Multi-target decision-making algorithm for intercepting ballistic missiles based on covariance adaptive model

Abstract

The invention relates to the field of missile interception, and is a multi-target decision algorithm for intercepting ballistic missiles based on a covariance adaptive model. Based on a given attack trajectory, a predicted hit point and a threat evaluation index set, threat values ​​of ballistic missile targets are calculated and sorted based on acquired data. Based on a decision variable allocation with constraints and a covariance adaptive sampling strategy, parameters such as the launch azimuth angle, the maximum negative attack angle and the launch position of interceptor missiles corresponding to different targets are determined. The algorithm can effectively have extremely high interception efficiency and accuracy in multi-target missile interception.

Description

Technical Field

[0001] The invention relates to the field of missile interception, and in particular to a multi-target decision algorithm for intercepting ballistic missiles based on a covariance adaptive model. Background Art

[0002] Driven by scientific and technological progress, precision guidance technology is constantly upgraded, improved and replaced. The hit probability, accuracy and anti-interference ability of missiles are getting higher and higher. It is becoming increasingly difficult for targets without interference and camouflage to survive in actual combat, which has brought huge challenges to air defense and anti-missile. The main technologies for destroying incoming missiles include fragmentation interception technology, firepower salvo suppression, and "many-on-one" interception methods of air defense missiles. The fragmentation interception and firepower salvo suppression interception action areas are limited, and the probability of successful interception is related to the density of firepower. The enemy can control the missile to avoid the action area. The "many-on-one" interception method of air defense missiles is not cost-effective. How to achieve successful interception of intercontinental ballistic targets with strong penetration capability and hypersonic flight characteristics, as well as the allocation of interception time and interception tasks are issues that urgently need to be solved in the prior art. For this reason, this application proposes a multi-target decision-making algorithm for intercepting ballistic missiles based on a covariance adaptive model. Summary of the invention

[0003] The purpose of the present invention is to provide a multi-target decision algorithm for intercepting ballistic missiles based on a covariance adaptive model to solve the problems raised in the above background technology.

[0004] To achieve the above object, the present invention provides a multi-objective decision-making algorithm for intercepting ballistic missiles based on a covariance adaptive model, comprising the following steps:

[0005] Step S1, determining the relevant parameters of the interceptor missile launch based on the given attack trajectory and predicted impact point;

[0006] Step S2, calculating and ranking the threat level values ​​of ballistic missile targets based on the threat level assessment index set and the acquired data;

[0007] Step S3, based on the decision variable allocation with constraints and the covariance adaptive sampling strategy, the parameters such as the launch azimuth angle, the maximum negative angle of attack and the launch position of the interceptor missile corresponding to different targets are determined.

[0008] Preferably, in step S1, according to the different predicted hit points of the multi-target attack missiles corresponding to the different ballistic characteristics of the interceptor missiles, for a given attack missile trajectory, the specific interceptor missile launch is selected according to the following rules:

[0009] G1. The angle between the interception plane and the attacking plane should be as small as possible;

[0010] G2. At the predicted impact point, the velocity angle between the interceptor missile and the attacking missile is as small as possible;

[0011] G3. Launch as early as possible.

[0012] Preferably, the interceptor missile launch time in step S1 is expressed as:

[0013] in, χ∈(0,π) represents the angle between the interception plane and the attack plane; A∈(0,π) represents the angle between the interceptor missile and the attacking missile at the predicted impact point; T L represents the interceptor missile launch time, T represents the interceptor missile launch time window length; α i ∈(0,1) is the indicator weight that needs to be customized by the user.

[0014] Preferably, the interceptor missile launch decision algorithm in step S1 is as follows:

[0015] Step 1: Initialize the trajectory of the interceptor projectile with the smallest negative angle of attack and use it to predict the hit point for comparison;

[0016] Step 2: Select a point at a certain time in the predicted trajectory of the attacking missile, calculate its distance from the interception position of the interceptor missile, and find the interceptor missile trajectory time index interceptor missile_Index with the smallest distance and the current interceptor missile trajectory sequence;

[0017] Step 3: If the difference between the interceptor missile height corresponding to the interceptor missile_Index and the altitude corresponding to the point of the attack missile at a certain time is less than 5 kilometers, go to Step 4. If the altitude difference is greater than 5 kilometers, the attack missile trajectory point is stepped by 10 points and goes to Step 2.

[0018] Step 4: Update the interceptor trajectory corresponding to the maximum negative attack angle of different program turns, and go to Step 2. If the last interceptor trajectory is traversed, the loop ends.

[0019] Preferably: In step S2, weighted calculation is used to determine the threat level w of the defense target o , the normalization formula of range threat value is:

[0020] The shooting height threat is mapped as follows:

[0021]

[0022] Where: x ij Indicates the ballistic altitude, calculated in km; Represents the corresponding minimum energy trajectory. The shutdown point velocity threat level can be processed by linear difference according to the change characteristics of the target shutdown point velocity. The formula is:

[0023] The remaining flight time threat level function can be processed by linear difference according to the characteristics of the attack missile flight time. The formula is:

[0024]

[0025] Preferably: step S2 uses the hierarchical analysis method to calculate the threat value of the ballistic missile target, and the specific process is: V1. establish a judgment matrix, V2. calculate the eigenvalue and the corresponding eigenvector, V3. normalize the eigenvector of the maximum eigenvalue for consistency check, V4. calculate the threat value of the ballistic missile target.

[0026] Preferably: the matrix for decision variable allocation in step S3 is

[0027]

[0028] Where: Decision variables When x i,j =1, it means that the i-th interception unit is responsible for intercepting the j-th target; when x i,j = 0 means that the i-th interception unit does not intercept the j-th target, and the interception units should meet certain constraints, mainly:

[0029]

[0030] Among them B i,j represents the interception mode of the i-th interception unit against the j-th target, B i,j =1 means that the interception unit uses a one-to-one interception mode to intercept the jth target, B i,j = 2 means that the interception unit uses the two-to-one interception mode to intercept the jth target, B i,j =3 means that the interception unit uses the three-interception-one interception mode to intercept the j-th target. The interception mode is given by the interception mode allocation software and input into the task allocation software; x i,j is a Boolean value used to determine whether the i-th interception unit is assigned to the j-th target; N i Represents the bomb load of the i-th interception unit.

[0031] Preferred: The MEDCA algorithm framework of the covariance adaptive sampling strategy in step S3 first randomly generates N solutions from the decision space as the initial population, and constructs an archive set After that, initialize the adaptive scaling factor s g and generate generation vector b n , where s g ,b n are all 1×N row vectors, corresponding to the N individuals in the population, and the initial value of each element is 1. During the population evolution process, the population is first Perform GK-FCM clustering to divide it into K clusters, and then evolve the population in sequence For each individual x in n , construct individual x n The adaptive covariance matrix Σ n , that is, by evolving individual x n The scaling factor s g n The covariance matrix of the class to which it belongs is scaled, and the scaled covariance matrix is ​​used as the covariance matrix of its sampling model, where: For x n The covariance matrix of the class to which it belongs. Then, around x n Sampling generates a trial solution ts, the environment selection operator evaluates the trial solution ts, and updates the archive set And generate generation vector b n After the population completes one evolution, based on the generation vector b n Calculate the adaptive scaling factor s g+1 , in calculating the adaptive scaling factor s g+1 In the above example, only the number of surviving generations of individuals in the past H evolutionary generations is considered. If the number of surviving generations of individuals exceeds the threshold, the number of surviving generations of individuals will no longer be accumulated. Then, the archive set Update population When the evolution termination condition is met, MEDCA returns to the population The set of non-dominated solutions in .

[0032] Preferably, the covariance adaptive sampling strategy in step S3 is as follows: first determine the individual x to be evolved n The adaptive covariance matrix Σ n , then, the adaptive covariance matrix Σ n Perform Cholesky decomposition, then, with x n is the mean, Σ n A Gaussian sampling model is constructed for the adaptive covariance matrix, and trial solutions ts are generated by random sampling. Then, polynomial mutation is performed on the trial solutions, and the trial solution genes outside the decision space are repaired. Finally, the trial solution set is output.

[0033] Preferably, the adaptive scaling factor updating step of the covariance adaptive sampling strategy in step S3 is as follows: first, the number of surviving generations of each individual in the population in the past H evolutionary generations is calculated: The upper limit of the number of generations that an individual can survive is H, and g represents the current number of generations of evolution of the population. After that, based on the number of generations that an individual can survive Calculate individual x n Covariance matrix scaling factor for the next evolution Scaling Factor The value range of is [0, 1], and the larger The value corresponds to a smaller value; otherwise, the smaller The value corresponds to a larger When the number of generations that an individual survives is close to the average number of generations that individuals in the population survive, the scaling factor Close to 0.5, finally, the covariance matrix scaling factor for the individual Make repairs.

[0034] Compared with the prior art, the present invention has the following beneficial effects:

[0035] The present invention calculates and sorts the threat values ​​of ballistic missile targets based on a given offensive trajectory, predicted hit point, and threat assessment index set, and determines the parameters such as the launch azimuth angle, maximum negative attack angle, and launch position of interceptor missiles corresponding to different targets based on the constraint-based decision variable allocation and covariance adaptive sampling strategy, so as to effectively achieve extremely high interception efficiency and accuracy in multi-target missile interception. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 is a flow chart of the present invention;

[0037] Figure 2 It is a diagram showing the change rule of the angle of attack of the missile of the present invention;

[0038] Figure 3 It is a schematic diagram of the launch time window of the interceptor missile of the present invention;

[0039] Figure 4 is a threat level assessment flow chart of the present invention;

[0040] Figure 5 It is a simulation ground-based attack and defense trajectory diagram of the present invention;

[0041] Figure 6 It is a simulated earth background solid system attack and defense trajectory map of the present invention;

[0042] Figure 7 It is a simulation diagram of interceptor missile speed of the present invention;

[0043] Figure 8 It is a simulation projectile-target distance diagram of the present invention;

[0044] Fig. 9 A full prediction hit point diagram for the simulation of the present invention;

[0045] Fig.10 It is a diagram of the maximum negative attack angle of the interceptor missile corresponding to the hit point predicted by the simulation of the present invention;

[0046] Fig.11 It is a simulation prediction hit point distance difference map of the present invention;

[0047] Fig.12 A simulation prediction hit point height map of the present invention;

[0048] Fig.13 The simulation prediction hit point and interception position distance diagram of the present invention;

[0049] Fig.14 It is a diagram of the launch time of an interceptor missile with different predicted hit points simulated by the present invention;

[0050] Fig.15 It is a latitude map of the simulation prediction hit point of the present invention;

[0051] Fig.16 It is a longitude diagram of the simulation prediction hit point of the present invention;

[0052] Fig.17 This is a time diagram of the attacking projectile corresponding to the simulation prediction hit point of the present invention. DETAILED DESCRIPTION

[0053] 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 implementation regulations described 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.

[0054] Example

[0055] See also Figure 1 , FIG. 1 is a preferred embodiment of the present invention, a multi-objective decision algorithm for intercepting ballistic missiles based on a covariance adaptive model, comprising the following steps:

[0056] Step S1, based on the given attack trajectory and predicted impact point, determine the interceptor missile launch time and other related parameters;

[0057] Step S2, calculating and ranking the threat level values ​​of ballistic missile targets based on the threat level assessment index set and the acquired data;

[0058] Step S3, based on the decision variable allocation with constraints and the covariance adaptive sampling strategy, the parameters such as the launch azimuth angle, the maximum negative angle of attack and the launch position of the interceptor missile corresponding to different targets are determined.

[0059] In this embodiment, the interceptor missile flight plan is determined before it is launched, and the guidance and control system controls the missile flight attitude according to the pre-calculated parameters to make it fly according to the predetermined trajectory. The boost phase flight pitch angle is an important design parameter in the interceptor missile flight plan design. The pitch angle directly determines the interception height and range of the missile in the longitudinal plane. The boost phase flight pitch angle of the interceptor missile is generally approximated by a fixed formula. Therefore, the design and calculation of the flight pitch angle becomes a problem of parameter selection of the approximate formula. The approximate formula of the interceptor missile flight pitch angle is:

[0060]

[0061] Among them, the vertical flight phase is from the initial moment to t1. The duration depends on the thrust-to-weight ratio K of the missile, which can be approximately expressed as t2 is the moment when the missile speed reaches Mach number 0.8, from t1 to t2 is the missile program turning stage; t3 is the end of the boost stage; γ(t) is the velocity inclination angle, α(t) is the missile's angle of attack, expressed as:

[0062]

[0063] Among them, α m is the maximum absolute value of the angle of attack in the subsonic section; t m is the time when the missile reaches the extreme value of the angle of attack, which is related to the specific performance of the missile. In the boost phase of the interceptor missile, the missile flies at a negative angle of attack. The approximate change law of α(t) is as follows: Figure 2 shown.

[0064] Furthermore, in addition to the above-mentioned boost phase pitch angle flight plan design in the longitudinal plane of the launch system, the interceptor missile's flight plan in the lateral direction of the launch system is also involved, and the interceptor missile launch azimuth angle μ is used as the design parameter to adjust the lateral deviation of the interceptor missile by adjusting the launch azimuth angle. Therefore, the present invention uses the interceptor missile launch time, launch azimuth angle, maximum negative angle of attack, and launch position as launch parameters.

[0065] In this embodiment, the interception time window is defined as the time period between the earliest launch time and the latest launch time of the interceptor missile, with the purpose of providing decision support for the ground anti-missile command and control system to select the interception time.

[0066] Furthermore, the interception time window of a ballistic missile is determined by many factors on both the offensive and defensive sides, including the range of the ballistic missile, ballistic characteristics, the location of the interceptor missile launch point, the range, interception altitude, the speed of the interceptor missile, and the early warning and tracking capabilities of the interceptor. The interception time window is mainly calculated by simulation based on the ballistic characteristics of the intercepting sides. After the deployment point of the interception unit is optimized and the interceptor missile launch point is fixed, the earlier the selected interceptor missile launch time (launch time) is, the greater the distance from the ballistic missile to the interceptor missile launch point is, and therefore, the higher the requirements for the interceptor missile projection capability are. Although selecting a later interception launch time can meet the interceptor missile projection capability requirements, the later the interception time is, the smaller the time window for implementing a secondary interception is, and therefore, the interception time cannot be too late.

[0067] Furthermore, the graphical representation of the interception time window is as follows Figure 3 As shown in the figure, o is the target missile launch point. At the initial time t0, the target missile is detected and the predicted trajectory is given. t2 is the earliest encounter time point between the interceptor missile and the target missile. Δt1 is the flight time of the interceptor missile to reach t2. Then the earliest launch time point of the interceptor missile is t1=t2-Δt1. t4 is the latest encounter time point between the interceptor missile and the target missile. Δt2 is the flight time of the interceptor missile to reach t4. Then the latest launch time point of the interceptor missile is t3=t4-Δt2. The interception time window can be expressed as T k =[t1,t3].

[0068] Furthermore, different predicted hit points correspond to different interceptor missile trajectory characteristics. For a given offensive trajectory, the specific interceptor missile launch time is selected according to the following rules:

[0069] (1) The angle between the interception plane and the attack plane is as small as possible;

[0070] (2) At the predicted impact point, the velocity angle between the interceptor and the attacking missile is as small as possible;

[0071] (3) The launch time should be as early as possible;

[0072] Among them, rule (1) means that when there is a deviation in the guidance radar or the offensive target is maneuvering, the interceptor missile has more maneuverability to make terminal guidance corrections; rule (2) means that the interceptor missile and the offensive missile have better conditions for handover of mid-terminal guidance; rule (3) means early detection and early interception, providing conditions for possible subsequent secondary interception.

[0073] Based on the above rules, define the indicator corresponding to each rule as p i , the weight of each rule indicator is α i , then the optimal launch time selection rule is:

[0074] in, χ∈(0,π) represents the angle between the interception plane and the attack plane; A∈(0,π) represents the angle between the interceptor missile and the attacking missile at the predicted impact point; T L represents the interceptor missile launch time, T represents the interceptor missile launch time window length; α i ∈(0,1) is the indicator weight that needs to be customized by the user.

[0075] Based on the above rules, when the specific predicted hit point, that is, the specific launch time, is determined, the launch azimuth and maximum negative attack angle of the interceptor missile can also be obtained. The interceptor missile take-off time decision algorithm is as follows:

[0076] Step 1: Initialize the trajectory of the interceptor projectile with the smallest negative angle of attack and use it to predict the hit point for comparison;

[0077] Step 2: Select a point at a certain time in the predicted trajectory of the attacking missile, calculate its distance from the interception position of the interceptor missile, and find the interceptor missile trajectory time index interceptor missile_Index with the smallest distance and the current interceptor missile trajectory sequence;

[0078] Step 3: If the difference between the interceptor missile height corresponding to the interceptor missile_Index and the altitude corresponding to the point of the attack missile at a certain time is less than 5 kilometers, go to Step 4; if the altitude difference is greater than 5 kilometers, the attack missile trajectory point is stepped by 10 points and goes to Step 2;

[0079] Step 4: Update the interceptor trajectory corresponding to the maximum negative attack angle of different program turns, and go to Step 2. If the last interceptor trajectory is traversed, end the loop.

[0080] Among them, when searching for the predicted hit point, the interceptor missile launch time corresponding to each predicted hit point can be obtained. If the predicted hit point is selected by adopting the strategy of first discovery, first interception, the corresponding interceptor missile launch time can be obtained.

[0081] In this embodiment, for the multi-target interception mode decision process, firstly, a threat assessment index set is established, including:

[0082] (1) By predicting the trajectory landing point and the landing point error radius, the geographical match is performed with the key points. If there is an overlapping area, it constitutes a threat. The missile attack area is divided into five levels according to the importance level and assigned corresponding scores, as shown in Table 1. The threat value of the defense target is determined by weighted calculation, and w is used. o express.

[0083] Table 1. Importance level of protected areas

[0084] grade Region Type Points Very high Key defense facility areas 9 high Command system area 7 generally Important hub area 5 Low Economic goals 3 Very low Overseas Regions 1

[0085] (2) Offensive missile range. The range refers to the geodetic distance from the launch location of an intercontinental ballistic missile to its landing location. It is measured in kilometers and is an important tactical and technical performance indicator for measuring the power of a missile. Each type of intercontinental ballistic missile has a minimum range and a maximum range. The greater the range of the offensive missile target, the greater the ability to destroy the target. It is a static threat indicator determined by the specific offensive missile target. The warhead equivalent and number carried by different types of intercontinental ballistic missiles are also very different. Therefore, the threat level of the target range is a linear change process, and the normalized formula for the range threat value is:

[0086]

[0087] (3) Offensive missile altitude. In missile combat, after the missile launch point is determined, there is a unique minimum energy trajectory. The theoretical shutdown speed required for this trajectory is the minimum. In reality, in order to increase the probability of penetration, the attacker will raise or lower the trajectory. The high trajectory has a steep shape and a faster reentry speed, while the low trajectory has a lower flight trajectory and can compress the flight time. Based on the above characteristics, the trajectory altitude threat is mapped as follows:

[0088]

[0089] Where: x ij Indicates the ballistic altitude, calculated in km; represents the corresponding minimum energy trajectory.

[0090] (4) Offensive missile (offensive ballistic missile) shutdown speed. The shutdown speed determines the reentry speed and attack power of the incoming ballistic missile target and is an important factor in determining the threat level of the ballistic missile target. The greater the target shutdown speed, the greater the target's flight speed in the middle and terminal stages, the higher the performance requirements for anti-missile detection and interception equipment, and the greater the difficulty of interception. The greater the impact energy and lethality on the defended target, the greater the threat level, and vice versa. According to the flight principle of ballistic missiles, the corresponding shutdown speed varies with the range of ballistic missiles. According to relevant research, generally speaking, the shutdown speed of short-range ballistic missiles is between 1 and 3 km / s, the shutdown speed of medium-range ballistic missiles is between 3 and 5.2 km / s, the shutdown speed of long-range ballistic missiles is between 5.2 and 6.5 km / s, and the shutdown speed of intercontinental ballistic missiles is greater than 6.5 km / s. Therefore, the threat level of the target shutdown speed can be processed by linear difference according to the characteristics of the target shutdown speed change. The formula is:

[0091]

[0092] (5) The remaining flight time of the attacking missile. The remaining flight time refers to the flight time of the incoming ballistic missile target from the moment it is detected by the early warning radar to the point of impact. Short time and fast pace are the outstanding characteristics of anti-missile operations. Therefore, the remaining flight time is an important factor in determining the threat level of the ballistic missile target. From the perspective of anti-missile operations, the shorter the remaining flight time, the shorter the time for the incoming ballistic missile target to fly to the defended target, and the shorter the combat time left for anti-missile detection, tracking, identification, accusation, interception and other links. The stronger the urgency, the greater the threat level; conversely, the smaller the threat level, the remaining flight time is generally calculated based on the target information detected by the early warning radar. Assuming that the early warning radar detects a certain time T K The ballistic target information is obtained by the anti-missile command and control system after intelligence integration and trajectory prediction, and the target landing time T is calculated. I , then the remaining flight time is the target landing time T I The time when the target is discovered T K time period, that is, t = T I -T K According to relevant research, the flight time of a ballistic missile is generally between 3 and 42 minutes. Generally speaking, the flight time of a short-range ballistic missile is between 180 and 600 seconds, the flight time of a medium-range ballistic missile is between 600 and 1000 seconds, the flight time of a long-range ballistic missile is between 1000 and 1500 seconds, and the flight time of an intercontinental ballistic missile is between 1500 and 2600 seconds. Considering that the reaction time of an anti-missile weapon system is generally more than 5 minutes, the remaining flight time threat level function can be processed by linear difference according to the characteristics of the ballistic missile flight time change. The formula is:

[0093]

[0094] The analytic hierarchy process (AHP) used in this embodiment is a multi-objective decision analysis method that combines qualitative and quantitative analysis. First, a judgment matrix is ​​established based on the influencing factors; then, the weight of each factor is obtained. After meeting the consistency requirements, the threat value of each target is calculated based on the weight of each factor and the actual data. The flow chart is as follows: Figure 4 As shown, specifically including:

[0095] (1) Establish a judgment matrix. First, based on the threat assessment index set, the six factors of ballistic missile identification type, military value of the defense area, offensive missile range, offensive missile altitude, offensive missile flight speed, and offensive missile warning time are set as influencing indicators. Then, through the analysis of the importance of each factor by experts and the reference table 2, the scores of each indicator are given. Finally, the relative values ​​between the factors are obtained to construct a judgment matrix.

[0096] Table 2 The impact scale of single indicator on threat degree

[0097] Scale Scale meaning 1 This factor has a slight impact on the threat level 3 The influence of this factor on the threat level is generally 5 This factor has a relatively important impact on the threat level 7 The impact of this factor on the threat level is important 9 This factor has a very important impact on the threat level 2，4，6，8，10 is the median of the above adjacent judgments

[0098] (2) Calculate the eigenvalues ​​and corresponding eigenvectors, and use the power method to solve the eigenvalues ​​of each matrix. The principle is to multiply the matrix with any vector so that the vector can be moved closer to the direction of its main eigenvector to obtain the final eigenvalue and the corresponding eigenvector.

[0099] (3) Perform a consistency check on it. The eigenvector corresponding to the maximum eigenvalue is normalized for consistency check. If the consistency is not met, it is necessary to readjust the matrix parameters to make it meet the consistency or directly invalidate the matrix data and then calculate the next one. The more factors the matrix has, the greater the possibility of its deviation. The corresponding relationship is shown in Table 3. Finally, the numerical average of each eigenvector that meets the consistency requirements is used as the final coefficient of the threat assessment model to obtain coefficients D1, D2, D3, D4, D5 and D6. The calculation formula is:

[0100]

[0101] Table 3 Average random consistency index R I

[0102]

[0103] (4) Calculate the threat level of the ballistic missile target. According to the threat level assessment index set, the acquired data (importance of the defended position, remaining flight time, range, target type and target model) are normalized and then weighted and calculated with the weight value of each factor to finally obtain the threat level. The final value is retained to two decimal places. The calculation formula of the threat level is:

[0104] W=D1w y +D2w o +D3w(L)+D4w(h)+D5w(v)+D6w(t)

[0105] In this embodiment, the decision variables and constraints are established, and the decision variable allocation matrix is:

[0106]

[0107] Where: Decision variables When x i,j =1, it means that the i-th interception unit is responsible for intercepting the j-th target; when x i,j When =0, it means that the i-th interception unit does not intercept the j-th target.

[0108] Furthermore, according to typical combat scenarios, certain constraints should be met between interception units, mainly:

[0109]

[0110] Among them B i,j represents the interception mode of the i-th interception unit against the j-th target, B i,j =1 means that the interception unit uses a one-to-one interception mode to intercept the jth target, B i,j = 2 means that the interception unit uses the two-to-one interception mode to intercept the jth target, B i,j =3 means that the interception unit uses the three-interception-one interception mode to intercept the j-th target. The interception mode is given by the interception mode allocation software and input into the task allocation software; x i,j is a Boolean value used to determine whether the i-th interception unit is assigned to the j-th target; N i Represents the bomb load of the i-th interception unit.

[0111] In this embodiment, in the covariance adaptive sampling strategy, the main feature of MEDCA is that a covariance adaptive sampling strategy CASS based on fuzzy clustering is introduced in the MEDA framework to adaptively balance the development and exploration of different evolutionary search stages. In MEDCA, CASS uses GK-FCM clustering to characterize the population distribution and divide the population into several classes. Through intra-class covariance sharing, a Gaussian model is constructed for each individual to jointly approximate the manifold of the Pareto solution set and sample to generate offspring. In the offspring generation, the individual's scaling factor scales the covariance matrix of the Gaussian model to assist the individual in development or exploration. The scaling factor is adaptively updated during the population evolution process based on the number of surviving generations of the individual to meet the individual's development and exploration preferences at different evolutionary stages. The MEDCA algorithm framework is shown in Algorithm 1 (Table 4).

[0112] Input: population size N, number of clusters K, historical generations H.

[0113] Output: The set of non-dominated solutions in .

[0114] Table 4 Algorithm 1MEDCA algorithm framework

[0115]

[0116] In Algorithm 1, N solutions are first randomly generated from the decision space as the initial population, and an archive set is constructed. (Line 1), after which the adaptive scaling factor s is initialized g and generate generation vector b n , where s g ,b nare all 1×N row vectors, corresponding to the N individuals in the population, and the initial value of each element is 1 (the second row). During the population evolution process, the population is first Perform GK-FCM clustering to divide it into K clusters (line 4), and then evolve the population in turn For each individual x in n , first, construct individual x n The adaptive covariance matrix Σ n (Line 6), that is, by evolving individual x n The scaling factor The covariance matrix of the class to which it belongs is scaled, and the scaled covariance matrix is ​​used as the covariance matrix of its sampling model, where: For x n The covariance matrix of the class, then around x n Sampling generates a trial solution ts (line 7), the environment selection operator evaluates the trial solution ts, and updates the archive set And generate generation vector b n (Line 8), after the population completes one evolution, based on the generation vector b n Calculate the adaptive scaling factor s g+1 (Line 10), in calculating the adaptive scaling factor s g+1 In the above example, only the number of surviving generations of individuals in the past H evolutionary generations is considered. If the number of surviving generations of individuals exceeds the threshold, the number of surviving generations of individuals will no longer be accumulated. Then, the archive set Update population (Line 12), when the evolution termination condition is met, MEDCA returns the population The set of non-dominated solutions in (line 14).

[0117] During the evolution process, individuals belonging to the same category have different preferences for development or exploration. CASS uses a clustering model to characterize the population distribution and introduces a scaling factor to perturb the search space centered on the individual to be evolved. The covariance matrix of the sampling model is scaled to control the sampling range to assist the individual in developing or exploring. CASS uses the covariance of the individual and the class to which it belongs to construct a multivariate Gaussian sampling model to generate offspring solutions. Through the intra-class covariance sharing mechanism, the computational complexity of the sampling model is reduced, and better exploration capabilities can be obtained with less computational overhead. The steps of CASS are shown in Algorithm 2 (Table 5). First, the individual x to be evolved is determined. n The adaptive covariance matrix Σ n (Line 11), then, the adaptive covariance matrix Σ n Perform Cholesky decomposition (line 22), then use x n is the mean, Σ nThe covariance matrix constructs a Gaussian sampling model, and randomly samples to generate trial solutions ts (line 3). Then, polynomial mutation is performed on the trial solutions, and the trial solution genes outside the decision space are repaired (lines 4-5). Finally, the trial solution set is output (line 6).

[0118] Input: Individual x n , the adaptive covariance matrix Σ n .

[0119] Output: Try to solve ts.

[0120] Table 5 Covariance adaptive sampling strategy of Algorithm 2

[0121]

[0122] Furthermore, the number of survival generations of an individual is a comprehensive expression of the results of environmental selection in the past evolutionary generations. As an attribute value of an evolving individual, the number of survival generations can not only reflect the quality of the individual in the current population, but also reflect the evolutionary state and search preference of the individual, that is, individuals with a large number of survival generations in the population have relatively good quality, and searching with development preference can better improve their quality; similarly, individuals with a small number of survival generations prefer exploration. MEDCA constructs an adaptive scaling factor based on the number of survival generations of the individual, scales the covariance matrix of the sampling model to control the sampling range, and satisfies the individual's development or exploration preference. Specifically, the number of survival generations of individuals in the population is mean normalized and mapped to [0, 1], while satisfying: individuals with a large number of survival generations correspond to a smaller scaling factor, thereby achieving local search; individuals with a small number of survival generations use a large scaling factor for global search. Algorithm 3 (shown in Table 6) gives the detailed steps for updating the adaptive scaling factor.

[0123] Input: Generate generation vector b n .

[0124] Output: Adaptive scaling factor s g+1 .

[0125] Table 6 Algorithm 3 adaptive scaling factor update

[0126]

[0127] In Algorithm 3, we first calculate the number of surviving generations of each individual in the population in the past H evolutionary generations. The upper limit of the number of generations that an individual can survive is H, and g represents the current evolutionary generation of the population (the first line). After that, based on the number of generations that an individual can survive Calculate individual x n Covariance matrix scaling factor for the next evolution As shown in row 2, the scaling factor The value range of is [0, 1], and the larger The value corresponds to a smaller value; otherwise, the smaller The value corresponds to a larger When the number of generations that an individual survives is close to the average number of generations that individuals in the population survive, the scaling factor Close to 0.5, finally, the covariance matrix scaling factor for the individual Repair to prevent high-quality individuals from falling into local optimal solutions when searching for development preferences due to too small a search range (lines 3-5).

[0128] The interception algorithm of the present application is simulated, and the launch time window of each attacking missile corresponding to the intercepting missile can be obtained by searching the predicted hit point as shown in Table 7 below:

[0129] Table 7 Interceptor missile interception time window

[0130]

[0131] According to the predicted hit point and the corresponding interceptor missile launch time, the time decision method of first find first intercept is adopted. Figure 5-Figure 17 The simulation results are the key data in the attack and defense confrontation results. Among them, the miss distances corresponding to the three attack missiles are all within a small range. At 600 seconds, Lambert orbit change is used to correct the zero control miss distance caused by factors such as the earth's rotation. For the southeast protection target, the interceptor missiles at interceptor point 1 are all at more predicted hit points, the height error threshold of the trajectory family comparison is 2 kilometers, the range error threshold is 0.5 kilometers, and the feasible interception interval is longer. The maximum negative attack angle feasible for intercepting the first attack missile is from 5.6 degrees to 9 degrees, the maximum negative attack angle feasible for intercepting the second attack missile is from 5.8 degrees to 9 degrees, and the maximum negative attack angle feasible for intercepting the third attack missile is from 5.1 degrees to 9 degrees. The feasible interception altitude range of the first attack missile is from 1610 kilometers to 1720 kilometers, the feasible interception altitude range of the second attack missile is from 1600 kilometers to 1750 kilometers, and the feasible interception altitude range of the third attack missile is from 1800 kilometers to 1960 kilometers. The launch time of the interceptor missile corresponding to the first offensive missile ranges from 800 seconds to 1500 seconds, the launch time of the interceptor missile corresponding to the second offensive missile ranges from 900 seconds to 1900 seconds, and the launch time of the interceptor missile corresponding to the third offensive missile ranges from 850 seconds to 1950 seconds.

[0132] The above content is a further detailed description of the present invention in combination with specific implementation methods. It cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, some simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as belonging to the scope of protection determined by the claims submitted for the present invention.

Claims

1. A multi-objective decision-making method for intercepting ballistic missiles based on a covariance adaptive model, characterized in that: The steps include: Step S1, determining the interceptor missile launch parameters based on the given attack trajectory and predicted impact point; Step S2, calculating and ranking the threat level values ​​of ballistic missile targets based on the threat level assessment index set and the acquired data; Step S3, based on the decision variable allocation with constraints and the covariance adaptive sampling strategy, determining the launch azimuth, maximum negative angle of attack and launch position parameters of the interceptor missile corresponding to different targets; The interceptor missile launch time in step S1 is expressed as: in, χ∈(0,π) represents the angle between the interception plane and the attack plane; A∈(0,π) represents the angle between the interceptor missile and the attacking missile at the predicted impact point; T L represents the interceptor missile launch time, T represents the interceptor missile launch time window length; α i ∈(0,1) is the indicator weight that needs to be customized by the user; The steps of the covariance adaptive sampling strategy in step S3 are: first determine the individual x to be evolved n The adaptive covariance matrix Σ n , then, the adaptive covariance matrix Σ n Perform Cholesky decomposition, then, with x n is the mean, Σ n A Gaussian sampling model is constructed for the adaptive covariance matrix, and trial solutions ts are generated by random sampling. Then, polynomial mutation is performed on the trial solutions, and the trial solution genes outside the decision space are repaired. Finally, the trial solution set is output.

2. The multi-objective decision-making method for intercepting ballistic missiles based on a covariance adaptive model according to claim 1, characterized in that: In step S1, different predicted hit points of multi-target attack missiles correspond to different interceptor missile trajectory characteristics. For a given attack missile trajectory, specific interceptor missile launch parameters are selected according to the following rules: G1. The angle between the interception plane and the attacking plane should be as small as possible; G2. At the predicted impact point, the velocity angle between the interceptor missile and the attacking missile is as small as possible; G3. Launch as early as possible.

3. The multi-objective decision-making method for intercepting ballistic missiles based on a covariance adaptive model according to claim 1, characterized in that: The interceptor missile take-off time decision algorithm is as follows: Step 1: Initialize the trajectory of the interceptor projectile with the smallest negative angle of attack and use it to predict the hit point for comparison; Step 2: Select a point at a certain time in the predicted trajectory of the attacking missile, calculate its distance from the interception position of the interceptor missile, and find the interceptor missile trajectory time index with the smallest distance and the current interceptor missile trajectory sequence, expressed as interceptor missile_Index; Step 3: If the difference between the interceptor missile height corresponding to the interceptor missile_Index and the altitude corresponding to the point of the attack missile at a certain time is less than 5 kilometers, go to Step 4. If the altitude difference is greater than 5 kilometers, the attack missile trajectory point is stepped by 10 points and goes to Step 2. Step 4: Update the interceptor trajectory corresponding to the maximum negative attack angle of different program turns, and go to Step 2. If the last interceptor trajectory is traversed, the loop ends.

4. The multi-objective decision-making method for intercepting ballistic missiles based on a covariance adaptive model according to claim 1, characterized in that: In step S2, weighted calculation is used to determine the threat level w of the defense target. o , the normalization formula of range threat value is: The shooting height threat is mapped as follows: Where: x ij Indicates the ballistic altitude, calculated in km; Represents the corresponding minimum energy trajectory. The shutdown point velocity threat level can be processed by linear difference according to the change characteristics of the target shutdown point velocity. The formula is: The remaining flight time threat level function performs linear difference processing according to the characteristics of the attack missile flight time change. Its formula is:

5. The multi-objective decision-making method for intercepting ballistic missiles based on a covariance adaptive model according to claim 4 is characterized in that: Step S2 uses the hierarchical analysis method to calculate the threat value of the ballistic missile target. The specific process is: V1. Establish a judgment matrix, V2. Calculate the eigenvalue and the corresponding eigenvector, V3. Normalize the eigenvector of the maximum eigenvalue for consistency check, V4. Calculate the threat value of the ballistic missile target.

6. The multi-objective decision-making method for intercepting ballistic missiles based on a covariance adaptive model according to claim 1, characterized in that: The matrix for decision variable assignment in step S3 is Where: Decision variables When x i,j =1, it means that the i-th interception unit is responsible for intercepting the j-th target; when x i,j = 0 means that the i-th interception unit does not intercept the j-th target, and the interception units should meet certain constraints, which are: Among them B i,j represents the interception mode of the i-th interception unit against the j-th target, B i,j =1 means that the interception unit uses a one-to-one interception mode to intercept the jth target, B i,j = 2 means that the interception unit uses the two-to-one interception mode to intercept the jth target, B i,j =3 means that the interception unit uses the three-interception-one interception mode to intercept the j-th target. The interception mode is given by the interception mode allocation software and input into the task allocation software; x i,j is a Boolean value used to determine whether the i-th interception unit is assigned to the j-th target; N i Represents the bomb load of the i-th interception unit.

7. The multi-objective decision-making method for intercepting ballistic missiles based on a covariance adaptive model according to claim 6 is characterized in that: The MEDCA algorithm framework of the covariance adaptive sampling strategy in step S3 first randomly generates N solutions from the decision space as the initial population and constructs an archive set After that, initialize the adaptive scaling factor s g and generate generation vector b n , where s g ,b n are all 1×N row vectors, corresponding to the N individuals in the population, and the initial value of each element is 1. During the population evolution process, the population is first Perform GK-FCM clustering to divide it into K clusters, and then evolve the population in sequence For each individual x in n , construct individual x n The adaptive covariance matrix Σ n , that is, by evolving individual x n The scaling factor The covariance matrix of the class to which it belongs is scaled, and the scaled covariance matrix is ​​used as the covariance matrix of its sampling model, where: For x n The covariance matrix of the class to which it belongs; then, around x n Sampling generates a trial solution ts, the environment selection operator evaluates the trial solution ts, and updates the archive set And generate generation vector b n After the population completes one evolution, based on the generation vector b n Calculate the adaptive scaling factor s g+1 , in calculating the adaptive scaling factor s g+1 In the above example, only the number of surviving generations of individuals in the past H evolutionary generations is considered. If the number of surviving generations of individuals exceeds the threshold, the number of surviving generations of individuals will no longer be accumulated. Then, the archive set Update population When the evolution termination condition is met, MEDCA returns to the population The set of non-dominated solutions in .

8. The multi-objective decision-making method for intercepting ballistic missiles based on a covariance adaptive model according to claim 1, characterized in that: The adaptive scaling factor update steps of the covariance adaptive sampling strategy in step S3 are as follows: First, calculate the number of surviving generations of each individual in the population in the past H evolutionary generations The upper limit of the number of generations that an individual can survive is H, and g represents the current evolutionary generation of the population. After that, based on the number of generations that an individual can survive Calculate individual x n Covariance matrix scaling factor for the next evolution Covariance matrix scaling factor The value range is [0, 1], and the covariance matrix scaling factor n=1,2,…,N, They are α g The mean, maximum, and minimum values ​​of the covariance matrix are: Close to 0.5, finally, the covariance matrix scaling factor for the individual Make repairs.

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