Cluster naval vessel air defense and anti-missile system capability change analysis method based on undirected topology

Abstract

The invention discloses an undirected topology-based cluster naval vessel air defense and anti-navigation system capability change analysis method, which comprises the following steps of: firstly, considering input attribute information of each naval vessel in a cluster, and constructing a corresponding cluster naval vessel undirected topological graph by taking each naval vessel as a node and taking a support relationship between the naval vessels as an edge; all nodes are traversed based on the undirected topological graph of the clustered naval vessel, node association information is obtained, the ability change of the air defense and anti-navigation system of the clustered naval vessel is analyzed, and the node association information comprises a node closed neighborhood, a node attack probability, a node weapon resource quantity and the like; based on the undirected topological graph of the clustered naval vessels, the most important node in the undirected topology is calculated in combination with a Roman control algorithm, the probability that each naval vessel is possibly attacked is calculated, and finally the air defense and anti-guide system capacity change of the clustered naval vessels is analyzed; results show that the method can effectively analyze the ability change of the air defense and anti-missile system of the cluster naval vessel.

Description

Technical Field

[0001] The invention relates to a method for analyzing the change in 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 structure has intensified the deep-seated needs 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] The study of combat effectiveness evaluation began in the United States and the Soviet Union. Since the 1960s, the United States has proposed a variety of effectiveness evaluation models, such as the WSEIAC model, the AN model, the AAM model, the ARINC model, etc., which can be used to solve the problem of combat effectiveness evaluation. After the 1990s, advanced information technology began to penetrate into all aspects of modern warfare, and the theory of combat effectiveness evaluation has also continued to evolve, becoming more systematic, autonomous, and intelligent. With the development of disciplinary methodologies such as fuzzy synthesis, operations research, material source analysis, and gray evaluation theory, combat effectiveness evaluation methods such as hierarchical analysis, gray evaluation method, and Bayesian network have emerged. With the rise of artificial intelligence, combat effectiveness evaluation can also be achieved using methods such as neural networks, intelligent decision-making, and genetic algorithms. Domestic research on combat effectiveness evaluation started a little later, and most of the research is the application or extension of foreign research results. The ADC method is used to study the combat effectiveness of ground-to-air missiles deployed by multiple firepower units, the ADC method is used to construct a combat effectiveness index system, the index method is used to construct a combat effectiveness index model, and the AHP method is used to determine the weights of combat capability indicators.

[0004] It can be seen that combat effectiveness evaluation is a hot issue in military research and a difficult issue 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 solve the deficiencies in the prior art, the present invention provides a method for analyzing the change in the capability of an air defense and anti-missile system of a cluster of ships based on an undirected topology. The method first considers the input attribute information of each ship in the cluster, and constructs a corresponding undirected topological graph of the cluster of ships with each ship as a node and the support relationship between the ships as an edge. The input attribute information of the ships includes plane two-dimensional coordinates, heading angles, interception near boundaries and interception far boundaries. Based on the undirected topological graph of the cluster of ships, all nodes are traversed to obtain node association information, and the change in the capability of the cluster of ships is analyzed. The node association information includes node closed neighborhood, node attack probability, node weapon resource quantity, etc. The change in the capability of the cluster air defense and anti-missile system is comprehensively analyzed from aspects such as ship attributes, ship support relationships and support capabilities.

[0006] In order to achieve the above-mentioned object of the invention, the present invention provides a method for analyzing the change of the capability of a cluster ship air defense and anti-missile system based on undirected topology, comprising the following steps: Step 1, considering the input attribute information of each ship in the cluster, taking each ship as a node and the support relationship between ships as an edge, construct an undirected topological graph, where the input attribute information of the ship includes plane two-dimensional coordinates, heading angle, interception angle, interception near boundary and interception far boundary.

[0007] Step 2: Based on the undirected topological graph of the clustered ships that has been constructed, 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 hit, the number of weapon resources of the nodes, etc.

[0008] Among them, the analysis method of the capability change of the cluster ship air defense and anti-missile system based on undirected topology is: first consider the The two-dimensional coordinates of the ships , Heading Angle , interception angle , Intercept near boundary and interception far boundary , in 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 If inside 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 ; Based on the constructed undirected topology , get the node Number , closed neighborhood , probability of being hit , the number of weapons 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 .

[0009] Preferably, step 1 specifically includes: Step 11, according to The two-dimensional coordinates of the ships , , heading angle , interception angle , Intercept near boundary and interception far boundary , in a two-dimensional plane, calculate the coordinates of the four vertices of the trapezoid , , , ; Step 12: Draw the first Ships can support area ; Step 13, in Ships can support area Random sampling points; Step 14, judgement Is the sampling point in Support area of ​​​​ships Inside, record in The number of points is ; Step 15, calculate , and determine whether it is greater than a given threshold ,like It is believed that Ships and There is a supportable relationship between the ships; Step 16: Take each ship as a node , the support relationship between ships is , constructing an undirected topology of clustered ships .

[0010] Preferably, 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: , , , , in, , Indicates The two-dimensional coordinates of the ships, Indicates The heading angle of the ship, Indicates The interception angle of the ship, Indicates The interception limit of the ships is Indicates The interception limit of a ship.

[0011] As a preferred method, 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 .

[0012] Preferably, in step 1, for the 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 .

[0013] As a preference, each ship is used as a node , the support relationship between ships is , constructing an undirected topology of clustered ships .

[0014] Preferably, step 2 specifically includes: Step 21: Calculate the undirected topology based on the Roman control algorithm The two most important nodes and , and the number of weapon resources given to the most important node is 90, and the number of weapon resources given to the remaining nodes is 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 given weapon resources is 90, and the number of given weapon resources for other nodes is 30.

[0015] 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 ; Step 23, according to and Expression in the adjustment phase, calculates the end time 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 is recalculated. The probability that all nodes other than , and according to Recalculate the combat capability of cluster ships during the adjustment phase ; Step 25: Calculate the combat capability of the cluster ships in the enemy encounter phase ; Step 26, during 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 ; Step 27: Calculate the combat capability of the cluster ships during the recovery phase ; Step 28, according to and The expression in the recovery phase calculates the end time of the recovery phase ; Step 29: Calculate the combat capability of the fleet in the final stage .

[0016] As a preferred option, in step 2, at the initial stage, the combat capability of the cluster ship air defense and anti-missile system There are the following expressions: , in, , Represents 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 of Representatives in The moments do 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: , 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 area indicates better mutual support between the two ships.

[0017] Preferably, in step 2, during the adjustment phase, the node The probability of being hit There are the following expressions: , in, Represents the total number of nodes, Indicates that except for the estimated hit node In addition, the enemy attacks the node The probability of Representation Node The degree of attack, estimated attack node That is, the initial stage node combat capability The strongest node.

[0018] As a preferred option, 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: , in, Indicates the end time of the adjustment phase, Representatives in The moments do not exist simultaneously on the ship and ship The number of sampling points in the support area during the adjustment phase is expressed as: , in, is the exponential constant coefficient, .

[0019] As a preferred option, 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: , in, Indicates the end of the enemy-meeting phase. It indicates the combat capability of the cluster ship air defense and anti-missile system at the end of the adjustment phase.

[0020] As a preferred option, 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: , in, Indicates the moment when the recovery phase is completed, Representatives in The moments do not exist simultaneously on the ship and ship The number of sampling points in the support area during the recovery phase is expressed as: , in, is the exponential constant coefficient, .

[0021] As a preferred option, 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: in, Representatives in The moments do not exist simultaneously on the ship and ship The number of sampling points in the supported area, .

[0022] Based on the same inventive concept, the present invention provides a cluster ship air defense and anti-missile system capability change analysis system based on undirected topology, comprising: The cluster ship undirected topology generation module considers the input attribute information of each ship in the cluster, takes each ship as a node, and the support relationship between ships as an edge to construct an undirected topology graph, where the ship attribute information includes plane two-dimensional coordinates, heading angle, interception angle, interception near boundary and interception far boundary; In addition, the cluster ship air defense and anti-missile system capability analysis module, based on the constructed undirected topology graph of cluster ships, traverses all nodes in the undirected topology, obtains the associated information of all nodes, and then analyzes the changes in the air defense and anti-missile system capabilities. The associated information of the nodes includes the closed neighborhood of the node, the probability of the node being hit, the number of weapon resources of the node, etc. 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 executable 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.

[0023] Beneficial effect: The method for analyzing the change of 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 topological graph of clustered ships with each ship as a node and the support relationship between ships as an edge. Then, based on the undirected topological graph of clustered ships, all nodes are traversed to obtain node association information and analyze the change of the capability of clustered ships. Based on step 1, the present invention models the supportable area as an isosceles trapezoid, which simplifies the overall calculation amount of the algorithm. Based on step 2, the present invention provides the air defense and anti-missile capabilities of the cluster ships at different times, and the corresponding changes in the supported areas, which takes into account the actual working status of the cluster ships more comprehensively. and changes in air defense and anti-missile capabilities , 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

[0024] Figure 1 is an overall flow chart of the method according to the embodiment of the present invention, Figure 2 is a flow chart of capability change analysis of a cluster ship air defense and anti-missile system based on undirected topology in an embodiment of the present invention. Figure 3It is a schematic diagram of the results of the analysis of the air defense and anti-missile capabilities of clustered ships according to the present invention. DETAILED DESCRIPTION

[0025] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. 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 creative work are within the scope of protection of the present invention.

[0026] Depend on Figure 1 As shown in the figure, first consider the input attribute information of each ship in the cluster, calculate the support area of ​​each ship, and judge whether the support areas between the two ships have enough overlapping area. If the overlapping area is large enough, it is considered that there is a support relationship between the two ships. Then, take each ship as a node and the support relationship between ships as an edge to construct the corresponding cluster ship undirected topological graph. The input attribute information of the ship includes plane two-dimensional coordinates, heading angle, interception near boundary and interception far boundary; then, based on the undirected topological graph of the cluster ship, traverse all nodes, obtain node association information, and analyze the changes in the ability of the cluster ship air defense and anti-missile system. The node association information includes node closed neighborhood, node attack probability, node weapon resource quantity, etc. Specifically: Combined with the input attribute information of the cluster ship, judge the support relationship between ships and construct an undirected topological graph; based on the undirected topological graph of the cluster ship, combined with the node association information, analyze the changes in the ability of the cluster ship air defense and anti-missile system.

[0027] Taking the change of the air defense and anti-missile system capability of the maritime air defense cluster ships as an example, the detailed implementation process of the embodiment of the present invention is described below, including the following steps: S1, construct an undirected topology based on the input attribute information of the cluster ships; 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 interception far boundary ; 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: , , , , in, , Indicates The two-dimensional coordinates of the ships, Indicates The heading angle of the ship, Indicates The interception angle of the ship, Indicates The interception limit of the ships is Indicates The interception limit of a ship.

[0028] Then, , , , The closed figure formed by connecting the four points as vertices in sequence is an isosceles trapezoid. Ships can support area ; S12, determine 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 a 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 ; 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; 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 given weapon resources is 90, and the number of given weapon resources for other nodes is 30; S22: Analyze the changes in the air defense and anti-missile system capabilities of the cluster ships in the initial stage; There are the following expressions: , in, , Represents 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 of Representatives in The moments do 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: , 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 area indicates better mutual support between the two ships.

[0029] 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 strike nodes in the initial stage, the estimated enemy strike nodes are recalculated. The probability that all nodes other than ,node The probability of being hit There are the following expressions: , in, Represents the total number of nodes, Indicates that except for the estimated hit node In addition, the enemy attacks the node The probability of Representation Node The degree of attack, estimated attack node That is, the initial stage node combat capability The strongest node.

[0030] according to Recalculate the combat capability of cluster ships during the adjustment phase There are the following expressions: , in, Indicates the end time of the adjustment phase, Representatives in The moments do not exist simultaneously on the ship and ship The number of sampling points in the support area during the adjustment phase is expressed as: , in, is the exponential constant coefficient, .

[0031] S24, analyze the changes in the air defense and anti-missile system capabilities of the cluster of ships during the enemy-facing phase; during the enemy-facing phase, when the enemy's firepower strikes, the combat capability of the air defense and anti-missile system of the cluster of ships There are the following expressions: , in, Indicates the end of the enemy-meeting phase. It indicates the combat capability of the cluster ship air defense and anti-missile system at the end of the adjustment phase.

[0032] S25, analysis and recovery phase, the air defense and anti-missile system capability of the cluster ships changes; after the enemy's attack ends, our cluster ships' air defense and anti-missile system begins to recover, and the system's combat capability There are the following expressions: , in, Indicates the moment when the recovery phase is completed, Representatives in The moments do not exist simultaneously on the ship and ship The number of sampling points in the support area during the recovery phase is expressed as: , in, is the exponential constant coefficient, .

[0033] 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: , in, Representatives in The moments do not exist simultaneously on the ship and ship The number of sampling points in the supported area, .

[0034] 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.

[0035] 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: Table 1 Parameters of the capability change method of cluster ship air defense and anti-missile system based on undirected topology Figure 3 The results of the analysis of the air defense and anti-missile capabilities of clustered ships by the algorithm proposed in the present invention are shown, wherein, 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 represented by the capability value of the entire ship; in the second adjustment stage, the capability of the entire system drops sharply, and 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 declining state 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 sunk costs of the system 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.

[0036] 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, takes each ship as a node, and the support relationship between the ships as an edge, to construct an undirected topological graph, wherein the attribute information of the ship includes a plane two-dimensional coordinate, a heading angle, an interception angle, an interception near boundary, and an interception far boundary; In addition, the cluster ship air defense and anti-missile system capability analysis module, based on the constructed undirected topology graph of cluster ships, traverses all nodes in the undirected topology, obtains the associated information of all nodes, and then analyzes the changes in the air defense and anti-missile system capabilities. The associated information of the nodes includes the closed neighborhood of the node, the probability of the node being hit, the number of weapon resources of the node, etc. The specific working process of each module described above can refer to the corresponding process in the aforementioned method embodiment, which will not be repeated here. The module division 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.

[0037] 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 executable 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.

[0038] Those skilled in the art can understand that the technical solution of the present invention, in essence or in other words, the part that contributes to the prior art, can be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for enabling a computer system (which may be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in the embodiment of the present invention. The storage medium includes: various media that can store computer programs, such as a USB flash drive, a mobile hard disk, a read-only memory ROM, a random access memory RAM, a magnetic disk or an optical disk.

[0039] 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 protection scope of the present invention.

Claims

1. A method for analyzing the change of the capability of the air defense and anti-missile system of clustered ships based on undirected topology, characterized in that: 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 to 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 cluster ships, obtain the associated information of all nodes, and then analyze the changes in the air defense and anti-missile system capabilities of the cluster ships. The associated information of the nodes includes the closed neighborhood of the nodes, the probability of the nodes being hit, and the number of weapon resources of the nodes.

2. The method for analyzing the change in the capability of the cluster 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 two-dimensional coordinates of the ships , , heading angle , interception angle , Intercept near boundary and interception far boundary , in a two-dimensional plane, calculate the coordinates of the four vertices of the trapezoid , , , ; Step 12: Draw the first Ships can support area ; Step 13, in Ships can support area Random sampling points; Step 14, judgement Is the sampling point in Support area of ​​​​ships Inside, record in The number of points is ; Step 15, calculate , and determine whether it is greater than a given threshold ,like It is believed that Ships and There is a supportable relationship between the ships; Step 16: Take each ship as a node , the support relationship between ships is , constructing an undirected topology of clustered ships .

3. The method for analyzing the change in the capability of the cluster ship air defense and anti-missile system based on undirected topology according to claim 1 is characterized in that: 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: in, , Indicates The two-dimensional coordinates of the ships, Indicates The heading angle of the ship, Indicates The interception angle of the ship, Indicates The interception limit of the ships is Indicates The interception distance of a ship.

4. The method for analyzing the change in the capability of the cluster 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: Calculate the undirected topology based on the Roman control algorithm The two most important nodes and , and the number of weapon resources given to the most important nodes is 90, and the number of weapon resources given to the remaining nodes is 30; 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 ; Step 23, according to and Expression in the adjustment phase, calculates the end time 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 is recalculated. The probability that all nodes other than , and according to Recalculate the combat capability of cluster ships during the adjustment phase ; Step 25: Calculate the combat capability of the cluster ships in the enemy encounter phase ; Step 26, during 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 ; Step 27: Calculate the combat capability of the cluster ships during the recovery phase ; Step 28, according to and The expression in the recovery phase calculates the end time of the recovery phase ; Step 29: Calculate the combat capability of the fleet in the final stage .

5. The method for analyzing the change in the capability of the cluster ship air defense and anti-missile system based on undirected topology according to claim 4 is characterized in that: In step 2, the initial stage, the combat capability of the cluster ship air defense and anti-missile system There are the following expressions: in, , Represents 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 , Representatives in The moments do 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: ， 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 area indicates better mutual support between the two ships.

6. The method for analyzing the change in the capability of the cluster 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, nodes The probability of being hit There are the following expressions: ， in, Represents the total number of nodes, Indicates that except for the estimated hit node In addition, the enemy attacks the node The probability of Representation Node The degree of attack, 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 cluster 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 of the cluster ship air defense and anti-missile system There are the following expressions: in, Indicates the end time of the adjustment phase, Representatives in The moments do not exist simultaneously on the ship and ship The number of sampling points in the support area during the adjustment phase is expressed as: ， in, is the exponential constant coefficient, .

8. The method for analyzing the change in the capability of the cluster 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 encounter phase, the combat capability of the cluster ship air defense and anti-missile system There are the following expressions: in, Indicates the end of the enemy-meeting phase. It indicates the combat capability of the cluster ship air defense and anti-missile system at the end of the adjustment phase.

9. The method for analyzing the change in the capability of the cluster 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 of the cluster ship air defense and anti-missile system There are the following expressions: in, Indicates the moment when the recovery phase is completed, Representatives in The moments do not exist simultaneously on the ship and ship The number of sampling points in the support area during the recovery phase is expressed as: in, is the exponential constant coefficient, .

10. The method for analyzing the change of the capability of the cluster ship air defense and anti-missile system based on undirected topology according to claim 4 is characterized in that: 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: ， in, Representatives in The moments do not exist simultaneously on the ship and ship The number of sampling points in the supported area, .

11. The capability change analysis system of cluster ship air defense and anti-missile system based on undirected topology is characterized by: The system is used to implement the change analysis method described in any one of claims 1 to 10, and comprises: a cluster ship undirected topology generation module, which considers the input attribute information of each ship in the cluster, takes each ship as a node, and the support relationship between the ships as an edge, and constructs an undirected topology graph, wherein the attribute information of the ship includes a plane two-dimensional coordinate, a heading angle, an interception angle, an interception near boundary, and an interception far boundary; In addition, the cluster ship air defense and anti-missile system capability analysis module, based on the constructed undirected topology graph of cluster ships, traverses all nodes in the undirected topology, obtains the associated information of all nodes, and then analyzes the changes in the air defense and anti-missile system capabilities. 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; Among them, the analysis method of the capability change of the cluster ship air defense and anti-missile system based on undirected topology is: first consider the The two-dimensional coordinates of the ships , Heading Angle , interception angle , Intercept near boundary and interception far boundary , in 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 If inside 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 ; Based on the constructed undirected topology , get the node Number , closed neighborhood , probability of being hit , the number of weapons resources , calculate the changes in the air defense and anti-missile system capabilities of cluster ships in five stages , respectively the initial stage, adjustment stage, enemy-facing 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 air defense and anti-missile system of clustered ships based on undirected topology are implemented according to any one of claims 1 to 10.

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