Capability change analysis method of cluster ship air defense and anti-missile system based on undirected topology

Abstract

The present invention discloses a method for analyzing changes in the capability of an air defense and anti-missile system of a cluster of ships based on an undirected topology. The method is as follows: first, input attribute information of each ship in the cluster is considered, and a corresponding undirected topology graph of the cluster of ships is constructed with each ship as a node and the support relationship between the ships as an edge; based on the undirected topology graph of the cluster of ships, all nodes are traversed, node association information is obtained, and changes in the capability of the air defense and anti-missile system of the cluster of ships are analyzed, where the node association information includes the closed neighborhood of the node, the probability of the node being attacked, the number of weapon resources of the node, etc.; based on the undirected topology graph of the cluster of ships, the most important nodes in the undirected topology are calculated in combination with the Roman control algorithm, and the probability that each ship may be attacked is calculated; finally, changes in the capability of the air defense and anti-missile system of the cluster of ships are analyzed; results show that the present invention can effectively analyze changes in the capability of the air defense and anti-missile system of the cluster of ships.

Description

Technical Field

[0001] The present invention relates to a method for analyzing changes in the capability of a cluster ship air defense and anti-missile system based on undirected topology, and belongs to the technical field of automatic control. Background Art

[0002] With the continuous emergence of new combat concepts and the accelerated deployment of traditional and new weapons in actual combat, the real threats facing aerospace defense are becoming more complex. The uncertainty of the world's military landscape has intensified the deep demand of various countries for the construction of advanced air defense and anti-missile systems, which has indirectly spawned a large number of advanced achievements in technical fields such as detection, command, and interception, and has become increasingly perfect and mature with the normalization and actual combat of air defense and anti-missile combat exercises.

[0003] Research on combat effectiveness assessment began in the United States and the Soviet Union. Since the 1960s, the United States has proposed a variety of effectiveness assessment models, such as the WSEIAC model, the AN model, the AAM model, and the ARINC model, all of which can be used to address combat effectiveness assessment issues. After the 1990s, advanced information technology began to permeate all aspects of modern warfare, and combat effectiveness assessment theory has continued to evolve, becoming more systematic, autonomous, and intelligent. With the development of disciplinary methodologies such as fuzzy synthesis, operations research, provenance analysis, and gray evaluation theory, combat effectiveness assessment methods such as the Analytic Hierarchy Process (AHP), gray evaluation methods, and Bayesian networks have emerged. With the rise of artificial intelligence, combat effectiveness assessment can also be implemented using methods such as neural networks, intelligent decision-making, and genetic algorithms. Domestic research on combat effectiveness assessment started later, and most studies are applications or extensions of international research findings. The ADC method was used to study the combat effectiveness of surface-to-air missiles deployed by multiple firepower units. The ADC method was used to construct a combat effectiveness indicator system, the index method was used to construct a combat effectiveness indicator model, and the AHP method was used to determine the weights of combat capability indicators.

[0004] Therefore, combat effectiveness evaluation is a hot topic in military research and a difficult problem in comprehensive evaluation. At present, the problem of imperfect combat effectiveness evaluation and the inability to quantify combat effectiveness evaluation values urgently needs further research. Summary of the Invention

[0005] In order to address the deficiencies in the prior art, the present invention provides a method for analyzing changes in the capabilities of a cluster ship air defense and anti-missile system based on undirected topology. The method first considers the input attribute information of each ship in the cluster, and constructs a corresponding undirected topology graph of the cluster ships with each ship as a node and the support relationship between the ships as an edge. The input attribute information of the ship includes plane two-dimensional coordinates, heading angle, interception near boundary and interception far boundary; based on the undirected topology graph of the cluster ships, all nodes are traversed to obtain node association information, and the changes in the capabilities of the cluster ships are analyzed. The node association information includes node closed neighborhood, node attack probability, node weapon resource quantity, etc. The method comprehensively analyzes the changes in the capabilities of the cluster air defense and anti-missile system from the aspects of ship attributes, ship support relationship and support capability.

[0006] To achieve the above-mentioned object, the present invention provides a method for analyzing the change in the capability of a clustered ship air defense and anti-missile system based on an undirected topology, comprising the following steps:

[0007] Step 1: Consider the input attribute information of each ship in the cluster, take each ship as a node and the support relationship between ships as an edge, and construct an undirected topological graph. The input attribute information of the ship includes plane two-dimensional coordinates, heading angle, interception angle, interception near boundary and interception far boundary.

[0008] Step 2: Based on the constructed undirected topological graph of the clustered ships, the associated information of all nodes is obtained to analyze the changes in the air defense and anti-missile system capabilities of the clustered ships. The associated information of the nodes includes the closed neighborhood of the nodes, the probability of the nodes being attacked, the number of weapon resources of the nodes, etc.

[0009] Among them, the analysis method of the capability change of cluster ship air defense and anti-missile system based on undirected topology is: first consider the Plane 2D coordinates of ships 、 Heading angle , interception angle , intercept near boundary and intercept far boundary , on a two-dimensional plane, calculate the Ships can support area Then, using the point sampling method, Ships can support area Random sampling points, and determine whether these points are in the Support area of ​​ships Inside, if The number of points within and Number of sampling points The ratio exceeds a given threshold , then it is considered that Ships and There is a support relationship between the ships; finally, each ship is a node , the support relationship between ships is , constructing an undirected topology of clustered ships ;

[0010] Based on the constructed undirected topology , get the node Number , closed neighborhood , probability of being hit 、Quantity of weapon resources , calculate the changes in the air defense and anti-missile system capabilities of cluster ships in five stages , respectively, the initial stage , Adjustment Phase , Enemy Phase , recovery phase and the final stage .

[0011] Preferably, step 1 specifically includes:

[0012] Step 11, according to Plane 2D coordinates of ships , , heading angle , interception angle , intercept near boundary and intercept far boundary , on a two-dimensional plane, calculate the coordinates of the four vertices of the trapezoid 、 、 、 ;

[0013] Step 12, draw the first Ships can support area ;

[0014] Step 13, in Ships can support area Random sampling points;

[0015] Step 14, judge Is the sampling point in Support area of ​​ships Inside, record in The number of points is ;

[0016] Step 15, calculate , and judge whether it is greater than a given threshold ,like It is believed that Ships and There is a supportable relationship between the ships;

[0017] Step 16: Take each ship as a node , the support relationship between ships is , constructing an undirected topology of clustered ships .

[0018] As a preference, in step 11, Ships can support area It is approximately an isosceles trapezoid. The coordinates of the four vertices of the trapezoid are expressed as follows:

[0019] ,

[0020] ,

[0021] ,

[0022] ,

[0023] in, , Indicates the The two-dimensional coordinates of the ships, Indicates the The heading angle of the ship, Indicates the The interception angle of the ship, Indicates the The interception limit of the ships is Indicates the The interception limit of 10 ships.

[0024] As a preference, in step 1, directly 、 、 、 The closed figure formed by connecting the four points as vertices in sequence is an isosceles trapezoid. Ships can support area .

[0025] Preferably, in step 1, for Ships can support area Randomly sampled from points, and determine whether these points are located in Support area of ​​ships Inside, record in The number of points in .

[0026] As a preference, each ship is used as a node , the support relationship between ships is , constructing an undirected topology of clustered ships .

[0027] Preferably, step 2 specifically includes:

[0028] Step 21: Calculate the undirected topology based on the Roman control algorithm The two most important nodes and , and the number of weapon resources is given to the most important node as 90, and the number of weapon resources is given to the remaining nodes as 30; in step 21, the number of weapon resources is a row vector, The distribution principle is that the two most important nodes and The number of weapon resources given is 90, and the number of weapon resources given to other nodes is 30.

[0029] Step 22: In the initial stage, calculate the capacity of each node , select the node with the largest capability as the estimated enemy attack node , the combat capability of the cluster ships in the initial stage is ;

[0030] Step 23, according to and Expression in the adjustment phase, calculates the end time of the adjustment phase ;

[0031] Step 24, in the adjustment phase, since the enemy attack node was incorrectly estimated in the initial phase, the estimated enemy attack node is recalculated. The probability that all nodes other than , and according to Recalculate the combat capability of cluster ships during the adjustment phase ;

[0032] Step 25: Calculate the combat capability of the cluster ships in the enemy encounter phase ;

[0033] Step 26, in the recovery phase, according to The combat capability of clustered ships at all times , and the combat capability of the cluster ships in the enemy-facing phase is , calculate the end time of the enemy phase ;

[0034] Step 27: Calculate the combat capability of the cluster ships during the recovery phase ;

[0035] Step 28, according to and The expression in the recovery phase calculates the end time of the recovery phase ;

[0036] Step 29: Calculate the combat capability of the cluster ships in the final stage .

[0037] As a preference, in step 2, in the initial stage, the combat capability of the cluster ship air defense and anti-missile system There are the following expressions:

[0038] ,

[0039] in, , Indicates the total number of nodes, Representation node The closed neighborhood of Representation node combat capability, Indicates the end time of the initial stage, Representation node The number of weapons resources, Representation node The number of weapons resources, represents the number of sampling points and , (the actual number of sampling points is 1000, but in order to make the subsequent results more obvious, , the subsequent stages Similarly, just show and The relative size relationship is sufficient). Representatives in The moment does not exist simultaneously on the ship and ship The number of sampling points in the support area is constant in the initial stage, that is:

[0040] ,

[0041] From the definition of the combat capability of the cluster ship air defense and anti-missile system, With ships and ships The overlapping area of the support area is related to The smaller the ship, and ships A larger overlap indicates better mutual support between the two ships.

[0042] As a preference, in step 2, during the adjustment phase, the node Probability of being hit There are the following expressions:

[0043] ,

[0044] in, Indicates the total number of nodes, Indicates that except for the estimated attack node In addition, the enemy attacks the node The probability of Representation node Degree, estimated attack node That is, the initial stage node combat capability The strongest node.

[0045] As a preference, in step 2, during the adjustment phase, the combat capability of the cluster ship air defense and anti-missile system There are the following expressions:

[0046] ,

[0047] in, Indicates the end time of the adjustment phase, Representatives in The moment does not exist simultaneously on the ship and ship The number of sampling points in the support area during the adjustment phase is expressed as:

[0048] ,

[0049] in, is the exponential constant coefficient, .

[0050] As a preference, in step 2, during the enemy encounter phase, the combat capability of the cluster ship air defense and anti-missile system There are the following expressions:

[0051] ,

[0052] in, Indicates the end of the enemy phase. It indicates the combat capability of the cluster ship air defense and anti-missile system at the end of the adjustment phase.

[0053] As a preference, in step 2, during the recovery phase, the combat capability of the cluster ship air defense and anti-missile system There are the following expressions:

[0054] ,

[0055] in, Indicates the moment when the recovery phase is completed, Representatives in The moment does not exist simultaneously on the ship and ship The number of sampling points in the support area during the recovery phase is expressed as:

[0056] ,

[0057] in, is the exponential constant coefficient, .

[0058] As a preference, in step 2, in the final stage, the combat capability of the cluster ship air defense and anti-missile system There are the following expressions:

[0059]

[0060] in, Representatives in The moment does not exist simultaneously on the ship and ship The number of sampling points in the supported area, .

[0061] Based on the same inventive concept, the present invention provides a system for analyzing the capability changes of a clustered ship air defense and anti-missile system based on an undirected topology, comprising:

[0062] The undirected topology generation module for clustered ships considers the input attribute information of each ship in the cluster, uses each ship as a node, and the support relationships between ships as edges to construct an undirected topology graph. The ship attribute information includes plane 2D coordinates, heading angle, interception angle, interception near bound, and interception far bound.

[0063] Furthermore, the module for analyzing the air defense and missile defense capabilities of swarm ships is based on the constructed undirected topology graph of swarm ships. It traverses all nodes in the undirected topology, obtains the associated information of all nodes, and then analyzes the changes in the air defense and missile defense capabilities. The associated information of the nodes includes the closed neighborhood of the node, the probability of the node being attacked, the number of weapon resources of the node, etc.

[0064] Based on the same inventive concept, the present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and runnable on the processor. When the computer program is loaded into the processor, it implements the steps of a method for analyzing changes in the capabilities of a cluster ship air defense and anti-missile system based on an undirected topology.

[0065] Beneficial Effects: The method for analyzing the change in the capability of the air defense and anti-missile system of clustered ships based on undirected topology proposed by the present invention first considers the input attribute information of each ship in the cluster, and constructs a corresponding undirected topology graph of the clustered ships with each ship as a node and the support relationship between ships as an edge. Then, based on the undirected topology graph of the clustered ships, all nodes are traversed to obtain node association information and analyze the change in the capability of the clustered ships. Based on step 1, the present invention models the supportable area as an isosceles trapezoid, which simplifies the overall computational complexity of the algorithm.

[0066] Based on step 2, the present invention provides the air defense and anti-missile capabilities of the clustered ships at different times, and the corresponding changes in the supported areas, which takes into account the actual working status of the clustered ships more comprehensively. For example, the changes in the supported range of each ship during the enemy encounter phase and changes in air and missile defense capabilities ,

[0067] The present invention will adopt the undirected topological calculation method of clustered ships proposed in the present invention, which can effectively characterize the support relationship and support capability between ships; the results show that the present invention can effectively analyze the changes in the air defense and anti-missile system capabilities of clustered ships. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 is an overall flow chart of the method according to an embodiment of the present invention,

[0069] Figure 2 Flowchart of capability change analysis of cluster ship air defense and anti-missile system based on undirected topology in an embodiment of the present invention.

[0070] Figure 3 This is a schematic diagram of the results of the present invention's analysis of the air defense and anti-missile capabilities of clustered ships. DETAILED DESCRIPTION

[0071] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0072] Depend on Figure 1As shown in the figure, the input attribute information of each ship in the cluster is first considered. The support area of each ship is calculated, and the overlap between the support areas of each ship is determined. If the overlap is large enough, a support relationship is considered between the two ships. An undirected topological graph of the clustered ships is then constructed, with each ship as a node and the support relationships between ships as edges. The input attribute information of the ships includes two-dimensional coordinates, heading angles, interception near bounds, and interception far bounds. Then, based on the undirected topological graph of the clustered ships, all nodes are traversed to obtain node association information, and the changes in the clustered ship air defense and anti-missile system capabilities are analyzed. Node association information includes node closed neighborhood, node attack probability, and node weapon resource quantity. Specifically, the input attribute information of the clustered ships is combined to determine the support relationships between ships and construct an undirected topological graph. Based on the undirected topological graph of the clustered ships and the node association information, the changes in the clustered ship air defense and anti-missile system capabilities are analyzed.

[0073] The following describes the detailed implementation process of the embodiment of the present invention, taking the change in the air defense and anti-missile system capability of a maritime air defense cluster ship as an example, including the following steps:

[0074] S1, constructs an undirected topology based on the input attribute information of the clustered ships;

[0075] Considering the input attribute information of the cluster ships, Take a ship as an example, including the plane two-dimensional coordinates 、 Heading angle , interception angle , intercept near boundary and intercept far boundary ;

[0076] S11, calculate the Ships can support area , can be approximated into an isosceles trapezoid. The coordinates of the four vertices of the trapezoid are expressed as follows:

[0077] ,

[0078] ,

[0079] ,

[0080] ,

[0081] in, , Indicates the The two-dimensional coordinates of the ships, Indicates the The heading angle of the ship, Indicates the The interception angle of the ship, Indicates the The interception limit of the ships is Indicates the The interception limit of 10 ships.

[0082] Then, 、 、 、 The closed figure formed by connecting the four points as vertices in sequence is an isosceles trapezoid. Ships can support area ;

[0083] S12, judge the Ships and Whether there is a support relationship between the two ships and generate an undirected topology, Ship support area Randomly sampled from points, of which , and calculate the Support area of ​​ships The number of points in The number of points in ; given threshold ,like It is believed that Ships and There is a support relationship between the ships; then, each ship is a node , the support relationship between ships is , constructing an undirected topology of clustered ships ;

[0084] S2, based on the undirected topological graph of clustered ships, analyze the changes in the air defense and anti-missile system capabilities of clustered ships;

[0085] S21, allocates weapon resources to all ship nodes, and uses the Roman control algorithm to calculate the undirected topology The two most important nodes and ;Weapon resource quantity is a row vector, The distribution principle is that the two most important nodes and The number of weapon resources given is 90, and the number of weapon resources given to other nodes is 30;

[0086] S22: Analyze the changes in the air defense and anti-missile system capabilities of the clustered ships in the initial stage; There are the following expressions:

[0087] ,

[0088] in, , Indicates the total number of nodes, Representation node The closed neighborhood of Representation node combat capability, Indicates the end time of the initial stage, Representation node The number of weapons resources, Representation node The number of weapons resources, represents the number of sampling points and , (the actual number of sampling points is 1000, but in order to make the subsequent results more obvious, , the subsequent stages Similarly, just show and The relative size relationship is sufficient). Representatives in The moment does not exist simultaneously on the ship and ship The number of sampling points in the support area is constant in the initial stage, that is:

[0089] ,

[0090] From the definition of the combat capability of the cluster ship air defense and anti-missile system, With ships and ships The overlapping area of the support area is related to The smaller the ship, and ships A larger overlap indicates better mutual support between the two ships.

[0091] S23, analysis and adjustment phase, the air defense and anti-missile system capabilities of the cluster ships change; in the adjustment phase, due to the incorrect estimation of the enemy's attack nodes in the initial phase, the estimated enemy attack nodes are recalculated. The probability that all nodes other than ,node Probability of being hit There are the following expressions:

[0092] ,

[0093] in, Indicates the total number of nodes, Indicates that except for the estimated attack node In addition, the enemy attacks the node The probability of Representation node Degree, estimated attack node That is, the initial stage node combat capability The strongest node.

[0094] according to Recalculate the combat capability of cluster ships during the adjustment phase There are the following expressions:

[0095] ,

[0096] in, Indicates the end time of the adjustment phase, Representatives in The moment does not exist simultaneously on the ship and ship The number of sampling points in the support area during the adjustment phase is expressed as:

[0097] ,

[0098] in, is the exponential constant coefficient, .

[0099] S24, analyze the changes in the air defense and anti-missile system capabilities of the clustered ships during the enemy-facing phase; during the enemy-facing phase, when enemy firepower strikes, the combat capability of the clustered ships' air defense and anti-missile system There are the following expressions:

[0100] ,

[0101] in, Indicates the end of the enemy phase. It indicates the combat capability of the cluster ship air defense and anti-missile system at the end of the adjustment phase.

[0102] S25, analysis and recovery phase, the air defense and anti-missile system capability of the cluster ships changes; after the enemy attack ends, the air defense and anti-missile system of our cluster ships begins to recover, and the system combat capability There are the following expressions:

[0103] ,

[0104] in, Indicates the moment when the recovery phase is completed, Representatives in The moment does not exist simultaneously on the ship and ship The number of sampling points in the support area during the recovery phase is expressed as:

[0105] ,

[0106] in, is the exponential constant coefficient, .

[0107] S26, analyze the changes in the air defense and anti-missile system capabilities of the cluster ships in the final stage; in the final stage, the air defense and anti-missile capabilities of our cluster ships are fully restored, and the combat capability of the air defense and anti-missile system of the cluster ships is There are the following expressions:

[0108] ,

[0109] in, Representatives in The moment does not exist simultaneously on the ship and ship The number of sampling points in the supported area, .

[0110] In this embodiment, MATLAB 2023a is used as the simulation software to verify the method for changing the capability of the cluster ship air defense and anti-missile system based on undirected topology proposed in the present invention.

[0111] The parameter settings of the capability change method of the cluster ship air defense and anti-missile system based on undirected topology are shown in Table 1:

[0112]

[0113] Table 1 Parameters of the capability change method of the swarm ship air defense and anti-missile system based on undirected topology

[0114] Figure 3The results of the algorithm proposed in the present invention on the analysis of the air defense and anti-missile capabilities of clustered ships are shown. In the first initial stage, the enemy's strike node is estimated to be the node with the strongest capability in the clustered ships, so the capability value of the node is used to represent the capability value of the entire ship; in the second adjustment stage, the capability of the entire system drops sharply. After discovering that the estimated enemy strike node in the initial stage is wrong, the air defense and anti-missile capabilities of the entire clustered ships are recalculated based on expectations, showing an upward trend; in the enemy-facing stage, the enemy strikes and some nodes of our clustered ships are destroyed, and the air defense and anti-missile capabilities show a decline due to factors such as ammunition consumption and node loss; in the recovery stage, the change in the rotation direction of the ship leads to an increase in the overlapping supportable area between ships, an increase in the supportability between ships, and a recovery trend of the air defense and anti-missile capabilities of the entire clustered ships; in the final stage, with the influence of the system's sunk costs such as ammunition consumption and node loss, the air defense and anti-missile capabilities of the entire clustered ship system tend to be constant, but are still lower than the initial state.

[0115] Based on the same inventive concept, an embodiment of the present invention discloses a method for changing the capability of a cluster ship air defense and anti-missile system based on an undirected topology, comprising: a cluster ship undirected topology generation module, which considers the input attribute information of each ship in the cluster, uses each ship as a node, and the support relationship between ships as an edge to construct an undirected topological graph, wherein the attribute information of the ships includes two-dimensional plane coordinates, heading angle, interception angle, interception near boundary, and interception far boundary;

[0116] Furthermore, the module for analyzing the air defense and missile defense capabilities of swarm ships is based on the constructed undirected topology graph of swarm ships. It traverses all nodes in the undirected topology, obtains the associated information of all nodes, and then analyzes the changes in the air defense and missile defense capabilities. The associated information of the nodes includes the closed neighborhood of the node, the probability of the node being attacked, the number of weapon resources of the node, etc.

[0117] The specific working process of each module described above can refer to the corresponding process in the aforementioned method embodiment and will not be repeated here. The division of the modules is only a logical function division, and there may be other division methods in actual implementation, such as multiple modules can be combined or integrated into another system.

[0118] Based on the same inventive concept, an embodiment of the present invention discloses an electronic device, including a memory, a processor, and a computer program stored in the memory and runnable on the processor. When the computer program is loaded into the processor, the steps of the method for changing the capability of the cluster ship air defense and anti-missile system based on undirected topology are implemented.

[0119] Those skilled in the art will appreciate that the technical solution of the present invention, or the portion that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes instructions for causing a computer system (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in the embodiments of the present invention. Storage media include various media capable of storing computer programs, such as USB flash drives, mobile hard drives, read-only memories (ROMs), random-access memories (RAMs), magnetic disks, or optical disks.

[0120] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for analyzing the change in the capability of the swarm ship air defense and anti-missile system based on undirected topology, characterized by: The method comprises the following steps: Step 1: Consider the input attribute information of each ship in the cluster, take each ship as a node and the support relationship between ships as an edge, and construct an undirected topological graph. The input attribute information of the ship includes plane two-dimensional coordinates, heading angle, interception angle, interception near boundary and interception far boundary. Step 2: Based on the constructed undirected topological graph of the clustered ships, the associated information of all nodes is obtained to analyze the changes in the air defense and anti-missile system capabilities of the clustered ships. The associated information of the nodes includes the closed neighborhood of the node, the probability of the node being hit, and the number of weapon resources of the node.

2. The method for analyzing the change in the capability of the clustered ship air defense and anti-missile system based on undirected topology according to claim 1 is characterized in that: Step 1 specifically includes: Step 11: According to the plane two-dimensional coordinate x of the i-th ship i ,y i , heading angle θ i , interception angle α i , intercept near boundary r min i and interception far boundary r max i , on a two-dimensional plane, calculate the coordinates A of the four vertices of the trapezoid 1i 、A 2i 、A 3i 、A 4i ; Step 12: Draw the support area S of the i-th ship based on the vertex coordinates i ; Step 13: In the support area S of the i-th ship i Randomly sample a=1000 points; Step 14, determine S i Is the sampling point in the support area S of the jth ship? j Inside, record in S j The number of points is μ; Step 15, calculate And judge whether it is greater than the given threshold ρ=0.1, if It is considered that there is a support relationship between the i-th ship and the j-th ship; Step 16: Take each ship as a node V and the support relationship between ships as an edge E to construct a cluster ship. The undirected topology G of the boat.

3. The method for analyzing the change in the capability of the swarm ship air defense and anti-missile system based on undirected topology according to claim 1 is characterized in that: In step 11, the i-th ship can support area S i It is approximately an isosceles trapezoid. The coordinates of the four vertices of the trapezoid are expressed as follows: Among them, x i ,y i represents the plane two-dimensional coordinates of the i-th ship, θ i represents the heading angle of the i-th ship, α i represents the interception angle of the i-th ship, r min i represents the interception limit of the i-th ship, r max i represents the interception limit of the i-th ship.

4. The method for analyzing the change in the capability of the swarm ship air defense and anti-missile system based on undirected topology according to claim 1 is characterized in that: Step 2 specifically includes: Step 21: Based on the Roman control algorithm, calculate the two most important nodes v in the undirected topology G. imp1 and v imp2 The most important node is given 90 weapon resources, and the remaining nodes are given 30 weapon resources; Step 22: In the initial stage, calculate the capacity of each node Select the node with the greatest capability as the estimated enemy attack node The combat capability of the cluster ships in the initial stage is Step 23, according to a im (t2) = 200 and a im (t) Expression in the adjustment phase, calculate the end time t2 of the adjustment phase; Step 24, in the adjustment phase, since the enemy attack node was incorrectly estimated in the initial phase, the estimated enemy attack node v is recalculated. i预估 The probability that all nodes other than i , and according to W i Recalculate the combat capability Q2(t) of the cluster ships during the adjustment phase; Step 25, calculate the combat capability Q3(t) of the cluster ships in the enemy encounter phase; Step 26, in the recovery phase, based on the combat capability Q4(t3) of the cluster ships at time t3 and the combat capability Q3(t3) of the cluster ships in the encounter phase, calculate the end time t3 of the encounter phase; Step 27, calculate the combat capability Q4(t) of the cluster ships in the recovery phase; Step 28, according to a im (t4) = 110 and a im (t) The expression in the recovery phase calculates the end time t4 of the recovery phase; a im (t) represents the number of sampling points that are not in the support areas of ship i and ship m at the same time at time t; Step 29, calculate the combat capability Q5(t) of the cluster ships in the final stage.

5. The method for analyzing the change in the capability of the swarm ship air defense and anti-missile system based on undirected topology according to claim 4 is characterized in that: In step 2, at the initial stage, the combat capability Q1(t) of the cluster ship air defense and anti-missile system is expressed as follows: Among them, i∈M, M represents the total number of nodes, N i Represents node v i The closed neighborhood of Represents node v i combat capability, t1 represents the end time of the initial stage, p i Represents node v i The number of weapon resources, p m Represents node v m The number of weapon resources, a represents the number of sampling points and a=300, a im (t) represents the number of sampling points that are not in the support area of ship i and ship m at the time t, and is a constant in the initial stage, that is: a im (t)=270,0≤t<t1 From the definition of the combat capability of the cluster ship air defense and anti-missile system, a im (t) is related to the overlapping area of support areas of ship i and ship m, a im The smaller (t) is, the larger the overlapping area between ship i and ship m is, indicating better mutual support between the two ships.

6. The method for analyzing the change in the capability of the swarm ship air defense and anti-missile system based on undirected topology according to claim 4 is characterized in that: In step 2, during the adjustment phase, node v i The probability of being hit W i There are the following expressions: Among them, M represents the total number of nodes, W i Indicates that except for the estimated attack node In addition, the enemy attacks node v i The probability of k i Represents node v i Degree, estimated attack node That is, the initial stage node combat capability The strongest node.

7. The method for analyzing the change in the capability of the swarm ship air defense and anti-missile system based on undirected topology according to claim 4 is characterized in that: In step 2, during the adjustment phase, the combat capability Q2(t) of the clustered ship air defense and anti-missile system is expressed as follows: Among them, t2 represents the end time of the adjustment phase, a im (t) represents the number of sampling points that are not in the support area of ship i and ship m at the same time at time t. The expression in the adjustment stage is: Where q=2 is the exponential constant coefficient, from im (t1)=a im (0) = 270.

8. The method for analyzing the change in the capability of the swarm ship air defense and anti-missile system based on undirected topology according to claim 4 is characterized in that: In step 2, during the enemy-engaging phase, the combat capability Q3(t) of the swarm ship air defense and anti-missile system is expressed as follows: Among them, t3 represents the end time of the enemy encounter phase, and Q(t2)=Q2(t2) represents the combat capability of the cluster ship air defense and anti-missile system at the end time of the adjustment phase.

9. The method for analyzing the change in the capability of the swarm ship air defense and anti-missile system based on undirected topology according to claim 4 is characterized in that: In step 2, during the recovery phase, the combat capability Q4(t) of the clustered ship air defense and anti-missile system is expressed as follows: Among them, t4 represents the time when the recovery phase is completed, a im (t) represents the number of sampling points that are not in the support area of ship i and ship m at the same time at time t. The expression in the recovery phase is: Where q=2 is the exponential constant coefficient, <h2 style=";text-align:left;direction:ltr">a<h2 style=";text-align:left;direction:ltr"> im <h2 style=";text-align:left;direction:ltr"> (t3)=a<h2 style=";text-align:left;direction:ltr"> im <h2 style=";text-align:left;direction:ltr"> (t2) = 200.

10. The method for analyzing the change in the capability of the swarm ship air defense and anti-missile system based on undirected topology according to claim 4 is characterized in that: In step 2, at the final stage, the combat capability Q5(t) of the clustered ship air defense and anti-missile system is expressed as follows: Among them, a im (t) represents the number of sampling points that are not in the support area of ship i and ship m at the same time at time t, a im (t4)=110.

11. The capability change analysis system of clustered ship air defense and anti-missile system based on undirected topology is characterized by: A system for implementing the change analysis method described in any one of claims 1 to 10, comprising: a cluster ship undirected topology generation module, which considers input attribute information of each ship in the cluster, uses each ship as a node, and uses support relationships between ships as edges to construct an undirected topology graph, wherein the attribute information of the ships includes plane two-dimensional coordinates, heading angle, interception angle, interception near boundary, and interception far boundary; Furthermore, the module for analyzing the air defense and missile defense capabilities of clustered ships is based on the constructed undirected topology graph of clustered ships. It traverses all nodes in the undirected topology, obtains the associated information of all nodes, and then analyzes the changes in the air defense and missile defense capabilities. The associated information of the nodes includes the closed neighborhood of the node, the probability of the node being attacked, and the number of weapon resources of the node. Among them, the analysis method of the capability change of the cluster ship air defense and anti-missile system based on undirected topology is as follows: First, consider the plane two-dimensional coordinate x of the i-th ship i 、y i Heading angle θ i , interception angle α i , intercept near boundary r mini and interception far boundary r maxi , on a two-dimensional plane, calculate the support area S of the i-th ship i Then, using the point-taking method, the i-th ship can support the area S i Randomly sample a points and determine whether these points are in the support area S of the jth ship. j If in S j The number of points μ and S i If the ratio of the number of sampling points a in the equation exceeds a given threshold ρ, it is considered that there is a support relationship between the i-th ship and the j-th ship. Finally, with each ship as a node V and the support relationship between ships as an edge E, an undirected topology G of the clustered ships is constructed. Based on the constructed undirected topology G, get the node v i Number i, closed neighborhood N i , probability of being hit W i 、Weapon resource quantity P i , calculate the capability change Q of the cluster ship air defense and anti-missile system in five stages, namely the initial stage, adjustment stage, enemy encounter stage, recovery stage and final stage.

12. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the computer program is loaded into the processor, the steps of the method for analyzing changes in the capability of the cluster ship air defense and anti-missile system based on undirected topology according to any one of claims 1 to 10 are implemented.

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