A group-dependent dual-layer heterogeneous dependency combat network recovery method under overload conditions

Abstract

The present invention relates to the technical field of combat network recovery methods, and in particular to a method for recovering a group-dependent combat network under overload conditions. The method comprises: establishing a combat physical network and a functional network, and based on these establishing a two-layer heterogeneous-dependent combat network model; establishing a cascading failure model for the combat network; recovering functional network nodes according to functional network recovery rules; recording the combat network failure and recovery process as the nth stage physical network failure, the nth stage functional network failure, and the nth stage two-layer heterogeneous-dependent combat network recovery; generating combat network simulation model data based on model network parameters; and attacking and recovering the combat network. The combat network modeling method described in the present invention fully considers the heterogeneity and directionality of the combat system, and simultaneously discusses the cascading failure scenario under overload conditions. This practical combat network modeling and recovery method addresses the combat system's anti-destruction issues in real combat situations and improves the combat system's robustness.

Description

Technical Field

[0001] The present invention relates to the technical field of double-layer heterogeneous dependency combat network recovery methods, and in particular to a group-dependent double-layer heterogeneous dependency combat network recovery method under overload conditions. Background Art

[0002] With the continuous development of information technology, networked and system-based combat modes have become the main form of future warfare. Efficient, interconnected, interoperable combat system networks can provide a strong guarantee for preparing for and winning wars, but they also become the main targets of attack during system confrontations, resulting in serious consequences such as "destroyed points, broken links, and paralyzed networks." Therefore, how to improve the robustness of combat system networks when attacked, adapt to damage through elasticity, and restore combat capabilities as much as possible has become a key and difficult issue in current research.

[0003] The development of interdisciplinary disciplines such as network science and complex systems theory has provided powerful tools for combat system modeling. By transforming complex and ever-changing systems into structural models through networking, it facilitates the study of combat system robustness. Generally speaking, improving network robustness can be categorized into prevention, optimization, and recovery strategies. However, the first two approaches have limitations in practice, such as the inability to prevent catastrophic events and excessive costs. Therefore, developing reasonable strategies to recover networks is increasingly becoming an option for improving robustness.

[0004] Chinese Patent Publication No. CN113568782A discloses a method, electronic device, and storage medium for dynamic recovery of a combat equipment system. The method comprises: obtaining attribute information of multiple equipment entities, constructing a hypernetwork model of the combat equipment system based on the attribute information; obtaining multiple candidate recovery strategies, and dynamically simulating the combat equipment system using the hypernetwork model based on the multiple candidate recovery strategies; calculating the combat effectiveness of the combat equipment system to determine the initial stabilization time, anti-interference stabilization time, and recovery stabilization time; calculating the system resilience value of the combat equipment system based on the combat effectiveness corresponding to the initial stabilization time, anti-interference stabilization time, and recovery stabilization time; determining multiple system resilience values ​​corresponding to the multiple candidate recovery strategies, selecting the candidate recovery strategy with the greatest system resilience as the optimal recovery strategy; and dynamically recovering the combat equipment system based on the optimal recovery strategy.

[0005] It can be seen that the invention has the following problems: when modeling the two-layer heterogeneous dependent combat network, the heterogeneity and directionality of the combat system and the cascading failure scenario under overload conditions are not fully considered, and the two-layer heterogeneous dependent combat network modeling and recovery method is inconsistent with reality. Summary of the Invention

[0006] To this end, the present invention provides a group-dependent double-layer heterogeneous dependency combat network recovery method under overload conditions, so as to overcome the problems in the prior art that the heterogeneity and directionality of the combat system and the cascading failure scenarios under overload conditions are not fully considered when modeling the double-layer heterogeneous dependency combat network, and the double-layer heterogeneous dependency combat network modeling and recovery methods are not consistent with reality.

[0007] To achieve the above objectives, the present invention provides a method for recovering a group-dependent, double-layer heterogeneous-dependency combat network under overload conditions, comprising:

[0008] Step S1: for the combat system, the combat units and combat relationships in the system are converted into nodes and edges, and combat physical networks G are established based on the nodes and edges. W and functional network G G , and based on the combat physical network G W and functional network G G Establish a two-layer heterogeneous dependent combat network model;

[0009] Step S2: establishing a cascading failure model for the dual-layer heterogeneous dependency combat network and defining attack patterns and robustness indicators for the dual-layer heterogeneous dependency combat network; wherein the cascading failure model includes conditional group dependency failure and cascading failure considering overload;

[0010] Step S3: sorting the boundary nodes of the physical network using a comprehensive importance index, selecting the top-ranked boundary nodes for restoration according to the physical network restoration ratio, and then restoring each node in the functional network according to the functional network restoration rule; wherein the importance index is the weighted sum of the normalized external degree and internal degree of the physical network nodes; the restoration rule of the functional network is to first restore the functional network nodes and dependent edges that have a dependency relationship with the preferred physical network boundary node, and then restore the original connection relationship between these nodes and the largest connected subgraph of the functional network. After restoring some nodes, the load of the restored nodes in the physical network and the functional network is 0.

[0011] Step S4: Based on step S3, the failure and recovery process of the dual-layer heterogeneous dependency combat network is recorded as the nth stage physical network failure, the nth stage functional network failure, the nth stage dual-layer heterogeneous dependency combat network recovery, and the nth stage functional network recovery, where n is a natural number.

[0012] Step S5, generating simulation model data for a two-layer heterogeneous dependent combat network according to different model network parameters; wherein the model network has different parameters, for the ER model network, the parameters are the connection probability between different nodes and the connection probability of the inter-layer network, for the Goh network parameters are the power exponent β = 2.3, the average degree <k>=6 and the connection probability of the inter-layer network; for the NW network, the parameters are K, the connection probability between different nodes and the connection probability of the inter-layer network;

[0013] Step S6, attacking the double-layer heterogeneous dependent combat network, and repeating steps S2 to S4 until the double-layer heterogeneous dependent combat network no longer fails or fails completely.

[0014] Furthermore, in step S1, the physical network is a simple undirected graph in which nodes include communication load and capacity, wherein each node of the physical network is divided into a node C having a communication function;

[0015] The functional network is a heterogeneous directed network whose nodes include business categories, business loads, and capacities, and is used to transfer intelligence information and command commands. The nodes of the functional network are divided into intelligence acquisition nodes O, intelligence processing nodes P, command decision nodes D, and combat response nodes A.

[0016] The double-layer heterogeneous dependency network G is a coupling network formed by the functional network being unidirectionally dependent on the physical network. The dependency network is represented by G D .

[0017] Furthermore, in step S2, the cascading failure model includes conditional group dependency failure and cascading failure considering overload; the asymmetric dependency failure rule is that for a dependent network node, when it is not in the largest connected subgraph or all dependent nodes fail, the node fails; for a dependent network node, when it is not in the largest connected subgraph, the node fails; the conditional group dependency failure rule introduces tolerance τ on the basis of the above, and when the failure ratio of the dependent node is greater than τ, the dependent node fails; wherein, the failure ratio refers to the failure ratio of the dependent nodes when a node group of the functional network depends on the physical network.

[0018] Furthermore, the load-considered cascading failure model includes initial load, node capacity, failure state determination, and capacity redistribution method, wherein the initial load L i (0) is the exponential power of the product of the node degree and the adjacent node degree, set Among them, κ is the adjustment parameter used to control the distribution of the initial load of the node, Γ i For node v i The subscript set of neighbor nodes;

[0019] For the node capacity Ci, set C i =L i (0)+λ·L(0) γ ,i=1,2,…N, where λ and γ are load regulation parameters, set λ>0, γ>0;

[0020] For the node failure state judgment, when the node load exceeds the capacity, the node is in a critical state of overload within the preset tolerance range μ, and the node failure probability is P i (t), set

[0021]

[0022] The load redistribution method considers the importance of both static and dynamic nodes. The allocation ratio of static nodes is set up The dynamic node allocation ratio is set up The comprehensive distribution ratio is Π ij ,set up Where η and 1-η are weights when the distribution ratio is mixed. Set η = 0.5, and update the load of the neighboring nodes of the node according to the following formula:

[0023] Furthermore, in step S2, the attack mode is to attack the physical network according to the corresponding attack ratio f, so that fN w The attack methods include random attacks and intentional attacks that prioritize node degrees.

[0024] Furthermore, in step S2, the robustness evaluation index is expressed as a comprehensive index of the number of combat kill links and the maximum connected subgraph size, and the combat kill link types include standard kill chain, kill chain with collaborative detection, kill chain with information interaction, kill chain with collaborative command and control, kill chain with collaborative detection and information interaction, kill chain with collaborative detection and command and kill chain with collaborative detection, command and control and information interaction.

[0025] Furthermore, the flow of information within the functional network depends on the communication nodes of the physical network. The functional network completely relies on the communication nodes of the physical network to calculate the number of kill chains. The functional network calculates the overall reachability matrix based on Boolean power to obtain the reachability matrix from node 0 to A.

[0026] set up

[0027] Taking the standard kill chain as an example, let The number of combat loops is obtained as:

[0028] S OPDA (G)=tr{[S oP ∧(S oC ×S CC ×S CP )]

[0029] ×[S PD ∧(S PC ×S CC ×S CD )]

[0030] ×[S DA ∧(S DC ×S CC ×S CA )]×S AO }

[0031] Among them, S OC and S CP etc. is the reachability matrix between functional nodes and communication nodes, ∧ is the Boolean sum operation, and the calculation method of the number of other kill chains is the same as the above method. Then the number of 7 kill chains is expressed as

[0032] The maximum connected subgraph size is expressed as the sum of the maximum connected subgraph sizes of the physical network and the functional network. The initial size S of the maximum connected subgraph size is set to huge (G) = N W +N G ;

[0033] For the unattacked dual-layer heterogeneous dependent combat network G, the number of kill chains targeting the dual-layer heterogeneous dependent combat network is recorded as S links (G), the maximum connected subgraph size for this two-layer heterogeneous dependent combat network is recorded as S huge (G), the network after the attack on the double-layer heterogeneous dependent combat network is recorded as G′, and the corresponding indicators are recorded as S links (G′) and S huge (G′), and then the robustness index R of the two-layer heterogeneous dependent combat network is obtained, setting

[0034]

[0035] Among them, θ is the scaling parameter of the number of kill chains, and 1-θ is the scaling parameter of the maximum connected subgraph size, and the default value of both is 0.5.

[0036] Furthermore, in step S3, the boundary node of the physical network is a failed node whose distance to its maximum connected subgraph is 1; when performing node recovery on the physical network, nodes are selected from the boundary node set according to the sum of the structural importance index and the capacity index, specifically:

[0037]

[0038] in, is the weighted sum of the normalized external and internal degrees, set

[0039]

[0040] Among them, k max is the maximum degree, is the normalized node capacity, set

[0041]

[0042] Among them, C max For the maximum capacity;

[0043] For the functional network, recovery is performed based on the recovery of the physical network nodes. The recovery rules are: first, restore the functional network nodes and dependent edges that have dependencies with the preferred physical network boundary nodes, and then restore the original connection relationships between these nodes and the maximum connected subgraph of the functional network. After some nodes of the physical network and the functional network are restored, the load of the restored nodes is 0.

[0044] Furthermore, in step S4, the specific process of the double-layer heterogeneous dependency combat network cyclic recovery includes:

[0045] S41, the physical network failure process at stage n,

[0046] (41a) If the physical network node v i If an overload occurs, the node v i Failure;

[0047] (41b) All nodes that are out of the maximum connected subgraph are invalid;

[0048] (41c) The load of the newly failed node is updated by spreading to the surrounding areas;

[0049] S42, the failure process of the functional network in the nth stage,

[0050] (42a) If the functional network node v i If the proportion of failed nodes in the nth stage of the physical network exceeds the limit τ, then node v i Failure;

[0051] (42b) If the functional network node v i If an overload occurs, the node v i Failure;

[0052] (42c) All nodes that are out of the maximum connected subgraph are invalid;

[0053] (42d) The load of the newly failed node spreads to the surrounding areas, triggering a new round of overload and disconnected cascading failures until there are no new failed nodes in the functional network at this stage;

[0054] S3, the nth stage double-layer heterogeneous dependent combat network recovery process,

[0055] (8) Find all failed nodes and restore them according to the rules described above. The recovery ratio of the physical network is α. All the edges of the restored nodes that originally existed with the current normal nodes are fully restored.

[0056] (9) Repeat steps (1) to (8) until the network reaches a stable state with no new failed nodes or a complete collapse state.

[0057] Furthermore, in step S5, the process of generating the dual-layer heterogeneous dependency combat network simulation model data includes:

[0058] According to the ER random network, Goh scale-free network and NW small-world network model algorithms, the corresponding network parameters are set and a model network of a specified scale is generated, which serves as the physical network and functional network subnets respectively. The dependencies between subnets are connected in a random dependency manner, and a fixed dependency scale is set.

[0059] Compared with the existing technology, the beneficial effect of the present invention lies in that the method of the present invention is rigorous in theory and has clear physical meaning. The established double-layer heterogeneous group-dependent and double-layer heterogeneous dependent combat network has a high degree of authenticity in depicting the combat system in real scenarios, and the proposed robustness indicators have practical significance.

[0060] Furthermore, the present invention enriches the applicable scenarios of the double-layer heterogeneous dependent combat network recovery method under cascading failure conditions from the perspective of physical layer and functional layer overload failure.

[0061] Furthermore, the method of the present invention has the characteristics of fast onset and few iterations in the recovery effect of a double-layer heterogeneous dependent combat network, and the recovered network has better combat capability. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 This is a flow chart of the method for recovering a group-dependent dual-layer heterogeneous-dependent combat network under an overload situation according to the present invention;

[0063] Figure 2 This is a schematic diagram of information flow in a functional network according to an embodiment of the present invention;

[0064] Figure 3 This is a schematic diagram of a two-layer heterogeneous dependency combat network according to an embodiment of the present invention;

[0065] Figure 4 This is a schematic diagram of a boundary node according to an embodiment of the present invention;

[0066] Figure 5 This is a schematic diagram of the recovery process of a dual-layer heterogeneous dependency combat network according to an embodiment of the present invention;

[0067] Figure 6 This is a comparison chart of the recovery effects of four methods under different subnet structures according to an embodiment of the present invention;

[0068] Figure 7 This is a comparison chart of the number of iterations of the four methods under different subnet structures according to the embodiment of the present invention;

[0069] Figure 8 This is a comparison chart of the recovery effects of four methods under different tolerances in an embodiment of the present invention;

[0070] Figure 9 This is a comparison chart of the recovery effects of four methods under different load parameters according to an embodiment of the present invention;

[0071] Figure 10 This is a comparison chart of the recovery effects of four methods under different capacity parameters in an embodiment of the present invention;

[0072] Figure 11 This is a comparison chart of the recovery effects of four methods under different capacity parameters in an embodiment of the present invention;

[0073] Figure 12 This is a comparison chart of the recovery effects of four methods under different parameters in the embodiment of the present invention;

[0074] Figure 13 This is a comparison chart of the recovery effects of four methods at different recovery ratios according to an embodiment of the present invention;

[0075] Figure 14 This is a comparison diagram of the average degree of the network after recovery using different methods according to the embodiment of the present invention;

[0076] Figure 15 This is a load comparison diagram after recovery using different methods according to an embodiment of the present invention. DETAILED DESCRIPTION

[0077] In order to make the objects and advantages of the present invention more clearly understood, the present invention is further described below in conjunction with embodiments; it should be understood that the specific embodiments described herein are merely used to explain the present invention and are not intended to limit the present invention.

[0078] The preferred embodiments of the present invention are described below with reference to the accompanying drawings. It should be understood by those skilled in the art that these embodiments are only used to explain the technical principles of the present invention and are not intended to limit the scope of protection of the present invention.

[0079] It should be noted that, in the description of the present invention, terms such as "up", "down", "left", "right", "inside", and "outside" indicating directions or positional relationships are based on the directions or positional relationships shown in the accompanying drawings. This is merely for the convenience of description and does not indicate or imply that the device or element must have a specific orientation, be constructed and operated in a specific orientation. Therefore, it should not be understood as a limitation on the present invention.

[0080] Furthermore, it should be noted that, in the description of the present invention, unless otherwise expressly specified or limited, the terms "mounted," "connected," and "connected" should be understood broadly. For example, they may refer to fixed, detachable, or integral connections; mechanical or electrical connections; direct or indirect connections through an intermediary; and internal communication between two components. Those skilled in the art will understand the specific meanings of these terms in the present invention based on specific circumstances.

[0081] See also Figure 1 As shown, it is a flow chart of the group-dependent double-layer heterogeneous dependency combat network recovery method under overload conditions of the present invention, including:

[0082] Step S1: for the combat system, the combat units and combat relationships in the system are converted into nodes and edges, and combat physical networks G are established based on the nodes and edges. W and functional network G G , and based on the combat physical network G W and functional network G G Establish a two-layer heterogeneous dependent combat network model;

[0083] Step S2: establishing a cascading failure model for the dual-layer heterogeneous dependency combat network and defining attack patterns and robustness indicators for the dual-layer heterogeneous dependency combat network; wherein the cascading failure model includes conditional group dependency failure and cascading failure considering overload;

[0084] Step S3: sorting the boundary nodes of the physical network using a comprehensive importance index, selecting the top-ranked boundary nodes for restoration according to the physical network restoration ratio, and then restoring each node in the functional network according to the functional network restoration rule; wherein the importance index is the weighted sum of the normalized external degree and internal degree of the physical network nodes; the restoration rule of the functional network is to first restore the functional network nodes and dependent edges that have a dependency relationship with the preferred physical network boundary node, and then restore the original connection relationship between these nodes and the largest connected subgraph of the functional network. After restoring some nodes, the load of the restored nodes in the physical network and the functional network is 0.

[0085] Step S4: Based on step S3, the failure and recovery process of the dual-layer heterogeneous dependency combat network is recorded as the nth stage physical network failure, the nth stage functional network failure, the nth stage dual-layer heterogeneous dependency combat network recovery, and the nth stage functional network recovery, where n is a natural number.

[0086] Step S5, generating simulation model data for a two-layer heterogeneous dependent combat network according to different model network parameters; wherein the model network has different parameters, for the ER model network, the parameters are the connection probability between different nodes and the connection probability of the inter-layer network, for the Goh network parameters are the power exponent β = 2.3, the average degree <k>=6 and the connection probability of the inter-layer network; for the NW network, the parameters are K, the connection probability between different nodes and the connection probability of the inter-layer network;

[0087] Step S6, attacking the double-layer heterogeneous dependent combat network, and repeating steps S2 to S4 until the double-layer heterogeneous dependent combat network no longer fails or fails completely.

[0088] See also Figure 2 and Figure 3 As shown, Figure 2 This is a schematic diagram of information flow in a functional network according to an embodiment of the present invention. Figure 3 This is a schematic diagram of a two-layer heterogeneous dependent combat network according to an embodiment of the present invention. In step S1, the physical network is a simple undirected graph in which nodes include communication load and capacity, wherein each node in the physical network is divided into a node C with communication function;

[0089] The functional network is a heterogeneous directed network whose nodes include business categories, business loads, and capacities, and is used to transfer intelligence information and command commands. The nodes of the functional network are divided into intelligence acquisition nodes O, intelligence processing nodes P, command decision nodes D, and combat response nodes A.

[0090] The double-layer heterogeneous dependency network G is a coupling network formed by the functional network being unidirectionally dependent on the physical network. The dependency network is represented by G D .

[0091] Specifically, in step S2, the cascading failure model includes conditional group dependency failure and cascading failure considering overload; the asymmetric dependency failure rule is that for a dependent network node, when it is not in the largest connected subgraph or all dependent nodes fail, the node fails; for a dependent network node, when it is not in the largest connected subgraph, the node fails; the conditional group dependency failure rule introduces tolerance τ on the basis of the above, and when the failure ratio of the dependent node is greater than τ, the dependent node fails; wherein, the failure ratio refers to the failure ratio of the dependent node when a node group of the functional network depends on the physical network.

[0092] Specifically, the load-considered cascading failure model includes initial load, node capacity, failure state determination, and capacity redistribution method, wherein the initial load L i (0) is the exponential power of the product of the node degree and the adjacent node degree, set Among them, κ is the adjustment parameter used to control the distribution of the initial load of the node, Γ i For node v i The subscript set of neighbor nodes;

[0093] For the node capacity Ci, set C i =L i (0)+λ·L(0) γ ,i=1,2,…N, where λ and γ are load regulation parameters, set λ>0, γ>0;

[0094] For the node failure state judgment, when the node load exceeds the capacity, the node is in a critical state of overload within the preset tolerance range μ, and the node failure probability is P i (t), set

[0095]

[0096] The load redistribution method considers the importance of both static and dynamic nodes. The allocation ratio of static nodes is set up The dynamic node allocation ratio is set up The comprehensive distribution ratio is Π ij ,set up Where η and 1-η are weights when the distribution ratio is mixed. Set η = 0.5, and update the load of the neighboring nodes of the node according to the following formula:

[0097] Specifically, in step S2, the attack method is to attack the physical network according to the corresponding attack ratio f, so that fN w The attack methods include random attacks and intentional attacks that prioritize node degrees.

[0098] Specifically, in step S2, the robustness evaluation index is expressed as a comprehensive index of the number of combat kill links and the maximum connected subgraph size. The combat kill link types include standard kill chain, kill chain with collaborative detection, kill chain with information interaction, kill chain with collaborative command and control, kill chain with collaborative detection and information interaction, kill chain with collaborative detection and command, and kill chain with collaborative detection, command and information interaction.

[0099] Specifically, the flow of information in the functional network depends on the communication nodes of the physical network. The functional network completely relies on the communication nodes of the physical network to calculate the number of kill chains. The functional network calculates the overall reachability matrix based on Boolean power to obtain the reachability matrix from node 0 to A.

[0100] set up

[0101] Taking the standard kill chain as an example, let The number of combat loops is obtained as:

[0102] S OPDA (G)=tr{[S oP ∧(S oC ×S CC ×S CP )]

[0103] ×[S PD ∧(S PC ×S CC ×S CD )]

[0104] ×[S DA ∧(S DC ×S CC ×S CA )]×S AO }

[0105] Among them, S oC and S CP etc. is the reachability matrix between functional nodes and communication nodes, ∧ is the Boolean sum operation, and the calculation method of the number of other kill chains is the same as the above method. Then the number of 7 kill chains is expressed as

[0106] The maximum connected subgraph size is expressed as the sum of the maximum connected subgraph sizes of the physical network and the functional network. The initial size S of the maximum connected subgraph size is set to huge (G) = N W +N G ;

[0107] For the unattacked dual-layer heterogeneous dependent combat network G, the number of kill chains targeting the dual-layer heterogeneous dependent combat network is recorded as S links (G), the maximum connected subgraph size for this two-layer heterogeneous dependent combat network is recorded as S huge (G), the network after the attack on the double-layer heterogeneous dependent combat network is recorded as G′, and the corresponding indicators are recorded as S links (G′) and S huge (G′), and then the robustness index R of the two-layer heterogeneous dependent combat network is obtained, setting

[0108]

[0109] Among them, θ is the scaling parameter of the number of kill chains, and 1-θ is the scaling parameter of the maximum connected subgraph size, and the default value of both is 0.5.

[0110] Specifically, in step S3, the boundary node of the physical network is a failed node whose distance to its maximum connected subgraph is 1; when recovering the nodes of the physical network, the boundary nodes are selected from the set of boundary nodes according to the sum of the structural importance index and the capacity index, specifically:

[0111]

[0112] in, is the weighted sum of the normalized external and internal degrees, set

[0113]

[0114] Among them, k max is the maximum degree, is the normalized node capacity, set

[0115]

[0116] Among them, C max For the maximum capacity;

[0117] For the functional network, recovery is performed based on the recovery of the physical network nodes. The recovery rules are: first, restore the functional network nodes and dependent edges that have dependencies with the preferred physical network boundary nodes, and then restore the original connection relationships between these nodes and the maximum connected subgraph of the functional network. After some nodes of the physical network and the functional network are restored, the load of the restored nodes is 0.

[0118] See also Figure 4 As shown, it is a schematic diagram of a boundary node in an embodiment of the present invention. In step S4, the specific process of cyclic recovery of the double-layer heterogeneous dependent combat network includes:

[0119] S41, the physical network failure process at stage n,

[0120] (41a) If the physical network node v i If an overload occurs, the node v i Failure;

[0121] (41b) All nodes that are out of the maximum connected subgraph are invalid;

[0122] (41c) The load of the newly failed node is updated by spreading to the surrounding areas;

[0123] S42, the failure process of the functional network in the nth stage,

[0124] (42a) If the functional network node v i If the proportion of failed nodes in the nth stage of the physical network exceeds the limit τ, then node v i Failure;

[0125] (42b) If the functional network node v i If an overload occurs, the node v i Failure;

[0126] (42c) All nodes that are out of the maximum connected subgraph are invalid;

[0127] (42d) The load of the newly failed node spreads to the surrounding areas, triggering a new round of overload and disconnected cascading failures until there are no new failed nodes in the functional network at this stage;

[0128] S3, the nth stage double-layer heterogeneous dependent combat network recovery process,

[0129] (8) Find all failed nodes and restore them according to the rules described above. The recovery ratio of the physical network is α. All the edges of the restored nodes that originally existed with the current normal nodes are fully restored.

[0130] (9) Repeat steps (1) to (8) until the network reaches a stable state with no new failed nodes or a complete collapse state.

[0131] Specifically, in step S5, the process of generating the dual-layer heterogeneous dependent combat network simulation model data includes:

[0132] According to the ER random network, Goh scale-free network and NW small-world network model algorithms, the corresponding network parameters are set and a model network of a specified scale is generated, which serves as the physical network and functional network subnets respectively. The dependencies between subnets are connected in a random dependency manner, and a fixed dependency scale is set.

[0133] Compared with the existing technology, the beneficial effect of the present invention lies in that the method of the present invention is rigorous in theory and has clear physical meaning. The established double-layer heterogeneous group-dependent and double-layer heterogeneous dependent combat network has a high degree of authenticity in depicting the combat system in real scenarios, and the proposed robustness indicators have practical significance.

[0134] Furthermore, the present invention enriches the applicable scenarios of the double-layer heterogeneous dependent combat network recovery method under cascading failure conditions from the perspective of physical layer and functional layer overload failure.

[0135] Furthermore, the method of the present invention has the characteristics of fast onset and few iterations in the recovery effect of a double-layer heterogeneous dependent combat network, and the recovered network has better combat capability.

[0136] Specifically, the working principle of the present invention includes: first, based on reality, a two-layer heterogeneous group-dependent combat network model is established, including a physical network, a functional network and a dependent network; second, the cascade failure process of dependency failure and overload failure and the attack mode are designed, and robustness indicators with combat significance are proposed; then, a cyclic process of physical network failure, functional network failure and recovery of the two-layer heterogeneous dependent combat network is designed, and a boundary node priority recovery (PRCI) method based on node capacity and importance is proposed.

[0137] Specifically, the parameter settings involved in this embodiment are:

[0138] The functional network size is N G =150, where N O =50, N P =40, N D =30, N A =30, the physical network is N W = 100. Set the parameters of the model network. The connection between different nodes in the ER network is f OO =0.02, f OP =0.03, f PP =0.05,f PD =0.03, f DD =0.05,f DA =0.03, f AA =0.03, f CC =0.07; Goh network power index β = 2.3, average degree <k>=6, different functional types are connected according to the parameters of ER network; NW network K = 2, the connection probability between functional nodes of the same type is f OO =0.08, f PP =0.1,f DD =0.14,f AA =0.14,f CC = 0.05, and the connection probabilities between different types are the same as those for the ER network. The functional network randomly depends on the physical network in a unidirectional manner, and the size of the dependency group is uniformly set to 5. To reduce randomness in the experiment, the above networks were generated 500 times according to the set parameters. During simulation, unless otherwise specified, the following default parameters were used: α = 0.6, τ = 0.6, κ = 0.5, λ = 1, γ = 1.1, μ = 0.3, and the initial node failure rate f was [0, 0.3].

[0139] In order to test the effectiveness of the PRCI method, it is compared with three benchmark methods: Random Recovery (RR), which randomly selects nodes for recovery from the boundary nodes according to the probability of recovery ratio; Prior Recovery based on Degree (PRD), which prioritizes boundary nodes with large degrees for recovery according to the descending order of the internal degrees of the nodes; Prior Recovery based on Local centrality (PRL), which prioritizes the frontier nodes for recovery according to the descending order of the local centrality index of the nodes.

[0140] Specifically, see Figure 6 As shown in FIG, which is a comparison diagram of the recovery effects of the four methods under different subnet structures according to an embodiment of the present invention, from the perspective of the recovery effects of subnets with different network structures, the PRCI method is the best.

[0141] Specifically, see Figure 7 As shown in FIG, which is a comparison chart of the number of iterations of the four methods under different subnet structures of the embodiment of the present invention, from the perspective of the number of iterations of the methods under different network structure subnets, the PRCI method has the advantages of fewer iteration steps and faster effect.

[0142] Specifically, see Figures 8 to 13 As shown, Figure 8 This is a comparison chart of the recovery effects of four methods under different tolerances in an embodiment of the present invention. Figure 9 This is a comparison chart of the recovery effects of four methods under different load parameters in the embodiment of the present invention. Figure 10 This is a comparison chart of the recovery effects of four methods under different capacity parameters in the embodiment of the present invention. Figure 11 This is a comparison chart of the recovery effects of four methods under different capacity parameters in the embodiment of the present invention. Figure 12 This is a comparison chart of the recovery effects of four methods under different parameters in the embodiment of the present invention. Figure 13 This is a comparison chart of the recovery effects of four methods under different recovery ratios according to an embodiment of the present invention. From the recovery effects under different parameters, taking the Goh subnet as an example, the PRCI method is the best and has good results.

[0143] Specifically, see Figure 14 and 15 As shown, Figure 14 This is a comparison chart of the average degree of the network after recovery using different methods according to the embodiment of the present invention. Figure 15 This is a load comparison chart after recovery using different methods in an embodiment of the present invention. From the perspective of the average degree and load after recovery, the result of the PRCI method is the best among the compared methods. When recovery resources are limited, using the PRCI method for node recovery can improve the robustness of the two-layer heterogeneous dependent combat network and enhance the combat capability of the system.

[0144] Thus far, the technical solutions of the present invention have been described in conjunction with the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art may make equivalent changes or substitutions to the relevant technical features, and the technical solutions after such changes or substitutions will fall within the scope of protection of the present invention.

[0145] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that the present invention is susceptible to various modifications and variations. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.< / k> < / k> < / k>

Claims

1. A method for recovering a group-dependent combat network under overload conditions, characterized in that: include: Step S1: for the combat system, the combat units and combat relationships in the system are converted into nodes and edges, and combat physical networks G are established based on the nodes and edges. W and functional network G G , and based on the combat physical network G W and functional network G G Establish a two-layer heterogeneous dependent combat network model; Step S2: establishing a cascading failure model for the dual-layer heterogeneous dependency combat network and defining attack patterns and robustness indicators for the dual-layer heterogeneous dependency combat network; wherein the cascading failure model includes conditional group dependency failure and cascading failure considering overload; Step S3: sorting the boundary nodes of the physical network using a comprehensive importance index, selecting the top-ranked boundary nodes for restoration according to the physical network restoration ratio, and then restoring each node in the functional network according to the functional network restoration rule. The importance index is the weighted sum of the normalized external degree and internal degree of the physical network nodes. The restoration rule of the functional network is to first restore the functional network nodes and dependent edges that have dependencies on the physical network boundary nodes, and then restore the original connection relationships between these nodes and the largest connected subgraph of the functional network. After restoring some nodes, the load of the restored nodes in the physical network and the functional network is 0. Step S4: Based on step S3, the failure and recovery process of the dual-layer heterogeneous dependency combat network is recorded as the nth stage physical network failure, the nth stage functional network failure, the nth stage dual-layer heterogeneous dependency combat network recovery, and the nth stage functional network recovery, where n is a natural number. Step S5, generating simulation model data for a two-layer heterogeneous dependent combat network according to different model network parameters; wherein the model network has different parameters, for the ER model network, the parameters are the connection probability between different nodes and the connection probability of the inter-layer network, for the Goh network parameters are the power exponent β = 2.3, the average degree <k> =6 and the connection probability of the inter-layer network; for the NW network, the parameters are K, the connection probability between different nodes and the connection probability of the inter-layer network;< / k> Step S6, attacking the double-layer heterogeneous dependent combat network, and repeating steps S2 to S4 until the double-layer heterogeneous dependent combat network no longer fails or fails completely.

2. The method for recovering a group-dependent combat network under overload conditions according to claim 1, characterized in that: In the step S1, The physical network is a simple undirected graph whose nodes include communication load and capacity, wherein each node of the physical network is divided into a node C with communication function; The functional network is a heterogeneous directed network whose nodes include business categories, business loads, and capacities, and is used to transfer intelligence information and command commands. The nodes of the functional network are divided into intelligence acquisition nodes O, intelligence processing nodes P, command decision nodes D, and combat response nodes A. The two-layer heterogeneous dependent combat network G is a coupling network formed by the functional network through unidirectional dependence on the physical network. The dependency network is represented by G D .

3. The method for recovering a group-dependent combat network under overload conditions according to claim 1, characterized in that: In step S2, the cascading failure model includes conditional group dependency failure and cascading failure considering overload; the conditional group dependency failure rule introduces tolerance τ on the basis of the above, and when the failure ratio of the dependent node is greater than τ, the dependent node fails; wherein, the failure ratio refers to the failure ratio of the dependent node when a node group of the functional network depends on the physical network.

4. The method for recovering a group-dependent combat network under overload conditions according to claim 3, characterized in that: The cascading failure model considering load includes initial load, node capacity, failure state judgment and capacity redistribution method, among which the initial load L i (0) is the exponential power of the product of the node degree and the neighbor node degree, set Among them, κ is the adjustment parameter used to control the distribution of the initial load of the node, Γ i For node v i The subscript set of neighbor nodes; For the node capacity Ci, set C i =L i (0)+λ·L(0) γ ,i=1,2,…N, where λ and γ are load regulation parameters, set λ>0, γ>0; For the node failure state judgment, when the node load exceeds the capacity, the node is in a critical state of overload within the preset tolerance range μ, and the node failure probability is P i (t), set The load redistribution method considers the importance of both static and dynamic nodes. The allocation ratio of static nodes is set up The dynamic node allocation ratio is set up The comprehensive distribution ratio is Π ij ,set up Where η and 1-η are weights when the distribution ratio is mixed. Set η = 0.5, and update the load of the neighboring nodes of the node according to the following formula:

5. The method for recovering a group-dependent combat network under overload conditions according to claim 1, characterized in that: In step S2, the attack mode is to attack the physical network according to the corresponding attack ratio f, so that fN W The attack methods include random attacks and intentional attacks that prioritize node degrees.

6. The method for recovering a group-dependent combat network under overload conditions according to claim 5, characterized in that: In step S2, the robustness index is expressed as a comprehensive index of the number of combat kill links and the maximum connected subgraph size. The combat kill link types include standard kill chain, kill chain with collaborative detection, kill chain with information interaction, kill chain with collaborative command and control, kill chain with collaborative detection and information interaction, kill chain with collaborative detection and command and kill chain with collaborative detection, command and control and information interaction.

7. The method for recovering a group-dependent combat network under overload conditions according to claim 6, characterized in that: The flow of information in the functional network depends on the communication nodes of the physical network. The functional network completely relies on the communication nodes of the physical network to calculate the number of kill chains. The functional network calculates the overall reachability matrix based on Boolean power to obtain the reachability matrix from node O to A. set up Taking the standard kill chain as an example, let The number of combat loops is obtained as: S OPDA (G)=tr{[S OP ∧(S OC ×S CC ×S CP )]×[S PD ∧(S PC ×S CC ×S CD )]×[S DA ∧(S DC ×S CC ×S CA )]×S AO } Among them, S OC and S CP etc. is the reachability matrix between functional nodes and communication nodes, ∧ is the Boolean sum operation, and the calculation method of the number of other kill chains is the same as the above method. Then the number of 7 kill chains is expressed as The maximum connected subgraph size is expressed as the sum of the maximum connected subgraph sizes of the physical network and the functional network, and the initial size of the maximum connected subgraph size is set to Shuge(G)=NW+NG; For the unattacked dual-layer heterogeneous dependent combat network G, the number of kill chains targeting the dual-layer heterogeneous dependent combat network is recorded as S links (G), the maximum connected subgraph size for this two-layer heterogeneous dependent combat network is recorded as S huge (G), the network after the attack on the double-layer heterogeneous dependent combat network is recorded as G′, and the corresponding indicators are recorded as S links (G′) and S huge (G′), and then the robustness index R of the two-layer heterogeneous dependent combat network is obtained, setting Among them, θ is the scaling parameter of the number of kill chains, and 1-θ is the scaling parameter of the maximum connected subgraph size, and the default value of both is 0.

5.

8. The method for recovering a group-dependent combat network under overload conditions according to claim 1, characterized in that: In step S3, the boundary node of the physical network is a failed node whose distance to its maximum connected subgraph is 1; when recovering the nodes of the physical network, the boundary nodes are selected from the set of boundary nodes according to the sum of the structural importance index and the capacity index, specifically: in, is the weighted sum of the normalized external and internal degrees, set Among them, k max is the maximum degree, is the normalized node capacity, set Among them, C max For the maximum capacity; For the functional network, recovery is performed based on the recovery of the physical network nodes. The recovery rules are: first, restore the functional network nodes and dependent edges that have dependencies on the physical network boundary nodes, and then restore the original connection relationships between these nodes and the maximum connected subgraph of the functional network. After the physical network and the functional network have restored some nodes, the load of the restored nodes is 0.

9. The method for recovering a group-dependent combat network under overload conditions according to claim 1, characterized in that: In step S4, the specific process of the double-layer heterogeneous dependent combat network cyclic recovery includes: S41, the physical network failure process at stage n, (41a) If the physical network node v i If an overload occurs, the node v i Failure; (41b) All nodes that are out of the maximum connected subgraph are invalid; (41c) The load of the newly failed node is updated by spreading to the surrounding areas; S42, the failure process of the functional network in the nth stage, (42a) If the functional network node v i If the proportion of failed nodes in the nth stage of the physical network exceeds the limit τ, then node v i Failure; (42b) If the functional network node v i If an overload occurs, the node v i Failure; (42c) All nodes that are out of the maximum connected subgraph are invalid; (42d) The load of the newly failed node spreads to the surrounding areas, triggering a new round of overload and disconnected cascading failures until there are no new failed nodes in the functional network at this stage; S3, the nth stage double-layer heterogeneous dependent combat network recovery process, (8) Find all failed nodes and restore them according to the rules described above. The recovery ratio of the physical network is α. All the edges of the restored nodes that originally existed with the current normal nodes are fully restored. (9) Repeat steps (1) to (8) until the network reaches a stable state with no new failed nodes or a complete collapse state.

10. The method for recovering a group-dependent combat network under overload conditions according to claim 1, characterized in that: In step S5, the process of generating the dual-layer heterogeneous dependency combat network simulation model data includes: According to the ER random network, Goh scale-free network and NW small-world network model algorithms, the corresponding network parameters are set and a model network of a specified scale is generated, which serves as the physical network and functional network subnets respectively. The dependencies between subnets are connected in a random dependency manner, and a fixed dependency scale is set.

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