence across the cross-layer structure, thus more comprehensively defining the initial load of upper-layer network nodes. In this way, nodes undertaking critical tasks in the command and control network can be identified more accurately, providing a reliable basis for subsequent load allocation and state determination, improving the accuracy and robustness of the entire network model, and enhancing its adaptability to complex network structures.
[0014] According to a preferred embodiment, the initial load of each node in the upper-layer network is calculated using the following formula: Upper-layer network nodes; among them, The degree of a node within a layer reflects its importance within that layer. For nodes Its dependent nodes The interlayer coupling strength between them and These are the adjustment parameters for intra-layer node density and inter-layer coupling strength, respectively.
[0015] This technique, by introducing a weighted calculation formula for intra-layer degree and inter-layer coupling strength, allows for a more flexible definition of the initial load on upper-layer network nodes. The parameters α and β can be adjusted according to actual needs, making the model more adaptable to different scenarios. This method balances the importance of nodes within their own layer with the impact of cross-layer interactions, improving the rationality of load distribution and enhancing the network model's ability to characterize complex structures, thereby improving the overall system stability and operational efficiency.
[0016] According to a preferred embodiment, the step of defining the initial load of a lower-level network node based on the characteristics of the lower-level network hierarchy and the definition method of the initial load of the upper-level network node includes: calculating the average coupling strength between the node and its dependent nodes; and calculating the initial load of the lower-level network node.
[0017] This technique, by combining the characteristics of lower-layer network hierarchy with the initial load definition of upper-layer nodes, enables a more reasonable calculation of the initial load of lower-layer nodes. Utilizing the average coupling strength between dependent nodes helps reflect the actual burden on lower-layer nodes in cross-layer interactions, improving the fairness and accuracy of load distribution. This approach enhances a comprehensive understanding of the network structure and improves the system's adaptability and operational efficiency in complex environments.
[0018] According to a preferred embodiment, in the step of defining the initial load of a lower-layer network node based on the characteristics of the lower-layer network hierarchy and the initial load definition method of the upper-layer network node, the formula for calculating the average coupling strength between a node and its dependent nodes is as follows: ;in, Dependent nodes and The interlayer coupling strength between layers.
[0019] This technical step, by calculating the average coupling strength between a node and its dependent nodes, more comprehensively reflects the overall burden of lower-level nodes in cross-layer interactions. Combined with the upper-layer load definition method, it helps improve the rationality and consistency of load distribution to lower-level nodes, enhances the adaptability to the network hierarchy, and thus improves the stability and operating efficiency of the overall system.
[0020] According to a preferred embodiment, in the step of defining the initial load of a lower-layer network node based on the characteristics of the lower-layer network hierarchy and the initial load definition method of the upper-layer network node, the formula for calculating the initial load of the lower-layer network node is as follows: Lower-level nodes; among which, This represents the total number of levels in the lower-level network. For the accusation node Level; This represents the degree of nodes within the layer.
[0021] This technique, by introducing a weighted combination of the number of levels and the degree within each level, combined with the average inter-level coupling strength, more accurately reflects the status and load characteristics of lower-level nodes in different levels. This method enhances the adaptability to network hierarchical structures, making load allocation more consistent with the organizational relationships and information interaction needs of actual command and control systems, thereby improving the accuracy of the model and the stability and efficiency of system operation.
[0022] This invention provides a system for defining the initial load of nodes in a two-layer interdependent command and control network from a second aspect. The system includes a processor, which comprises a coupling strength calculation module, an upper-layer load definition module, and a lower-layer load definition module. The coupling strength calculation module is used to define the inter-layer coupling strength based on the betweenness centrality of nodes. The upper-layer load definition module is used to define the initial load of upper-layer network nodes based on a nonlinear weighted sum of inter-layer coupling strength and intra-layer node degree. The lower-layer load definition module is used to define the initial load of lower-layer network nodes based on the hierarchical characteristics of the lower-layer network and the definition method of the initial load of upper-layer network nodes. Integrating the above steps, a complete algorithm flow for defining the initial load of nodes in a two-layer interdependent command and control network is constructed.
[0023] According to a preferred embodiment, the formula for calculating the initial load of each node in the upper-layer network by the upper-layer load definition module is as follows: Upper-layer network nodes; among them, The degree of a node within a layer reflects its importance within that layer. For nodes Its dependent nodes The interlayer coupling strength between them and These are the adjustment parameters for intra-layer node density and inter-layer coupling strength, respectively.
[0024] According to a preferred embodiment, the lower-layer load definition module is configured to: calculate the average coupling strength between a node and its dependent nodes; and calculate the initial load of the lower-layer network nodes.
[0025] The advantages of the system of this invention compared to the prior art are as follows: First, drawing on the degree-based definition of inter-layer coupling strength, a method for calculating inter-layer coupling strength based on node betweenness centrality is proposed to measure the tightness of information exchange between dependent nodes; second, combining intra-layer node degree and inter-layer coupling strength, a method for defining the initial load of upper-layer network nodes is proposed, so that node load can simultaneously reflect intra-layer importance and cross-layer coupling importance; third, a mean coupling strength is defined to measure the average coupling strength between a node and all dependent nodes; finally, combining the hierarchical characteristics of the lower-layer network, intra-layer node degree, and average inter-layer node coupling strength, a method for defining the initial load of lower-layer network nodes is proposed to ensure that load distribution conforms to organizational hierarchy and cross-layer dependency characteristics.
[0026] This invention fully considers the local importance of nodes, cross-layer coupling relationships, network hierarchical characteristics, and information transmission capabilities in a two-layer interdependent command and control network. It effectively reduces the risk of cascading failures, enhances the network's resilience, and provides important theoretical support and engineering reference value for improving the robustness of command and control networks. Attached Figure Description
[0027] Figure 1 is a comparison of network node survival rates under different values of adjustment parameters α and β during a deliberate attack provided by the present invention; Figure 2 is a comparison of network node survival rates under different values of adjustment parameters α and β during a random attack provided by the present invention; Figure 3 is a comparison of network node survival rates under different initial load definition methods during a deliberate attack provided by the present invention; Figure 4 is a comparison of network node survival rates under different initial load definition methods during a random attack provided by the present invention; Figure 5 is a comparison of network load retention rates under different initial load definition methods during a deliberate attack provided by the present invention; Figure 6 is a comparison of network load retention rates under different initial load definition methods during a random attack provided by the present invention. Detailed Implementation
[0028] The following is a detailed explanation with reference to the accompanying drawings.
[0029] Example 1: This invention provides a system for defining the initial load of nodes in a two-layer interdependent command and control network. The system includes a processor. The processor is configured to execute a method for defining the initial load of nodes in a two-layer interdependent command and control network. The processor includes a coupling strength calculation module, an upper-layer load definition module, and a lower-layer load definition module.
[0030] The initial load definition method for the nodes of the two-layer interdependent command and control network of the present invention is as follows.
[0031] S100: Defines the interlayer coupling strength based on node betweenness centrality, and defines the initial load of upper-layer network nodes based on the nonlinear weighted sum of interlayer coupling strength and intralayer node degree.
[0032] S110: The coupling strength calculation module is used to define the interlayer coupling strength based on node betweenness centrality.
[0033] To characterize the importance of inter-layer dependencies, we draw upon and integrate the degree-based definition of inter-layer coupling strength from the above steps to define inter-layer coupling strength based on node betweenness centrality. Node betweenness centrality is a core indicator in network analysis for measuring the importance of nodes, representing the degree to which a node acts as a bridge or intermediary in the network.
[0034] Preferably, the formula for calculating the interlayer coupling strength based on node betweenness centrality is: ; ;in, For upper-layer network nodes, For lower-level network nodes; For nodes betweenness, For nodes betweenness; For nodes and The number of shortest paths between them. For nodes With nodes The nodes passed through in the shortest path between The quantity. and Multiplication is used to measure their importance as key bridge nodes in the network.
[0035] S120: The upper-layer load definition module defines the initial load of nodes in the upper-layer network based on a nonlinear weighted sum of inter-layer coupling strength and intra-layer node degree. Preferably, the initial load of each node in the upper-layer network is determined based on the inter-layer coupling strength of node betweenness centrality.
[0036] Preferably, the initial load of each node in the upper-layer network is calculated using the following formula: Upper-layer network nodes; among them, The degree of a node within a layer is the degree of node i within its own layer, reflecting the importance of the node within that layer. For nodes Its dependent nodes The interlayer coupling strength between them and These are the adjustment parameters for intra-layer node density and inter-layer coupling strength, respectively.
[0037] S200: The lower-layer load definition module defines the initial load of lower-layer network nodes based on the characteristics of the lower-layer network hierarchy and the initial load definition method of the upper-layer network nodes.
[0038] S210: Calculate the average coupling strength between a node and its dependent nodes.
[0039] The formula for calculating the average coupling strength between a node and its dependent nodes is: ;in, Dependent nodes With nodes The interlayer coupling strength between layers.
[0040] S220: Calculate the initial load of the lower-level network nodes.
[0041] The formula for calculating the initial load of lower-level network nodes is: Lower-level nodes; among which, This represents the total number of levels in the lower-level network. For the accusation node Level; This represents the degree of nodes within the layer.
[0042] S300: Integrates the functions of the above modules to construct a complete algorithm flow for defining the initial load of nodes in a two-layer interdependent command and control network.
[0043] S400: Nonlinear capacity model for computing nodes.
[0044] The formula for the nonlinear capacity model of a computing node is: .
[0045] In the above formula, and This is a capacity adjustment parameter used to measure the maximum capacity of a node. This indicates the initial load of the corresponding layer network node, including the initial load of the upper layer node and the lower layer node.
[0046] S500: Sets up a node status discrimination mechanism and divides nodes into three states: normal, overloaded, or failed, and determines the load distribution strategy based on the remaining capacity.
[0047] S510: Set up a node status determination mechanism.
[0048] The formula for calculating the node state is: .
[0049] In the above formula, rand is a random number between 0 and 1; Let be the failure probability of node i; This is a nonlinear capacity model for nodes.
[0050] S520: Calculate the load distribution strategy for overloaded and failed nodes.
[0051] The formula for calculating the load distribution strategy for overloaded and failed nodes is as follows: .
[0052] In the above formula, Indicates an overloaded or failed node. The neighboring nodes, the overloaded nodes have loads to be allocated. The load to be assigned to the failed node is .
[0053] The initial load of a node consists of the node’s intra-layer importance and inter-layer coupling strength. While reflecting the importance of nodes, it also takes into account the hierarchical characteristics of the command and control network and the significant feature of cross-layer information interaction. This not only improves the accuracy and robustness of the model, but also more comprehensively reflects the complexity and diversity of real networks.
[0054] To verify the rationality and applicability of the proposed method, a simulation comparative analysis was designed to evaluate the network's resilience from three aspects: different attack strategies, different inter-layer and intra-layer weight adjustment parameters, and different initial load definition methods.
[0055] Experimental Subjects and Initial Settings: An abstract air defense command and control network was used, with 420 upper-level nodes and 160 lower-level nodes. Two strategies were employed: deliberate attack and random attack. To reduce the impact of randomness, each simulation experiment was run independently 50 times, and the average value was used as the statistical result.
[0056] (1) Simulation analysis of adjusting parameters α and β.
[0057] To verify the applicability and performance of the node initial load definition method proposed in this invention under different intra-layer and inter-layer weight parameter values, a comparative analysis of node survival rates under different combinations of α and β was conducted. Parameters α and β are used to adjust the degree of influence of intra-layer and inter-layer weighting on the nonlinearity of the initial load, respectively.
[0058] Figure 1 shows the distribution of network node survival rates under a deliberate attack with different values of adjustment parameters α and β. Figure 2 shows the distribution of network node survival rates under a random attack with different values of adjustment parameters α and β. In Figures 1 and 2, the X-axis represents the dimensionless adjustment parameter α for intra-layer load weight, used to characterize the influence of intra-layer connection strength on initial load distribution; the Y-axis represents the dimensionless adjustment parameter β for inter-layer coupling weight, reflecting the weight ratio of cross-layer connections in the initial load distribution; and the Z-axis represents the node survival rate F (ranging from 0 to 1). In Figures 1 and 2, the color bars from blue to red represent survival rates from low to high.
[0059] As shown in Figure 1, under a deliberate attack, when the adjustment parameter α of the load weight within the layer increases from 0.5 to 0.8, the node survival rate increases from approximately 0.49 (0.486207) to approximately 0.67 (0.67069), indicating that moderately increasing the load weight within the layer can significantly enhance the carrying capacity of critical nodes and the resilience of the network. When the adjustment parameter α of the load weight within the layer exceeds 0.8, the increase in survival rate tends to level off, indicating that the marginal benefit of continuing to increase the weight within the layer is limited.
[0060] As shown in Figure 2, the overall survival rate is low under random attack scenarios, with a peak value of approximately 0.43 (0.433621). The peak value corresponds to adjustment parameters α=0.8 and β=0.7. The surface is relatively flat overall, indicating that the load impact caused by random attacks is more evenly distributed in the network. The system is less sensitive to changes in the adjustment parameters α of intra-layer load weights and β of inter-layer coupling weights. A moderate adjustment parameter β of inter-layer coupling weights helps to disperse the impact between layers and suppress the further propagation of local failures.
[0061] Combining Figures 1 and 2, we can see that under deliberate attacks (Figure 1), the peak survival rate is higher and the surface fluctuations are more pronounced, indicating a stronger reliance on the protection of critical nodes. Under random attacks (Figure 2), the surface shifts downwards overall and the differences decrease, reflecting a more even impact of random damage on the overall structure. Based on the combined performance of the two attack modes, α=0.8 and β=0.7 can be considered as a superior parameter combination, which can maintain high node survival rate and network robustness simultaneously under both deliberate and random failure scenarios.
[0062] Therefore, considering the results of both attack strategies, the initial load adjustment parameters were selected as α=0.8 and β=0.7 in subsequent simulations to ensure that the model has good resilience under both deliberate and random attacks.
[0063] (2) Simulation analysis of initial load definitions for different nodes.
[0064] ① Node survival rate analysis under different initial load definition methods.
[0065] To verify the rationality and applicability of the proposed initial load definition method, the node survival rates of seven initial load definition methods (1-the method of this invention (considering hierarchy), 2-node degree method, 3-node betweenness method, 4-node strength and neighbor degree method, 5-the method of this invention (not considering hierarchy), 6-degree-neighbor betweenness weighted method, 7-degree-neighbor degree weighted method) were compared and analyzed under deliberate and random attacks, as shown in Figures 3 and 4.
[0066] Figure 3 is a schematic diagram comparing the network node survival rates under different initial load definition methods of the present invention under deliberate attacks. Figure 4 is a schematic diagram comparing the network node survival rates under different initial load definition methods of the present invention under random attacks. The horizontal and vertical axes and the numbers of the seven methods in Figure 4 have the same meanings as in Figure 3, and the colors are only used to distinguish the methods.
[0067] In Figures 3 and 4, the horizontal axis represents the node deletion ratio p (range 0-1), and the vertical axis represents the node survival rate F (range 0-1). The different colored curves correspond to seven initial load definition methods: 1-the method of this invention (considering hierarchy), 2-node degree, 3-node betweenness, 4-node strength and neighbor degree (node strength refers to the sum of the weights of the edges connected to the node, and neighbor degree refers to the degree of the nodes directly connected to the node; this method defines the initial load by combining the two), 5-the method of this invention (not considering hierarchy), 6-degree-neighbor betweenness weighted and 7-degree-neighbor degree weighted; the colors are only used to distinguish the methods.
[0068] As shown in Figure 3, when p>0.23, the performance differences of each method are obvious: the node degree method and the node betweenness method (2, 3) collapse first, and the method that relies only on a single-layer static structure has the worst resilience. This is because degree and betweenness mainly reflect the static structural characteristics of nodes and fail to fully reflect cross-layer dependencies, which makes the network more prone to cascading failures when key nodes are removed. Methods 4, 6 and 7, which are based on node and neighbor attributes, are slightly improved when p>0.32, but because they do not explicitly consider inter-layer dependencies, some dependent nodes lack sufficient load-bearing capacity, and cross-layer dependency failures are more serious, causing the fault to spread rapidly in the two-layer network. Although the improved method (5) that does not consider the hierarchy has improved, the load is still not balanced enough. Overall, the load definition method (1) that considers the hierarchy in this invention always maintains the highest survival rate under the same deletion ratio, indicating that the introduction of hierarchical coupling and betweenness adjustment can significantly enhance the carrying capacity of key nodes and network stability.
[0069] As shown in Figure 4, the survival rate of each method under random attack shows a smooth downward trend with increasing p, and no sudden collapse occurs, indicating that the structural damage is relatively uniform. At this time, the method (1) considering the hierarchy of the present invention still maintains the highest survival rate curve, especially in the p>0.5 interval, which is more obvious, verifying that the method also has good robustness in non-directional random perturbation scenarios.
[0070] Combining Figures 3 and 4, it can be seen that under deliberate attacks (Figure 3), the survival rate curve drops sharply and collapses are concentrated, indicating that the network is extremely sensitive to high-load, high-between-number critical nodes, and system performance is mainly constrained by hierarchical coupling and load distribution strategies. Under random attacks (Figure 4), the curve is relatively flat, with damage spreading gradually, relying more on network-wide load balancing and cross-layer redundancy configuration. Therefore, the initial load definition method proposed in this invention, which considers both hierarchical structure and betweenness adjustment, can effectively improve the overall robustness of two-layer interdependent command and control networks under both targeted destruction and random disturbance scenarios.
[0071] ② Load retention rate analysis of different initial load definition methods. Further, taking the above seven initial load definition methods as the object, the network load retention rate under deliberate attack and random attack was compared and analyzed, as shown in Figures 5 and 6.
[0072] Figure 5 is a schematic diagram comparing the network load retention rates of different initial load definition methods under intentional attacks according to the present invention. Figure 6 is a schematic diagram comparing the network load retention rates of different initial load definition methods under random attacks according to the present invention.
[0073] In Figures 5 and 6, the horizontal axis represents the node deletion ratio p (ranging from 0 to 1), and the vertical axis represents the network load retention rate R (ranging from 0 to 1), used to measure the effective load capacity maintained by the network after an attack. Different colored curves correspond to seven initial load definition methods: 1-The method of this invention (considering hierarchy), 2-Node degree, 3-Node betweenness, 4-Node strength and neighbor degree, 5-The method of this invention (not considering hierarchy), 6-Degree-Neighbor betweenness weighted, 7-Degree-Neighbor degree weighted. The colors are only used to distinguish the methods.
[0074] As shown in Figure 5, when p>0.25, the load retention rates of each method begin to diverge significantly: the node degree method (2) falls into the collapse range first, with the weakest resilience; the reason is that it only considers the local importance of nodes and fails to accurately define the initial load of some key edge nodes, resulting in poor performance. The node betweenness method (3) is slightly improved by introducing global information; methods 4, 6 and 7 take into account both local and some global features, and their stability is better than the former two, but they still cannot accurately reflect the role of key nodes between layers; although method 5 considers a certain degree of inter-layer influence, it ignores hierarchical dependence, and the load distribution is still unbalanced.
[0075] In contrast, the load definition method (1) of the present invention, which considers the hierarchy, maintains the highest load retention rate throughout the entire attack process, indicating that it has stronger robustness in complex deliberate attack scenarios and can effectively suppress cascading failures and delay system mutations.
[0076] As shown in Figure 6, under random attack conditions, the load retention rate of each method shows a smooth downward trend with increasing p, without any drastic changes. The hierarchical method (1) of this invention still maintains the best performance, and can maintain a high load level even when p>0.6, indicating that it also has good adaptability under random failure scenarios. This is mainly due to the fact that this method comprehensively characterizes the importance of nodes at different levels, within layers and between layers, so that the load is more evenly distributed in the network, thereby enhancing redundancy and shock resistance.
[0077] Combining Figures 5 and 6, it can be seen that under deliberate attacks (Figure 5), the curve declines more sharply, and the failure of critical nodes easily induces centralized system mutations. The system robustness is mainly affected by the load distribution strategy and hierarchical dependency structure. Under random attacks (Figure 6), the curve changes more gently, the network damage is more dispersed, and the degradation process exhibits gradual characteristics, relying more on overall load balancing and cross-layer redundancy design. Therefore, the results of both types of attacks jointly demonstrate that the initial load definition method considering hierarchical dependencies proposed in this invention can maintain a high load retention rate and system stability under different attack modes, effectively suppress cascading failures, and significantly improve the resilience of two-layer interdependent command and control networks.
[0078] As described above, the proposed method for defining the initial load of nodes in a two-layer interdependent command and control network, through design simulation and comparative analysis, evaluates the network's resilience from three aspects: different attack strategies, different inter-layer and intra-layer weight adjustment parameters, and different initial load definition methods. It demonstrates high levels of performance in both node survival rate and load retention rate, effectively improving network robustness while fully satisfying the hierarchical and cross-layer dependency characteristics of the command and control network. This indicates that the method of this invention has significant advantages in suppressing cascading failures and provides valuable reference for command and control network modeling and resilience optimization.
[0079] It should be noted that the specific embodiments described above are exemplary. Those skilled in the art can devise various solutions inspired by the disclosure of this invention, and these solutions all fall within the scope of this invention and its protection. Those skilled in the art should understand that this specification and its accompanying drawings are illustrative and not intended to limit the scope of the claims. The scope of protection of this invention is defined by the claims and their equivalents. This specification contains multiple inventive concepts; terms such as "preferredly," "according to a preferred embodiment," or "optionally" indicate that the corresponding paragraph discloses an independent concept. The applicant reserves the right to file divisional applications based on each inventive concept.
Claims
1. A method for defining the initial load of nodes in a two-layer interdependent command and control network, characterized in that, The method includes: defining the initial load of upper-layer network nodes based on the nonlinear weighted sum of inter-layer coupling strength and intra-layer node degree; defining the initial load of lower-layer network nodes based on the characteristics of lower-layer network hierarchy and the definition method of the initial load of upper-layer network nodes; and integrating the above steps to construct a complete algorithm flow for defining the initial load of nodes in a two-layer interdependent command and control network.
2. The method according to claim 1, characterized in that, The steps for defining the initial load of upper-layer network nodes based on the nonlinear weighted sum of inter-layer coupling strength and intra-layer node degree include: defining the inter-layer coupling strength based on node betweenness centrality, and determining the initial load of each node in the upper-layer network based on the inter-layer coupling strength based on node betweenness centrality.
3. The method according to claim 1 or 2, characterized in that, The formula for calculating the interlayer coupling strength based on node betweenness centrality is: ； ;in, For upper-layer network nodes, For lower-level network nodes; For nodes betweenness, For nodes betweenness; For nodes and The number of shortest paths between them. For nodes With nodes The nodes passed through in the shortest path between The quantity.
4. The method according to any one of claims 1 to 3, characterized in that, The formula for calculating the initial load of each node in the upper-layer network is: Upper-layer network nodes; among them, The degree of a node within a layer reflects its importance within that layer. For nodes Its dependent nodes The interlayer coupling strength between them and These are the adjustment parameters for intra-layer node density and inter-layer coupling strength, respectively.
5. The method according to any one of claims 1 to 4, characterized in that, The steps for defining the initial load of a lower-level network node based on the characteristics of the lower-level network hierarchy and the definition method of the initial load of the upper-level network node include: calculating the average coupling strength between the node and its dependent nodes; and calculating the initial load of the lower-level network node.
6. The method according to any one of claims 1 to 5, characterized in that, In the step of defining the initial load of a lower-layer network node based on the characteristics of the lower-layer network hierarchy and the definition method of the initial load of the upper-layer network node, the formula for calculating the average coupling strength between the node and its dependent nodes is as follows: ;in, Dependent nodes and The interlayer coupling strength between layers.
7. The method according to any one of claims 1 to 6, characterized in that, In the step of defining the initial load of lower-layer network nodes based on the characteristics of the lower-layer network hierarchy and the definition method of the initial load of upper-layer network nodes, the formula for calculating the initial load of lower-layer network nodes is as follows: Lower-level nodes; among which, This represents the total number of levels in the lower-level network. For the accusation node Level; This represents the degree of nodes within the layer.
8. A two-layer interdependent command and control network node initial load definition system, characterized in that, The system includes a processor, which comprises: a coupling strength calculation module, defining the interlayer coupling strength based on node betweenness centrality; an upper-layer load definition module, defining the initial load of upper-layer network nodes based on a nonlinear weighted sum of interlayer coupling strength and intra-layer node degree; and a lower-layer load definition module, defining the initial load of lower-layer network nodes based on the lower-layer network hierarchy characteristics and the upper-layer network node initial load definition method; integrating the above steps to construct a complete algorithm flow for defining the initial load of nodes in a two-layer interdependent command and control network.
9. The system according to claim 8, characterized in that, The formula for calculating the initial load of each node in the upper-layer network by the upper-layer load definition module is as follows: Upper-layer network nodes; among them, The degree of a node within a layer reflects its importance within that layer. For nodes Its dependent nodes The interlayer coupling strength between them and These are the adjustment parameters for intra-layer node density and inter-layer coupling strength, respectively.
10. The system according to claim 8 or 9, characterized in that, The lower-layer load definition module is configured to: calculate the average coupling strength between a node and its dependent nodes; and calculate the initial load of the lower-layer network nodes.