Granular hypernetwork-based air defense and anti-guide killing net model construction and evaluation method

Abstract

The invention discloses a construction and evaluation method of an air defense and anti-conductance killing net model based on a granularity super network, and belongs to the technical field of combat systems, and the construction method of the air defense and anti-conductance killing net model based on the granularity super network comprises task analysis, functional component modeling, connection edge modeling and an air defense and anti-conductance killing net system architecture model based on the granularity super network. According to the invention, four types of nodes of target, early warning, decision making and strike are abstracted from an air defense and anti-missile combat system based on a combat ring theory, and an air defense and anti-missile killing network model based on a granularity super network is established; the energy reduction degree, the energy recovery rate, the recovery degree and the structural elasticity of the air-defense anti-conductance killing network based on the granularity super network are all superior to those of an air-defense anti-conductance system based on a traditional network, and meanwhile, a combat ability evaluation method based on the graduatory binary semantic fuzziness is provided, so that the node attribute index membership degree is accurately determined; and carrying out quantitative evaluation on the combat ring capability and the overall combat capability of the air defense anti-missile killing network.

Description

Technical Field

[0001] The present invention belongs to the technical field of combat systems, and in particular relates to a method for constructing and evaluating an air defense and anti-missile kill network model based on a granular hypernetwork. Background Art

[0002] Faced with the future aerospace threats that are multi-dimensional, diverse, agile and changeable across the entire domain, the air defense and anti-missile system may face the danger of node failure, link loss, and system dysfunction. How to reasonably construct an air defense and anti-missile combat system, build an air defense and anti-missile kill network, enhance the comprehensive flexibility of the system, and ensure that the air defense and anti-missile system continues to provide defense capabilities on the battlefield has become a hot issue in the current research in the field of air defense and anti-missile.

[0003] Domestic and foreign scholars have conducted many studies on the modeling and evaluation of combat systems. First, in terms of system modeling, there are four main methods. The first is a modeling method based on a multi-view architecture, such as a modeling method based on the DoDAF system framework. This method can intuitively display the combat process, but lacks quantitative information mapping; the second is an entity-based modeling method, such as an agent-based modeling method. This method can display the entities and their attributes in the combat system, but lacks information interaction between entities; the third is a modeling method based on structural decomposition, such as a modeling method based on a combat ring or kill chain. This method can display the logic of combat activities, but lacks consideration of global capabilities; the fourth is a modeling method based on complex network theory, such as a modeling method based on hypernetwork theory. This method can perform dynamic modeling and analysis, but lacks consideration of the granularity of entity nodes, and the use of hypernetworks alone for modeling cannot describe the kill loop of the air defense and anti-missile kill network. Therefore, a modeling method based on the theory of hypernetworks and combat rings is needed, and granular analysis is performed, which can not only describe the structure and attribute characteristics of the combat system in detail, but also effectively calculate the kill chain and prepare for elasticity evaluation.

[0004] There are four main methods for evaluating the resilience of combat architecture. The first is a resilience evaluation method based on decomposition and comprehensive analysis, such as establishing an indicator system, standardizing indicators, aggregating indicators, and obtaining the numerical values ​​of evaluation indicators. The advantage is that different indicators can be set according to different systems, which has a certain degree of flexibility, but it is too dependent on the rationality of the establishment of the indicator system. The second is a resilience evaluation method based on simulation, such as a threat-driven command information system resilience capability evaluation test method, a simulation method based on AnyLogic, and a simulation method based on Monte Carlo. The simulation-based resilience evaluation can simulate the dynamic process of the system well, but due to the complexity of the system, the comprehensiveness of resilience is often ignored, and most literature cannot provide actual simulation exercises. The third is a resilience evaluation method based on the resilience triangle, such as a resilience quantification model based on effectiveness thresholds. The resilience evaluation method based on the elastic triangle is mainly used to evaluate the recovery process and cannot comprehensively measure the system's anti-destruction and recovery. The fourth is a resilience evaluation method based on the effectiveness change curve. The resilience evaluation method based on the effectiveness change curve can overcome the defects of the resilience evaluation method based on the elastic triangle and can describe the overall damage degree, damage rate, recovery degree, and recovery rate of the combat system in detail. Summary of the invention

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

[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 a granular hypernetwork, comprising 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 relationship between the equipment, and the combat application process;

[0009] S1.2, Functional Component Modeling

[0010] According to the equipment attributes, the equipment in the air defense and anti-missile kill network system is defined as target nodes, early warning nodes, decision nodes and strike nodes;

[0011] S1.3, Connectivity modeling

[0012] According to the closed process of the combat loop, the actual combat process of the air defense and anti-missile kill network and the interaction relationship between equipment components adopt the following six connection methods. The edge set of the air defense and anti-missile kill network based on the granular hypernetwork is expressed as:

[0013]

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

[0015] The intelligence sharing edge S→S indicates a bidirectional edge in which equipment functional component nodes in the early warning system 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 of the early warning equipment transmitting information such as target characteristics, categories, positions, and speeds to the command and control equipment functional component nodes, 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 transmission edge D→D indicates a unidirectional edge in which the command and control equipment at all levels in the air defense and anti-missile system transmits intelligence information according to the command link after fusing and processing it.

[0018] The command edge D→A indicates a unidirectional edge where the command equipment node transmits the interception and strike command to the soft and hard strike node. The information transmission capability and information processing capability from the command node to the strike node include the time, sending and receiving rate, accuracy, information connectivity, transmission rate, transmission quality, communication quality, and communication delay of the interception weapon.

[0019] The strike edge A→T refers to the one-way edge formed by the interception and strike of the air strike target node by the functional component nodes of various soft and hard kill equipment. In the operation of the air defense and anti-missile kill network, the kill classification of air strike targets includes electronic soft kill and firepower hard kill. Soft kill refers to the activity of using electronic weapons to interfere with, reduce or destroy the electronic devices of air strike targets, thereby making them lose their combat capability; hard kill refers to the activity of destroying air strike targets with weapons such as missiles and artillery.

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

[0021]

[0022] In formula (21), V represents the set of all nodes, E represents the set of all edges, and V M represents a tuple of granularity and the level to which it belongs, L represents a set of level types, q i represents the functional property of granularity, lt ,l s ,l d ,l a They 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 capability, strike capability, target capability, communication capability, spatial location capability, capacity, and consumption time;

[0024] The expression formula of the early warning capability is: They represent the detection distance, scanning frequency, maneuvering speed, detection accuracy, and recognition probability of the equipment functional component node respectively;

[0025] The expression formula of the accusation capability is: They represent the response time, receiving and sending rate, and accuracy of the equipment functional component nodes respectively;

[0026] The expression formula of the striking ability is: They represent the strike accuracy, killing radius, interference power, and maneuvering speed of the equipment functional component nodes respectively;

[0027] The expression formula of the target capability is: They respectively represent the stealth coefficient, photoelectric resistance coefficient, radar resistance coefficient, infrared resistance coefficient, maneuvering speed, survival coefficient, warning time and receiving power of the equipment functional component node;

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

[0029] The expression formula of the spatial position capability is: Represents the equipment function component q in the air defense and anti-missile killing network i The spatial position of is an important factor in the equipment of the air defense and anti-missile combat system, and is related to the number and quality of the kill network combat loop. i ,y i ,z i Respectively represent the three-dimensional coordinates of the functional components of the equipment in space;

[0030] The capacity is expressed as follows: Represents the equipment function component q in the air defense and anti-missile killing network i capacity, that is, the number of air raid targets detected by early warning equipment at the same time, the number of command and control equipment that processes command information and commands equipment at the same time, and the number of channels for strike equipment to intercept air raid targets at the same time;

[0031] The expression formula of the consumption time is: Represents the equipment function component q in the air defense and anti-missile killing network i The time consumed refers to the time consumed by the early warning equipment to detect targets, the decision-making nodes to process information, the command and control system to prepare for strikes, and the time consumed by intercepting and striking in the formation of the air defense and anti-missile kill network combat loop.

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

[0033]

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

[0035] Represents the radar scanning frequency. In the process of air defense and anti-missile operations, considering the stealth performance of early warning equipment and targets, the expression formula is:

[0036]

[0037] In formula (3), 0<k<1 represents the environmental adjustment parameter, Represents the detection accuracy in node S The membership function of They represent the radar detection distance and maneuvering speed respectively, A represents the specified detection range, Indicates the photoelectric resistance coefficient, radar resistance coefficient, and infrared resistance coefficient of the target node T The membership function of the three indicators is: Indicates their respective weights;

[0038] Tracking probability P t The expression formula is:

[0039]

[0040]

[0041] In formulas (4), (5), and (6), p tr Indicates the tracking capability of the detected target, p z Indicates the anti-tracking capability of air strike targets;

[0042] Identification probability P r The expression formula is:

[0043]

[0044] In formula (7), represents the recognition probability.

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

[0046]

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

[0048]

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

[0050] Furthermore, in step S1.3 The factors affecting the information processing capability of node D include the response time P1 DD , transceiver rate Accuracy Then node D i With D j The expression formula of the influencing factors between (i≠j) is:

[0051]

[0052] In formulas (13), (14), (15), Indicates the response time of different nodes, Indicates the consumption time of the node, represents the sending and receiving rate of different nodes, Indicates the accuracy of different nodes.

[0053] Further, the interference probability of the soft kill to destroy the air raid target in step S1.3 is and suppression probability The expression formula for description is:

[0054]

[0055] In formulas (16), (17), (18), represents the maneuvering speed of the strike node, Indicates interception weapon node A i Launch to kill target node T j The time spent, Indicates the killing radius of the attack node, Indicates the distance from the interception weapon to the target, Respectively represent the maneuvering speed and warning time of the target node, represents the interference power of the attack node, represents the survival coefficient and receiving power of the target node, represents the coordinate difference between the attack node i and the target node j;

[0056] Hard kill damage to air strike targets using hit probability and probability of damage The expression formula for description is:

[0057]

[0058] In formulas (19) and (20), represents the maneuvering speed of attacking node m, represents the killing radius of the attack node m, represents the straight-line distance between the attack node m and the target node n, They represent the maneuvering speed and warning time of the target node n respectively, Indicates interception weapon node A m Launch to hit target T n The time spent, Indicates the distance between the interceptor missile and the target is When A m To T n The membership function of damage, represents the membership function of the target node survival coefficient, Represent the corresponding coefficients respectively.

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

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

[0061] S2.2, evaluate the anti-destruction capability of the combat system. The anti-destruction capability indicators of the combat system include three stages: being attacked, capability degradation and capability recovery;

[0062] S2.3, evaluate from the perspective of combat capability. Combat capability indicators include the anti-destruction capability and the recovery capability of the kill net.

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

[0064] S2.1.1, Calculate the number of nodes R 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 edges;

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

[0068] The degree distribution refers to the probability distribution of node degrees p(λ). When a combat system is deliberately attacked, the degree of the combat system follows a power law distribution, that is,

[0069] p(λ)~λ -γ (twenty three)

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

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

[0072]

[0073] In formula (24), p(λ) represents the probability that the node degree is λ, μ is the average degree of the network, that is, the average value of the degrees 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 invulnerability of the combat system.

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

[0075] R C Indicates the degree of clustering of combat system nodes, and defines the clustering coefficient of combat system nodes as C i :

[0076]

[0077] In formula (25), represents the actual number of edges that the adjacent node cluster has, and K represents the number of clusters;

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

[0079]

[0080] In formula (26), R N Indicates the number of nodes. A combat system with a higher clustering coefficient has better cohesion and is more conducive to mutual support;

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

[0082] The number of combat loops is the number of kill chains, and the number of combat loops is calculated using the transfer matrix and the arrival matrix;

[0083] Transfer matrix: Let A ij is about node v i With node v j The transfer matrix between them, if there is a relationship between two nodes, then the element a ij =1, otherwise a ij = 0, when node v i With node v j For nodes of the same type, A ij represents a homogeneous adjacency matrix;

[0084] Arrival Matrix: A ij and A jk is the adjacent transfer matrix, and A ij The arrival node and A jk The starting nodes are of the same type,

[0085] The node transfer of the combat ring is obtained according to the transfer matrix, so the arrival matrix of the standard combat ring for the air strike target T is expressed as

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

[0087] In formula (27), A TS ,A SD ,A DA ,A AT They represent the arrival matrices from the target node to the warning node, the warning node to the decision node, the decision node to the strike node, and the strike node to the target node for the target T respectively;

[0088] The number of standard combat rings for air strike target T in the air defense and anti-missile killing network is

[0089]

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

[0091] Furthermore, the combat capability is evaluated by using a combat capability evaluation method based on Pythagorean binary semantic fuzziness:

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

[0093]

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

[0095] Complete the combat mission according to the standard combat cycle, and set the uncertainty of the early warning node, decision node, strike node and target node as I S ,I D ,I A ,I T , let the uncertainty of the edge in the completed combat loop be I TS ,I SS ,I SD ,I DD ,I DA ,I AT , assuming that there are m targets in total, and the number of combat loops for the i-th target is n, then the uncertainty of the j-th combat loop for the i-th target is determined by both the nodes and the edges, that is,

[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] Then the uncertainty information of all combat loops of the i-th target is:

[0098]

[0099] The combat effectiveness of this combat loop 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 killing network against all m targets is:

[0102]

[0103] In formulas (30) to (33), I T ,I S ,I D ,I A Respectively represent the uncertainty of the task completion capabilities of the target node, warning node, decision node, and strike node, I TS ,I SS ,I SD ,I DD ,I DA ,I AT I represents the uncertainty of the ability to complete the mission on the early warning side, intelligence sharing side, intelligence side, command transmission side, command side, and strike side, respectively. ij represents the uncertainty of the jth combat loop of the i-th target, C i represents the combat effectiveness against the i-th target, I i represents the uncertainty information of all combat loops of the i-th target, C represents the overall combat effectiveness of all m targets, and λ i is the importance weight or threat level weight of the target node.

[0104] Furthermore, the anti-destruction performance of the kill net is determined by the energy degradation degree and energy degradation rate of the kill net. The energy degradation degree d of the kill net system is:

[0105]

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

[0107]

[0108] Invulnerability R d It is expressed as:

[0109] R d =exp(-d·v d ) (36)

[0110] The recovery of the kill net is determined by the degree and rate of recovery of the kill net. The degree of recovery of the kill net system r is:

[0111]

[0112] Killnet system regeneration rate v r for:

[0113]

[0114] The recovery R r It is expressed as:

[0115] R r =exp(r·v r ) (39)

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

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

[0118] In formulas (34) to (40), t0, t a ,t d ,t r ,t s They represent the time when the battle starts, the time when the attack occurs, the time when the ability decreases to the lowest point, the time when the ability starts to recover, and the time when the ability recovery is completed. C(t0), C(t a )、C(t d )、C(t r )、C(t s ) represent t0, t a ,t d ,t r ,t s The system combat capability at a certain moment, d represents the degree of system capability decline, v d Indicates the rate of system capacity decline, R d represents the system's invulnerability, r represents the system's ability to recover, and v r Represents the rate of system recovery, R rRepresents system recovery, R I Represents architectural resilience.

[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, warning, decision-making, and attack, and establishes an air defense and anti-missile kill network model based on a granular super network. The energy degradation degree, energy recovery rate, recovery degree, and structural elasticity of the air defense and anti-missile kill network based on the granular super network are better than those of the air defense and anti-missile system based on the traditional network. Therefore, the air defense and anti-missile kill network model based on the granular super network has certain advantages.

[0120] (2) The present invention proposes a combat capability assessment method based on Pythagorean binary semantic fuzziness by constructing a model architecture of network system nodes and edges, thereby achieving accurate determination of the membership of node attribute indicators and simultaneously achieving quantitative assessment of the combat loop capability and overall combat capability of the air defense and anti-missile kill network under complex indicator data. BRIEF DESCRIPTION OF THE DRAWINGS

[0121] Figure 1 It is a principle block diagram of an embodiment of the method for constructing an air defense and anti-missile kill network model based on a granular hypernetwork of the present invention.

[0122] Figure 2 It is a schematic diagram of the dynamic changes in the elasticity of the air defense and anti-missile killing network.

[0123] Figure 3 It is a topology diagram of the air defense and anti-missile system based on the traditional network.

[0124] Figure 4 It is a topological diagram of the air defense and anti-missile system based on the hypernetwork.

[0125] Figure 5 It is the number of combat cycles of the four nodes of the air defense and anti-missile system: target, early warning, decision-making, and strike.

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

[0127] Figure 7 This is a comparison chart of the elasticity of the air defense and anti-missile system under the random attack strategy.

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

[0129] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

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

[0131] S1.1, Task Analysis

[0132] During air defense and anti-missile operations, analyze the weapons and equipment of the air defense and anti-missile kill network, the relationship between equipment, and the combat application process.

[0133] S1.2, Functional Component Modeling

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

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

[0136] The expression formula of early warning capability is: They respectively represent the detection distance, scanning frequency, maneuvering speed, detection accuracy, and recognition probability of the equipment functional component node.

[0137] The expression formula of accusation capability is: They respectively represent the response time, receiving and sending rate, and accuracy of the equipment functional component nodes.

[0138] The expression formula of strike capability is: They respectively represent the strike accuracy, killing radius, interference power, and maneuvering speed of the equipment functional component node.

[0139] The expression formula of target capability is: They respectively represent the stealth coefficient, anti-photoelectric coefficient, anti-radar coefficient, anti-infrared coefficient, maneuvering speed, survivability coefficient, warning time and receiving power of the equipment functional component node.

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

[0141] The expression formula of spatial position ability is: Represents the equipment function component q in the air defense and anti-missile killing network i The spatial position of is an important factor in the equipment of the air defense and anti-missile combat system, and is related to the number and quality of the kill network combat loop. i ,y i ,z iThey respectively represent the three-dimensional coordinates of the equipment functional components in space.

[0142] The capacity expression formula is: Represents the equipment function component q in the air defense and anti-missile killing network i The capacity is the number of air raid targets detected by early warning equipment at the same time, the number of command and control equipment that processes command information and commands equipment at the same time, and the number of channels for strike equipment to intercept air raid targets at the same time.

[0143] The expression formula for consuming time is: Represents the equipment function component q in the air defense and anti-missile killing network i The time consumed refers to the time consumed by the early warning equipment to detect targets, the decision-making nodes to process information, the command and control system to prepare for strikes, and the time consumed by intercepting and striking in the formation of the air defense and anti-missile kill network combat loop.

[0144] S1.3, Connectivity modeling

[0145] According to the closed process of the combat loop, the actual combat process of the air defense and anti-missile kill network and the interaction relationship between equipment components adopt the following six connection methods. The edge set of the air defense and anti-missile kill network based on the granular hypernetwork is expressed as:

[0146]

[0147] It is the early warning edge T→S, which means that the air defense and anti-missile early warning detection system implements a full-area early warning on the enemy target, mainly obtaining the threat type, speed, altitude, direction of the target node, predicting the possible movement trajectory of the target, etc., forming a one-way edge from the target to the intelligence system, which can measure the early warning capability of the air defense and anti-missile kill network S functional component on the target T.

[0148] The actual combat process of the air defense and anti-missile kill network includes detection, tracking and identification. The detection probability P of the early warning radar is f The expression formula is:

[0149]

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

[0151] Represents the radar scanning frequency. In the process of air defense and anti-missile operations, considering the stealth performance of early warning equipment and targets, the expression formula is:

[0152]

[0153] In formula (3), 0<k<1 represents the environmental adjustment parameter, Represents the detection accuracy in node S The membership function of They represent the radar detection distance and maneuvering speed respectively, A represents the specified detection range, Indicates the photoelectric resistance coefficient, radar resistance coefficient, and infrared resistance coefficient of the target node T The membership function of the three indicators is: Indicates their respective weights;

[0154] Tracking probability P t The expression formula is:

[0155]

[0156] In formulas (4), (5), and (6), p tr Indicates the tracking capability of the detected target, p z Indicates the anti-tracking capability of air strike targets;

[0157] Identification probability P r The expression formula is:

[0158]

[0159] In formula (7), represents the recognition probability.

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

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

[0162]

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

[0164]

[0165]

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

[0167] It is the intelligence edge S→D, which means that the early warning equipment transmits information such as target characteristics, categories, positions, and speeds to the one-way edge of the command and control equipment functional component node, as well as the intelligence edge shared by the friendly combat system. S represents the sending information of the functional component node, and D represents the receiving information of the node.

[0168] It is the command and control transmission edge D→D, which refers to the unidirectional edge in which the command and control equipment at all levels in the air defense and anti-missile system fuses and processes the intelligence information and then transmits it according to the command link.

[0169] The factors affecting the information processing capability of node D include the response time P1 DD , transceiver rate Accuracy P3 DD , then node D i With D j The expression formula of the influencing factors between (i≠j) is:

[0170]

[0171] In formulas (13), (14), (15), Indicates the response time of different nodes, Indicates the consumption time of the node, represents the sending and receiving rate of different nodes, Indicates the accuracy of different nodes.

[0172] The command edge D→A indicates a unidirectional edge in which the command equipment node transmits the interception and strike command to the soft and hard strike node. The information transmission capability and information processing capability from the command node to the strike node include the time, sending and receiving rate, accuracy, information connectivity, transmission rate, transmission quality, communication quality, and communication delay of the interception weapon.

[0173] The strike edge A→T refers to the unidirectional edge formed by the interception and strike of air strike target nodes by various soft and hard kill equipment functional component nodes. In the air defense and anti-missile kill network operations, the kill classification of air strike targets includes electronic soft kill and firepower hard kill. Soft kill refers to the use of electronic weapons to interfere with air strike targets, reduce or destroy their electronic devices, thereby making them lose their combat capability; hard kill refers to the use of missiles, artillery and other weapons to destroy air strike targets.

[0174] The probability of soft-kill destruction of air raid targets using interference and suppression probability The expression formula for description is:

[0175]

[0176] In formulas (16), (17), (18), represents the maneuvering speed of the strike node, Indicates interception weapon node A i Launch to kill target node T j The time spent, Indicates the killing radius of the attack node, Indicates the distance from the interception weapon to the target, Respectively represent the maneuvering speed and warning time of the target node, represents the interference power of the attack node, represents the survival coefficient and receiving power of the target node, Represents the coordinate difference between the attack node i and the target node j.

[0177] Hard kill damage to air strike targets using hit probability and probability of damage The expression formula for description is:

[0178]

[0179] In formulas (19) and (20), represents the maneuvering speed of attacking node m, represents the killing radius of the attack node m, represents the straight-line distance between the attack node m and the target node n, They represent the maneuvering speed and warning time of the target node n respectively, Indicates interception weapon node A m Launch to hit target T n The time spent, Indicates the distance between the interceptor missile and the target is When Am To T n The membership function of damage, represents the membership function of the target node survival coefficient, Represent the corresponding coefficients respectively.

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

[0181]

[0182] In formula (21), V represents the set of all nodes, E represents the set of all edges, and V M represents a tuple of granularity and the level to which it belongs, L represents a set of level types, q i represents the functional property of granularity, l t ,l s ,l d ,l a They represent the target layer, early warning layer, decision-making layer and strike layer respectively.

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

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

[0185] The evaluation method of the air defense and anti-missile kill network combat system is:

[0186] S2.1.1, Calculate the number of nodes R 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 edges;

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

[0190] The degree distribution refers to the probability distribution of node degrees p(λ). When a combat system is deliberately attacked, the degree of the combat system follows a power law distribution, that is,

[0191] p(λ)~λ -γ (twenty three)

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

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

[0194]

[0195] In formula (24), p(λ) represents the probability that the node degree is λ, μ is the average degree of the network, that is, the average value of the degrees 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 invulnerability of the combat system.

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

[0197] R C Indicates the degree of clustering of combat system nodes, and defines the clustering coefficient of combat system nodes as C i :

[0198]

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

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

[0201]

[0202] In formula (26), R N Indicates the number of nodes. A combat system with a higher clustering coefficient has better cohesion and is more conducive to mutual support;

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

[0204] The number of combat rings is the number of kill chains, and the number of combat rings is calculated using the transfer matrix and the arrival matrix.

[0205] Transfer matrix: Let A ij is about node v i With node v j The transfer matrix between them, if there is a relationship between two nodes, then the element a ij =1, otherwise a ij = 0, when node v i With node v j For nodes of the same type, A ij Represents a homogeneous adjacency matrix.

[0206] Arrival Matrix: A ij and Ajk is the adjacent transfer matrix, and A ij The arrival node and A jk The starting nodes of the same type, the node transfer of the combat ring is obtained according to the transfer matrix, then the arrival matrix of the standard combat ring for the air strike target T is expressed as

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

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

[0209] The number of standard combat rings for air strike target T in the air defense and anti-missile killing network is

[0210]

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

[0212] S2.2, evaluate the anti-destruction capability of the combat system. The anti-destruction capability indicators of the combat system include three stages: being attacked, capability degradation and capability recovery. Figure 2 As shown, t0 represents the initial combat capability of the air defense and anti-missile killing network, t a Indicates the time when the combat system is attacked, t d Indicates the moment when the combat system capability declines to the lowest point, t r Indicates the moment when the combat system capability begins to recover, t s Indicates the time when the combat system capability is restored, t e Indicates the moment when the combat system completes its action. During this process, the degree and rate of the combat system's capability decline after being hit, and the degree and rate of combat capability recovery are important factors in judging the anti-destruction capability of the air defense and anti-missile kill network.

[0213] S2.3, evaluate from the perspective of combat capability. Combat capability indicators include the anti-destruction capability and the recovery capability of the kill net.

[0214] The combat capability is evaluated by using the combat capability evaluation method based on Pythagorean binary semantic fuzzy:

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

[0216]

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

[0218] Complete the combat mission according to the standard combat cycle, and set the uncertainty of the early warning node, decision node, strike node and target node as I S ,I D ,I A ,I T , let the uncertainty of the edge in the completed combat loop be I TS ,I SS ,I SD ,I DD ,I DA ,I AT , assuming that there are m targets in total, and the number of combat loops for the i-th target is n, then the uncertainty of the j-th combat loop for the i-th target is determined by both the nodes and the edges, that is:

[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] Then the uncertainty information of all combat loops of the i-th target is:

[0221]

[0222] The combat effectiveness of this combat loop 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 killing network against all m targets is:

[0225]

[0226] In formulas (30) to (33), I T ,I S ,I D ,I A Respectively represent the uncertainty of the task completion capabilities of the target node, warning node, decision node, and strike node, I TS ,I SS ,I SD ,I DD ,I DA ,I AT I represents the uncertainty of the ability to complete the mission on the early warning side, intelligence sharing side, intelligence side, command transmission side, command side, and strike side, respectively. ij represents the uncertainty of the jth combat loop of the i-th target, C i represents the combat effectiveness against the i-th target, I i represents the uncertainty information of all combat loops of the i-th target, C represents the overall combat effectiveness of all m targets, and λ i is the importance weight or threat level weight of the target node.

[0227] The anti-destruction performance of the kill net is determined by the energy degradation degree and energy degradation rate of the kill net. The energy degradation degree d of the kill net system is:

[0228]

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

[0230]

[0231] Invulnerability R d It is expressed as:

[0232] R d =exp(-d·v d ) (36)

[0233] The recovery of the kill net is determined by the degree and rate of recovery of the kill net. The degree of recovery of the kill net system r is:

[0234]

[0235] Killnet system regeneration rate v r for:

[0236]

[0237] The recovery R r It is expressed as:

[0238] R r =exp(r·v r ) (39)

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

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

[0241] In formulas (34) to (40), t0, t a ,t d ,t r ,t s They represent the time when the battle starts, the time when the attack occurs, the time when the ability decreases to the lowest point, the time when the ability starts to recover, and the time when the ability recovery is completed. C(t0), C(t a )、C(t d )、C(t r )、C(t s ) represent t0, t a ,t d ,t r ,t s The system combat capability at a certain moment, d represents the degree of system capability decline, v d Indicates the rate of system capacity decline, R d represents the system's invulnerability, r represents the system's ability to recover, and v r Represents the rate of system recovery, R r Represents system recovery, R I Represents architectural resilience.

[0242] The related noun concepts in this embodiment are explained as follows:

[0243] <1> Meta-Path K is a path defined on the hypernetwork H = (V, E) and represents the node v i , v j (i≠j) relation sequence, where v k ∈V,e j ∈E.

[0244] <2> The operational loop (OL) refers to the closed loop formed by the detection, command and control, strike and other weapon equipment entities in the weapon equipment system and the enemy target entities according to the established combat mission. That is, when the network node is attacked, or when the target does not appear, it can only be called an air defense and anti-missile system, and it cannot constitute a kill net. Only when the target appears in the air and is captured by the radar can the operational loop be formed, and it is possible to form a kill net.

[0245] <3> The System Architecture of Air Defense and Antimissile Kill Web (OA-ADAKW) decomposes the multifunctional weapons and equipment that perform air defense and antimissile combat missions into a large number of simple-function sensors, command and control, and strike functional components, and relies on communication network integration to form a dynamic kill web.

[0246] <4> Granular hypernetwork is a collection of nodes and edges in a hypernetwork, which is an abstract collection of multiple attribute information. It is the granular space of the hypernetwork. For network units with multiple attributes, we define them as functional components, and the edges between functional components are defined as connected parts. Defining granular hypernetwork is helpful to describe the network structure and analyze the internal operation mechanism of the network. Granular hypernetwork is represented as

[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 of the granularity, U i =∪U ip (p∈Q i )=[δ a ,δ b ,…,δ k ](δ a ,δ b ,…,δ k ∈[0,1]), indicating a vector with attributes, U ip represents the attribute threshold of the network granularity p, f:V→U represents the information function for extracting the network granularity attribute; e i = {Q i1 ,Q i2 ,…Q ij} represents the network granularity Q i , Q j The relationship between E = {e1, e2, …, e m} represents the set of hypernetwork granularity association relations; L = {l1,l 2, …,l α} represents the set of hierarchical networks in the granular hypernetwork; A tuple representing a granularity at the same level as the granularity, and satisfying the following conditions:

[0249] (1)

[0250] (2)

[0251] From the above definition, we can see that the system nodes are diverse in types, have different functions, and have complex relationships. The system operates in an intertwined and parallel manner, with outstanding node heterogeneity and association complexity.

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

[0253] Table 1 Structural characteristics and attributes of the air defense and anti-missile killing network

[0254]

[0255] According to the definition of granular hypernetwork, granular hypernetwork is a multi-heterogeneous network formed by connecting heterogeneous granular networks with multiple attributes through multiple connection methods. As can be seen from Table 1, the characteristic attributes of the air defense and anti-missile kill network are very similar to those of the granular hypernetwork. The granular hypernetwork can be used to well describe the architecture and internal information flow relationship of the air defense and anti-missile kill network, and combined with the combat ring theory, it can well describe the combat process and dynamic changes.

[0256] <6> In order to conveniently describe 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 the air defense and anti-missile kill network architecture

[0258]

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

[0260] In order to facilitate the analysis of different levels of air defense and anti-missile kill network architecture 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, that is, the early warning, command, and strike attributes of the functional components are directly inherited to the combat unit.

[0261] In order to conveniently use the combat ring theory to describe the combat process of the air defense and anti-missile kill network, it is assumed that the incoming target is an attribute of the air defense and anti-missile kill network system granularity, that is, the attribute vector of the air defense and anti-missile kill network granularity can be [δ s ,δ d ,δ a ,δ t], indicating that it has the attributes of early warning, accusation, attack and target,

[0262] According to Table 2, f(s ij )=[1,0,0,0] means it only has warning attribute, f(d ik )=[0,1,0,0] means it only has the accusation attribute, f(a il )=[0,0,1,0] means it only has the attack attribute, f(t ih )=[0,0,0,1] means it only has target attributes, combat unit O 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 ) has four basic types, as shown in Table 3.

[0264] Table 3 Classification of node attribute types in the air defense and anti-missile kill network system

[0265]

[0266] <8> Fine-grained air defense and anti-missile kill network structure: It refers to the configuration relationship of the internal functions of the combat unit based on the basic configuration of the combat unit, which is recorded as OA0. OA0 represents the various functional components or certain types of weapons and equipment of the air defense and anti-missile kill network. It is the physical structure layer of the air defense and anti-missile kill network. This article defines it as the component layer. According to Definition 1,

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

[0268] Among them, V0 represents the set of functional components, E0 represents the set of edges connecting functional components, and V M0 and L0 represents the functional component level and its tuple belonging to this level.

[0269] <9> Coarse-grained air defense and anti-missile kill network structure: It is based on the basic configuration of combat units, describes the configuration relationship between the functions of combat units, and can form different functional networks within the air defense and anti-missile kill network system, denoted as OA i =(i=1,2,3,4), then OA i It refers to a combat unit that can conduct independent operations, such as a tactical air defense and anti-missile combat unit. This paper defines it as the system layer. According to Definition 3,

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

[0271] Among them, V i Represents a combat unit set, E i represents the edge set of combat units, V Mi and L i A pair representing a combat unit level and the units that belong to this level.

[0272] <10> Modeling of air defense and anti-missile kill network system based on granular 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, attack and target nodes, which is one of the meta-paths. However, in actual combat, completing an air defense and anti-missile combat mission often requires associating multiple similar nodes, or in order to improve combat efficiency, multiple nodes need to be coordinated to achieve the expansion of the standard combat loop to the generalized combat loop. The meta-path of the generalized combat loop corresponds to the kill chain one by one. According to the research in the literature

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

[0274] Table 4 Common meta-paths and meanings of air defense and anti-missile kill network

[0275]

[0276] 1. Initial conditions

[0277] In order to verify the advantages of the air defense and anti-missile kill network based on the granular hypernetwork, the air defense and anti-missile kill network based on the granular hypernetwork is compared with the air defense and anti-missile system architecture based on the traditional network, and the scenario is set as follows:

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

[0279] (2) Each tactical command center is composed of three air defense and anti-missile combat battalions and one 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 firepower unit.

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

[0282] After analysis, this architecture has node R N=30, of which there are 5 target nodes, 12 warning nodes, 4 decision nodes, and 9 strike nodes. Due to the restrictions on the direction of the target and the type of weapon equipment, the target node T1 can only be discovered by the warning nodes S1, S2, S3, and S4, and the assigned command node D2 controls the strike nodes A1, A2, and A3 to kill the target node T1; the target nodes T2 and T3 can only be discovered by the warning nodes S5, S6, S7, and S8, and the assigned command node D3 controls the strike nodes A4, A5, and A6 to kill the target nodes T2 and T3; the target nodes T4 and T5 can only be discovered by the warning nodes S9, S10, S11, S12, S13, S14, S15, S16, S17, S18, S19, S20, S21, S22, S23, S24, S25, S26, S27, S28, S29, S30, S31, S32, S33, S34, S35, S36, S37, S38, S39, S40, S41, S42, S43, S44, S45, S46, S47, S48, S49, S40, S49, S40, S41, S4 10 ,S 11 ,S 12 It is discovered that the assigned command node D4 controls the attack nodes A7, A8, and A9 to kill the target nodes T4 and T5.

[0283] like Figure 3 As shown in Figure 2, the figure is generated by the network analysis software UCINET. Based on the traditional network-based air defense and anti-missile architecture, after the early warning node captures the target intelligence data, it is unable to share the intelligence information due to the limitations of equipment models and networks. The intelligence information can only be transmitted 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 its own strike equipment. According to formula (22), the network clustering coefficient based on the traditional air defense and anti-missile architecture is 0.9222.

[0284] like Figure 4 As shown in the figure, based on the air defense and anti-missile killing network of granular hypernetwork, after the early warning node finds the target, each node can share intelligence data with each other to form air situation data, which can be obtained on demand by the regional command and control center according to combat needs. The command and control centers at all levels can not only control the assigned strike nodes, but also control other strike nodes across domains. However, according to the requirements of the system's limitations, the information capacity of each tactical command and control center that can simultaneously receive intelligence data is set to quantitative i D =8 (i=2,3,4), and the maximum number of command and attack nodes is 6. According to formula (22), the network clustering coefficient of the air defense and anti-missile kill network based on the granular hypernetwork is 1.4556. Compared with the air defense and anti-missile system architecture based on the traditional network, the resilience increases by 57.84%.

[0285] 2. Operation process and number of operations

[0286] In order to compare the flexibility of the above two regional air defense and anti-missile system models, different attack strategies and recovery strategies are set during the combat process. Assume that the initial combat time is t0=0 and the time of being attacked is t a = 300s, the time for the attacked node to completely fail is t d=480s, Δt=60s, and the time to enable different recovery strategies is 2Δt. Since the backup node has the same function as the failed node, the restored function level 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, that is, C(t0)=1, and the strength of the two types of attack modes is δ=0.1, that is, the number of nodes attacked N r =[N R ·δ]=3. In the case of random attack strategy, the air defense and anti-missile system nodes or links to be attacked are not specified. In the case of deliberate attack strategy, the attack is carried out according to the importance of each type of node. The importance of nodes is sorted according to the degree of the node, that is, the more combat rings the node is in, the greater the degree. According to the formula, the number of combat rings each node is in is as follows: Figure 5 shown.

[0287] 3. Attack and recovery strategies

[0288] In the initial stage, the air defense and anti-missile kill network based on the granular super network adopts the traditional network connection, so the number of air defense and anti-missile combat rings that meet the mission requirements is consistent with the number of combat rings based on the traditional network. A =240, when a deliberate attack is carried out, the warning nodes S5~S 12 , decision-making node D1, and attack nodes A4~A9 of three types of high importance nodes are attacked one each; when implementing random attacks, the warning nodes S1~S 12 , decision-making nodes D1~D2, attack nodes A1~A93, each attack 1 node. Enable the super network connection mode, and adopt the reconnection, backup, replacement, and repair recovery strategies to restore the system capacity.

[0289] 4. Verification Analysis

[0290] 4.1 Assessment of the resilience of the air defense and anti-missile kill network under the deliberate attack strategy

[0291] According to the node attack strategy, the D1, D3, and D4 nodes are prioritized in this case, but considering the actual equipment system, the command and control system is set to only process 8 warning information at the same time and command a maximum of 6 attack nodes at the same time. Reconnect, repair, and replace strategies are implemented for the air defense and anti-missile system based on traditional networks and granular hyper networks.

[0292] (1) After the hyper-network-based air defense and anti-missile kill network is attacked, the system nodes are a Reconnection recovery is performed at any time, and the number of combat rings at this time is The super network reconnection strategy is adopted, with an average recovery time of 2Δt. The time required to recover D1 is Δt, and then D3 and D4 are recovered to form a complete air defense and anti-missile combat ring of 48, 120, and 240 respectively.

[0293] (2) When the hyper-network-based air defense and anti-missile system has no backup, it can be reconnected by repairing the nodes, with an average recovery time of 3Δt.

[0294] (3) After the air defense and anti-missile system based on the traditional communication network is attacked, the attacked nodes are completely ineffective and cannot be immediately reconnected or repaired. If there is a backup, the only option is to use random repair and reconnection, first restore D3, then restore D1 and D4. The average recovery time is 2Δt, and the number of air defense and anti-missile combat rings increases by 36, 60, and 240 respectively.

[0295] (4) Similarly, when the air defense and anti-missile system based on the traditional communication network has no backup, it can only be restored by repairing the nodes, and the average recovery time is 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 And as shown in Table 5.

[0297] Table 5 Comparison of elastic parameters of air defense and anti-missile system 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 Evaluation of the elasticity of the air defense and anti-missile kill network under the random attack strategy

[0300] According to the node attack strategy, the three nodes D2, S3, and A8 are prioritized in this case, but considering the actual equipment system, the command and control system is set to only be able to process 8 warning information at the same time and command a maximum of 6 attack nodes at the same time. Reconnection, repair, and replacement strategies are implemented for the air defense and anti-missile system based on traditional networks and granular hyper networks.

[0301] (1) After the air defense and anti-missile killing network based on the granular hypernetwork is attacked, the system nodes are a Reconnection recovery is performed at any time, and the number of combat rings at this time is The super network reconnection strategy is adopted, with an average recovery time of 2Δt. The recovery time required for D2 is Δt, and then S3 and A8 are restored to form a complete air defense and anti-missile combat ring of 196, 208, and 240 respectively.

[0302] (2) When the air defense and anti-missile system based on the granular hypernetwork has no backup, it can be reconnected by repairing the nodes, and the average recovery time reaches 3Δt.

[0303] (3) After the air defense and anti-missile system based on the granular traditional network is attacked, the attacked nodes are completely ineffective and cannot be reconnected and repaired immediately. If there is a backup, the only option is to use random repair and reconnection, first restore A8, then S3 and D2. The average recovery time is 2Δt, and the increase in the number of air defense and anti-missile combat rings is 125, 143, and 240 respectively.

[0304] (4) Similarly, when the traditional network-based air defense and anti-missile system has no backup, it can only be restored by repairing the nodes, and the average recovery time is 3Δt.

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

[0306] Table 6 Comparison of elastic parameters of air defense and anti-missile system under random attack strategy

[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 Killnet Functional Component Modeling

[0310] According to the air defense and anti-missile combat capability evaluation method in 3.1, the indicators with empirical membership formulas are calculated directly, and the remaining indicators are calculated using Pythagorean binary semantic fuzzy sets; according to the combat cycle process and sequence, the experts first judge the five target nodes, and the indicator evaluation results are shown in Table 7.

[0311] Table 7 Evaluation table of indicators of target class nodes

[0312]

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

[0314] Table 8 Capacity requirements and weighted information values ​​of target 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

[0320]

[0321] The indicator satisfaction degree and weighted information value of the early warning node are shown in Table 10

[0322] Table 10 Capacity requirements and weighted information values ​​of early warning node indicators

[0323]

[0324] Again, by using the empirical formula to calculate the four decision nodes, the indicators meet the capacity requirements and the weighted information values ​​are shown in Table 11.

[0325] Table 11 Capacity requirements and weighted information values ​​of decision-making node indicators

[0326]

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

[0328] Table 12 Evaluation table of various indicators of attack nodes

[0329]

[0330] Continued

[0331]

[0332]

[0333] The indicators of attack nodes meet the capability requirements and weighted capability values ​​as shown in Table 13.

[0334] Table 13 Capability requirements and weighted information values ​​of strike node indicators

[0335]

[0336] 5.2 Modeling the connection edges of the air defense and anti-missile killing network

[0337] Based on the capability value and information entropy of the air defense and anti-missile network edge, it is assumed that the capability value and information entropy of the network edge 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, and it is 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 air defense and anti-missile kill network connection edges

[0339]

[0340]

[0341] According to the calculation method of kill net combat capability, the combat capability of the traditional air defense and anti-missile kill net and the super network-based air defense and anti-missile kill net against five targets is as follows: Figure 8 shown.

[0342] 6. Results Analysis

[0343] (1) By Figure 6 and Figure 7 It can be concluded that under the same conditions, the energy degradation degree, energy recovery rate, recovery degree and structural elasticity of the air defense and anti-missile kill network based on the granular hypernetwork are better than those of the air defense and anti-missile system based on the traditional network, which illustrates the superiority of the air defense and anti-missile kill network model based on the granular hypernetwork.

[0344] (2) With redundant backup, no matter what kind of network system it is, when it is attacked, its recovery speed is higher than when it is without redundant backup. Therefore, while accelerating the construction of air defense and anti-missile systems, we should also pay attention to the construction of battlefield weapons and equipment reserves to improve system resilience.

[0345] (3) Comparing the attack strategies, under the conditions of deliberate attack strategies, no matter which air defense and anti-missile system is used, it will target nodes with higher contribution rates. Compared with the random attack strategy, this attack method obviously reduces the system's energy consumption 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 more important system nodes, it is necessary to strengthen position camouflage protection, electronic attack and defense, and mobility performance to prevent important nodes from being interfered with and attacked, so as to ensure that the air defense and anti-missile kill network system can play its due role.

[0346] (4) Figure 8 The results reflect the combat capability of the air defense and anti-missile system based on two types of networks against five targets, and illustrate that the capability evaluation method of the air defense and anti-missile kill network based on improved information entropy can effectively evaluate the network system with relatively high heterogeneity. By constructing the model architecture of the nodes and edges of the network system, an evaluation method based on Pythagorean binary semantic fuzziness is proposed, which realizes the accurate determination of the membership of the node attribute index. Combined with the empirical formula, the quantitative evaluation of the combat loop capability and overall combat capability of the air defense and anti-missile kill network under the condition of complex indicator data is realized.

[0347] (5) Under the same conditions of early warning, decision-making and strike equipment, the combat capability of the air defense and anti-missile kill network based on the granular super network against the five targets is higher than that based on the traditional network, among which 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 based on the traditional network. This shows the importance of breaking the traditional fixed system information flow architecture and accelerating the construction of a system network based on the granular super network. At present, while vigorously developing high-performance weapons and equipment, coordinating the decoupling of weapons and equipment, realizing intelligence information sharing, accelerating the construction of system intelligence, and improving the flexibility of the air defense and anti-missile system are also important links in the construction of the air defense and anti-missile system.

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

Claims

1. A method for constructing an air defense and anti-missile kill network model based on a granular hypernetwork, characterized in that: The following steps are involved: 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 relationship between the equipment, and the combat application process; S1.2, Functional Component Modeling According to the equipment attributes, the equipment in the air defense and anti-missile kill network system is defined as target nodes, early warning nodes, decision nodes and strike nodes; S1.3, Connectivity modeling According to the closed process of the combat loop, the actual combat process of the air defense and anti-missile kill network and the interaction relationship between equipment components adopt the following six connection methods. The edge set of the air defense and anti-missile kill network based on the granular hypernetwork is expressed as: The early warning edge T→S indicates that the air defense and anti-missile early warning detection system implements global early warning on enemy targets, mainly obtaining the threat type, speed, altitude, and direction of the target node, predicting the possible movement trajectory of the target, etc., forming a one-way edge from the target to the intelligence system, which can measure the early warning capability of the air defense and anti-missile kill network S functional component on the target T; The intelligence sharing edge S→S indicates a bidirectional edge in which equipment functional component nodes in the early warning system share target information with each other, and measures the information transmission capability of S-type functional component nodes; The intelligence edge S→D represents the one-way edge of the early warning equipment transmitting information such as target characteristics, categories, positions, and speeds to the command and control equipment functional component nodes, 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. The command transmission edge D→D indicates a unidirectional edge in which the command and control equipment at all levels in the air defense and anti-missile system transmits intelligence information according to the command link after fusing and processing it. The command edge D→A indicates a unidirectional edge where the command equipment node transmits the interception and strike command to the soft and hard strike node. The information transmission capability and information processing capability from the command node to the strike node include the time, sending and receiving rate, accuracy, information connectivity, transmission rate, transmission quality, communication quality, and communication delay of the interception weapon. The strike edge A→T refers to the one-way edge formed by the interception and strike of the air strike target node by the functional component nodes of various soft and hard kill equipment. In the operation of the air defense and anti-missile kill network, the kill classification of air strike targets includes electronic soft kill and firepower hard kill. Soft kill refers to the activity of using electronic weapons to interfere with, reduce or destroy the electronic devices of air strike targets, thereby making them lose their combat capability; hard kill refers to the activity of destroying air strike targets with weapons such as missiles and artillery. S1.4, the air defense and anti-missile kill network architecture model based on granular hypernetwork is expressed as: In formula (21), V represents the set of all nodes, E represents the set of all edges, and V M represents a tuple of granularity and the level to which it belongs, L represents a set of level types, q i represents the functional property of granularity, l t ,l s ,l d ,l a They 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 killing network model based on a granular hypernetwork according to claim 1 is characterized in that: The equipment attributes in step S1.2 include early warning capability, command capability, strike capability, target capability, communication capability, spatial location capability, capacity, and consumption time; The expression formula of the early warning capability is: They represent the detection distance, scanning frequency, maneuvering speed, detection accuracy, and recognition probability of the equipment functional component node respectively; The expression formula of the accusation capability is: They represent the response time, receiving and sending rate, and accuracy of the equipment functional component nodes respectively; The expression formula of the striking ability is: They represent the strike accuracy, killing radius, interference power, and maneuvering speed of the equipment functional component nodes respectively; The expression formula of the target capability is: They respectively represent the stealth coefficient, photoelectric resistance coefficient, radar resistance coefficient, infrared resistance coefficient, maneuvering speed, survival coefficient, warning time and receiving power of the equipment functional component node; The expression formula of the communication is: communication i ={x1,x2,…,x5}, where x1,x2,…,x5 represent the communication coverage, transmission speed, communication quality, communication capacity, and communication delay of the equipment functional components respectively; The expression formula of the spatial position capability is: Represents the equipment function component q in the air defense and anti-missile killing network i The spatial position of is an important factor in the equipment of the air defense and anti-missile combat system, and is related to the number and quality of the kill network combat loop. i ,y i ,z i Respectively represent the three-dimensional coordinates of the functional components of the equipment in space; The capacity is expressed as follows: Represents the equipment function component q in the air defense and anti-missile killing network i capacity, that is, the number of air raid targets detected by early warning equipment at the same time, the number of command and control equipment that processes command information and commands equipment at the same time, and the number of channels for strike equipment to intercept air raid targets at the same time; The expression formula of the consumption time is: Represents the equipment function component q in the air defense and anti-missile killing network i The time consumed refers to the time consumed by the early warning equipment to detect targets, the decision-making nodes to process information, the command and control system to prepare for strikes, and the time consumed by intercepting and striking in the formation of the air defense and anti-missile kill network combat loop.

3. The method for constructing an air defense and anti-missile killing network model based on a granular hypernetwork according to claim 1 is characterized in that: The actual combat process of the air defense and anti-missile killing network in step S1.3 includes discovery, tracking and identification. The discovery probability P of the early warning radar is f The expression formula is: In formula (2), g i represents the probability that the early warning detection equipment finds the air raid target in the i-th scan, Represents the radar scanning frequency. In the process of air defense and anti-missile operations, considering the stealth performance of early warning equipment and targets, the expression formula is: In formula (3), 0<k<1 represents the environmental adjustment parameter, Represents the detection accuracy in node S The membership function of They represent the radar detection distance and maneuvering speed respectively, A represents the specified detection range, Indicates the photoelectric resistance coefficient, radar resistance coefficient, and infrared resistance coefficient of the target node T The membership function of the three indicators is: Indicates their respective weights; Tracking probability P t The expression formula is: In formulas (4), (5), and (6), p tr Indicates the tracking capability of the detected target, p z Indicates the anti-tracking capability of air strike targets; Identification probability P r The expression formula is: In formula (7), represents the recognition probability.

4. The method for constructing an air defense and anti-missile killing network model based on a granular hypernetwork according to claim 1 is characterized in that: In step S1.3 The intelligence sharing edge S→S includes five indicators related to information transmission capability, P i SS (i=1,2,3,4,5) is the node S i With S j The information transmission rate between (i≠j) is P1 SS ,rate quality capacity and delay for: in, Represents node S i With S j The distance between i -x j ,y i -y j 、z i -z j Respectively represent S i With S j The difference between the coordinates of two points; In the above formula, represents the detection distance between two different nodes, represents the scanning frequency of two different nodes, represents the maneuvering speed of two different nodes, represents the detection accuracy of two different nodes, Represents the identification frequency of two different nodes.

5. The method for constructing an air defense and anti-missile killing network model based on a granular hypernetwork according to claim 1 is characterized in that: In step S1.3 The factors affecting the information processing capability of node D include the response time P1 DD , transceiver rate Accuracy Then node D i With D j The expression formula of the influencing factors between (i≠j) is: In formulas (13), (14), (15), Indicates the response time of different nodes, Indicates the consumption time of the node, represents the sending and receiving rate of different nodes, Indicates the accuracy of different nodes.

6. The method for constructing an air defense and anti-missile killing network model based on a granular hypernetwork according to claim 1 is characterized in that: The interference probability of soft kill on the air raid target in step S1.3 is and suppression probability The expression formula for description is: In formulas (16), (17), (18), represents the maneuvering speed of the strike node, Indicates interception weapon node A i Launch to kill target node T j The time spent, Indicates the killing radius of the attack node, Indicates the distance from the interception weapon to the target, Respectively represent the maneuvering speed and warning time of the target node, represents the interference power of the attack node, represents the survival coefficient and receiving power of the target node, represents the coordinate difference between the attack node i and the target node j; Hard kill damage to air strike targets using hit probability and probability of damage The expression formula for description is: In formulas (19) and (20), represents the maneuvering speed of attacking node m, represents the killing radius of the attack node m, represents the straight-line distance between the attack node m and the target node n, They represent the maneuvering speed and warning time of the target node n respectively, Indicates interception weapon node A m Launch to hit target T n The time spent, Indicates the distance between the interceptor missile and the target is When A m To T n The membership function of damage, represents the membership function of the target node survival coefficient, Represent the corresponding coefficients respectively.

7. An evaluation method for an air defense and anti-missile kill network model based on a granular hypernetwork is characterized in that: The following steps are involved: S2.1, evaluate the model's air defense and anti-missile kill network combat system; S2.2, evaluate the anti-destruction capability of the combat system. The anti-destruction capability indicators of the combat system include three stages: being attacked, capability degradation and capability recovery; S2.3, evaluate from the perspective of combat capability. Combat capability indicators include the anti-destruction capability and the recovery capability of the kill net.

8. The evaluation method of the air defense and anti-missile killing network model based on granular hypernetwork according to claim 7 is characterized by: The evaluation method of the air defense and anti-missile kill network combat system in step S2.1 is: S2.1.1, Calculate the number of nodes R in the air defense and anti-missile kill network N Number of edges R E ; In formula (22), V represents the set of all nodes, and E represents the set of all edges; S2.1.2, Degree elasticity R of air defense and anti-missile kill network nodes P ; The degree distribution refers to the probability distribution of node degrees p(λ). When a combat system is deliberately attacked, the degree of the combat system follows a power law distribution, that is, p(λ)~λ -γ (23) In formula (23), p(λ) represents the probability that the node degree is λ, λ is the degree of the node, and γ is an exponent greater than 1, which determines the shape of the power law distribution. The more uneven the degree distribution is, the lower the invulnerability of the system network is; When a combat system is attacked randomly, the degree of the combat system follows the Poisson distribution, that is, In formula (24), p(λ) represents the probability that the node degree is λ, μ is the average degree of the network, that is, the average value of the degrees 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 invulnerability of the combat system. S2.1.3, Calculate the elasticity of the clustering coefficient R of the air defense and anti-missile killing network C ; R C Indicates the degree of clustering of combat system nodes, and defines the clustering coefficient of combat system nodes as C i : In formula (25), represents the actual number of edges that the adjacent node cluster has, and K represents the number of clusters; The clustering coefficient C of the air defense and anti-missile kill network combat system is In formula (26), R N Indicates the number of nodes. A combat system with a higher clustering coefficient has better cohesion and is more conducive to mutual support; S2.1.4, Calculate the number of air defense and anti-missile kill network combat rings R A ; The number of combat loops is the number of kill chains, and the number of combat loops is calculated using the transfer matrix and the arrival matrix; Transfer matrix: Let A ij is about node v i With node v j The transfer matrix between them, if there is a relationship between two nodes, then the element a ij =1, otherwise a ij = 0, when node v i With node v j For nodes of the same type, A ij represents a homogeneous adjacency matrix; Arrival Matrix: A ij and A jk is the adjacent transfer matrix, and A ij The arrival node and A jk The starting nodes are of the same type, The node transfer of the combat ring is obtained according to the transfer matrix, so the arrival matrix of the standard combat ring for the air strike target T is expressed as A TSDAT =A TS *A SD *A DA *A AT (27) In formula (27), A TS ,A SD ,A DA ,A AT They represent the arrival matrices from the target node to the warning node, the warning node to the decision node, the decision node to the strike node, and the strike node to the target node for the target T respectively; The number of standard combat rings for air strike target T in the air defense and anti-missile killing network is In formula (28), |T| represents the number of target nodes, N TSDAT Represents the number of combat rings for all target nodes, A TSDAT (i,i) represents the number of combat rings for the i-th target node.

9. The evaluation method of the air defense and anti-missile kill network model based on granular hypernetwork according to claim 7 is characterized in that: The combat capability is evaluated by using a combat capability evaluation method based on Pythagorean binary semantic fuzzy: For a given Pythagorean binary semantic fuzzy number Its index membership function is expressed as: In formula (29), s θ represents the language scale, Indicates the difference in language information, represents the Pythagorean fuzzy number, represents the degree of membership, represents non-membership; Complete the combat mission according to the standard combat cycle, and set the uncertainty of the early warning node, decision node, strike node and target node as I S ,I D ,I A ,I T , let the uncertainty of the edge in the completed combat loop be I TS ,I SS ,I SD ,I DD ,I DA ,I AT , assuming that there are m targets in total, and the number of combat loops for the i-th target is n, then the uncertainty of the j-th combat loop for the i-th target is determined by both the nodes and the edges, that is, I ij =I S +I D +I A +I T +I TS +I SS +I SD +I DD +I DA +I AT (30) Then the uncertainty information of all combat loops of the i-th target is: The combat effectiveness of this combat loop against the i-th target is: C i =exp(-I i ) (32) The overall combat capability of the air defense and anti-missile killing network against all m targets is: In formulas (30) to (33), I T ,I S ,I D ,I A Respectively represent the uncertainty of the task completion capabilities of the target node, warning node, decision node, and strike node, I TS ,I SS ,I SD ,I DD ,I DA ,I AT I represents the uncertainty of the ability to complete the mission on the early warning side, intelligence sharing side, intelligence side, command transmission side, command side, and strike side, respectively. ij represents the uncertainty of the jth combat loop of the i-th target, C i represents the combat effectiveness against the i-th target, I i represents the uncertainty information of all combat loops of the i-th target, C represents the overall combat effectiveness of all m targets, and λ i is the importance weight or threat level weight of the target node.

10. The evaluation method of the air defense and anti-missile killing network model based on granular hypernetwork according to claim 7 is characterized by: The anti-destruction performance of the kill net is determined by the energy degradation degree and energy degradation rate of the kill net. The energy degradation degree d of the kill net system is: Kill net system energy reduction rate v d for: Invulnerability R d It is expressed as: R d =exp(-d·v d ) (36) The recovery of the kill net is determined by the degree and rate of recovery of the kill net. The degree of recovery of the kill net system r is: Killnet system regeneration rate v r for: The recovery R r It is expressed as: R r =exp(r·v r ) (39) The structural elasticity of the kill net system is: R I =R d *R r (40) In formulas (34) to (40), t0, t a ,t d ,t r ,t s They represent the time when the battle starts, the time when the attack occurs, the time when the ability decreases to the lowest point, the time when the ability starts to recover, and the time when the ability recovery is completed. C(t0), C(t a )、C(t d )、C(t r )、C(t s ) represent t0, t a ,t d ,t r ,t s The system combat capability at a certain moment, d represents the degree of system capability decline, v d Indicates the rate of system capacity decline, R d represents the system's invulnerability, r represents the system's ability to recover, and v r Represents the rate of system recovery, R r Represents system recovery, R I Represents architectural resilience.

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