CN110782062A - Many-to-many packet interception target distribution method and system for air defense system - Google Patents
Many-to-many packet interception target distribution method and system for air defense system Download PDFInfo
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Abstract
The invention discloses a many-to-many group interception target distribution method and system for an air defense system, which can distribute reasonable interception bombs to each target in the situation that a plurality of missiles intercept a plurality of targets for operation, realize group interception of the plurality of targets and improve the cooperative operation capability among the plurality of interception bombs. The method of the invention has the following main advantages: 1) according to the kinematics characteristics of the bullet eyes in the interception battle, an interception probability function considering the interception precision and the energy required for interception is constructed, and the method is suitable for many-to-many interception battle situations; 2) the target distribution method can realize the optimal target distribution under the fixed grouping constraint and the self-adaptive grouping constraint, can realize the grouping interception and the cooperative combat of a plurality of targets, and the common target distribution method does not have the grouping capability, so the method can effectively improve the cooperative combat capability among a plurality of intercepted bombs.
Description
Technical Field
The invention relates to the technical field of guidance control and decision optimization, in particular to a many-to-many grouping interception target distribution method and system for an air defense system.
Background
Weapon target distribution is one of important subjects in the field of guidance control and decision optimization, and different interception missiles are distributed for different attacking targets, so that a plurality of missiles have good battle positions relative to the targets, and good initial conditions are provided for tasks including cooperative detection, guidance and the like. Considering that in the situation that a plurality of missiles intercept a plurality of targets for operation, different intercepted missiles are different from different targets in initial position conditions. If a plurality of interception bombs with large array bit condition difference are distributed to the same target, the cooperative interception of the target can be difficult to realize. Therefore, in the case of many-to-many interception battles, reasonable interception resources must be allocated to each target first to form a battle situation of intercepting different targets in groups, so that the advantage of cooperative battles can be exerted to the greatest extent in a subsequent guidance link, that is, many-to-many grouping interception target allocation is required.
In air defense combat, aiming at a plurality of attacking targets, the intercepting efficiency needs to be accurately evaluated and calculated according to the relative kinematics characteristics of the missile. The design of the common interception probability function mainly comprises a method based on the information of the distance of the bullet, the information of the angle of the bullet and the prediction of the miss distance. However, the magnitude of the overload and the miss distance required for the subsequent interception bomb cannot be accurately estimated only based on the information of the projectile distance or the projectile angle, the magnitude of the energy required for the subsequent interception bomb cannot be estimated only based on the information of the predicted miss distance, and the comprehensive estimation of the interception precision and the energy required is difficult to realize in the conventional method. Therefore, how to evaluate the interception efficiency and calculate the interception probability from two aspects of the interception precision and the energy required by interception has important value and practical application significance.
The weapon target distribution problem is the most important problem in the front section of many-to-many interception battles, and the distribution result directly influences the overall battle efficiency. The solution space size of the target distribution problem can be exponentially increased along with the increase of the number of the interception bombs and the number of the targets, and the problem belongs to a typical integer programming problem. The existing target allocation methods all use the optimal total attack probability in many-to-many combat as an index, and adopt a common integer programming solution or a heuristic optimization algorithm to solve. The method has no capability of grouping attack, and is applied to the situation that the number of the intercepting bombs distributed to some targets is too large or too small in many-to-many intercepting battle situations, so that some targets break through a defense system in serious conditions and serious threats are generated to defenders. In many-to-many air defense interception battles, the threat degree of targets is different due to the self attributes of the targets and the initial position, so that the number and the position of interception bombs of one party are required to be integrated to carry out grouping attack on different targets, and each target is guaranteed to be allocated with enough interception resources. How to realize the optimal target distribution under the grouping constraint condition in many-to-many interception battles is a technical problem to be broken through.
Disclosure of Invention
The invention aims to provide a many-to-many grouping interception target distribution method and system for an air defense system, and the method and system are used for solving the problem of low cooperative combat capability caused by unreasonable weapon target distribution in the existing many-to-many interception combat.
In order to achieve the purpose, the invention provides the following scheme:
a many-to-many packet interception target assignment method for an air defense system, the method comprising:
acquiring initial motion parameters of an interception bullet group and a target group; the initial motion parameters comprise the speed vector, the course angle and the line-of-sight angle of each intercepted bullet in the intercepted bullet group as well as the speed vector and the course angle of each target in the target group;
determining the miss distance between the intercepting bullet and the target, the visual line angle rate of the bullet and the time required for the intercepting bullet to hit the moving target according to the initial motion parameters;
determining the interception probability of the interception bullet on the target according to the miss distance between the interception bullet and the target, the visual line angle rate of the bullet and the time required by the interception bullet to hit the moving target;
determining a target distribution strategy according to the interception probability of the interception bomb to the target; the target allocation strategy comprises a target allocation strategy under fixed grouping constraint and a target allocation strategy under self-adaptive grouping constraint;
taking the target distribution strategy as a fitness function of an artificial bee colony algorithm, and calculating by adopting the artificial bee colony algorithm to obtain a target distribution optimal solution under the target distribution strategy; and the target distribution optimal solution is the target number of the target intercepted by each interception bullet.
Optionally, the determining, according to the initial motion parameter, the miss distance between the intercepting bullet and the target, the line-of-sight angular rate of the bullet and the time required for the intercepting bullet to hit the moving target specifically includes:
using a formula
Determining the miss distance between the interception bomb and the target; wherein, the delta S is the miss distance between the interception bullet and the target;
θ
Mindicating the course angle of the intercepted missile; q represents the line of sight angle of the bullet; v
MRepresenting the velocity of the interceptor projectile; v
TRepresenting the speed of the target; theta
TRepresenting a heading angle of the target; t is t
goRepresenting the residual flight time of the interception bomb, and tau representing the inertia time constant of the interception bomb guidance system;
using a formula
Determining the visual angle rate of the bullet; wherein
Representing the angular rate of the line of sight of the bullet; r represents the relative distance between the interceptor projectile and the target;
using a formula
Determining the time required for an intercepting bullet to hit a moving targetA (c) is added; wherein T is
goRepresenting the time required for the interception bomb to hit the moving target; n represents the effective navigation ratio of the guidance system.
Optionally, the determining the interception probability of the interception bullet on the target according to the miss distance between the interception bullet and the target, the line-of-sight angular rate of the bullet and the time required for the interception bullet to hit the moving target specifically includes:
determining interception probability under the miss distance index according to the miss distance between the interception bullet and the target;
determining the interception probability under the visual angle rate index according to the visual angle rate of the bullet;
determining the interception probability under the index of time required for interception according to the time required by the interception bullet to hit the moving target;
and determining the interception probability of the interception bomb to the target according to the interception probability under the miss distance index, the interception probability under the line-of-sight angular rate index and the interception probability under the interception required time index.
Optionally, the determining the interception probability of the interception bullet to the target according to the interception probability under the miss distance index, the interception probability under the line-of-sight angular rate index, and the interception probability under the interception required time index specifically includes:
using a formula
Determining the interception probability of an interception bomb to a target; wherein P is
ijRepresenting the interception probability of the ith interception bullet to the jth target; p
ΔS(i,j)Representing the interception probability under the miss distance index;
representing the interception probability under the time index required by interception;
representing the interception probability under the line-of-sight angular rate index, β
ΔSThe weight under the off-target amount index is represented,
representing the weight of the interception time index;
the representation represents the weight under the line-of-sight angular rate index.
Optionally, the determining a target distribution policy according to the interception probability of the interception bomb to the target specifically includes:
determining a target distribution strategy under fixed grouping constraint according to the interception probability of the interception bomb to the target
Where m represents the number of interceptor bombs and n represents the number of targets; v
jRepresents the value of the jth target; x
ijIndicating whether the ith interception bullet is allocated to the jth target; q
jG
jAnd S
iH
iRespectively are penalty function terms;
determining a target distribution strategy under the self-adaptive grouping constraint according to the interception probability of the interception bomb to the target
U
jE
jA penalty function term that is an upper bound of the allocation number; l is
jF
jA penalty function term for assigning a lower bound to the number.
A many-to-many packet interception target distribution system for an air defense system, the system comprising:
the initial motion parameter acquisition module is used for acquiring initial motion parameters of the intercepted bullet group and the target group; the initial motion parameters comprise the speed vector, the course angle and the line-of-sight angle of each intercepted bullet in the intercepted bullet group as well as the speed vector and the course angle of each target in the target group;
the motion parameter determining module is used for determining the miss distance between the intercepting bullet and the target, the line-of-sight angular rate of the bullet and the time required by the intercepting bullet to hit the moving target according to the initial motion parameters;
the interception probability determining module is used for determining the interception probability of the interception bullet on the target according to the miss distance between the interception bullet and the target, the visual line angle rate of the bullet and the time required by the interception bullet to hit the moving target;
the target distribution strategy determining module is used for determining a target distribution strategy according to the interception probability of the interception bomb to the target; the target allocation strategy comprises a target allocation strategy under fixed grouping constraint and a target allocation strategy under self-adaptive grouping constraint;
the target distribution module is used for taking the target distribution strategy as a fitness function of an artificial bee colony algorithm and calculating by adopting the artificial bee colony algorithm to obtain a target distribution optimal solution under the target distribution strategy; and the target distribution optimal solution is the target number of the target intercepted by each interception bullet.
Optionally, the motion parameter determining module specifically includes:
a miss amount determination unit for employing a formula
Determining the miss distance between the interception bomb and the target; wherein, the delta S is the miss distance between the interception bullet and the target;
θ
Mindicating the course angle of the intercepted missile; q represents the line of sight angle of the bullet; v
MRepresenting the velocity of the interceptor projectile; v
TRepresenting the speed of the target; theta
TRepresenting a heading angle of the target; t is t
goRepresenting the residual flight time of the interception bomb, and tau representing the inertia time constant of the interception bomb guidance system;
a bullet eye line of sight angular rate determining unit for adopting a formula
Determining the visual angle rate of the bullet; wherein
Representing the angular rate of the line of sight of the bullet; r represents the relative distance between the interceptor projectile and the target;
an interception required time determining unit for adopting a formula
Determining the time required for intercepting the moving target in the impact; wherein T is
goRepresenting the time required for the interception bomb to hit the moving target; n represents the effective navigation ratio of the guidance system.
Optionally, the interception probability determining module specifically includes:
the interception probability determining unit under the miss distance index is used for determining the interception probability under the miss distance index according to the miss distance between the interception bullet and the target;
the interception probability determining unit under the visual angle rate index is used for determining the interception probability under the visual angle rate index according to the visual angle rate of the bullet;
the interception probability determining unit under the interception required time index is used for determining the interception probability under the interception required time index according to the time required by the interception bullet to hit the moving target;
and the interception probability determining unit is used for determining the interception probability of the interception bomb to the target according to the interception probability under the miss distance index, the interception probability under the line-of-sight angular rate index and the interception probability under the interception required time index.
Optionally, the interception probability determining unit specifically includes:
an interception probability determining subunit for employing a formula
Determining the interception probability of an interception bomb to a target; wherein P is
ijRepresenting the interception probability of the ith interception bullet to the jth target; p
ΔS(i,j)Representing the interception probability under the miss distance index;
representing the interception probability under the time index required by interception;
representing the interception probability under the line-of-sight angular rate index, β
ΔSThe weight under the off-target amount index is represented,
representing the weight of the interception time index;
the representation represents the weight under the line-of-sight angular rate index.
Optionally, the target allocation policy determining module specifically includes:
a target distribution strategy determining unit under the fixed grouping constraint, which is used for determining the target distribution strategy under the fixed grouping constraint according to the interception probability of the interception bomb to the target
Where m represents the number of interceptor bombs and n represents the number of targets; v
jRepresents the value of the jth target; x
ijIndicating whether the ith interception bullet is allocated to the jth target; q
jG
jAnd S
iH
iRespectively are penalty function terms;
a target distribution strategy determining unit under the adaptive grouping constraint, which is used for determining the target distribution strategy under the adaptive grouping constraint according to the interception probability of the interception bomb to the target
U
jE
jA penalty function term that is an upper bound of the allocation number; l is
jF
jA penalty function term for assigning a lower bound to the number.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention provides a many-to-many group interception target distribution method and system for an air defense system, which can distribute reasonable interception bombs to each target in the situation that a plurality of missiles intercept a plurality of targets for operation, realize group interception of the plurality of targets and improve the cooperative operation capacity among the plurality of interception bombs. The method of the invention has the following main advantages: 1) according to the kinematics characteristics of the bullet eyes in the interception battle, an interception probability function considering the interception precision and the energy required for interception is constructed, and the method is suitable for many-to-many interception battle situations; 2) the target distribution method can realize the optimal target distribution under the fixed grouping constraint and the self-adaptive grouping constraint, can realize the grouping interception and the cooperative combat of a plurality of targets, and the common target distribution method does not have the grouping capability, so the method can effectively improve the cooperative combat capability among a plurality of intercepted bombs.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a flow chart of a many-to-many packet interception target distribution method for an air defense system according to the present invention;
FIG. 2 is a schematic diagram of a bullet relative kinematics model and motion parameters provided by the present invention;
FIG. 3 is a diagram illustrating an integer encoding method according to the present invention;
FIG. 4 is a schematic structural diagram of a many-to-many packet interception target distribution system for an air defense system according to the present invention;
FIG. 5 is a target assignment result under a fixed grouping constraint, which is solved by the embodiment of the present invention;
FIG. 6 is a graph of an optimal value of an objective function under a fixed grouping constraint according to an embodiment of the present invention;
FIG. 7 is a target assignment result under adaptive grouping constraint solved by the embodiment of the present invention;
fig. 8 is a graph of an optimal value of an objective function under adaptive grouping constraint according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention provides a method and a system for distributing many-to-many group interception targets for an air defense system, and aims to design a target distribution algorithm with group constraint, so that in a situation of a plurality of targets intercepted by a plurality of missiles, reasonable interception bombs can be distributed to each target, the group interception of the plurality of targets is realized, the cooperative fighting capacity among the plurality of interception bombs is improved, and the problem of low cooperative fighting capacity caused by unreasonable distribution of weapon targets in the existing many-to-many interception fighting is solved.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Fig. 1 is a flowchart of a many-to-many packet interception target allocation method for an air defense system according to the present invention. Referring to fig. 1, the method for allocating many-to-many packet interception targets for an air defense system provided by the present invention specifically includes:
step 101: and acquiring initial motion parameters of the intercepting bullet group and the target group. The initial motion parameters comprise the speed vector, the course angle and the line-of-sight angle of each intercepted bullet in the intercepted bullet group and the speed vector and the course angle of each target in the target group.
Fig. 2 is a schematic diagram of a bullet relative kinematics model and motion parameters provided by the present invention. In FIG. 2, M denotes an interception bullet, T denotes an interception target (simply referred to as target in the present invention), and V
MCCRepresenting the velocity vector of the intercepted projectile under the condition of interception triangle, EIP representing the expected interception point, η representing the advance angle under the condition of meeting the interception triangle, V
MRepresenting the velocity vector of the interceptor projectile; v
TA velocity vector representing the target; r denotes the interceptor missile and the targetThe relative distance therebetween; q represents the line of sight angle of the bullet; theta
MIndicating the course angle of the intercepted missile; theta
TRepresenting a heading angle of the target; ψ represents the heading angle error of the interceptor missile.
Step 102: and determining the miss distance between the intercepting bullet and the target, the visual line angle rate of the bullet and the time required for the intercepting bullet to hit the moving target according to the initial motion parameters.
The step 102 specifically includes:
establishing a relative kinematics model of the interception bullet and the target
The relative motion relationship between the interceptor projectile and the target is as follows:
wherein, V
MAnd V
TRespectively representing the speed of the interception bomb and the target, r representing the relative distance between the interception bomb and the target,
representing the rate of change of the relative distance between the interceptor projectile and the target, q and
representing the eye angle and eye angular velocity, theta, respectively
MAnd theta
TRespectively representing the heading angles of the interceptor missile and the target,
and
respectively representing the course angle change rate of the intercepted missile and the target, a
MAnd a
TThe normal acceleration of the interceptor projectile and the target are indicated, respectively.
The leading angle η satisfying the intercept triangle condition is defined as follows:
the current heading angle error psi of the interceptor projectile is defined as follows:
the miss distance Δ S between the interceptor projectile and the target can be expressed as:
wherein, t
goRepresenting the remaining flight time of the interceptor projectile and tau representing the inertial time constant of the guidance system of the interceptor projectile.
Time T required for intercepting bullet to hit moving target
goThe definition is as follows:
where N represents the effective navigation ratio of the guidance system.
Step 103: and determining the interception probability of the intercepted bomb to the target according to the miss distance between the intercepted bomb and the target, the visual line angle rate of the target and the time required by the intercepted bomb to hit the moving target.
Constructing an interception probability function by adopting relative motion parameters of the interception bomb and the target:
selecting the miss distance delta S between the interception bullet and the target as an index for evaluating the interception precision, and selecting the visual line angular rate of the bullet
And the time T required for intercepting the moving target in the impact
goAs an index for evaluating the energy requirement of the interceptor projectile. For the air defense system, three indexes are taken
The smaller the interception probability of the interception bomb to the target.
And designing an interception probability function under three indexes of miss distance, required interception time and line-of-sight angular rate by adopting a negative exponential function. The interception probability of the ith interception bullet to the jth target under the three indexes is respectively defined as follows:
where m and n represent the number of interceptor bombs and targets, respectively,. DELTA.S (i, j), T
go(i, j) and
respectively representing the miss distance, the required interception time and the line-of-sight angular rate of the ith interception bomb to the jth target, P
ΔS(i,j)、
And
respectively representing the interception probability under three interception probability indexes of miss distance, required interception time and line-of-sight angular rate,
and
respectively representing the default values of the interception probabilities, delta, under the three indexes of the interception probabilities
ΔS、
And
and respectively representing the average value of three interception probability indexes of all m interception bombs relative to n targets.
The interception probability of the ith interception bullet to the jth target is defined as follows:
wherein, β
ΔS，βT
goAnd
respectively representing the weights under three interception probability indexes of miss distance, required interception time and line-of-sight angular rate, and satisfying the following conditions:
step 104: and determining a target distribution strategy according to the interception probability of the interception bomb to the target.
In many-to-many interception combat situations, the problem of target allocation is to make the total interception probability maximum at that moment by determining the number of interception bombs allocated to each target, modeling the total interception probability as follows:
wherein, P
ijRepresents the interception probability of the ith interception bullet to the jth target, X
ijIndicating whether the ith interception bullet is allocated to the jth target or not, if X is
ij1, the ith block is assigned to the jth target, if X
ij0, meaning that the ith block is not assigned to the jth target, V
jRepresenting the value of the jth target.
In the interception battle, a target with a larger threat allows a plurality of interception bullets to be distributed for interception. When the number of the interception bullets allocated to a certain target exceeds a certain number, the number of the interception bullets allocated to the target is continuously increased, which causes waste of interception resources, and in a serious case, the total interception probability may be deteriorated. The number of interceptor bombs assigned to each target should be less than the set upper limit. Further, assume that each interceptor bullet must be assigned to a target. The allocation number constraint is expressed as:
wherein, B
jThe upper limit of the number of the interception bombs allocated to the jth target.
And determining a target distribution strategy according to the interception probability of the intercepted missile to the target, wherein the target distribution strategy comprises a target distribution strategy under fixed grouping constraint and a target distribution strategy under adaptive grouping constraint.
In many-to-many interception battles, if only the total interception probability is considered to be optimal, the number of the intercepted bombs allocated to some targets is too large, while the number of the intercepted bombs allocated to some targets is too small or even the intercepted bombs are not allocated to some targets, so that some targets break through the air defense system and threaten defenders. In addition, the threat degree of an incoming target is different due to the self-attribute of the target and the position of the shot, so that the number of the shots intercepted by the party, the initial conditions and other factors need to be integrated to perform group interception on different targets.
And (3) designing a fixed grouping strategy by adopting a penalty function method:
setting the quantity of the intercepted bullets distributed to each target as a fixed value according to the difference of the value and the threat degree of the target, wherein the target distribution problem at the moment needs to meet two constraints, and obtaining a target distribution strategy under the fixed grouping constraint after weighting the two equality constraints:
wherein
Wherein A is
jIs the number of the interception bullets distributed to the jth target and meets the requirement
Q
jAnd S
iThe penalty function coefficients, Q, of the jth target and the ith interception projectile respectively
jG
jAnd S
iH
iRespectively, penalty function terms. Two penalty function terms representing deviations of the dispensing result from the set grouping constraintTo the extent that the assignment deviates more strongly from the grouping constraint, the values of the penalty function term and the objective function are larger. When solving the objective assignment problem, if the objective function value is no longer reduced and the value of the penalty function term is 0, it is said that the optimal objective assignment satisfying the fixed grouping constraint is achieved.
Adopting a penalty function method to design a self-adaptive grouping strategy:
in order to avoid that each target is allocated with too many or too few numbers of the intercepting bullets, the number of the intercepting bullets allowed to be allocated to each target is set as an interval according to the value of the target and the fighting requirement, namely, the upper limit and the lower limit of the number of the intercepting bullets allocated to each target are determined. The target allocation problem at this time needs to satisfy two inequality constraints and one equality constraint:
wherein, B
jUpper limit of the number of interceptor bombs allocated to the jth target, C
jIs the lower limit of the number of interceptor bombs assigned to the jth target. And processing and weighting the three constraint conditions to obtain a target distribution strategy under the self-adaptive grouping constraint:
wherein, U
j、L
jAnd S
iThe penalty function coefficient of the upper limit of the jth target distribution number, the penalty function coefficient of the lower limit of the jth target distribution number and the penalty function coefficient of the ith interception bullet are respectively. U shape
jE
j，L
jF
jPenalty function terms respectively for the upper limit and the lower limit of the distribution number, the two penalty function terms representing the degree of deviation of the distribution result from the set distribution number interval, if the distribution number is in the set distribution number interval, the value of the penalty function term in the objective function is 0, if the distribution number is not in the set distribution number interval,the value of the penalty function term in the objective function is not 0. When solving the target distribution problem, if the target function is not reduced any more and the value of each penalty function term is 0, the optimal target distribution meeting the self-adaptive grouping constraint is realized.
In practical application, a user can select and adopt a target allocation strategy under a fixed grouping constraint condition or a target allocation strategy under a self-adaptive grouping constraint condition according to actual needs, and the allocation result can meet corresponding setting according to the grouping constraint condition given by the user.
Step 105: taking the target distribution strategy as a fitness function of an artificial bee colony algorithm, and calculating by adopting the artificial bee colony algorithm to obtain a target distribution optimal solution under the target distribution strategy; and the target distribution optimal solution is the target number of the target intercepted by each interception bullet.
The invention solves the problem of many-to-many packet interception target distribution by adopting an artificial bee colony algorithm. The invention relates to a many-to-many grouping interception target distribution problem of an air defense system, which belongs to an integer programming problem, and adopts an artificial bee colony algorithm with high convergence rate and excellent overall performance to solve, wherein the solving principle is as follows:
firstly, according to the combat requirement, a fixed grouping interception and self-adaptive grouping strategy is selected, and the number or the upper limit and the lower limit of the intercepted bullets allocated to each target are determined according to the target value, the battlefield environment and other factors. Secondly, initializing the artificial bee colony, randomly generating the bee colony, and dividing the bee colony into an employment bee colony and an observation bee colony which are equal in scale according to the fitness function value. Then, local search is carried out on each employed bee, fitness function values are calculated, and whether the honey source is updated or not is judged according to the fitness value of the new honey source. Then, the probability of selecting honey source by the observation bees is calculated and the honey source is updated, and whether the honey source is updated or not is judged similarly to the stage of employing bees. Finally, judging whether the internal circulation frequency of the algorithm of the round exceeds the allowed maximum internal circulation frequency, if so, abandoning the honey source, changing the current employed bees into the scout bees and randomly generating a new honey source, recording the optimal solution found by all the bees, judging whether the external circulation termination condition of the algorithm is met, if so, exiting the algorithm output result, and if not, continuing the algorithm circulation of the next round; if not, recording the optimal solution found by all the bees, judging whether the optimal solution meets the outer loop termination condition of the algorithm, if so, exiting the algorithm output result, and if not, continuing the next round of algorithm loop.
Specifically, the step 105 of using the target distribution strategy as a fitness function of an artificial bee colony algorithm, and obtaining the optimal solution of target distribution under the target distribution strategy by using the artificial bee colony algorithm includes:
the many-to-many grouping interception target distribution problem of the air defense system belongs to an integer programming problem, and an artificial bee colony algorithm with high convergence rate and excellent overall performance is adopted for solving. The target distribution strategies under the two grouping constraint conditions provided by the invention are used as the fitness function of the artificial bee colony method. Initializing parameters of an artificial bee colony algorithm, and taking the bee colony scale as 2SN, wherein the initial population scales of the employed bee and the investigation bee are SN, the optimization record variable of the ith bee in the artificial bee colony algorithm is recorded as trial (i), the upper limit number of a certain food source which is not updated continuously is recorded as limit, and the maximum cycle number of the algorithm is recorded as MaxFES. The search dimension of the individual vector, i.e. the dimension of the solution of the target allocation problem, is taken to be D. The target distribution problem is a typical multi-constraint integer programming problem, when solving with an artificial bee colony algorithm, rounding and encoding operations need to be performed on individuals in the artificial bee colony method, so as to establish mapping with the actual target distribution problem, and an integer encoding flow is shown in fig. 3. X in FIG. 2
iRepresenting the target allocation result of the ith bee; m1: catch bomb 1, M2: catch bomb 2, M3: interceptor projectile 3, M4: catch bomb 4, M5: catch bomb 5, M6: catch bomb 6, M7: catch bomb 7, M8: catch bomb 8, M9: catch bomb 9, M10: an interception bullet 10; t1 target 1, T2 target 2, T3 target 3, T4 target 4, T5 target 5, T6 target 6; missile, intercepting bullet mark; target: and (4) marking the target.
Under the condition that m missiles intercept n targets, the solution of the target distribution problem is an m-dimensional integer vector
Wherein
Is an integer from 1 to n, indicating that the kth block is assigned a subscript of
The object of (1). If there are 10 interceptor bombs intercepting 6 targets, result X is distributed
i＝[5,2,3,2,6,4,1,1,5,3]As shown in fig. 2, it means that a block bomb 1 is assigned to a target 5, a block bomb 2 is assigned to the target 2, a block bomb 3 is assigned to the target 3, a block bomb 4 is assigned to the target 2, a block bomb 5 is assigned to the target 6, a block bomb 6 is assigned to the target 4, a block bomb 7 and a block bomb 8 are assigned to the target 1, a block bomb 9 is assigned to the target 5, and a block bomb 10 is assigned to the target 3.
The method for solving the problem of many-to-many grouping interception target distribution of the air defense system based on the artificial bee colony algorithm comprises the following steps:
the first step is as follows: according to the combat demand, selecting a target distribution strategy under fixed grouping constraint or a target distribution strategy under self-adaptive grouping constraint, and determining the number of the intercepted bullets or the upper and lower limit numbers distributed to each target according to factors such as target value, battlefield environment and the like;
the second step is that: and initializing the artificial bee colony. The standard number 2SN of the bee colony, the continuously non-updated upper limit of a certain food source and the maximum cycle number MaxFES of the algorithm are set. Randomly generating an artificial bee colony with the scale of 2SN, dividing the bee colony into a employment bee colony with the scale of SN and an observation bee colony, and initializing an optimization record variable (i) to be 0;
the third step: performing neighborhood search on each employed bee and calculating a fitness function value; the fitness function is a target distribution strategy under the constraint of fixed grouping
Or target allocation strategy under adaptive grouping constraint
The fourth step: if the fitness of the new honey source is better than that of the old honey source, replacing the old honey source with the new honey source, and enabling the triel (i) to be 0, otherwise, keeping the old honey source, and enabling the triel (i) to be triel (i) + 1;
the fifth step: calculating the selection probability p of honey source
iEach observation bee has a probability p
iSelecting a new honey source, and calculating a corresponding fitness function value;
and a sixth step: similar to the hiring bee phase, if the fitness of the new honey source is better than that of the old honey source, replacing the old honey source with the new honey source, and making the triel (i) 0, otherwise keeping the old honey source and updating the triel (i);
the seventh step: judging whether the real (i) is larger than the continuously non-updated upper limit; if yes, go to the eighth step; otherwise, turning to the ninth step;
eighth step: abandoning the honey source, changing the ith employment bee into a scout bee, and randomly generating a new honey source in a solution space;
the ninth step: recording the optimal results found by all the bees at present, and judging whether the termination conditions of the algorithm are met; if yes, finishing the algorithm to output a result; otherwise go to the third step.
The output result of the artificial bee colony algorithm is the optimal solution of target distribution, and an m-dimensional integer vector is used
Is output in the form of (1). According to the vector
The target number of the target intercepted by each intercepted bullet can be determined, so that the optimal distribution of a plurality of intercepted bullets is realized.
Aiming at the situation of many-to-many interception combat of the air defense system, the invention constructs an interception probability function which simultaneously considers interception precision and energy required for interception by using relative motion parameters of the bullets, and provides a target distribution method with fixed grouping constraint and self-adaptive grouping constraint, so that the optimal weapon target distribution under the grouping constraint condition can be realized, good initial conditions can be provided for multi-bullet cooperative combat, and the improvement of the overall interception efficiency of the air defense system is facilitated.
Based on the target distribution method provided by the present invention, the present invention further provides a many-to-many packet interception target distribution system for an air defense system, fig. 4 is a schematic structural diagram of the many-to-many packet interception target distribution system for the air defense system provided by the present invention, referring to fig. 4, the system includes:
an initial motion parameter obtaining module 401, configured to obtain initial motion parameters of an intercepted bullet group and a target group; the initial motion parameters comprise the speed vector, the course angle and the line-of-sight angle of each intercepted bullet in the intercepted bullet group as well as the speed vector and the course angle of each target in the target group;
a motion parameter determining module 402, configured to determine, according to the initial motion parameter, a miss distance between the intercepted projectile and the target, a line-of-sight velocity of the projectile, and a time required for the intercepted projectile to hit the moving target;
an interception probability determining module 403, configured to determine an interception probability of an intercepted bullet on a target according to a miss distance between the intercepted bullet and the target, the line-of-sight angular rate of the bullet, and a time required for the intercepted bullet to hit the moving target;
a target distribution policy determining module 404, configured to determine a target distribution policy according to the probability of interception of the intercepted missile to the target; the target allocation strategy comprises a target allocation strategy under fixed grouping constraint and a target allocation strategy under self-adaptive grouping constraint;
a target distribution module 405, configured to use the target distribution strategy as a fitness function of an artificial bee colony algorithm, and obtain an optimal solution of target distribution under the target distribution strategy by using the artificial bee colony algorithm; and the target distribution optimal solution is the target number of the target intercepted by each interception bullet.
The motion parameter determining module 402 specifically includes:
a miss amount determination unit for employing a formula
Determining the miss distance between the interception bomb and the target; wherein Delta S is the interception bomb and the targetThe amount of miss;
θ
Mindicating the course angle of the intercepted missile; q represents the line of sight angle of the bullet; v
MRepresenting the velocity of the interceptor projectile; v
TRepresenting the speed of the target; theta
TRepresenting a heading angle of the target; t is t
goRepresenting the residual flight time of the interception bomb, and tau representing the inertia time constant of the interception bomb guidance system;
a bullet eye line of sight angular rate determining unit for adopting a formula
Determining the visual angle rate of the bullet; wherein
Representing the angular rate of the line of sight of the bullet; r represents the relative distance between the interceptor projectile and the target;
an interception required time determining unit for adopting a formula
Determining the time required for intercepting the moving target in the impact; wherein T is
goRepresenting the time required for the interception bomb to hit the moving target; n represents the effective navigation ratio of the guidance system.
The interception probability determination module 403 specifically includes:
the interception probability determining unit under the miss distance index is used for determining the interception probability under the miss distance index according to the miss distance between the interception bullet and the target;
the interception probability determining unit under the visual angle rate index is used for determining the interception probability under the visual angle rate index according to the visual angle rate of the bullet;
the interception probability determining unit under the interception required time index is used for determining the interception probability under the interception required time index according to the time required by the interception bullet to hit the moving target;
and the interception probability determining unit is used for determining the interception probability of the interception bomb to the target according to the interception probability under the miss distance index, the interception probability under the line-of-sight angular rate index and the interception probability under the interception required time index.
The interception probability determining unit specifically includes:
an interception probability determining subunit for employing a formula
Determining the interception probability of an interception bomb to a target; wherein P is
ijRepresenting the interception probability of the ith interception bullet to the jth target; p
ΔS(i,j)Representing the interception probability under the miss distance index;
representing the interception probability under the time index required by interception;
representing the interception probability under the line-of-sight angular rate index, β
ΔSThe weight under the off-target amount index is represented,
representing the weight of the interception time index;
the representation represents the weight under the line-of-sight angular rate index.
The target allocation policy determining module 404 specifically includes:
a target distribution strategy determining unit under the fixed grouping constraint, which is used for determining the target distribution strategy under the fixed grouping constraint according to the interception probability of the interception bomb to the target
Where m represents the number of interceptor bombs and n represents the number of targets; v
jRepresents the value of the jth target; x
ijIndicating whether the ith interception bullet is allocated to the jth target; q
jG
jAnd S
iH
iRespectively, penalty functionsAn item;
a target distribution strategy determining unit under the adaptive grouping constraint, which is used for determining the target distribution strategy under the adaptive grouping constraint according to the interception probability of the interception bomb to the target
U
jE
jA penalty function term that is an upper bound of the allocation number; l is
jF
jA penalty function term for assigning a lower bound to the number.
The effectiveness of the method provided by the invention is verified by a specific embodiment of the many-to-many packet interception target distribution of the air defense system. The specific implementation steps of this embodiment are as follows:
(1) initial motion parameter setting for intercepting group of bullets and target group
In the present embodiment, 10 interceptor bombs (numbered from M1-M10) are set to intercept 6 targets (numbered from T1-T6) in an attack manner, the initial motion parameters of the interceptor bombs and the target group are shown in table 1 and table 2, and the battlefield value of each target is also given in table 2.
TABLE 1 initial motion parameters for intercepting a group of projectiles
TABLE 2 initial motion parameters of the target group and the battlefield value of each target
In the table, X (km) indicates a position in the X-axis direction, and Y (km) indicates a position in the Y-axis direction.
(2) Interception probability calculation and grouping parameter setting
In the present embodiment, the effective navigation ratio N of the guidance system is taken to be 4, and weights β under three interception probability indexes are set
ΔS＝0.5，
The interception probability matrix shown in table 3 is obtained by calculation using the interception probability function of the present invention:
TABLE 3 interception probability matrix of interception bullet group to target group
The values in table 3 are the calculated interception probabilities.
Initializing parameters in the manual bee colony algorithm: the population size SN of an initial employed bee or a scout bee is taken as 100, the optimization record variable trial (i) is taken as 0, the upper limit number of continuous non-updating of a certain food source is taken as limit as 100, the maximum cycle number of the algorithm is taken as MaxFES as 10000 m, wherein m is the number of the interception bullets.
According to the battlefield value V of each target
jAnd interception probability P
ijSetting the number of the interception bombs allocated to the 1 st, 2 nd, 3 rd, 4 th, 5 th and 6 th targets under the fixed grouping constraint condition to be 2,1 st, 3 th, 2 th and 1 st respectively, namely, a ═ a [, a [
j]＝[2,1,1,3,2,1]The penalty function coefficient is taken as Q
j0.05, j 1,2, n and S
i0.02, i ═ 1,2, …, m; the upper limit numbers of the interception bombs allocated to the 1 st, 2 nd, 3 rd, 4 th, 5 th and 6 th targets are respectively 2,2 nd and 2 th, and the lower limit numbers are respectively 1 st, i.e. B ═ B [ B ]
j]＝[2,2,2,2,2,2]，C＝[C
j]＝[1,1,1,1,1,1]The penalty function coefficient is taken as U
j＝0.05，L
j0.05, j 1,2, n and S
i＝0.02，i＝1,2,…,m。
(3) Analysis of simulation results
Fig. 5 is a target assignment result under a fixed grouping constraint, which is solved by the embodiment of the present invention. Fig. 6 is a graph of the optimal value of the objective function under the constraint of a fixed grouping according to the embodiment of the present invention. Fig. 7 is a target assignment result under the adaptive grouping constraint solved by the embodiment of the present invention. Fig. 8 is a graph of an optimal value of an objective function under adaptive grouping constraint according to an embodiment of the present invention. In the figure, Missile is a marker of an interception bullet, Target is a marker of a Target, vector is a marker of the interception bullet and a Target velocity vector, X (km) represents the position along the X-axis direction, and Y (km) represents the position along the Y-axis direction; the Cycle number is the number of times for solving the artificial bee colony algorithm, and the Optimal value is the Optimal value of the objective function.
As can be seen from fig. 5, under the fixed grouping constraint, the number of the interceptor bombs allocated to each target is consistent with the set allocation number; as can be seen from fig. 6, the curve of the optimal value of the objective function converges fast, and as the number of iterations increases, the optimal value remains unchanged, and the objective allocation under the constraint of fixed grouping is realized. As can be seen from fig. 7, under the adaptive grouping constraint, the number of the interception bullets allocated to each target is within the set upper and lower limit intervals of the allocation number; as can be seen from FIG. 8, the optimal value curve of the objective function quickly converges to near the optimal value, and the objective distribution under the adaptive grouping constraint is realized. The two distribution methods both realize the optimal target distribution under the grouping constraint condition, are beneficial to the cooperative combat among subsequent interception bombs, and verify the effectiveness of the target distribution method provided by the invention.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (10)
1. A many-to-many packet interception target assignment method for an air defense system, the method comprising:
acquiring initial motion parameters of an interception bullet group and a target group; the initial motion parameters comprise the speed vector, the course angle and the line-of-sight angle of each intercepted bullet in the intercepted bullet group as well as the speed vector and the course angle of each target in the target group;
determining the miss distance between the intercepting bullet and the target, the visual line angle rate of the bullet and the time required for the intercepting bullet to hit the moving target according to the initial motion parameters;
determining the interception probability of the interception bullet on the target according to the miss distance between the interception bullet and the target, the visual line angle rate of the bullet and the time required by the interception bullet to hit the moving target;
determining a target distribution strategy according to the interception probability of the interception bomb to the target; the target allocation strategy comprises a target allocation strategy under fixed grouping constraint and a target allocation strategy under self-adaptive grouping constraint;
taking the target distribution strategy as a fitness function of an artificial bee colony algorithm, and calculating by adopting the artificial bee colony algorithm to obtain a target distribution optimal solution under the target distribution strategy; and the target distribution optimal solution is the target number of the target intercepted by each interception bullet.
2. The method according to claim 1, wherein the determining of the miss distance between the intercepting bomb and the target, the visual line angle rate of the bomb and the time required for the intercepting bomb to hit the moving target according to the initial motion parameters specifically comprises:
using a formula
Determining the miss distance between the interception bomb and the target; wherein, the delta S is the miss distance between the interception bullet and the target;
θ
Mindicating the course angle of the intercepted missile; q represents the line of sight angle of the bullet; v
MRepresenting the velocity of the interceptor projectile; v
TRepresenting the speed of the target; theta
TRepresenting a heading angle of the target; t is t
goRepresenting the residual flight time of the interception bomb, and tau representing the inertia time constant of the interception bomb guidance system;
using a formula
Determining the visual angle rate of the bullet; wherein
Representing the angular rate of the line of sight of the bullet; r represents the relative distance between the interceptor projectile and the target;
using a formula
Determining the time required for intercepting the moving target in the impact; wherein T is
goRepresenting the time required for the interception bomb to hit the moving target; n represents the effective navigation ratio of the guidance system.
3. The many-to-many grouping interception target distribution method for the air defense system according to claim 1, wherein the determining the interception probability of the interception bullet to the target according to the miss distance between the interception bullet and the target, the bullet sight line angle rate and the time required for the interception bullet to hit the moving target specifically comprises:
determining interception probability under the miss distance index according to the miss distance between the interception bullet and the target;
determining the interception probability under the visual angle rate index according to the visual angle rate of the bullet;
determining the interception probability under the index of time required for interception according to the time required by the interception bullet to hit the moving target;
and determining the interception probability of the interception bomb to the target according to the interception probability under the miss distance index, the interception probability under the line-of-sight angular rate index and the interception probability under the interception required time index.
4. The many-to-many group interception target distribution method for the air defense system according to claim 3, wherein the determining of the interception probability of the interception bomb to the target according to the interception probability under the miss distance index, the interception probability under the line-of-sight angular rate index, and the interception probability under the interception required time index specifically includes:
using a formula
Determining the interception probability of an interception bomb to a target; wherein P is
ijRepresenting the interception probability of the ith interception bullet to the jth target; p
ΔS(i,j)Representing the interception probability under the miss distance index;
representing the interception probability under the time index required by interception;
representing the interception probability under the line-of-sight angular rate index, β
ΔSThe weight under the off-target amount index is represented,
representing the weight of the interception time index;
the representation represents the weight under the line-of-sight angular rate index.
5. The many-to-many packet interception target distribution method for the air defense system according to claim 4, wherein the determining a target distribution strategy according to the interception probability of the interception bomb to the target specifically includes:
determining a target distribution strategy under fixed grouping constraint according to the interception probability of the interception bomb to the target
Where m represents the number of interceptor bombs and n represents the number of targets; v
jRepresents the value of the jth target; x
ijIndicating whether the ith interception bullet is allocated to the jth target; q
jG
jAnd S
iH
iRespectively are penalty function terms;
determining a target distribution strategy under the self-adaptive grouping constraint according to the interception probability of the interception bomb to the target
U
jE
jA penalty function term that is an upper bound of the allocation number; l is
jF
jA penalty function term for assigning a lower bound to the number.
6. A many-to-many packet interception target distribution system for an air defense system, the system comprising:
the initial motion parameter acquisition module is used for acquiring initial motion parameters of the intercepted bullet group and the target group; the initial motion parameters comprise the speed vector, the course angle and the line-of-sight angle of each intercepted bullet in the intercepted bullet group as well as the speed vector and the course angle of each target in the target group;
the motion parameter determining module is used for determining the miss distance between the intercepting bullet and the target, the line-of-sight angular rate of the bullet and the time required by the intercepting bullet to hit the moving target according to the initial motion parameters;
the interception probability determining module is used for determining the interception probability of the interception bullet on the target according to the miss distance between the interception bullet and the target, the visual line angle rate of the bullet and the time required by the interception bullet to hit the moving target;
the target distribution strategy determining module is used for determining a target distribution strategy according to the interception probability of the interception bomb to the target; the target allocation strategy comprises a target allocation strategy under fixed grouping constraint and a target allocation strategy under self-adaptive grouping constraint;
the target distribution module is used for taking the target distribution strategy as a fitness function of an artificial bee colony algorithm and calculating by adopting the artificial bee colony algorithm to obtain a target distribution optimal solution under the target distribution strategy; and the target distribution optimal solution is the target number of the target intercepted by each interception bullet.
7. The many-to-many packet interception target distribution system for an air defense system according to claim 6, wherein said motion parameter determination module specifically comprises:
a miss amount determination unit for employing a formula
Determining the miss distance between the interception bomb and the target; wherein, the delta S is the miss distance between the interception bullet and the target;
θ
Mindicating the course angle of the intercepted missile; q represents the line of sight angle of the bullet; v
MRepresenting the velocity of the interceptor projectile; v
TRepresenting the speed of the target; theta
TRepresenting a heading angle of the target; t is t
goRepresenting the residual flight time of the interception bomb, and tau representing the inertia time constant of the interception bomb guidance system;
a bullet eye line of sight angular rate determining unit for adopting a formula
Determining the visual angle rate of the bullet; wherein
Representing the angular rate of the line of sight of the bullet; r represents the relative distance between the interceptor projectile and the target;
an interception required time determining unit for adopting a formula
Determining the time required for intercepting the moving target in the impact; wherein T is
goRepresenting the time required for the interception bomb to hit the moving target; n represents the effective navigation ratio of the guidance system.
8. The many-to-many packet interception target distribution system for an air defense system according to claim 6, wherein the interception probability determination module specifically comprises:
the interception probability determining unit under the miss distance index is used for determining the interception probability under the miss distance index according to the miss distance between the interception bullet and the target;
the interception probability determining unit under the visual angle rate index is used for determining the interception probability under the visual angle rate index according to the visual angle rate of the bullet;
the interception probability determining unit under the interception required time index is used for determining the interception probability under the interception required time index according to the time required by the interception bullet to hit the moving target;
and the interception probability determining unit is used for determining the interception probability of the interception bomb to the target according to the interception probability under the miss distance index, the interception probability under the line-of-sight angular rate index and the interception probability under the interception required time index.
9. The many-to-many packet interception target distribution system for an air defense system according to claim 8, wherein the interception probability determining unit specifically includes:
an interception probability determining subunit for employing a formula
Determining the interception probability of an interception bomb to a target; wherein P is
ijRepresenting the interception probability of the ith interception bullet to the jth target; p
ΔS(i,j)Representing the interception probability under the miss distance index;
representing the interception probability under the time index required by interception;
representing angle of sightProbability of interception in rate index β
ΔSThe weight under the off-target amount index is represented,
representing the weight of the interception time index;
the representation represents the weight under the line-of-sight angular rate index.
10. The many-to-many packet interception target distribution system for an air defense system according to claim 9, wherein the target distribution policy determining module specifically includes:
a target distribution strategy determining unit under the fixed grouping constraint, which is used for determining the target distribution strategy under the fixed grouping constraint according to the interception probability of the interception bomb to the target
Where m represents the number of interceptor bombs and n represents the number of targets; v
jRepresents the value of the jth target; x
ijIndicating whether the ith interception bullet is allocated to the jth target; q
jG
jAnd S
iH
iRespectively are penalty function terms;
a target distribution strategy determining unit under the adaptive grouping constraint, which is used for determining the target distribution strategy under the adaptive grouping constraint according to the interception probability of the interception bomb to the target
U
jE
jA penalty function term that is an upper bound of the allocation number; l is
jF
jA penalty function term for assigning a lower bound to the number.
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| CN112880488A (en) * | 2021-02-08 | 2021-06-01 | 上海机电工程研究所 | Master-slave bomb overall layout system and master-slave bomb cooperative detection method |
| CN113791633A (en) * | 2021-08-05 | 2021-12-14 | 北京航空航天大学 | Cyclic veto target allocation method based on maximum marginal profit |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN112880488A (en) * | 2021-02-08 | 2021-06-01 | 上海机电工程研究所 | Master-slave bomb overall layout system and master-slave bomb cooperative detection method |
| CN113791633A (en) * | 2021-08-05 | 2021-12-14 | 北京航空航天大学 | Cyclic veto target allocation method based on maximum marginal profit |
| CN113791633B (en) * | 2021-08-05 | 2023-12-15 | 北京航空航天大学 | Circulation overrule target distribution method based on maximum marginal benefit |
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Application publication date: 20200211 |