CN117371256B - Multi-type multi-number platform deployment setting scheme planning method - Google Patents
Multi-type multi-number platform deployment setting scheme planning method Download PDFInfo
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Abstract
The invention relates to a method for planning a deployment setting scheme of multiple types and multiple numbers of platforms, and belongs to the field of application of scheme planning technology. In order to only know the attack direction of a target and the deployment problem of two types of platforms with optimal total interception effect under the condition that the areas can be deployed by the platforms on the my side, the method for optimizing the deployment of the multiple types and the multiple types of platforms is provided, the method relates to the cooperative deployment of the two types and the multiple types of platforms, solves the problem of determining the position of the platforms, and ensures that after the platform I is deployed, the platform II performs blind supplement on the weak links of the deployment, and the reliability of completing the target interception task is highest. A method for planning a deployment setting scheme of a plurality of types and a plurality of platforms comprises the following steps: 1. constructing a system coordinate system, determining a second representation of a system actual killing domain under the system coordinate system, determining an optimal deployment position III of two I-type platforms, and performing blind supplement by using four II-type platforms aiming at weak links of the I-type platforms.
Description
Technical Field
The invention relates to a scheme planning method for setting a plurality of platforms of multiple types, and belongs to the technical field of scheme planning.
Background
The optimal deployment of the platform is a key problem to be solved in the urgent need of constructing an interception system and improving the working efficiency of the system. In order to achieve a better interception effect, defensive parties usually adopt multiple platforms of multiple types to complement each other and optimize deployment, and ensure optimal interception efficiency for all incoming targets.
Because the attack target does not have the functions of positioning and tracking the attack target and automatically transferring the track, how to optimally deploy the two types of platforms under the condition that only the attack direction of the target and the deployable area of the platform on the my side are known, so that the optimal total interception effect is realized, and the technical problem to be solved is urgently.
Disclosure of Invention
The invention aims to solve the problem that in the prior art, only the attack direction of a target is known, and the deployment problem of two types of platforms with optimal total interception effect is met under the condition that a region can be deployed by a platform on the side, and provides a multi-type multi-number platform optimizing deployment method.
In order to solve the problems, the multi-type multi-number platform deployment setting scheme planning method is realized through the following technical scheme:
the deployment optimization deployment method for the multiple types and the multiple numbers of platforms is characterized by comprising the following steps of: the method comprises the following steps:
1. constructing a system coordinate system, and determining the representation of the actual kill domain of the system under the system coordinate system
Taking the North Tiandong coordinate system NUE as a reference to establish a new coordinate systemIn the new coordinate system, the actual kill domain is；
2. Determining optimal deployment locations for two type I platforms
Determining the optimal radar normal direction of each deployment position in each I-type platform in a constructed system coordinate system, determining a nonlinear 0-1 integer programming model according to the optimal position, and obtaining the optimal deployment positions of the two I-type platforms through calculation;
3. aiming at weak links of the type I platform, four type II platforms are used for blind supplement
In the system coordinate system constructed in the first step, calculating the time length of each II-type platform interception arc section and emission arc section and the optimal radar normal angle matrix of each target position, establishing a model of the optimal placement position of four II-type platforms, and determining the optimal placement point position.
Preferably, the specific steps of the first step are as follows:
the system has the coordinates of the north-east coordinate systemThe normal direction of the radar isToIs the origin of coordinatesFrom the slaveLooking in the positive direction of the axisA plane surface of the glass fiber reinforced plastic plate,rotation of the shaft unit vector clockwiseObtaining a new vectorToIs the origin of coordinates, parallel toIs the coordinate axis of the direction of (a)Direction andthe same is true of the fact that,and (3) withThe axes are parallel and in the same direction,is determined to meet the right hand rule, and a new coordinate system is established；
The north eastern coordinate system NUE is a celestial coordinate system with a fixed relation with the rotation axis of the earth, in the north eastern coordinate system, the eastern is an E axis, the north is an N axis, and the direction perpendicular to the ground and pointing to the zenith is a U axis;
the attack direction of the target is that the track of the target is inProjection vector of planeKill domain coordinate systemMiddle coordinate axisAnd (3) withParallel, and opposite in direction,shaft and method for producing the sameThe included angle of the axes is a vectorAnd (3) withIncluded angle of axesThis angle may be negative;
the coordinate system isIn a coordinate systemFrom the slaveClockwise rotation of the shaft in normal plane viewObtaining;
target track is onIs the inverse of the projection vector of (a)，
Wherein:，-initial moment target isCoordinates of the coordinate system;，-the falling point moment is aimed atCoordinates of the coordinate system;
definition of the definitionAxial unit vector=Thus (a)Included angle of (a)
（1）；
If it isThenIf (if)ThenThe method comprises the steps of carrying out a first treatment on the surface of the According to formula (1), there is；
At the position ofThe two side boundaries of the kill domain are expressed as by spherical coordinatesAndthus atIn the coordinate system, two side boundaries of the theoretical kill domain are respectively expressed as,,
At the position ofAndunder the coordinate system, the near boundaries are spherical surfaces with the minimum killing inclined distance as the radius, and the far boundaries are spherical surfaces with the maximum killing inclined distance as the radius;
at the position ofIn the coordinate system, the near and far ranges are respectively 70km and 200km, which are expressed as spherical coordinates,,
At the position ofIn the coordinate system, the high and low boundaries can be expressed as rectangular coordinates,,
The high near-range is determined by the maximum pitch angle of the platform radar, whereIn the coordinate system, the spherical coordinates are used for representing；
The actual killing area of the incoming target is the overlapping part of the radar sector and the theoretical killing area, and the actual killing area is usually reduced at the position of the radar sector, which is close to the maximum azimuth angles at the two sides of the radar, and is influenced by the radar sector;
when (when)When the method is used, one side of the killing domain is a boundary of one side of the radar sector, and the killing domain in the radar sector is an actual killing domain;
when (when)When the killing domain is not in the radar sector, the actual killing domain does not exist for the target;
the actual kill domain is the intersection of the theoretical kill domain and the radar sector whenThe two side boundaries of the real killing domain are
Thus there is
At the position ofIn the coordinate system, the actual kill domain can be expressed as follows by means of spherical coordinates and rectangular coordinates
。
Preferably, the deploying position in the second step refers to dividing the deploying area into 500 grids according to the area parallel to the coordinate axis, and selecting the midpoint of each grid as the optional deploying position.
Preferably, the determining the optimal radar normal direction of each deployment position in the I-type platform in the second step includes the following steps:
A. determining a coordinate parameter equation for each deployment location at system coordinates
Giving out ballistic trajectory data of m incoming targets and N deployment position coordinate data, and obtaining the position of each target according to the ballistic trajectory data of each targetThe coordinates in the coordinate system are fitted to obtain the change relation of each coordinate along with time t, namelyWherein；
Given 500 deployable positions of the platform, for the firstTaking the normal direction of the radar as the position coordinatesIn the system coordinate systemUnder the condition, three coordinate parameter equations of a certain attack target are
B. Determining an objective function
The time when the ith target falls within the actual kill zone，Is a decision variable, whereinIndicating the time of the closest intercept point for the ith target bit,representing the time of the i-th target bit furthest from the intercept point,andmust fall on the boundary of the actual kill zone,
order the，Representing the time when the ith target falls in the actual killing area, solving the optimal normal direction of the radar for constructing an optimization model, wherein the objective function is all targetsThe sum is maximum, thereby ensuring that the sum of the time length of the interception arc section and the emission arc section is the longest, and the objective function is that；
C. Determining constraint conditions of the objective function in the step B
The constraint conditions of the high and low limits are
Wherein,representing coordinates of a platform deployed at a kth position under a NUE coordinate system;
the U-axis coordinate when the ith incoming target position is furthest blocked,the U-axis coordinate of the ith attack target position when the closest interception point is shown;
the far and near constraint conditions are that
Representing that the distance from the ith attack target to the platform deployed at the kth position is between far and near bounds;
the pitch angle constraint condition of the system missile is as followsI.e.，
There are then the following constraints
When (when)I.e.When the actual killing domain is defined, the side constraint needs to be satisfied asI.e.And because ofThus there is
When meeting the requirements，When the constraint is that
D. Aiming at variables according to the objective function determined in the step B and the constraint conditions determined in the step CAnd solving the optimal radar normal direction for each deployment position by adopting a variable step search algorithm.
Preferably, determining the nonlinear 0-1 integer programming model with the optimal position in the second step includes determining the nonlinear 0-1 integer programming model with the sum of the emitting arcs of m targets under two I-type platforms as a target or determining the nonlinear 0-1 integer programming model with the sum of the emitting arcs of m targets under two I-type platforms as a target.
Preferably, the nonlinear 0-1 integer programming model is determined by taking the sum distribution balance of the m targets in the transmitting arc segments under two I-type platforms as a target, and specifically comprises the following steps:
A. introducing a 0-1 variable
B. Determining an objective function
The length of the emission arc section of the ith target falling in the two actual killing areas of the system isOrder-makingAims at hopeing that the time lengths of m targets are relatively balanced and have little difference, so thatThen there is an objective function；
C. Determining constraints
Only s positions can be selected to place the I-type platform, so the constraint condition is that
The distance between any two systems is at least 5km, and the constraint conditions are scaled, so the constraint conditions are that
Adding a filtering matrixWhen the distance between the two deployment locations is less than 5km, it means that the two locations cannot deploy two platforms simultaneously, i.e.Therefore, after the filtering condition is introduced, the searching area in solving can be simplified, and the searching efficiency is improved;
wherein the method comprises the steps ofThen the constraint is thatWherein:-vectors consisting of 0-1 variables corresponding to N position points;-distance matrix, elementRepresenting the distance from the ith position to the jth position;
order theDefinition of the 0-1 variableTo make as many targets as possible fall within the actual kill zone, i.e. to meet constraints；
D. According to the objective function of the step B and the constraint condition of the step C, the following planning model is established
E. And D, solving the model obtained in the step D by adopting traversal calculation, and finding out an optimal solution.
Preferably, the determining the nonlinear 0-1 integer programming model by taking the sum of the emission arc segments of m targets under two I-type platforms as a target specifically comprises the following steps:
A. introducing a 0-1 variable
B. Determining an objective function
The length of the emission arc section of the ith target falling in the two actual killing areas of the system isTwo platforms fall into actual killing for m targetsThe arc length and the longest of the fields, i.eThen there is an objective function；
C. Determining constraints
Only s positions can be selected to place the I-type platform, so the constraint condition is that
The distance between any two platforms is at least 5km, and the constraint conditions are scaled, so the constraint conditions are that
Adding a filtering matrixWhen the distance between the two deployment locations is less than 5km, it means that the two locations cannot deploy two platforms simultaneously, i.e.Therefore, after the filtering condition is introduced, the searching area in solving can be simplified, and the searching efficiency is improved;
wherein the method comprises the steps ofThen the constraint isWherein:-vectors consisting of 0-1 variables corresponding to N position points;-distance matrix, elementRepresenting the distance from the ith position to the jth position;
order theDefinition of the 0-1 variableTo make as many targets as possible fall within the actual kill zone, i.e. to meet constraints；
D. According to the objective function of the step B and the constraint condition of the step C, the following planning model is established
E. And D, solving the model obtained in the step D by adopting traversal calculation, and finding out an optimal solution.
Preferably, the step three of calculating the duration of the type II platform interception arc segment and the emission arc segment includes the following steps:
A. determining type II platform parameters, specifically as follows: -45 ° -azimuth of system radar; 0-75 DEG-system high-low angle; the two planes of azimuth determination areAndthe method comprises the steps of carrying out a first treatment on the surface of the The depression angle determines the plane asA plane; elevation angle determination plane isThe method comprises the steps of carrying out a first treatment on the surface of the The furthest detection round surface is；
Wherein:-RCS of the target;-radar detection radius in km;
the farthest detection point is the point which satisfies the following constraint condition and has the smallest moment
Calculating the time corresponding to the farthest detection point as，Is the furthest detection radius;
the actual kill domain is represented as follows
The missile can only encounter with the target in the killing area, and the missile flies along a straight line, and the flying track and the target are the same as those of the missileFace (i.e) Included angle of (1)；
Setting a target at a certain momentThe spherical coordinates of the track areRectangular coordinates areOnly at the momentWhen the target is in the killing domain, and satisfiesIs the point located on the interception arc, then there is
The point satisfying the above is the largest in timeThe corresponding point is the nearest interception point, and the moment is the smallestIs the furthest interception point;
the coordinates of the track point when the target is detected are as followsThe system takes a period of timeThe missile is launched after the rear of the missile,for the minimum reaction time of the system of 12s, the missile can be launched only after the minimum reaction time of the system is 12s, and the coordinates of the track points are as followsAfter the missile is launched, toFlying at km/s along a straight line to the expected interception position of the target, wherein the coordinates of the track point areThus there is
Taking outThenThe point corresponding to the moment is the furthest interception point;
the length of time of the interception arc segment is then，
According to the time of the furthest interception pointThe corresponding track coordinates areThe time of the furthest emission point is thenThe time of the nearest interception point isThe corresponding track coordinates areThe time of the emission point isThe length of the obtained transmitting arc section is。
Preferably, the calculating the optimal radar normal angle matrix for each target position in the third step includes the following steps:
A. determining an objective function
For the ith target, the jth position, the model of the optimal radar normal direction is found as follows:
setting the maximum time and the minimum time of the ith target falling in the actual killing area asAndthen has an objective function of，
B. Determining constraints
The constraint conditions of the high and low limits are
The far and near constraint conditions are that
The pitch angle constraint of the system missile is as followsI.e.Then there are the following constraints
When (when)I.e.When the actual killing domain is defined, the side constraint needs to be satisfied asI.e.And because of
Thus there is
Thus when meeting When there is a constraint condition that
C. Aiming at variables according to the objective function determined in the step A and the constraint conditions determined in the step BSolving the optimal radar normal direction of the platform II according to each deployment position by adopting a variable step length search algorithm；
D. Constructing an optimal radar normal direction matrix for each target
Constructing an optimal radar normal direction matrix for each targetIf no matter what direction normal direction is selected, the ith target cannot fall into the actual killing area of the platform II placed at the jth positionOtherwiseThe intersection arc section duration of the target track and the actual killing area for the ith attack is the platform at the jth position.
Preferably, the establishing a model of the optimal placement positions of the four II-type platforms in the third step, and determining the optimal placement point positions include the following steps:
A. introducing a 0-1 variable，Representing the sum of the lengths of time for which the jth target is located in the actual killing area after the two platforms I are placed;
B. determining an objective function
C. B, solving the objective function obtained in the step B by adopting traversal calculation, and finding an optimal solution to obtain an optimal deployment area;
D. and B, after the optimal deployment area is determined, searching again in the cell grid intervals of the optimal deployment area by utilizing the step length limited by the steps A to C, so that the optimal deployment point position is determined.
The method is based on the performance of the front middle section reverse guiding platform I, the longest total length of the transmitting arc section is taken as a deployment optimization target, an optimization model is constructed, constraint conditions of the model are easy to operate in a matrix, searching and calculating are facilitated, and therefore algorithm efficiency is improved; based on the platform II with the tail end inverted, aiming at weak links deployed by the platform I, calculating an optimal radar normal angle matrix aiming at a specific target construction model, and determining an optimal normal direction by adopting variable step search.
According to the method, the determination of the optimal deployment position in the area is converted into the determination of the optimal deployment position of the grid center point, the continuous search is converted into the discrete search, so that 0-1 variable is introduced, a planning model is built, although a linear planning model cannot be built, the nonlinear constraint of the model is less, and the optimal deployment position can be calculated quickly through variable step search.
As the performance parameters of the two types of platforms have larger difference, the cooperative problem of the multiple types of platforms is decomposed, and for the platform I, the total interception effect of all targets is comprehensively considered as a target, and a model is built; for platform II, building a model for each target; the two models can be effectively fused.
Drawings
Fig. 1: the flow diagram of the invention;
fig. 2:and (3) withA coordinate system;
fig. 3:spherical coordinates of a coordinate system;
fig. 4: theoretical kill domain NUE in the coordinate system;
fig. 5: impact points of m targets and N alternative location schematics.
Detailed Description
The following description of the present invention will be given with reference to the accompanying drawings, which are used to further explain the constitution of the present invention.
Example 1. The deployment optimization deployment method for the multi-type multi-number platform as shown in fig. 1 comprises the following steps:
1. constructing a system coordinate system, and determining the representation of the actual kill domain of the system under the system coordinate system
Taking the North Tiandong coordinate system NUE as a reference to establish a new coordinate systemIn the new coordinate system, the actual kill domain is
2. Determining optimal deployment locations for two type I platforms
In the system coordinate system constructed in the first step, determining the optimal radar normal direction of each deployment position in each I-type platform, determining a nonlinear 0-1 integer programming model according to the optimal position, and obtaining the optimal deployment positions of the two I-type platforms through calculation;
3. aiming at weak links of the type I platform, four type II platforms are used for blind supplement
In the system coordinate system constructed in the first step, calculating the time length of each II-type platform interception arc section and emission arc section and the optimal radar normal angle matrix of each target position, establishing a model of the optimal placement position of four II-type platforms, and determining the optimal placement point position.
The method comprises the following specific steps:
the system has the coordinates of the north-east coordinate systemThe normal direction of the radar isToIs the origin of coordinatesFrom the slaveLooking in the positive direction of the axisA plane surface of the glass fiber reinforced plastic plate,rotation of the shaft unit vector clockwiseObtaining a new vectorToIs the origin of coordinates, parallel toIs the coordinate axis of the direction of (a)Direction andthe same is true of the fact that,and (3) withThe axes are parallel and in the same direction,is determined to meet the right hand rule, and a new coordinate system is establishedAs shown in fig. 2-3;
the north eastern coordinate system NUE is a celestial coordinate system with a fixed relation with the rotation axis of the earth, in the north eastern coordinate system, the eastern is an E axis, the north is an N axis, and the direction perpendicular to the ground and pointing to the zenith is a U axis;
the attack direction of the target is that the track of the target is inProjection vector of planeKill domain coordinate systemMiddle coordinate axisAnd (3) withParallel, and opposite in direction,shaft and method for producing the sameThe included angle of the axes is a vectorAnd (3) withIncluded angle of axesThis angle may be negative;
the coordinate system isIn a coordinate systemFrom the slaveClockwise rotation of the shaft in normal plane viewObtaining;
target track is onIs the inverse of the projection vector of (a)；
Wherein:，——the initial time is aimed atCoordinates of the coordinate system;，-the falling point moment is aimed atCoordinates of the coordinate system;
definition of the definitionAxial unit vector=Thus (a)Included angle of (a)
（1）
If it isThenIf (if)Then；
According to formula (1), there is
At the position ofThe two side boundaries of the kill domain are expressed as by spherical coordinatesAndthus atIn the coordinate system, two side boundaries of the theoretical kill domain are respectively expressed as,,
At the position ofAndunder the coordinate system, the near boundaries are spherical surfaces with the minimum killing inclined distance as the radius, and the far boundaries are spherical surfaces with the maximum killing inclined distance as the radius;
at the position ofIn the coordinate system, the near and far ranges are respectively 70km and 200km, which are expressed as spherical coordinates,,
At the position ofIn the coordinate system, the high and low boundaries can be expressed as rectangular coordinates,,
The high near-range is determined by the maximum pitch angle of the platform radar, whereIn the coordinate system, the spherical coordinates are used for representing；
The actual killing area of the incoming target is the overlapping part of the radar sector and the theoretical killing area, and the actual killing area is usually reduced at the position of the radar sector, which is close to the maximum azimuth angles at the two sides of the radar, and is influenced by the radar sector;
when (when)When the method is used, one side of the killing domain is a boundary of one side of the radar sector, and the killing domain in the radar sector is an actual killing domain;
when (when)When the killing domain is not in the radar sector, the actual killing domain does not exist for the target;
the actual kill domain is the intersection of the theoretical kill domain and the radar sector whenThe two side boundaries of the real killing domain are
Thus there is
At the position ofIn the coordinate systemThe actual kill zone can be expressed as follows by means of spherical coordinates and rectangular coordinates
。
The deployment position in the second step refers to dividing the deployment area into 500 grids according to the area parallel to the coordinate axis, and selecting the midpoint of each grid as an optional deployment position.
The determining the optimal radar normal direction of each deployment position in the I-type platform in the second step comprises the following steps:
A. determining a coordinate parameter equation for each deployment location at system coordinates
Giving out ballistic trajectory data of m incoming targets and N deployment position coordinate data, and obtaining the position of each target according to the ballistic trajectory data of each targetThe coordinates in the coordinate system are fitted to obtain the change relation of each coordinate along with time t, namelyWherein
Given 500 deployable positions of the platform, for the firstTaking the normal direction of the radar as the position coordinatesIn the system coordinate systemUnder the condition, three coordinate parameter equations of a certain attack target are
B. Determining an objective function
The time when the ith target falls within the actual kill zone，Is a decision variable, whereinIndicating the time of the closest intercept point for the ith target bit,representing the time of the i-th target bit furthest from the intercept point,andmust fall on the boundary of the actual kill zone,
order the，Representing the time when the ith target falls in the actual killing area, solving the optimal normal direction of the radar for constructing an optimization model, wherein the objective function is all targetsThe sum is maximum, thereby ensuring that the sum of the time length of the interception arc section and the emission arc section is the longest, and the objective function is that；
C. Determining constraint conditions of the objective function in the step B
The constraint conditions of the high and low limits areWherein,representing coordinates of a platform deployed at a kth position under a NUE coordinate system;
the U-axis coordinate when the ith incoming target position is furthest blocked,the U-axis coordinate of the ith attack target position when the closest interception point is shown;
the far and near constraint conditions are that
Representing that the distance from the ith attack target to the platform deployed at the kth position is between far and near bounds;
the pitch angle constraint condition of the system missile is as followsI.e.There are then the following constraints
When (when)I.e.When the actual killing domain is defined, the side constraint needs to be satisfied asI.e.，
And because ofThus there is
When meeting the requirements When the constraint is that
D. Aiming at variables according to the objective function determined in the step B and the constraint conditions determined in the step CAnd solving the optimal radar normal direction for each deployment position by adopting a variable step search algorithm.
And in the second step, determining the nonlinear 0-1 integer programming model by using the optimal position comprises determining the nonlinear 0-1 integer programming model by using the sum and the distribution balance of the m targets transmitting arc segments under the two I-type platforms as targets or determining the nonlinear 0-1 integer programming model by using the sum and the sum of the m targets transmitting arc segments under the two I-type platforms as targets.
The nonlinear 0-1 integer programming model which aims at balancing the sum distribution of the emission arc segments of m targets under two I-type platforms specifically comprises the following steps:
A. introducing a 0-1 variable
B. Determining an objective function
The length of the emission arc section of the ith target falling in the two actual killing areas of the system isOrder-makingAims at hopeing that the time lengths of m targets are relatively balanced and have little difference, so that；
Then there is an objective function
C. Determining constraints
Only s positions can be selected to place the I-type platform, so the constraint condition is that
The distance between any two systems is at least 5km, and the constraint conditions are scaled, so the constraint conditions are that
Adding a filtering matrixWhen the distance between the two deployment locations is less than 5km, it means that the two locations cannot deploy two platforms simultaneously, i.e.Therefore, after the filtering condition is introduced, the searching area in solving can be simplified, and the searching efficiency is improved;
wherein the method comprises the steps of
Then the constraint is thatWherein:-vectors consisting of 0-1 variables corresponding to N position points;-distance matrix, elementRepresenting the distance from the ith position to the jth position;
order theDefinition of the 0-1 variable
To make as many targets as possible fall within the actual kill zone, i.e. to meet constraints；
D. According to the objective function of the step B and the constraint condition of the step C, the following planning model is established
E. And D, solving the model obtained in the step D by adopting traversal calculation, and finding out an optimal solution.
The nonlinear 0-1 integer programming model which takes the sum of the emission arc segments of m targets under two I-type platforms as a target comprises the following steps:
A. introducing a 0-1 variable
B. Determining an objective function
The length of the emission arc section of the ith target falling in the two actual killing areas of the system isThe two platforms are the longest and the duration of arc segments of m targets falling into the actual killing domain, namelyThen there is an objective function；
C. Determining constraints
Only s positions can be selected to place the I-type platform, so the constraint condition is that
The distance between any two platforms is at least 5km, and the constraint conditions are scaled, so the constraint conditions are that
Adding a filtering matrixWhen the distance between the two deployment locations is less than 5km, it means that the two locations cannot deploy two platforms simultaneously, i.e.Therefore, after the filtering condition is introduced, the searching area in solving can be simplified, and the searching efficiency is improved;
wherein the method comprises the steps of
Then the constraint is thatWherein:-vectors consisting of 0-1 variables corresponding to N position points;-distance matrix, elementRepresenting the distance from the ith position to the jth position;
order theDefinition of the 0-1 variable
To make as many targets as possible fall within the actual kill zone, i.e. to meet constraints；
D. According to the objective function of the step B and the constraint condition of the step C, the following planning model is established
E. And D, solving the model obtained in the step D by adopting traversal calculation, and finding out an optimal solution.
The step III of calculating the time length of the II-type platform interception arc section and the emission arc section comprises the following steps:
A. determining type II platform parameters, specifically as follows: -45 ° -azimuth of system radar; 0-75 DEG-system high-low angle; the two planes of azimuth determination areAndthe method comprises the steps of carrying out a first treatment on the surface of the The depression angle determines the plane asA plane; elevation angle determination plane is；
The furthest detection round surface isThe method comprises the steps of carrying out a first treatment on the surface of the Wherein:-RCS of the target;-radar detection radius in km;
the farthest detection point is the point which satisfies the following constraint condition and has the smallest moment
Calculating the time corresponding to the farthest detection point as，For the most distant detection of the radius,
the actual kill domain is represented as follows
The missile can only encounter with the target in the killing area, and the missile flies along a straight line, and the flying track and the target are the same as those of the missileThe face isIncluded angle of (1)；
Setting a target at a certain momentThe spherical coordinates of the track areRectangular coordinates areOnly at the momentWhen the target is in the killing domain, and satisfiesIs the point located on the interception arc, then there is
The point satisfying the above is the largest in timeThe corresponding point is the nearest interception point, and the moment is the smallestIs the furthest interception point;
the coordinates of the track point when the target is detected are as followsThe system takes a period of timeThe missile is launched after the rear of the missile,for the minimum reaction time of the system of 12s, the missile can be launched only after the minimum reaction time of the system is 12s, and the coordinates of the track points are as followsAfter the missile is launched, toFlying at km/s along a straight line to the expected interception position of the target, wherein the coordinates of the track point areThus there is
Taking outThenThe point corresponding to the moment is the furthest interception point;
the length of time of the interception arc segment is thenAccording to the time of the furthest interception pointThe corresponding track coordinates areThe time of the furthest emission point is thenThe time of the nearest interception point isThe corresponding track coordinates areThe time of the emission point isThe length of the obtained transmitting arc section is。
The calculating of the optimal radar normal angle matrix of each target position in the third step comprises the following steps:
A. determining an objective function
For the ith target, the jth position, the model of the optimal radar normal direction is found as follows:
setting the maximum time and the minimum time of the ith target falling in the actual killing area asAndthen has an objective function of，
B. Determining constraints
The constraint conditions of the high and low limits are
The far and near constraint conditions are that
The pitch angle constraint of the system missile is as followsI.e.Then there are the following constraints
When (when)I.e.When the actual killing domain is defined, the side constraint needs to be satisfied asI.e.，
And because ofThus there is
Thus when meeting When there is a constraint condition that
C. Aiming at variables according to the objective function determined in the step A and the constraint conditions determined in the step BSolving the optimal radar normal direction of the platform II according to each deployment position by adopting a variable step length search algorithm；
D. Constructing an optimal radar normal direction matrix for each target
Constructing an optimal radar normal direction matrix for each targetIf no matter what direction normal direction is selected, the ith target cannot fall into the actual killing area of the platform II placed at the jth positionOtherwiseThe intersection arc section duration of the target track and the actual killing area for the ith attack is the platform at the jth position.
In the third step, the building of the model of the optimal placement position of the four type II platforms and the determination of the optimal placement point position comprise the following steps:
A. introducing a 0-1 variable，Representing the sum of the lengths of time for which the jth target is located in the actual killing area after the two platforms I are placed;
B. determining an objective function
C. B, solving the objective function obtained in the step B by adopting traversal calculation, and finding an optimal solution to obtain an optimal deployment area;
D. and B, after the optimal deployment area is determined, searching again in the cell grid intervals of the optimal deployment area by utilizing the step length limited by the steps A to C, so that the optimal deployment point position is determined.
Example 2
Simulation experiments were performed using the method described in example 1.
The simulation experiment is aimed at 6 attack targets, 500 deployment positions, 2I-type platforms and 4 II-type platforms, and finally two optimal placement parameters of the system are obtained through variable step-size traversal search calculation, wherein the optimal placement parameters are shown in table 1.
Table 1 two type I platform optimal placement parameters
After the two platforms are selected, the emission arc segment duration and the interception arc segment duration corresponding to the 6 targets are shown in table 2. The distance between the two platforms was 8413.63m, about 8.4km.
TABLE 2 emission arc duration and interception arc duration (unit: s)
And after the I-type platform is deployed, performing blind supplement by using the II-type platform aiming at weak links of the I-type platform. By calculation, it can be obtained that platform II is in 500 positions, and for 6 targets, the target can fall into the normal direction with the largest actual killing area range, so that. Table 3 counts the number of positions where the target can fall into the actual killing area, among 500 positions for each target. Table 4 shows the optimal position and optimal normal direction of platform II for each target, and according to the estimation criterion of platform I, 6 targets are given, and for each position, according to the three-dimensional coordinate data and optimal normal direction, the intersection arc length matrix of the ith target track and actual killing area for the jth position can be calculated。
TABLE 3 number of locations where attacks can be implemented for each target platform II
TABLE 4 optimal position and optimal normal direction (Unit: s) for each target platform II
After the two systems are selected, the sum of the time lengths of the emission arc sections of the 6 targets is arranged from small to large, and the time lengths of the 6 targets are sequentially 5 # targets, 3 # targets, 1 # targets, 2 # targets, 4 # targets and 6 # targets. Since only 4 type II platforms can be installed, no. 5, no. 3, no. 1 and No. 2 targets were selected, and therefore, after the I, II platforms were installed, the total emission arc duration and interception arc duration for the 6 targets are shown in table 5.
Table 5I, type II platform total time length (unit: s) for 6 target emitting arcs and intercepting arcs
As can be seen from table 5, after the type II platform is added, the average value of the total duration of each target emission arc segment and the total duration of each interception arc segment is increased, and the mean square error is reduced, which indicates that the distribution of each target is more balanced after the type II platform is added.
Claims (2)
1. The optimized deployment method for the multi-type multi-reverse-guiding platform is characterized by comprising the following steps of: the method comprises the following steps:
1. constructing a system coordinate system, and determining the representation of the actual kill domain of the system under the system coordinate system
Taking the North Tiandong coordinate system NUE as a reference to establish a new coordinate system，
The system has the coordinates of the north-east coordinate systemThe normal direction of the radar is +.>To->Is the origin of coordinates +.>From->The direction of the positive axis is +.>Plane (S)>The axis unit vector rotates clockwise +.>Obtaining a new vector->To->Is the origin of coordinates, parallel to->The direction of (2) is coordinate axis>Direction and->Same (I)>And->The axes are parallel and equidirectional, and->Is determined to satisfy the right hand rule, a new coordinate system is established +.>；
The attack direction of the target is that the track of the target is inProjection vector of plane->Killer Domain coordinate System->Middle coordinate axis->And->Parallel and opposite directions ++>Shaft and->The included angle of the axes is vector->And->Included angle of shaft->This angle is negativeIs a kind of device for the treatment of a cancer;
the coordinate system is->In the coordinate system +.>From->Clockwise rotation of the shaft in forward plane view +.>Obtaining;
target track is onThe inverse vector of the projection vector of (2) is +.>Wherein: />，/>-initial moment target->Coordinates of the coordinate system; />，/>-the falling point moment is targeted at +.>Coordinates of the coordinate system;
definition of the definitionAxle unit vector->=/>Thus->Included angle of (a)(1) If->Then->If (if)Then->；
According to formula (1), there isThe method comprises the steps of carrying out a first treatment on the surface of the At->The spherical coordinates are used under the system, and two side boundaries of the killing domain are expressed as +.>And->Thus is +.>In the coordinate system, two side boundaries of the theoretical kill domain are respectively expressed as
,/>In->And->Under the coordinate system, the near boundaries are spherical surfaces with the minimum killing inclined distance as the radius, and the far boundaries are spherical surfaces with the maximum killing inclined distance as the radius;
at the position ofIn the coordinate system, using spherical coordinates, near and far distances of 70km and 200km, respectively, are denoted +.>,,
At the position ofIn the coordinate system, the high and low bounds are expressed as +.>,/>,
The high near-range is determined by the maximum pitch angle of the platform radar, whereIn the coordinate system, the spherical coordinates are used for representing；
The actual killing area of the incoming target is the superposition of the radar sector and the theoretical killing area, and the actual killing area is reduced when the radar sector is influenced by the radar sector at the position of the radar sector close to the maximum azimuth angles at the two sides of the radar;
when (when)When the method is used, one side of the killing domain is a boundary of one side of the radar sector, and the killing domain in the radar sector is an actual killing domain;
when (when)When the killing domain is not in the radar sector, the actual killing domain does not exist for the target;
the actual kill domain is the intersection of the theoretical kill domain and the radar sector whenThe two side boundaries of the real killing domain are
，There is +.>；
At the position ofIn the coordinate system, the actual kill domain is expressed as follows by means of spherical coordinates and rectangular coordinates
；
2. Determining optimal deployment locations for two type I platforms
In the system coordinate system constructed in the first step, determining the optimal radar normal direction of each deployment position in each I-type platform, determining a nonlinear 0-1 integer programming model according to the optimal position, and obtaining the optimal deployment positions of the two I-type platforms through calculation;
determining the optimal radar normal direction for each deployment location in a type I platform comprises the steps of:
A. determining a coordinate parameter equation for each deployment location at system coordinates
Giving out ballistic trajectory data of m incoming targets and N deployment position coordinate data, and obtaining the position of each target according to the ballistic trajectory data of each targetThe coordinates in the coordinate system are fitted to obtain the change relation of each coordinate along with the time t, namely +.>Wherein->；
Given 500 deployable positions of the platform, for the firstThe position coordinates are taken as the radar normal direction>In the system coordinate system->Under the condition, three coordinate parameter equations of a certain attack target are
；
B. Determining an objective function
The time when the ith target falls within the actual kill zone，/>Is a decision variable, wherein->Indicating the maximum moment when the i-th target falls in the actual killing zone, < >>Indicating the minimum moment when the i-th target falls in the actual killing zone, +.>And->Must fall on the boundary of the actual kill zone,
order the；/>Representing the time when the ith target falls in the actual killing area, solving the optimal normal direction of the radar for constructing an optimization model, wherein the objective function is +.>The sum is maximum, thereby ensuring that the sum of the time length of the interception arc section and the emission arc section is the longest, and the objective function is that
；
C. Determining constraint conditions of the objective function in the step B
The constraint conditions of the high and low limits are
Wherein->Representing coordinates of a platform deployed at a kth position under a NUE coordinate system;
u-axis coordinate representing the i-th incoming target position furthest from the interception point, +.>The U-axis coordinate of the ith attack target position when the closest interception point is shown;
the far and near constraint conditions are that
The method comprises the steps of carrying out a first treatment on the surface of the Representing that the distance from the ith attack target to the platform deployed at the kth position is between far and near bounds;
the pitch angle constraint condition of the system missile is as followsI.e. +.>There are then the following constraints
When->I.e.In the time, according to the definition of the actual killing domain, the side boundary constraint needs to be satisfied as +.>I.e. +.>And because ofThus there is，/>When meeting the following requirements
，When the constraint is that
D. Aiming at variables according to the objective function determined in the step B and the constraint conditions determined in the step CSolving an optimal radar normal direction for each deployment position by adopting a variable step search algorithm;
determining a nonlinear 0-1 integer programming model by using an optimal position comprises determining the nonlinear 0-1 integer programming model by using the sum distribution balance of the transmitting arc segments of m targets under two I-type platforms as a target or determining the nonlinear 0-1 integer programming model by using the sum of the transmitting arc segments of m targets under two I-type platforms as a target;
the nonlinear 0-1 integer programming model which takes the sum distribution balance of m targets transmitting arc segments under two I-type platforms as a target comprises the following steps:
A. the 0-1 variable was introduced:
B. determining an objective function: the length of the emission arc section of the ith target falling in the actual killing area of the two systems is +.>Let->The purpose is to hope that the durations of the m targets are relatively balanced, not much different, let +.>Then there is an objective functionC, determining constraint conditions: only s positions can be selected to place the I-shaped platform, so the constraint condition is +.>Any two ofThe distance between the systems is at least 5km, and the constraint conditions are scaled, so the constraint conditions are +.>Adding a filter matrix->When the distance between the two deployment locations is less than 5km, it means that the two deployment locations cannot deploy two platforms simultaneously, i.e. +.>Therefore, after the filtering condition is introduced, the searching area in solving can be simplified, and the searching efficiency is improved;
wherein the method comprises the steps ofThe constraint is then +.>Wherein: />-vectors consisting of 0-1 variables corresponding to N position points; />-distance matrix, element->Representing the distance from the ith position to the jth position;
definition of the 0-1 variableTo make as many targets as possible fall within the actual kill zone, i.e. to meet constraints；
D. According to the objective function of the step B and the constraint condition of the step C, the following planning model is established
E. D, solving the model obtained in the step D by adopting traversal calculation, and finding out an optimal solution;
the nonlinear 0-1 integer programming model which takes the sum of the emission arc segments of m targets under two I-type platforms as a target comprises the following steps:
A. the 0-1 variable was introduced:B. determining an objective function: the length of the emission arc section of the ith target falling in the actual killing area of the two systems is +.>Order-makingThe two platforms are the longest and the duration of the arc section of the m targets falling into the actual killing domain, namely +.>Then there is an objective function->；
C. Determining constraint conditions:
only s positions can be selected to place the I-shaped platform, so the constraint conditions are that:the distance between any two platforms is at least 5km, and the constraint conditions are scaled, so the constraint conditions are +.>Adding a filtering matrixWhen the distance between the two deployment locations is less than 5km, it means that the two deployment locations cannot deploy two platforms simultaneously, i.e. +.>Therefore, after the filtering condition is introduced, the searching area in solving can be simplified, and the searching efficiency is improved;
wherein the method comprises the steps ofThe constraint is then +.>Wherein: />-vectors consisting of 0-1 variables corresponding to N position points; />-distance matrix, element->Representing the distance from the ith position to the jth position;
definition of the 0-1 variableTo make as many targets as possible fall within the actual kill zone, i.e. to meet constraints；
D. According to the objective function of the step B and the constraint condition of the step C, the following planning model is established
E. Solving the modulus obtained in step D by adopting traversal calculationModel, find the optimal solution;
3. aiming at weak links of the type I platform, four type II platforms are used for blind supplement
In the system coordinate system constructed in the first step, calculating the time length of each II-type platform interception arc section and emission arc section and the optimal radar normal angle matrix of each target position, establishing a model of the optimal placement position of four II-type platforms and determining the optimal deployment point position;
the time length of the II-type platform interception arc section and the emission arc section comprises the following steps:
A. determining type II platform parameters, specifically as follows: -45 ° -azimuth of system radar; 0-75 DEG-system high-low angle; the two planes of azimuth determination areAnd->The method comprises the steps of carrying out a first treatment on the surface of the The depression angle determines the plane as +.>A plane; elevation determination plane +.>The method comprises the steps of carrying out a first treatment on the surface of the The furthest detection round surface is +.>；
Wherein:-RCS of the target; />-radar detection radius in km;
the farthest detection point is the point which satisfies the following constraint condition and has the smallest moment
Calculating the corresponding time of the furthest detection point as +.>，/>For the furthest detection radius
The actual kill domain is represented as follows
The missile can only encounter with the target in the killing area, and the missile flies along a straight line, and the flying track and +.>The included angle of the faces is->；
Setting a target at a certain momentThe spherical coordinates of the track are +.>Rectangular coordinates are +.>Only at the momentWhen the target is located in the killing domain, and satisfy +.>Is the point located on the interception arc, then there is
Maximum time in the points satisfying the above +.>The corresponding point is the nearest interception point, the moment is the smallest +.>Is the furthest interception point;
the coordinates of the track point when the target is detected are as followsThe system goes by a period of>The missile is launched after the rear of the missile,for the minimum reaction time of the system of 12s, the missile can be launched only after that, and the coordinates of the track point are +.>After the missile is launched, the following formula is->Flying at km/s along a straight line to the expected interception position of the target, where the trajectory point coordinates are +.>Thus there is
Get->Then->Corresponding to the momentThe point is the furthest intercept point;
the length of time of the interception arc segment is thenThe method comprises the steps of carrying out a first treatment on the surface of the According to the time of the furthest interception point->The corresponding track coordinates are +.>The time of the furthest emission point is then +.>The time to nearest interception point is +.>The corresponding track coordinates are +.>The time of the emission point isThe length of the obtained emission arc section is +.>；
The method for calculating the optimal radar normal angle matrix of each target position comprises the following steps:
A. determining an objective function: for the ith target, the jth position, the model of the optimal radar normal direction is found as follows: setting the maximum time and the minimum time of the ith target falling in the actual killing area asAnd->Then has an objective function of，
B. Determining constraint conditions: the constraint conditions of the high and low limits areThe far and near constraint conditions are thatThe pitch angle constraint of the system missile is->I.e.Then there are the following constraints
When->I.e.When the actual killing domain is defined, the side constraint needs to be satisfied asI.e. +.>And because ofThere is +.> Thus when meeting，/>
When there is a constraint of-> C. According to the objective function determined in step A and the constraint conditions determined in step B, for the variable +.>Solving the optimal radar normal direction of the platform II aiming at each deployment position by adopting a variable step length search algorithm>The method comprises the steps of carrying out a first treatment on the surface of the D. Constructing an optimal radar normal direction matrix for each target:
constructing an optimal radar normal direction matrix for each targetIf no matter what direction normal direction is selected, the ith target cannot fall into the actual killing area of the platform II placed at the jth position +.>Otherwise->Is the j thThe platform at the position is used for intersecting arc segment duration of the ith attack target track and the actual killing area;
establishing a model of the optimal placement positions of four II-type platforms and determining the optimal placement positions comprises the following steps:
A. the 0-1 variable was introduced:，/>representing the sum of the lengths of time for which the jth target is located in the actual killing area after the two platforms I are placed;
B. determining an objective function:，/>c, solving the objective function obtained in the step B by adopting traversal calculation, and finding out an optimal solution to obtain an optimal deployment area;
D. and B, after the optimal deployment area is determined, searching again in the cell grid intervals of the optimal deployment area by utilizing the step length limited by the steps A to C, so that the optimal deployment point position is determined.
2. The multi-type multi-homing platform optimal deployment method of claim 1, wherein: the deployment position in the second step refers to dividing the deployment area into 500 grids according to the area parallel to the coordinate axis, and selecting the midpoint of each grid as an optional deployment position.
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