Air defense and anti-missile killing net model construction and evaluation method based on granularity super network

Abstract

The application discloses a method for constructing and evaluating an air defense anti-missile killing net model based on a granularity super network, and belongs to the technical field of combat systems.The method for constructing the air defense anti-missile killing net model based on the granularity super network comprises task analysis, function component modeling, connection edge modeling and an air defense anti-missile killing net architecture model based on the granularity super network.The application abstracts four types of nodes, i.e., targets, early warning, decision and attack, from an air defense anti-missile combat system based on a combat loop theory, and establishes an air defense anti-missile killing net model based on the granularity super network.The energy reduction degree, energy recovery rate, recovery degree and structural elasticity of the air defense anti-missile killing net based on the granularity super network are all superior to those of an air defense anti-missile system based on a traditional network.Meanwhile, a combat capability evaluation method based on Pythagorean binary semantic fuzziness is proposed, the membership degree of node attribute indexes is accurately determined, and the combat loop capability of the air defense anti-missile killing net and the overall combat capability are quantitatively evaluated.

Description

Technical Field

[0001] This invention belongs to the field of combat system technology, specifically involving a method for constructing and evaluating an air defense and anti-missile kill network model based on granular hypernetworks. Background Technology

[0002] Faced with future multi-dimensional, diverse, and agile aerospace threats, air defense and missile defense systems may face the dangers of node failure, link disruption, and system inoperability. How to rationally construct an air defense and missile defense combat system, build an air defense and missile defense kill network, improve the system's overall resilience, and ensure that the air defense and missile defense system can continuously provide defensive capabilities on the battlefield has become a hot research topic in the field of air defense and missile defense.

[0003] Numerous studies have been conducted by scholars both domestically and internationally regarding the modeling and evaluation of combat systems. Firstly, in terms of system modeling, there are four main approaches: First, modeling methods based on multi-view architectures, such as those based on the DoDAF framework, which can intuitively display the combat process but lacks quantitative information mapping; second, entity-based modeling methods, such as agent-based methods, which can display entities and their attributes within the combat system but lack information interaction between entities; third, modeling methods based on structural decomposition, such as those based on combat loops or kill chains, which can display the logic of combat activities but lack consideration of global capabilities; and fourth, modeling methods based on complex network theory, such as those based on hypernetwork theory, which can perform dynamic modeling and analysis but lacks consideration of the granularity of entity nodes, and using hypernetworks alone cannot describe the kill loop of an air defense and missile defense kill network. Therefore, a modeling approach based on hypernetworks and combat loops, with granular analysis, is needed. This approach can not only describe the structure and attribute characteristics of the combat system in detail but also effectively calculate kill chains, preparing for resilient assessment.

[0004] There are currently four main methods for assessing the resilience of operational architectures: First, there are resilience assessment methods based on decomposition, synthesis, and analysis, such as establishing an indicator system, standardizing indicators, aggregating indicators, and acquiring evaluation indicator values. The advantage is that different indicators can be set for different systems, offering a certain degree of flexibility, but it relies too heavily on the rationality of the indicator system. Second, there are simulation-based resilience assessment methods, such as a threat-driven command information system resilience assessment test method, AnyLogic-based simulation methods, and Monte Carlo simulation methods. Simulation-based resilience assessment can effectively simulate the dynamic processes of the system, but due to the complexity of the system, it often ignores the comprehensiveness of resilience, and most literature cannot provide actual simulation exercises. Third, there are resilience assessment methods based on the resilience triangle, such as resilience quantification models based on effectiveness thresholds. These methods are mainly used to assess the recovery process and cannot comprehensively measure the system's survivability and recoverability. Fourth, there are resilience assessment methods based on effectiveness change curves. These methods overcome the shortcomings of the resilience triangle approach and can provide a detailed characterization of the overall damage level, damage rate, recovery level, and recovery rate of the operational system. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide a method for constructing and evaluating an air defense and anti-missile kill network model based on granular hypernetworks.

[0006] The technical solution adopted to solve the above technical problems is: a method for constructing an air defense and anti-missile kill network model based on granular hypernetworks, including the following steps:

[0007] S1.1, Task Analysis

[0008] In the process of air defense and anti-missile operations, analyze the weapons and equipment of the air defense and anti-missile kill network, the relationships between the equipment, and the operational procedures.

[0009] S1.2, Functional Component Modeling

[0010] Based on equipment attributes, the equipment in the air defense and anti-missile kill network system is defined as target nodes, early warning nodes, decision-making nodes, and strike nodes.

[0011] S1.3, Connecting Edge Modeling

[0012] Based on the operational loop closure process, the actual operational flow of the air defense and anti-missile kill network and the interaction relationships between equipment components adopt the following six connection methods. Therefore, the set of edges in the air defense and anti-missile kill network based on granular hypernetworks is represented as follows:

[0013]

[0014] The warning edge T→S indicates that the air defense and anti-missile early warning and detection system implements full-domain early warning for enemy targets. It mainly obtains the threat type, speed, altitude, and direction of the target node, and predicts the possible movement trajectory of the target, forming a one-way edge from the target to the intelligence system. It can measure the early warning capability of the air defense and anti-missile kill network S functional component for target T.

[0015] The intelligence sharing edge S→S represents a bidirectional edge within the early warning system where functional component nodes of equipment share target information with each other, and measures the information transmission capability of S-type functional component nodes.

[0016] The intelligence edge S→D represents the one-way edge through which the early warning equipment transmits information such as target characteristics, type, location, and speed to the functional component nodes of the command and control equipment, as well as the intelligence edge shared by the friendly combat system. S represents the information sent by the functional component node, and D represents the information received by the node.

[0017] The command and control transmission edge D→D represents a one-way edge in the air defense and anti-missile system where command and control equipment at all levels transmit intelligence information through a command link after fusion processing.

[0018] Command and control edge D→A represents a one-way edge where the command and control equipment node transmits interception and strike commands to the soft and hard strike nodes. The information transmission and information processing capabilities from the command and control node to the strike node include the interception weapon's time, transmit and receive rate, accuracy, information connectivity, transmission rate, transmission quality, communication quality, and communication latency.

[0019] The term "A→T" refers to a unidirectional edge formed by the interception and attack of air-attack target nodes by various soft and hard kill equipment functional component nodes. In the operation of the air defense and anti-missile kill network, the kill classification of air-attack targets includes two categories: electronic soft kill and firepower hard kill. Soft kill refers to the activities of using electronic weapons to interfere with, reduce or destroy the electronic devices of air-attack targets, thereby rendering them incapable of combat. Hard kill refers to the activities of using missiles, artillery and other weapons to destroy air-attack targets.

[0020] S1.4, the air defense and anti-missile kill network system architecture model based on granular hypernetwork is represented as follows:

[0021]

[0022] In formula (21), V represents the set of all nodes, E represents the set of all connected edges, and V M q represents a tuple of granularity and its corresponding level, L represents the set of level types, and q represents the set of levels. i The functional attribute representing granularity, lt ,l s ,l d ,l a These represent the target layer, early warning layer, decision-making layer, and strike layer, respectively.

[0023] Furthermore, the equipment attributes in step S1.2 include early warning capability, command and control capability, strike capability, target capability, communication capability, spatial positioning capability, capacity, and time consumption.

[0024] The formula for expressing the aforementioned early warning capability is: These represent the detection range, scanning frequency, maneuvering speed, detection accuracy, and recognition probability of the equipment's functional component nodes, respectively.

[0025] The formula for expressing the aforementioned accusation capability is: These represent the response time, transmit / receive rate, and accuracy of the equipment's functional component nodes, respectively.

[0026] The formula for expressing the aforementioned striking capability is: These represent the strike accuracy, kill radius, jamming power, and maneuver speed of the equipment's functional component nodes, respectively.

[0027] The formula for expressing the target capability is: These represent the stealth coefficient, anti-electro-optical coefficient, anti-radar coefficient, anti-infrared coefficient, maneuverability, survivability, early warning time, and receiving power of the equipment's functional component nodes, respectively.

[0028] The expression formula for the aforementioned communication is: communication i = {x1, x2, ..., x5}, where x1, x2, ..., x5 represent the communication coverage, transmission speed, communication quality, communication capacity, and communication latency of the equipment's functional components, respectively;

[0029] The formula for expressing the spatial positioning capability is as follows: The q indicates the functional component of the air defense and anti-missile kill network. i The spatial location is a crucial factor in air defense and anti-missile combat systems, affecting the quantity and quality of the kill network's operational links. i ,y i ,z i These represent the three-dimensional coordinates of the equipment's functional components in space.

[0030] The formula for expressing the capacity is: The q indicates the functional component of the air defense and anti-missile kill network. i The capacity refers to the number of air attack targets that early warning equipment can detect simultaneously, the number of command and control equipment that can process command information and control equipment simultaneously, and the number of channels through which strike equipment can intercept air attack targets simultaneously.

[0031] The formula for expressing the time consumed is: The q indicates the functional component of the air defense and anti-missile kill network. i The time consumed refers to the time spent by early warning equipment in detecting targets, decision-making nodes in processing information, command and control systems in preparing for strikes, and intercepting strikes in the formation of an air defense and anti-missile kill network combat ring.

[0032] Furthermore, the actual combat process of the air defense and anti-missile kill network in step S1.3 includes detection, tracking, and identification, and the detection probability P of the early warning radar... f The formula is as follows:

[0033]

[0034] In formula (2), g i This represents the probability that the early warning detection equipment detects the air attack target in the i-th scan.

[0035] The frequency of the radar scan, when considered in air defense and anti-missile operations, taking into account the stealth capabilities of early warning equipment and targets, is expressed by the following formula:

[0036]

[0037] In formula (3), 0 < k < 1 represents the environmental regulation parameter. Indicates the detection accuracy in node S membership function, These represent the radar detection range and the maneuvering speed, respectively, with A representing the specified detection range. This represents the photoelectric resistance coefficient, radar resistance coefficient, and infrared resistance coefficient of target node T. The membership functions of the three indicators, Indicate their respective weights;

[0038] Tracking probability P t The formula for expressing it is:

[0039]

[0040]

[0041] In formulas (4), (5), and (6), p tr p represents the ability to track detected targets. z Indicates the anti-tracking capability of air attack targets;

[0042] Recognition probability P r The formula for expressing it is:

[0043]

[0044] In formula (7), This indicates the probability of recognition.

[0045] Furthermore, in step S1.3 The intelligence-sharing edge S→S includes five indicators related to information transmission capabilities, P i SS (i = 1, 2, 3, 4, 5) is node S i With S j The information transmission rate P1 between (i≠j) SS ,rate quality capacity and delay for:

[0046]

[0047] in, Represents node S i With S j The distance between them, x i -x j y i -y j z i -z j S represents i With S j The difference between the coordinates of two points;

[0048]

[0049] In the above formula, This represents the detection distance between two different nodes. This indicates the scanning frequency of two different nodes. This represents the maneuvering speed of two different nodes. This indicates the detection accuracy of two different nodes. This indicates the recognition frequency of two different nodes.

[0050] Furthermore, in step S1.3 Factors affecting the information processing capability of node D include response time P1 DD Send and receive rate accuracy Then node D i With D j The formula for expressing the influencing factors between (i≠j) is:

[0051]

[0052] In formulas (13), (14), (15), This indicates the response time of different nodes. This indicates the time consumed by the node. This indicates the transmit / receive rate of different nodes. This indicates the accuracy of different nodes.

[0053] Furthermore, in step S1.3, the soft-kill attack on the air strike target is affected by interference probability. and suppression probability The formula for describing this is:

[0054]

[0055] In formulas (16), (17), (18), Indicates the speed of movement of the attacking node. Indicates intercept weapon node A i Launched to kill target node T j The time taken This indicates the kill radius of the target node. Indicates the distance between the intercepting weapon and the target. These represent the target node's maneuver speed and warning time, respectively. This indicates the interference power of the attacking node. This represents the target node's survivability coefficient and received power. This represents the coordinate difference between the attack node i and the target node j;

[0056] Hard kill damage to airstrike targets is determined by hit probability. and probability of destruction The formula for describing this is:

[0057]

[0058] In formulas (19) and (20), This represents the speed of movement of the node m being attacked. This represents the kill radius of the node m. This represents the straight-line distance between the attack node m and the target node n. Let n represent the target node's speed and the warning time, respectively. Indicates intercept weapon node A m Launched to target T n The time taken This indicates the distance between the interceptor missile and the target is... At that time, A m For T n The membership function of the damage. The membership function represents the survival coefficient of the target node. These represent the corresponding coefficients.

[0059] The evaluation method using the air defense and anti-missile kill network model based on granular hypernetworks includes the following steps:

[0060] S2.1, evaluate the air defense and anti-missile kill network combat system of the model;

[0061] S2.2, assess the resilience of the combat system. The resilience indicators of the combat system include three stages: being attacked, capability decline, and capability recovery.

[0062] S2.3 assesses operational capabilities, with operational capability indicators including the kill network's resilience and recoverability.

[0063] Furthermore, the evaluation method for the air defense and anti-missile kill network combat system in step S2.1 is as follows:

[0064] S2.1.1, Calculate the number R of nodes in the air defense and anti-missile kill network. N Number of edges R E ;

[0065]

[0066] In formula (22), V represents the set of all nodes and E represents the set of all connected edges;

[0067] S2.1.2, the degree of elasticity R of the air defense and anti-missile kill network nodes. P ;

[0068] The degree distribution refers to the probability distribution p(λ) of the node degrees. When a deliberate attack is launched on a combat system, the degree of the combat system follows a power-law distribution, i.e.

[0069] p(λ)~λ -γ (twenty three)

[0070] In formula (23), p(λ) represents the probability that a node has a degree of λ, where λ is the degree of the node and γ is an exponent greater than 1. It determines the shape of the power law distribution. The more uneven the degree distribution, the lower the resilience of the system network.

[0071] When a combat system is attacked randomly, the degree of the combat system follows a Poisson distribution, that is...

[0072]

[0073] In formula (24), p(λ) represents the probability that a node has a degree of λ, μ is the average degree of the network, that is, the average degree of all nodes in the network, e is the base of the natural logarithm, and λ! represents the factorial. The more uniform the degree distribution, the lower the survivability of the combat system.

[0074] S2.1.3, Calculate the elasticity R of the air defense and anti-missile kill network aggregation coefficient. C ;

[0075] R C The degree of clustering of nodes in a combat system is represented by the clustering coefficient C. i :

[0076]

[0077] In formula (25), This represents the actual number of edges connected to adjacent node clusters, where K represents the number of clusters.

[0078] The concentration coefficient C of the air defense and anti-missile kill network combat system is

[0079]

[0080] In formula (26), R N The number of nodes indicates that a combat system with a high aggregation coefficient has good cohesion and is easy to support each other.

[0081] S2.1.4, Calculate the number R of the air defense and anti-missile kill network combat rings. A ;

[0082] The number of combat rings is the same as the number of kill chains. The number of combat rings is calculated using the transition matrix and the arrival matrix.

[0083] Transition matrix: Let A ij It's about node v i With node v j The transition matrix between nodes, if there is a relationship between the two nodes, then the element a... ij =1, otherwise a ij =0, when node v i With node v j When they are nodes of the same type, A ij Represents a homogeneous adjacency matrix;

[0084] Arrival Matrix: A ij and A jk Let A be the adjacent transition matrix. ij The arrival node and A jk The starting nodes are of the same type.

[0085] The node transitions of the operational loop are obtained from the transition matrix. Therefore, the arrival matrix of the standard operational loop for an air-attack target T is represented as follows:

[0086] A TSDAT =A TS *A SD *A DA *A AT(27)

[0087] In formula (27), A TS A SD A DA A AT Let T represent the arrival matrices from the target node to the early warning node, from the early warning node to the decision node, from the decision node to the attack node, and from the attack node to the target node, respectively.

[0088] The standard operational ring number for an air defense and anti-missile kill network targeting an air-attack target T is:

[0089]

[0090] In formula (28), |T| represents the number of target nodes, N TSDAT A represents the number of combat rings for all target nodes. TSDAT (i,i) represents the number of combat rings for the i-th target node.

[0091] Furthermore, the combat capability assessment adopts a combat capability assessment method based on Pythagorean binary semantic fuzzy logic:

[0092] For a given Pythagorean binary semantic fuzzy number Its membership function is expressed as:

[0093]

[0094] In formula (29), Indicates language scale, Indicates the degree of difference in linguistic information. Represents the Pythagorean fuzzy number. Indicates membership degree. Indicates non-membership degree;

[0095] To complete the combat mission according to the standard operational cycle, the uncertainty of the early warning node, decision-making node, strike node, and target node is set as I. S ,I D ,I A ,I T Let I be the uncertainty of completing the edge in the combat loop. TS ,I SS ,I SD ,I DD ,I DA ,I AT Assuming there are m targets in total, and n operational rings exist for the i-th target, then the uncertainty of the j-th operational ring for the i-th target is determined by both the nodes and the edges, i.e.

[0096] I ij=I S +I D +I A +I T +I TS +I SS +I SD +I DD +I DA +I AT (30)

[0097] The uncertainty information of all operational loops for the i-th target is:

[0098]

[0099] The combat effectiveness of this combat ring against the i-th target is:

[0100] C i =exp(-I i (32)

[0101] The overall combat capability of the air defense and anti-missile kill network against all m targets is:

[0102]

[0103] In formulas (30) to (33), I T ,I S ,I D ,I A I represents the uncertainty in the mission completion capabilities of the target node, early warning node, decision-making node, and strike node, respectively. TS ,I SS ,I SD ,I DD ,I DA ,I AT These represent the uncertainties in the mission completion capabilities of the early warning edge, intelligence sharing edge, intelligence edge, command and control transmission edge, command and control edge, and strike edge, respectively. ij C represents the uncertainty of the j-th operational loop of the i-th target. i I represents the combat effectiveness against the i-th target. i Let C represent the amount of uncertainty information in all operational loops of the i-th target, and let λ represent the overall operational effectiveness of all m targets. i The weight is the importance weight or threat level weight of the target node.

[0104] Furthermore, the survivability of the kill net is determined by the degree and rate of energy reduction of the kill net system, and the degree of energy reduction d of the kill net system is:

[0105]

[0106] Kill net system energy reduction rate vd for:

[0107]

[0108] R-resistance d Represented as:

[0109] R d =exp(-d·v d (36)

[0110] The resilience of the kill web is determined by the degree and rate of reactivation of the kill web system. The degree of reactivation r of the kill web system is:

[0111]

[0112] Kill net system reactivation rate v r for:

[0113]

[0114] Then the restorative R r Represented as:

[0115] R r =exp(r·v r (39)

[0116] The structural flexibility of the kill net system is:

[0117] R I =R d *R r (40)

[0118] In formulas (34) to (40), t0 and t a t d t r t s These represent the moments at the start of combat, the moment of being attacked, the moment when the ability decline reaches its lowest point, the moment when the ability begins to recover, and the moment when the ability recovery is complete, respectively, C(t0) and C(t). a ), C(t) d ), C(t) r ), C(t) s ) represent t0 and t respectively a t d t r t s Real-time system combat capability, d represents the degree of decline in system capability, v d R represents the rate at which the system's capability decreases. d The system's resilience is represented by r, which indicates the degree of its recovery capability. r R represents the rate at which the system recovers. rIndicates system recoverability, R I This indicates architectural flexibility.

[0119] The beneficial effects of the present invention are as follows: (1) The present invention adopts the combat ring theory to abstract the air defense and anti-missile combat system into four types of nodes: target, early warning, decision-making and strike, and establishes an air defense and anti-missile kill network model based on granular hypernetwork. The air defense and anti-missile kill network based on granular hypernetwork has better energy reduction, energy recovery rate, recovery degree and structural elasticity than the air defense and anti-missile system based on traditional network. Therefore, the air defense and anti-missile kill network model based on granular hypernetwork has certain advantages.

[0120] (2) This invention proposes a combat capability assessment method based on Pythagorean binary semantic fuzzy by constructing a model architecture of network system nodes and edges, which realizes the accurate determination of the membership degree of node attribute indicators, and at the same time realizes the quantitative assessment of the combat ring capability and overall combat capability of the air defense and anti-missile kill network under complex indicator data. Attached Figure Description

[0121] Figure 1 This is a schematic diagram of an embodiment of the air defense and anti-missile kill network model construction method based on granular hypernetworks of the present invention.

[0122] Figure 2 This is a schematic diagram illustrating the dynamic elastic changes of the air defense and anti-missile kill net.

[0123] Figure 3 This is a topology diagram of an air defense and anti-missile system based on traditional networks.

[0124] Figure 4 This is a topology diagram of an air defense and missile defense system based on hypernetworks.

[0125] Figure 5 It refers to the operational links of the four types of nodes in the air defense and anti-missile system: target, early warning, decision-making, and strike.

[0126] Figure 6 This is a comparison chart of the resilience of air defense and anti-missile systems under a deliberate attack strategy.

[0127] Figure 7 This is a comparison chart of the resilience of air defense and anti-missile systems under random attack strategies.

[0128] Figure 8 This is a comparison chart of the target capabilities of air defense and anti-missile kill networks based on different networks. Detailed Implementation

[0129] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0130] like Figure 1 As shown, the method for constructing an air defense and anti-missile kill network model based on granular hypernetworks includes the following steps:

[0131] S1.1, Task Analysis

[0132] In the process of air defense and anti-missile operations, analyze the weapons and equipment of the air defense and anti-missile kill network, the relationships between the equipment, and the operational procedures.

[0133] S1.2, Functional Component Modeling

[0134] Based on equipment attributes, the equipment in the air defense and anti-missile kill network system is defined as target nodes, early warning nodes, decision-making nodes, and strike nodes.

[0135] Equipment attributes include early warning capability, command and control capability, strike capability, target acquisition capability, communication capability, spatial positioning capability, capacity, and consumption time.

[0136] The formula for expressing early warning capability is: These represent the detection range, scanning frequency, maneuvering speed, detection accuracy, and recognition probability of the equipment's functional component nodes, respectively.

[0137] The formula for expressing accusatory capacity is: These represent the response time, transmit / receive rate, and accuracy of the equipment's functional component nodes, respectively.

[0138] The formula for expressing striking power is: These represent the strike accuracy, kill radius, jamming power, and maneuver speed of the equipment's functional component nodes, respectively.

[0139] The formula for expressing the target capability is: These represent the stealth coefficient, anti-electro-optical coefficient, anti-radar coefficient, anti-infrared coefficient, maneuverability, survivability, early warning time, and receiving power of the equipment's functional component nodes, respectively.

[0140] The formula for expressing communication is: communication i ={x1,x2,…,x5}, where x1,x2,…,x5 represent the communication coverage, transmission speed, communication quality, communication capacity, and communication latency of the equipment's functional components, respectively.

[0141] The formula for expressing spatial location capability is: The q indicates the functional component of the air defense and anti-missile kill network. i The spatial location is a crucial factor in air defense and anti-missile combat systems, affecting the quantity and quality of the kill network's operational links. i ,y i ,z iThese represent the three-dimensional coordinates of the equipment's functional components in space.

[0142] The formula for representing capacity is: The q indicates the functional component of the air defense and anti-missile kill network. i The capacity refers to the number of air attack targets that early warning equipment can detect simultaneously, the number of command and control equipment that can process command information and control equipment simultaneously, and the number of channels through which strike equipment can intercept air attack targets simultaneously.

[0143] The formula for expressing the time consumed is: The q indicates the functional component of the air defense and anti-missile kill network. i The time consumed refers to the time spent by early warning equipment in detecting targets, decision-making nodes in processing information, command and control systems in preparing for strikes, and intercepting strikes in the formation of an air defense and anti-missile kill network combat ring.

[0144] S1.3, Connecting Edge Modeling

[0145] Based on the operational loop closure process, the actual operational flow of the air defense and anti-missile kill network and the interaction relationships between equipment components adopt the following six connection methods. Therefore, the set of edges in the air defense and anti-missile kill network based on granular hypernetworks is represented as follows:

[0146]

[0147] The warning edge T→S indicates that the air defense and anti-missile early warning and detection system implements full-domain early warning for enemy targets. It mainly obtains the threat type, speed, altitude, and direction of the target node, and predicts the possible movement trajectory of the target, forming a one-way edge from the target to the intelligence system. It can measure the early warning capability of the air defense and anti-missile kill network S functional component for target T.

[0148] The actual operational process of an air defense and anti-missile kill network includes detection, tracking, and identification, with the detection probability P of the early warning radar being... f The formula is as follows:

[0149]

[0150] In formula (2), g i This represents the probability that the early warning detection equipment detects the air attack target in the i-th scan.

[0151] The frequency of the radar scan, when considered in air defense and anti-missile operations, taking into account the stealth capabilities of early warning equipment and targets, is expressed by the following formula:

[0152]

[0153] In formula (3), 0 < k < 1 represents the environmental regulation parameter. Indicates the detection accuracy in node S membership function, These represent the radar detection range and the maneuvering speed, respectively, with A representing the specified detection range. This represents the photoelectric resistance coefficient, radar resistance coefficient, and infrared resistance coefficient of target node T. The membership functions of the three indicators, Indicate their respective weights;

[0154] Tracking probability P t The formula for expressing it is:

[0155]

[0156] In formulas (4), (5), and (6), p tr p represents the ability to track detected targets. z Indicates the anti-tracking capability of air attack targets;

[0157] Recognition probability P r The formula for expressing it is:

[0158]

[0159] In formula (7), This indicates the probability of recognition.

[0160] The intelligence-sharing edge S→S represents a bidirectional edge within the early warning system where functional component nodes of equipment share target information with each other, and measures the information transmission capability of S-type functional component nodes.

[0161] The intelligence-sharing edge S→S includes five indicators related to information transmission capabilities, P i SS (i = 1, 2, 3, 4, 5) is node S i With S j The information transmission rate P1 between (i≠j) SS ,rate Quality P3 SS ,capacity and delay for:

[0162]

[0163] in, Represents node S i With S j The distance between them, x i -x j y i -y j z i -zj S represents i With S j The difference between the coordinates of two points;

[0164]

[0165]

[0166] In the above formula, This represents the detection distance between two different nodes. This indicates the scanning frequency of two different nodes. This represents the maneuvering speed of two different nodes. This indicates the detection accuracy of two different nodes. This indicates the recognition frequency of two different nodes.

[0167] The intelligence edge S→D represents the one-way edge through which the early warning equipment transmits information such as target characteristics, type, location, and speed to the functional component nodes of the command and control equipment, as well as the intelligence edge shared by the friendly combat system. S represents the information sent by the functional component node, and D represents the information received by the node.

[0168] The command and control transmission edge D→D represents a unidirectional edge in the air defense and anti-missile system where command and control equipment at all levels transmit intelligence information through a command link after fusion processing.

[0169] Factors affecting the information processing capability of node D include response time P1 DD Send and receive rate Accuracy P3 DD Then node D i With D j The formula for expressing the influencing factors between (i≠j) is:

[0170]

[0171] In formulas (13), (14), (15), This indicates the response time of different nodes. This indicates the time consumed by the node. This indicates the transmit / receive rate of different nodes. This indicates the accuracy of different nodes.

[0172] Command and control edge D→A represents a one-way edge where the command and control equipment node transmits interception and strike commands to the soft and hard strike nodes. The information transmission and processing capabilities from the command and control node to the strike node include the interception weapon's time, transmit / receive rate, accuracy, information connectivity, transmission rate, transmission quality, communication quality, and communication latency.

[0173] The term "A→T" refers to a unidirectional edge formed by the interception and attack of various soft and hard kill equipment functional component nodes on air attack target nodes. In the operation of the air defense and anti-missile kill network, the kill classification of air attack targets includes two categories: electronic soft kill and firepower hard kill. Soft kill refers to the activities of using electronic weapons to interfere with, reduce or destroy the electronic devices of air attack targets, thereby rendering them incapable of combat. Hard kill refers to the activities of using missiles, artillery and other weapons to destroy air attack targets.

[0174] The probability of soft-kill damage to airstrike targets is determined by interference. and suppression probability The formula for describing this is:

[0175]

[0176] In formulas (16), (17), (18), Indicates the speed of movement of the attacking node. Indicates intercept weapon node A i Launched to kill target node T j The time taken This indicates the kill radius of the target node. Indicates the distance between the intercepting weapon and the target. These represent the target node's maneuver speed and warning time, respectively. This indicates the interference power of the attacking node. This represents the target node's survivability coefficient and received power. This represents the coordinate difference between the attack node i and the target node j.

[0177] Hard kill damage to airstrike targets is determined by hit probability. and probability of destruction The formula for describing this is:

[0178]

[0179] In formulas (19) and (20), This represents the speed of movement of the node m being attacked. This represents the kill radius of the node m. This represents the straight-line distance between the attack node m and the target node n. Let n represent the target node's speed and the warning time, respectively. Indicates intercept weapon node A m Launched to target T n The time taken This indicates the distance between the interceptor missile and the target is... At that time, Am For T n The membership function of the damage. The membership function represents the survival coefficient of the target node. These represent the corresponding coefficients.

[0180] S1.4, the air defense and anti-missile kill network system architecture model based on granular hypernetwork is represented as follows:

[0181]

[0182] In formula (21), V represents the set of all nodes, E represents the set of all connected edges, and V M q represents a tuple of granularity and its corresponding level, L represents the set of level types, and q represents the set of levels. i The functional attribute representing granularity, l t ,l s ,l d ,l a These represent the target layer, early warning layer, decision-making layer, and strike layer, respectively.

[0183] The evaluation method for the air defense and anti-missile kill network model based on granular hypernetworks includes the following steps:

[0184] S2.1, evaluate the air defense and anti-missile kill network combat system of the model;

[0185] The evaluation method for an air defense and anti-missile kill network combat system is as follows:

[0186] S2.1.1, Calculate the number R of nodes in the air defense and anti-missile kill network. N Number of edges R E ;

[0187]

[0188] In formula (22), V represents the set of all nodes and E represents the set of all connected edges;

[0189] S2.1.2, the degree of elasticity R of the air defense and anti-missile kill network nodes. P ;

[0190] The degree distribution refers to the probability distribution p(λ) of the node degrees. When a deliberate attack is launched on a combat system, the degree of the combat system follows a power-law distribution, i.e.

[0191] p(λ)~λ -γ (twenty three)

[0192] In formula (23), p(λ) represents the probability that a node has a degree of λ, where λ is the degree of the node and γ is an exponent greater than 1. It determines the shape of the power law distribution. The more uneven the degree distribution, the lower the resilience of the system network.

[0193] When a combat system is attacked randomly, the degree of the combat system follows a Poisson distribution, that is...

[0194]

[0195] In formula (24), p(λ) represents the probability that a node has a degree of λ, μ is the average degree of the network, that is, the average degree of all nodes in the network, e is the base of the natural logarithm, and λ! represents the factorial. The more uniform the degree distribution, the lower the survivability of the combat system.

[0196] S2.1.3, Calculate the elasticity R of the air defense and anti-missile kill network aggregation coefficient. C .

[0197] R C The degree of clustering of nodes in a combat system is represented by the clustering coefficient C. i :

[0198]

[0199] In formula (25), This represents the actual number of edges that adjacent node clusters have, and K represents the number of clusters.

[0200] The concentration coefficient C of the air defense and anti-missile kill network combat system is:

[0201]

[0202] In formula (26), R N The number of nodes indicates that a combat system with a high aggregation coefficient has good cohesion and is easy to support each other.

[0203] S2.1.4, Calculate the number R of the air defense and anti-missile kill network combat rings. A .

[0204] The number of combat rings is the same as the number of kill chains. The number of combat rings is calculated using the transition matrix and the arrival matrix.

[0205] Transition matrix: Let A ij It's about node v i With node v j The transition matrix between nodes, if there is a relationship between the two nodes, then the element a... ij =1, otherwise a ij =0, when node v i With node v j When they are nodes of the same type, A ij This represents a homogeneous adjacency matrix.

[0206] Arrival Matrix: A ij and Ajk Let A be the adjacent transition matrix. ij The arrival node and A jk If the starting nodes are of the same type, and the node transitions of the combat ring are obtained based on the transition matrix, then the arrival matrix of the standard combat ring for an air attack target T is represented as follows:

[0207] A TSDAT =A TS *A SD *A DA *A AT (27)

[0208] In formula (27), A TS A SD A DA A AT Let T represent the arrival matrices from the target node to the early warning node, from the early warning node to the decision node, from the decision node to the attack node, and from the attack node to the target node, respectively.

[0209] The standard operational ring number for an air defense and anti-missile kill network targeting an air-attack target T is:

[0210]

[0211] In formula (28), |T| represents the number of target nodes, N TSDAT A represents the number of combat rings for all target nodes. TSDAT (i,i) represents the number of combat rings for the i-th target node.

[0212] S2.2 assesses the resilience of the combat system, which includes three phases: attack, capability degradation, and capability recovery. For example... Figure 2 As shown, t0 represents the initial operational capability of the air defense and missile defense kill network, t a t indicates the moment when the combat system is attacked. d t represents the moment when the combat system's capability declines to its lowest point. r This indicates the moment when the combat system's capabilities begin to recover. s The moment when the combat system's capabilities are fully restored, t e This indicates the moment when the combat system completes its operations. During this process, the degree and rate of capability decline after the combat system is attacked, as well as the degree and rate of capability recovery, are important factors in assessing the resilience of the air defense and anti-missile kill network.

[0213] S2.3 assesses operational capabilities, with operational capability indicators including the kill network's resilience and recoverability.

[0214] Combat capability assessment employs a Pythagorean binary semantic fuzzy combat capability assessment method:

[0215] For a given Pythagorean binary semantic fuzzy number Its membership function is expressed as:

[0216]

[0217] In formula (29), Indicates language scale, Indicates the degree of difference in linguistic information. Represents the Pythagorean fuzzy number. Indicates membership degree. Indicates non-membership degree;

[0218] To complete the combat mission according to the standard operational cycle, the uncertainty of the early warning node, decision-making node, strike node, and target node is set as I. S ,I D ,I A ,I T Let I be the uncertainty of completing the edge in the combat loop. TS ,I SS ,I SD ,I DD ,I DA ,I AT Assuming there are m targets in total, and n operational rings exist for the i-th target, then the uncertainty of the j-th operational ring for the i-th target is determined by both the nodes and the edges, i.e.:

[0219] I ij =I S +I D +I A +I T +I TS +I SS +I SD +I DD +I DA +I AT (30)

[0220] The uncertainty information of all operational loops for the i-th target is:

[0221]

[0222] The combat effectiveness of this combat ring against the i-th target is:

[0223] C i =exp(-I i (32)

[0224] The overall combat capability of the air defense and anti-missile kill network against all m targets is:

[0225]

[0226] In formulas (30) to (33), I T ,I S ,I D ,I A I represents the uncertainty in the mission completion capabilities of the target node, early warning node, decision-making node, and strike node, respectively. TS ,I SS ,I SD ,I DD ,I DA ,I AT These represent the uncertainties in the mission completion capabilities of the early warning edge, intelligence sharing edge, intelligence edge, command and control transmission edge, command and control edge, and strike edge, respectively. ij C represents the uncertainty of the j-th operational loop of the i-th target. i I represents the combat effectiveness against the i-th target. i Let C represent the amount of uncertainty information in all operational loops of the i-th target, and let λ represent the overall operational effectiveness of all m targets. i The weight is the importance weight or threat level weight of the target node.

[0227] The resilience of a kill net is determined by the degree and rate of energy reduction within the kill net system. The degree of energy reduction d in the kill net system is:

[0228]

[0229] Kill net system energy reduction rate v d for:

[0230]

[0231] R-resistance d Represented as:

[0232] R d =exp(-d·v d (36)

[0233] The resilience of the kill web is determined by the degree and rate of reactivation of the kill web system. The degree of reactivation r of the kill web system is:

[0234]

[0235] Kill net system reactivation rate v r for:

[0236]

[0237] Then the restorative R r Represented as:

[0238] R r =exp(r·v r (39)

[0239] The structural flexibility of the kill net system is:

[0240] R I =R d *R r (40)

[0241] In formulas (34) to (40), t0 and t a t d t r t s These represent the moments at the start of combat, the moment of being attacked, the moment when the ability decline reaches its lowest point, the moment when the ability begins to recover, and the moment when the ability recovery is complete, respectively, C(t0) and C(t). a ), C(t) d ), C(t) r ), C(t) s ) represent t0 and t respectively a t d t r t s Real-time system combat capability, d represents the degree of decline in system capability, v d R represents the rate at which the system's capability decreases. d The system's resilience is represented by r, which indicates the degree of its recovery capability. r R represents the rate at which the system recovers. r Indicates system recoverability, R I This indicates architectural flexibility.

[0242] The relevant terms and concepts in this embodiment are explained as follows:

[0243] <1> A meta-path K is a path defined on the hypernetwork H = (V, E), representing a node v i v j The relational sequence of (i≠j) Where v k ∈V, e j ∈E.

[0244] <2> An operational loop (OL) refers to a closed loop formed by detection, command and control, and strike weapon systems and enemy target entities within a weapon system, according to a predetermined operational mission. In other words, when a network node is attacked, or when the target is not present, it can only be considered an air defense and anti-missile system, not a kill network. Only when a target appears in the air and is detected by radar can an operational loop be formed, potentially leading to a kill network.

[0245] <3> The System Architecture of Air Defense and Antimissile Kill Web (OA-ADAKW) is a system that breaks down multifunctional weapons and equipment that perform air defense and antimissile combat missions into a large number of simple sensor, command and control, and strike functional components, and integrates them with a communication network to form a dynamic kill web.

[0246] <4> Granular hypernetworks abstract the two core elements of a hypernetwork—nodes and edges—into a collection with multiple attributes, forming the granular space of the hypernetwork. Network units with multiple attributes are defined as functional components, and edges between functional components are defined as connected components. Defining granular hypernetworks facilitates a vivid description of the network structure and analysis of its internal operating mechanisms. Granular hypernetworks are represented as follows:

[0247] H = (V, E, V) M ,L) (1)

[0248] Where, V=(Q i U i ,f i (i = 1, 2, ..., n) represents the information granularity of the hypernetwork, where Q i ={q ia ,q ib ,…,q ik} is a non-empty finite set, representing the set of functional attributes at the granularity level, U i =∪U ip (p∈Q i )=[δ a ,δ b ,…,δ k ](δ a ,δ b ,…,δ k ∈[0,1]), representing a vector with attributes, U ip The attribute threshold for network granularity p is represented by f:V→U, which represents the information function for extracting network granularity attributes; e i ={Q i1 Q i2 ,…Q ij} represents the network granularity Q i Q j The relationship between E and E is: E = {e1, e2, ..., e}. m} represents the set of hypernetwork granular relationships; L = {l1, l2, l3, l4, l5, l6, l7, l8, l9, l1, l1, l1, l2, l3 ...1, l2, l3, l1, l2, l3, 2, …,l α} represents the set of hierarchical networks in a granular supernetwork; This represents a pair of granularities that belong to the same level and satisfy the following conditions:

[0249] (1)

[0250] (2)

[0251] As can be seen from the above definition, its system has diverse node types, different functions, and complex relationships. The system operates in an intertwined and parallel manner, exhibiting prominent node heterogeneity and complex relationships.

[0252] <5> Taking air defense and anti-missile kill networks as the object, the characteristics of granular hypernetworks and air defense and anti-missile kill network architectures are summarized and analyzed, as shown in Table 1.

[0253] Table 1. Structural characteristics and attributes of air defense and anti-missile kill nets

[0254]

[0255] According to the definition of granular hypernetworks, granular hypernetworks are multi-layered heterogeneous networks formed by connecting heterogeneous granular networks with multiple attributes through various connection methods. As can be seen from Table 1, the characteristics of air defense and anti-missile kill networks are very similar to those of granular hypernetworks. Granular hypernetworks can be used to describe the system architecture and internal information flow relationships of air defense and anti-missile kill networks well, and combined with the operational loop theory, they can effectively describe the operational process and dynamic changes.

[0256] <6> To facilitate the description of the architecture of the air defense and anti-missile kill network, its network topology units are defined as shown in Table 2.

[0257] Table 2. Topological Units of Air Defense and Missile Defense Kill Network Architecture

[0258]

[0259] <7> Attribute inheritance relationship of air defense and anti-missile kill network

[0260] To facilitate the analysis of the different levels of air defense and anti-missile kill network structure formed by granularity differences, we propose an attribute inheritance relationship, that is, the combat unit is a relatively stable configuration composed of different functional components, and the early warning, command and control, and strike attributes of the functional components are directly inherited to the combat unit.

[0261] To facilitate the description of the air defense and missile defense kill network operational process using operational loop theory, it is assumed that the incoming target is an attribute of the air defense and missile defense kill network system granularity, that is, the attribute vector of the air defense and missile defense kill network granularity can be [δ s ,δ d ,δ a ,δ tThe symbols ] respectively indicate that it possesses the attributes of early warning, accusation, strike, and target.

[0262] According to Table 2, f(s) ij ) = [1,0,0,0] indicates that it only has the warning attribute, f(d ik ) = [0,1,0,0] indicates that it only has the accusation attribute, f(a il ) = [0,0,1,0] indicates that it only has the attack attribute, f(t) ih The value of [0,0,0,1] indicates that the combat unit O only possesses target attributes. i By {s ij ,d ik ,a il ,t ih}composition,

[0263] f(O i )=f(s ij )∨f(d ik )∨f(a il )∨f(t ih Obviously, f(O) i There are four basic types, as shown in Table 3.

[0264] Table 3 Classification of Node Attribute Types in Air Defense and Anti-Missile Kill Network System

[0265]

[0266] <8> Fine-grained air defense and anti-missile kill network structure: This refers to the configuration relationship describing the internal functions of a combat unit based on the basic configuration of the combat unit, denoted as OA0. OA0 represents the various functional components of the air defense and anti-missile kill network or a certain type of weapon system, and is the physical structural layer of the air defense and anti-missile kill network. This paper defines it as the component layer. According to Definition 1, we know...

[0267] OA0 = H0 = < V0, E0, V M0 L0>

[0268] Where V0 represents the set of functional components, E0 represents the set of edges connecting functional components, and V M0 L0 represents the functional component hierarchy and the tuples belonging to this hierarchy.

[0269] <9> Coarse-grained air defense and missile defense kill network structure: This refers to a structure based on combat units as the basic configuration, describing the functional configuration relationships between combat units, and capable of forming different functional networks within the air defense and missile defense kill network system, denoted as OA. i = (i = 1, 2, 3, 4), then OA i This refers to combat units capable of independent operations, such as tactical-level air defense and anti-missile combat units; this is defined as the system layer in this paper. According to Definition 3...

[0270] OA i =H i = <V i E i V Mi ,L i >

[0271] Among them, V i E represents the set of combat units. i V represents the edge set of combat units. Mi and L i This represents the operational unit level and the binary group belonging to that level.

[0272] <10> Modeling of Air Defense and Missile Defense Kill Network System Based on Granularity Hypernetwork

[0273] According to the definition of the combat loop, the standard air defense and anti-missile kill network combat loop is a kill loop composed of early warning, command and control, strike and target nodes, which is one of the meta-paths. However, in actual combat, to complete an air defense and anti-missile combat mission, it is often necessary to associate multiple similar nodes, or to improve combat efficiency, multiple nodes need to cooperate to realize the expansion of the standard combat loop to the generalized combat loop. The meta-paths of the generalized combat loop correspond one-to-one with the kill chain. According to the research in the literature

[26] , it can be deduced that the kill chain of the air defense and anti-missile kill network mainly consists of the following 8 types, as shown in Table 4.

[0274] Table 4 Commonly Used Metapaths and Meanings in Air Defense and Anti-Missile Kill Networks

[0275]

[0276] 1. Initial conditions

[0277] To verify the advantages of the air defense and missile defense kill network based on granular supernetworks, the air defense and missile defense kill network based on granular supernetworks is compared with the air defense and missile defense system architecture based on traditional networks, and the following scenarios are set:

[0278] (1) One regional command and control center, with three tactical command and control centers under it;

[0279] (2) Each tactical command center is equipped with 3 air defense and anti-missile combat battalions and 1 early warning radar;

[0280] (3) Each air defense and anti-missile combat battalion is equipped with one air defense guidance radar and one air defense and anti-missile fire unit.

[0281] (4) During the air defense and anti-missile operations, there were a total of 5 air attack targets.

[0282] After analysis, this system architecture has node R N=30, including 5 target nodes, 12 early warning nodes, 4 decision-making nodes, and 9 strike nodes. Due to the limitations of the target's direction of attack and weapon type, target node T1 can only be detected by early warning nodes S1, S2, S3, and S4, and the assigned command and control node D2 controls strike nodes A1, A2, and A3 to destroy target node T1; target nodes T2 and T3 can only be detected by early warning nodes S5, S6, S7, and S8, and the assigned command and control node D3 controls strike nodes A4, A5, and A6 to destroy target nodes T2 and T3; target nodes T4 and T5 can only be detected by early warning nodes S9, S1, S2, S3, and S4. 10 ,S 11 ,S 12 The system detects and, under the control of the assigned command node D4, attacks nodes A7, A8, and A9 to kill target nodes T4 and T5.

[0283] like Figure 3 As shown, this figure was generated by the network analysis software UCINET. In the traditional air defense and anti-missile system architecture, after the early warning node captures target intelligence data, due to the limitations of equipment models and networks, it is impossible to share intelligence information. It can only transmit intelligence information to the regional command and control center or directly to the corresponding tactical command and control center. The tactical command and control center can only control the strike equipment under its jurisdiction. According to formula (22), the network aggregation coefficient based on the traditional air defense and anti-missile system architecture is 0.9222.

[0284] like Figure 4 As shown, in the air defense and missile defense kill network based on granular hypernetworks, after the early warning nodes detect a target, each node can share intelligence data to form air situation data, which is then acquired by the regional command and control center as needed for operations. Command and control centers at all levels can control not only their assigned strike nodes but also other strike nodes across domains. However, due to system limitations, the information capacity that each tactical command and control center can simultaneously receive intelligence data is set to a quantitative limit. i D =8 (i=2,3,4), and the maximum number of command and control nodes is 6. Using formula (22), the network aggregation coefficient of the air defense and anti-missile kill network based on granular hypernetworks is 1.4556. Compared with the air defense and anti-missile system architecture based on traditional networks, the resilience increases by 57.84%.

[0285] 2. Operation process and operational phases

[0286] To compare the resilience of the two regional air defense and missile defense system models mentioned above, different attack and recovery strategies are set during the combat process. Let the initial combat time be t0 = 0, and the time of attack be t_0. a =300s, the time t is the time it takes for the attacked node to completely fail. d=480s, Δt=60s, the time to activate different recovery strategies is 2Δt. Since the backup node and the failed node have the same function, the level of restored function is the same, while the replacement node can only restore part of the function. At the initial combat moment, both regional air defense and anti-missile combat systems meet the interception mission requirements, i.e., C(t0)=1, and the intensity of both types of attack modes is δ=0.1, i.e., the number of attacking nodes N. r =[N R ·δ]=3. In a random attack strategy, no specific air defense or missile defense system node or link is specified for attack. In a deliberate attack strategy, attacks are conducted according to the importance ranking of various nodes. Node importance is ranked by degree; the more operational rings a node belongs to, the higher its degree. The number of operational rings a node belongs to is calculated using the formula as follows: Figure 5 As shown.

[0287] 3. Attack and Recovery Strategies

[0288] In the initial stage, the air defense and missile defense kill network based on granular hypernetworks adopts traditional network connections. Therefore, the number of air defense and missile defense operational loops that meet mission requirements is the same as the number of operational loops based on traditional networks, R. A =240, when a deliberate attack is launched, its early warning nodes S5~S 12 One attack is launched on each of the three high-importance nodes: decision-making node D1, and attack nodes A4-A9. During random attacks, warning nodes S1-S9 are also targeted. 12 One node from each of the decision-making nodes (D1-D2) and the attack nodes (A1-A93) will be attacked. Hypernetwork connectivity will be enabled, and reconnection, backup, replacement, and repair / recovery strategies will be employed to restore system capabilities.

[0289] 4. Verification Analysis

[0290] 4.1 Resilience Assessment of Air Defense and Missile Defense Kill Network under Deliberate Attack Strategy

[0291] Based on the node-based strike strategy, nodes D1, D3, and D4 are prioritized for attack in this case study. However, considering the actual equipment system, the command and control system is designed to process only eight early warning messages simultaneously and can command a maximum of six strike nodes at the same time. Strategies such as reconnection, repair, and replacement are employed for air defense and missile defense systems based on traditional networks and granular hypernetworks.

[0292] (1) After being attacked, the system nodes of the hypernetwork-based air defense and anti-missile kill network are in t a Reconnection and recovery are initiated immediately, at which point the number of combat rings is [number missing]. The system consists of three operational loops. Employing a super-network reconnection strategy, the average recovery time is 2Δt. The time required to recover D1 is Δt, followed by the recovery of D3 and D4, resulting in complete air defense and anti-missile operational loops of 48, 120, and 240 respectively.

[0293] (2) In the absence of backup, the air defense and anti-missile system based on the super network can be reconnected by repairing nodes, with an average recovery time of 3Δt.

[0294] (3) When an air defense and anti-missile system based on traditional communication networks is attacked, the attacked nodes become completely ineffective and cannot immediately carry out actions such as reconnection and repair. Even with backups, the only option is to perform random repairs and reconnections, first restoring D3, then D1 and D4, with an average recovery time of 2Δt. The number of air defense and anti-missile combat rings increases by 36, 60, and 240 respectively.

[0295] (4) Similarly, in the absence of backups, the air defense and anti-missile system based on traditional communication networks can only be restored by repairing nodes, with an average recovery time of 3Δt.

[0296] In summary, the final solution results and elasticity measurement data of the air defense and anti-missile system under deliberate attack are as follows: Figure 6 As shown in Table 5.

[0297] Table 5 Comparison of Elastic Parameters of Air Defense and Anti-Missile Systems under Deliberate Attack Strategy

[0298] plan d <![CDATA[v d ]]> r <![CDATA[v r ]]> <![CDATA[R d ]]> <![CDATA[R r ]]> R 1 0.9000 2.2000 0.9000 1.8333 0.1381 5.2068 0.7191 2 0.9000 4.6667 0.9000 1.5555 0.0150 4.0550 0.0608 3 0.9500 2.2000 0.9500 1.8333 0.1237 5.7067 0.7059 4 0.9500 4.6667 0.9500 1.5555 0.0119 4.3830 0.0522

[0299] 4.2 Resilience Assessment of Air Defense and Missile Defense Kill Network under Random Attack Strategy

[0300] Based on the node-based strike strategy, the case prioritizes striking nodes D2, S3, and A8. However, considering the actual equipment system, the command and control system is designed to handle only eight early warning messages simultaneously and can command a maximum of six strike nodes at the same time. Strategies such as reconnection, repair, and replacement are employed for air defense and missile defense systems based on traditional networks and granular hypernetworks.

[0301] (1) After being attacked, the air defense and anti-missile kill network based on granular hypernetworks has a system node at t a Reconnection and recovery are initiated immediately, at which point the number of combat rings is [number missing]. The system consists of three operational loops. A super-network reconnection strategy is adopted, with an average recovery time of 2Δt. Recovery requires D2 time of Δt, followed by the recovery of S3 and A8, forming complete air defense and anti-missile operational loops of 196, 208, and 240 respectively.

[0302] (2) In the absence of backup, the air defense and anti-missile system based on granular hypernetwork can be reconnected by repairing nodes, with an average recovery time of 3Δt.

[0303] (3) In air defense and anti-missile systems based on granular traditional networks, after being attacked, the attacked nodes become completely ineffective and cannot be immediately reconnected and repaired. Even with backups, the only option is to perform random repairs and reconnections, first restoring A8, then S3 and D2, with an average recovery time of 2Δt. The number of air defense and anti-missile combat rings increases by 125, 143, and 240 respectively.

[0304] (4) Similarly, in the absence of backups, the air defense and anti-missile system based on traditional networks can only be restored by repairing nodes, with an average recovery time of 3Δt.

[0305] In summary, the final solution results and elasticity measurement data of the air defense and anti-missile system under random attack are as follows: Figure 7 As shown in Table 6.

[0306] Table 6 Comparison of Elastic Parameters of Air Defense and Anti-Missile Systems under Random Attack Strategies

[0307] plan d <![CDATA[v d ]]> r <![CDATA[v r ]]> <![CDATA[R d ]]> <![CDATA[R r ]]> R 1 0.2958 2.2000 0.2958 1.8333 0.5216 1.7201 0.8972 2 0.2958 4.6667 0.2958 1.5555 0.2514 1.5844 0.3983 3 0.6292 2.2000 0.6292 1.8333 0.2505 3.1692 0.7940 4 0.6292 4.6667 0.6292 1.5555 0.0531 2.6610 0.1412

[0308] 5. Combat capability of the air defense and anti-missile kill network

[0309] 5.1 Modeling of Kill Net Functional Components

[0310] According to the air defense and anti-missile combat capability assessment method in 3.1, for indicators with membership empirical formulas, the calculation is performed directly, and the remaining indicators are calculated using Pythagorean binary semantic fuzzy sets. According to the combat loop process and sequence, experts first evaluate the five target nodes, and the evaluation results of their indicators are shown in Table 7.

[0311] Table 7 Evaluation Table of Target Nodes

[0312]

[0313] The target-type node indicators meet the capability requirements and the weighted information content values ​​are shown in Table 8.

[0314] Table 8. Capability Requirement and Weighted Information Values ​​of Target Category Node Indicators

[0315]

[0316] Secondly, experts evaluated the 12 early warning nodes, and the evaluation results are shown in Table 9.

[0317] Table 9 Evaluation Table of Indicators for Early Warning Nodes

[0318]

[0319] Continued table

[0320]

[0321] Table 10 shows the required performance of indicators for early warning nodes and their weighted information content.

[0322] Table 10 Capability Requirements and Weighted Information Values ​​for Early Warning Node Indicators

[0323]

[0324] Next, the indicators for the four decision nodes were calculated using empirical formulas, and their required capability and weighted information values ​​are shown in Table 11.

[0325] Table 11 Capability Requirements and Weighted Information Values ​​for Decision-Making Node Indicators

[0326]

[0327] Finally, experts evaluated the nine strike points, and the evaluation results are shown in Table 12.

[0328] Table 12 Evaluation Table of Various Indicators for Strike-Type Nodes

[0329]

[0330] Continued table

[0331]

[0332]

[0333] Table 13 shows the degree to which the performance indicators of attack-type nodes meet the capability requirements and their weighted capability values.

[0334] Table 13 Capability Demand and Weighted Information Values ​​for Strike-Related Node Indicators

[0335]

[0336] 5.2 Modeling the connecting edges of the air defense and anti-missile kill network

[0337] Based on the capability values ​​and information entropy of the edges of the air defense and anti-missile network, it is assumed that the capability values ​​and information entropy of the edges of the air defense and anti-missile kill network based on the traditional network and the air defense and anti-missile kill network based on the super network are the same. It is also assumed that the capability values ​​and information entropy of the same type of TS, SS, SD, DD, DA, and AT are the same, as shown in Table 14.

[0338] Table 14 Capability values ​​and information entropy of the connecting edges of the air defense and anti-missile kill network

[0339]

[0340]

[0341] Based on the kill network combat capability calculation method, the combat capabilities of traditional air defense and anti-missile kill networks and hypernetic air defense and anti-missile kill networks against five targets are as follows: Figure 8 As shown.

[0342] 6. Results Analysis

[0343] (1) Through Figure 6 and Figure 7 It can be concluded that, under the same conditions, the air defense and anti-missile kill network based on granular hypernetworks has better energy reduction, energy recovery rate, recovery degree, and structural elasticity than the air defense and anti-missile system based on traditional networks, which demonstrates the superiority of the air defense and anti-missile kill network model based on granular hypernetworks.

[0344] (2) With redundant backups, regardless of the network system, the recovery speed after being attacked is higher than that without redundant backups. Therefore, while accelerating the construction of air defense and anti-missile systems, we should also attach importance to the construction of battlefield weapon and equipment reserves to improve the system's resilience.

[0345] (3) In contrast to attack strategies, under the condition of deliberate attack strategy, regardless of the type of air defense and anti-missile system, the attack is aimed at nodes with high contribution rates. Compared with random attack strategy, this attack method significantly reduces the system's energy by more than 45%. Therefore, in the process of system construction and actual combat, it is necessary to strengthen the modularization, decentralization and networking of the system. For important system nodes, it is necessary to strengthen the camouflage protection of the positions, electronic attack and defense, and mobility performance to prevent important nodes from being interfered with and to ensure that the air defense and anti-missile kill network system can play its due role.

[0346] (4) Figure 8 This study reflects the operational capabilities of air defense and missile defense systems based on two types of networks against five targets, demonstrating that the capability assessment method for air defense and missile defense kill networks based on improved information entropy can effectively evaluate network systems with relatively high heterogeneity. By constructing a model architecture of network system nodes and edges, a judgment method based on Pythagorean binary semantic fuzzy logic is proposed, achieving accurate determination of the membership degree of node attribute indicators. Combined with empirical formulas, a quantitative assessment of the operational capabilities of the air defense and missile defense kill network's operational loops and overall operational capabilities is achieved under complex indicator data conditions.

[0347] (5) Under the same conditions of early warning, decision-making, and strike equipment, the air defense and anti-missile kill network based on granular hypernetwork has a higher combat capability against five targets than the air defense and anti-missile kill network based on traditional network. Specifically, T1 is 32.2% higher, T2 is 22.9% higher, T3 is 29.6% higher, T4 is 38.7% higher, and T5 is 18.3% higher. The overall combat strength is 28.2% higher than that of the air defense and anti-missile kill network based on traditional network. This shows the importance of breaking the traditional fixed system information flow architecture and accelerating the construction of the air defense and anti-missile kill network based on granular hypernetwork. At present, while vigorously developing high-performance weapons and equipment, coordinating the decoupling of weapons and equipment, realizing intelligence information sharing, accelerating the intelligent construction of the system, and improving the flexibility of the air defense and anti-missile system are also an indispensable part of the construction of the air defense and anti-missile system.

[0348] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention.

Claims

1. A method for constructing an air defense and anti-missile kill network model based on granular hypernetworks, characterized in that, Includes the following steps: S1.1, Task Analysis In the process of air defense and anti-missile operations, analyze the weapons and equipment of the air defense and anti-missile kill network, the relationships between the equipment, and the operational procedures. S1.2, Functional Component Modeling Based on equipment attributes, the equipment in the air defense and anti-missile kill network system is defined as target nodes, early warning nodes, decision-making nodes, and strike nodes. S1.3, Connecting Edge Modeling Based on the operational loop closure process, the actual operational flow of the air defense and anti-missile kill network and the interaction relationships between equipment components adopt the following six connection methods. Therefore, the set of edges in the air defense and anti-missile kill network based on granular hypernetworks is represented as follows: （1） For early warning of border This indicates that the air defense and anti-missile early warning and detection system implements full-domain early warning for enemy targets, obtains the threat type, speed, altitude and direction of target nodes, predicts the possible movement trajectory of the target, forms a one-way edge from the target to the intelligence system, and can measure the early warning capability of the air defense and anti-missile kill network S functional component for target T. For intelligence sharing This refers to the bidirectional edge that allows equipment functional component nodes within the early warning system to share target information with each other, and measures the information transmission capability of S-class functional component nodes. For intelligence This indicates that the early warning equipment transmits target characteristics, category, location, and speed information to the functional component nodes of the command and control equipment via a one-way edge, as well as the intelligence edge shared by the friendly combat system. S represents the information sent by the functional component node, and D represents the information received by the node. For the charge transmission edge This refers to a one-way link in the air defense and anti-missile system where command and control equipment at all levels transmit intelligence information through a fusion and processing process along the command link. Accusation of the side This indicates that the command and control equipment node transmits the interception and strike command to the soft and hard strike nodes via a one-way edge. The information transmission and processing capabilities from the command and control node to the strike node include the interception weapon's time, transmission and reception rate, accuracy, information connectivity, transmission rate, transmission quality, communication quality, and communication latency. To combat border This refers to the one-way edge formed by the interception and attack of various soft and hard kill equipment functional component nodes on air attack target nodes. In the process of air defense and anti-missile kill network operations, the kill classification of air attack targets includes two categories: electronic soft kill and firepower hard kill. Soft kill refers to the activities of using electronic weapons to interfere with, reduce or destroy the electronic devices of air attack targets, thereby rendering them incapable of combat. Hard kill refers to the activities of using missiles and artillery weapons to destroy air attack targets. S1.4, the air defense and anti-missile kill network system architecture model based on granular hypernetwork is represented as follows: （21） In formula (21), Let E represent the set of all nodes, and let E represent the set of all connected edges. The tuple represents the granularity and its corresponding level, where L represents the set of level types. Functional attributes representing granularity These represent the target layer, early warning layer, decision-making layer, and strike layer, respectively.

2. The method for constructing an air defense and anti-missile kill network model based on granular hypernetworks according to claim 1, characterized in that: The equipment attributes in step S1.2 include early warning capability, command and control capability, strike capability, target capability, communication capability, spatial positioning capability, capacity, and time consumption. The formula for expressing the aforementioned early warning capability is: , These represent the detection range, scanning frequency, maneuvering speed, detection accuracy, and recognition probability of the equipment's functional component nodes, respectively. The formula for expressing the aforementioned accusation capability is: , These represent the response time, transmit / receive rate, and accuracy of the equipment's functional component nodes, respectively. The formula for expressing the aforementioned striking capability is: , These represent the strike accuracy, kill radius, jamming power, and maneuver speed of the equipment's functional component nodes, respectively. The formula for expressing the target capability is: , These represent the stealth coefficient, anti-electro-optical coefficient, anti-radar coefficient, anti-infrared coefficient, maneuverability, survivability, early warning time, and receiving power of the equipment's functional component nodes, respectively. The expression formula for the aforementioned communication is: , These respectively represent the communication coverage, transmission speed, communication quality, communication capacity, and communication latency of the equipment's functional components; The formula for expressing the spatial positioning capability is as follows: This indicates the functional components of the air defense and anti-missile kill network. The spatial location is a crucial factor in air defense and anti-missile combat systems, affecting the quantity and quality of the kill network's operational links. These represent the three-dimensional coordinates of the equipment's functional components in space. The formula for expressing the capacity is: This indicates the functional components of the air defense and anti-missile kill network. The capacity refers to the number of air attack targets that early warning equipment can detect simultaneously, the number of command and control equipment that can process command information and control equipment simultaneously, and the number of channels through which strike equipment can intercept air attack targets simultaneously. The formula for expressing the time consumed is: This indicates the functional components of the air defense and anti-missile kill network. The time consumed refers to the time spent by early warning equipment in detecting targets, decision-making nodes in processing information, command and control systems in preparing for strikes, and intercepting strikes in the formation of an air defense and anti-missile kill network combat ring.

3. The method for constructing an air defense and anti-missile kill network model based on granular hypernetworks according to claim 1, characterized in that: The actual combat process of the air defense and anti-missile kill network in step S1.3 includes detection, tracking, and identification, and the detection probability of the early warning radar. The formula is as follows: （2） In formula (2), Indicates that the early warning and detection equipment is in the The probability of detecting an airstrike target in a second scan. The frequency of the radar scan, when considered in air defense and anti-missile operations, taking into account the stealth capabilities of early warning equipment and targets, is expressed by the following formula: （3） In formula (3), Indicates environmental control parameters. Indicates the detection accuracy in node S membership function, These represent the radar detection range and the maneuvering speed, respectively, with A representing the specified detection range. This represents the photoelectric resistance coefficient, radar resistance coefficient, and infrared resistance coefficient of target node T. The membership functions of the three indicators, Indicate their respective weights. ; Tracking probability The formula for expressing it is: （4） （5） （6） In formulas (4), (5) and (6), Indicates the ability to track detected targets. Indicates the anti-tracking capability of air attack targets; Recognition probability The formula for expressing it is: （7） In formula (7), This indicates the probability of recognition.

4. The method for constructing an air defense and anti-missile kill network model based on granular hypernetworks according to claim 1, characterized in that: In step S1.3 For intelligence sharing This includes five indicators related to information transmission capabilities. It is a node and Information transmission rate between ,rate ,quality ,capacity and delay , , ,for: （8） in, , representing a node and The distance between them , , They represent and The difference between the coordinates of two points; （9） （10） （11） （12） In the above formula, This represents the detection distance between two different nodes. This indicates the scanning frequency of two different nodes. This represents the maneuvering speed of two different nodes. This indicates the detection accuracy of two different nodes. This indicates the recognition frequency of two different nodes.

5. The method for constructing an air defense and anti-missile kill network model based on granular hypernetworks according to claim 1, characterized in that: In step S1.3 Factors affecting the information processing capability of node D include response time. Send and receive rate Accuracy ,in Then the node and The formula for expressing the influencing factors between them is: （13） （14） （15） In formulas (13), (14), (15), This indicates the response time of different nodes. This indicates the time consumed by the node. This indicates the transmit / receive rate of different nodes. This indicates the accuracy of different nodes.

6. The method for constructing an air defense and anti-missile kill network model based on granular hypernetworks according to claim 1, characterized in that: In step S1.3, the soft-kill attack on the air strike target is affected by interference probability. and suppression probability The formula for describing this is: （16） （17） （18） In formulas (16), (17), (18), Indicates the speed of movement of the attacking node. Indicates intercepting weapon nodes Launched to kill target node The time taken This indicates the kill radius of the target node. Indicates the distance between the intercepting weapon and the target. These represent the target node's maneuver speed and warning time, respectively. This indicates the interference power of the attacking node. This represents the target node's survivability coefficient and received power. , , Indicates the node to be attacked With the target node The coordinate difference; Hard kill damage to airstrike targets is determined by hit probability. and probability of destruction The formula for describing this is: （19） （20） In formulas (19) and (20), Indicates the node to be attacked speed of movement Indicates the node to be attacked kill radius, Indicates the node to be attacked and target node The straight-line distance Representing the target node respectively The speed of movement and the warning time, Indicates intercepting weapon nodes Launched to the target The time taken This indicates the distance between the interceptor missile and the target is... hour, right The membership function of the damage. The membership function represents the survival coefficient of the target node. , These represent the corresponding coefficients.

7. An evaluation method for an air defense and anti-missile kill network model based on granular hypernetworks, employing the air defense and anti-missile kill network model based on granular hypernetworks as described in claim 1, characterized in that... Includes the following steps: S2.1, evaluate the air defense and anti-missile kill network combat system of the model; S2.2, assess the resilience of the combat system. The resilience indicators of the combat system include three stages: being attacked, capability decline, and capability recovery. S2.3 assesses operational capabilities, with operational capability indicators including the kill network's resilience and recoverability.

8. The evaluation method for the air defense and anti-missile kill network model based on granular hypernetworks according to claim 7, characterized in that: The evaluation method for the air defense and anti-missile kill network combat system in step S2.1 is as follows: S2.1.1 Calculate the number of nodes in the air defense and anti-missile kill network. Number of edges ; （22） In formula (22), Represents the set of all nodes. This represents the set of all connected edges; S2.1.2, Degree of elasticity of air defense and anti-missile kill network nodes ; Degree distribution refers to the probability distribution of node degrees. When a deliberate attack is launched against a combat system, the degree of the combat system follows a power-law distribution, that is... （23） In formula (23), Indicates node degree as The probability, It is the degree of the node. As an exponent greater than 1, it determines that the more uneven the shape distribution of the power-law distribution, the lower the resilience of the system network. When a combat system is attacked randomly, the degree of the combat system follows a Poisson distribution, that is... （24） In formula (24), Indicates node degree as The probability, It is the average degree of the network, that is, the average degree of all nodes in the network. It is the base of the natural logarithm. The more uniform the degree distribution, the lower the survivability of the combat system; S2.1.3, Calculate the elasticity of the aggregation coefficient of the air defense and anti-missile kill network. ; This indicates the degree of clustering of nodes in a combat system, and the clustering coefficient of these nodes is defined as follows: : （25） In formula (25), This represents the actual number of connected edges that a cluster of adjacent nodes possesses. Indicates the number of clusters; The concentration coefficient C of the air defense and anti-missile kill network combat system is （26） In formula (26), The number of nodes indicates that a combat system with a high aggregation coefficient has good cohesion and is easy to support each other. S2.1.4, Calculate the number of combat rings in the air defense and anti-missile kill network. ; The number of combat rings is the same as the number of kill chains. The number of combat rings is calculated using the transition matrix and the arrival matrix. Transition matrix: Let It's about nodes. With nodes The transition matrix between nodes, if the two nodes are related, then the elements in it... ,otherwise When node With nodes When they are nodes of the same type, Represents a homogeneous adjacency matrix; Arrival Matrix: and Let be the adjacent transition matrices, and Arrival node and The starting nodes are of the same type. The node transitions of the operational loop are obtained from the transition matrix. Therefore, the arrival matrix of the standard operational loop for an air-attack target T is represented as follows: （27） In formula (27), They represent the targets respectively. The arrival matrix from the target node to the early warning node, from the early warning node to the decision node, from the decision node to the strike node, and from the strike node to the target node; Air defense and anti-missile kill network targeting air attack targets The standard number of combat rings is （28） In formula (28), Indicates the number of target nodes. This indicates the number of combat rings for all target nodes. Indicates the first The number of combat rings for each target node.

9. The evaluation method for the air defense and anti-missile kill network model based on granular hypernetworks according to claim 7, characterized in that: The aforementioned combat capability assessment employs a combat capability assessment method based on Pythagorean binary semantic fuzzy logic. For a given Pythagorean binary semantic fuzzy number Its membership function is expressed as: （29） In formula (29), Indicates language scale, Indicates the degree of difference in linguistic information. Represents the Pythagorean fuzzy number. Indicates membership degree. Indicates non-membership degree; To complete combat missions according to a standard operational cycle, the uncertainties at the early warning node, decision-making node, strike node, and target node are set as follows: Let the uncertainty of completing the edge in the combat loop be . Assuming there are a total The first goal, targeting the first The number of combat rings for each target is: Then for the first one, The first goal The uncertainty of each combat loop is determined by both the nodes and the edges, namely... （30） Then the first The amount of uncertainty information for all operational links of a target is: （31） The combat ring against the first The operational effectiveness of each target is: （32） The air defense and anti-missile kill network is effective against all The overall combat capability of the target is: （33） In formulas (30) to (33), These represent the uncertainties in the task completion capabilities of the target node, early warning node, decision-making node, and strike node, respectively. These respectively represent the uncertainty in the mission completion capabilities of the early warning edge, intelligence sharing edge, intelligence edge, command and control transmission edge, command and control edge, and strike edge. Indicates the first The first goal The uncertainty of each operational link Indicates the first The operational effectiveness of each target. Indicates the first The amount of uncertainty information in all operational links of a target Indicates all Overall operational effectiveness of each target The weight is the importance weight or threat level weight of the target node.

10. The evaluation method for the air defense and anti-missile kill network model based on granular hypernetworks according to claim 7, characterized in that: The survivability of the kill net is determined by the degree and rate of energy reduction of the kill net system. for: （34） Killnet system energy reduction rate for: （35） Damage resistance Represented as: （36） The recoverability of the kill web is determined by the degree and rate of reactivation of the kill web system. for: （37） Kill net system reactivation rate for: （38） Then restorative Represented as: （39） The structural flexibility of the kill net system is: （40） In formulas (34) to (40), , , , , These represent the moments at the start of combat, the moment of being attacked, the moment when abilities reach their lowest point, the moment when abilities begin to recover, and the moment when abilities are fully recovered, respectively. , , , , They represent , , , , Real-time system combat capability Indicates the degree of decline in system capability. Indicates the rate at which the system's capability declines. Indicates the system's resilience. Indicates the degree of system resilience. The rate that indicates the system's recovery capability. Indicates system resilience. This indicates architectural flexibility.

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