CN117606295A - Multi-target optimization method for trajectory of sweep-changing wing guided rocket projectile - Google Patents
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Abstract
The invention relates to a multi-target optimization method for the trajectory of a swept wing guided rocket projectile, which comprises the following steps: based on the instant balance assumption, taking the sweep angle of the missile wing into consideration, constructing a longitudinal plane ballistic motion equation of the guided rocket with the variable sweep wing; adopting a sweep-changing wing and glide range-increasing technology, and constructing a sweep-changing wing guided rocket projectile trajectory multi-target optimization model by taking a sweep-back angle and an attack angle of a missile wing as control variables for a glide segment trajectory; and solving the multi-target optimization model of the trajectory of the variable sweep wing guided rocket projectile by adopting a multi-target genetic algorithm. Compared with the prior art, the invention has the remarkable advantages that: the method considers the deformation strategy of the missile wing and the change of the attack angle of the rocket projectile simultaneously, ensures good aerodynamic performance of the rocket projectile in the flight process, solves and obtains the Pareto front with optimal tail end speed and range by utilizing a multi-target genetic algorithm, and improves the flight performance of the rocket projectile with the variable sweep wing to the greatest extent.
Description
Technical Field
The invention relates to the technical field of aerodynamics and trajectory of rocket projectiles, in particular to a method for optimizing multiple targets of a sweep-changing wing guided rocket projectile trajectory.
Background
The traditional fixed wing rocket projectile has the limitation in design that the optimal performance can be obtained only under a specific flight condition, and the performance potential of the rocket projectile cannot be fully exerted. In contrast, the variable-profile guided rocket projectile has the capability of improving mechanical properties by changing the structure of the variable-profile guided rocket projectile, can maintain optimal pneumatic performance in the whole flight mission process, and improves the remote accurate striking capability and the ultra-remote firepower pressing capability of the rocket projectile.
Document 1: the Chinese patent No. 109506517A discloses a method for optimizing the trajectory of a guided missile with constraint, and the optimization scheme aims at the trajectory optimization method of a guided missile with an unchangeable shape, and does not study the trajectory optimization problem of the guided missile with the changeable shape.
Document 2: the Chinese patent No. 113094807A discloses a deformation track optimization method of a deformed aircraft, which is used for researching the deformation strategy track optimization problem of the deformed aircraft, mainly focusing on the optimization of a single target problem of the track, and not researching the multi-target optimization problem of the deformed aircraft.
Disclosure of Invention
The invention aims to provide a multi-target optimization method for the trajectory of a guided rocket projectile with variable sweep wings, which solves the problem that the fixed-profile rocket projectile is inadaptive in flight by utilizing a dynamic change strategy for adjusting the sweep angle of the sweep wings in the flight process of the guided rocket projectile with variable sweep wings, realizes the optimization requirements for two mutually conflicting optimization targets of the rocket projectile range and the terminal striking force, and gives consideration to the terminal speed, the terminal striking force and the rocket projectile flight performance when the rocket projectile range is improved.
The technical solution for realizing the purpose of the invention is as follows:
a method for optimizing multiple targets of a sweep-changing wing guided rocket projectile trajectory, comprising the following steps:
based on the instant balance assumption, taking the sweep angle of the missile wing into consideration, constructing a longitudinal plane ballistic motion equation of the guided rocket with the variable sweep wing;
adopting a sweep-changing wing and glide range-increasing technology, and constructing a sweep-changing wing guided rocket projectile trajectory multi-target optimization model by taking a sweep-back angle and an attack angle of a missile wing as control variables for a glide segment trajectory;
and solving the multi-target optimization model of the trajectory of the variable sweep wing guided rocket projectile by adopting a multi-target genetic algorithm.
Further, the longitudinal plane ballistic motion equation of the swept wing guided rocket projectile is as follows:
in the formula (1): v represents the velocity of the rocket projectile; θ represents the ballistic dip; s represents the range; h represents the shooting height; p represents engine thrust; g represents gravitational acceleration; alpha represents the angle of attack; m represents the mass of the rocket projectile; m is m s Representing mass flow rate; d represents air resistance; l represents lift;
the calculation formula of the resistance and the lift force is as follows:
in the formula (2): s represents a reference area; ρ represents the air density; ma represents the flight Mach number; χ represents the sweep angle of the missile wing; c (C) D (Ma, alpha, X) and C L (Ma, α, χ) represents the drag coefficient and the lift coefficient, respectively;
in the formula (3), C Dα2 (Ma,χ)、C Dα (Ma,χ)、C D0 (Ma,χ)、C Lα (Ma,χ)、C L0 (Ma, χ) represents the fitting coefficients for the sweep χ and Mach number Ma of the missile wing.
Further, the sweep-changing wing guided rocket projectile trajectory multi-target optimization model specifically comprises the following steps:
when the state variable satisfies the ballistic constraint, an optimal control variable is sought such that the objective function j= [ J ] 1 ,J 2 ]Taking the maximum value; wherein the objective function J 1 Representing the firing range of the rocket, the objective function J 2 Representing the end attack speed of the rocket projectile;
state variable x (t) = [ V, θ, s, h] T Control variable u (t) = [ α, χ ]] T 。
Further, the ballistic constraint conditions are specifically:
(1) Initial state constraints:
x 0 ＝[V 0 ,θ 0 ,s 0 ,h 0 ] T ；
wherein: x is x 0 Representing an initial limit value of the state variable x (t), V 0 Represents an initial flight speed limit value, θ 0 Representing the initial ballistic dip limit value s 0 Represents an initial range limit value, h 0 Representing an initial fly-height limit value;
(2) End state constraints:
wherein: h (t) f )、V(t f )、θ(t f ) Respectively representing the tail end height, the tail end flying speed and the tail end trajectory dip angle; t is t f Indicating the attack moment of the end, h f Representing the end height limit value, V f Represents the limit value of the terminal flying speed, theta f Representing the terminal ballistic dip limit;
(3) Process constraints:
wherein: q represents dynamic pressure, q max Represents the maximum dynamic pressure, n y Indicating normal overload, n ymax Indicating a maximum normal overload;
(4) Control variable constraints:
wherein: alpha min 、α max Respectively represent the minimum value and the maximum value of the attack angle alpha, χ min 、χ max Representing the minimum and maximum values of the sweep χ of the missile wing, respectively.
Further, the multi-objective genetic algorithm is solved, and the specific solving process is as follows:
s1, using a direct targeting method to control the variable in a time interval [ t ] 0 ,t f ]Discretizing, and converting the ballistic optimization problem solved by the continuous sweep-changing wing guided rocket projectile trajectory multi-target optimization model into a nonlinear programming problem; wherein t is 0 Representing the initial firing time, t, of the rocket projectile f Representing the end striking time of the rocket projectile;
s2, solving a nonlinear programming problem by adopting a non-dominant ordering multi-objective genetic algorithm NSGA-II with elite strategy.
Further, solving a nonlinear programming problem by adopting a non-dominant ordering multi-objective genetic algorithm NSGA-II with elite strategy, wherein the specific solving flow is as follows;
s21, randomly generating an initial population in the constraint of meeting the upper limit and the lower limit of the control variable;
s22, intersecting and mutating individuals in the initial population to generate new offspring;
s23, combining the newly generated offspring with the selected father to form a mixed population; non-dominated sorting is carried out on the mixed population, wherein the non-dominated sorting is carried out according to the optimized performance of the mixed population individuals in the variable sweep wing guided rocket projectile trajectory multi-target optimization model, and all the mixed population individuals are distributed into all non-dominated layers;
s24, evaluating the degree of density of solutions around the individuals of the mixed population, and calculating the degree of congestion of the individuals of each mixed population in each non-dominant layer;
i distance ＝1/(Δd i +1)
wherein Δd i Indicating the crowding distance, i, of the ith mixed population individual distance Represents the crowding degree of the ith mixed population individual, M is the total number of objective functions,an mth objective function value for individual i+1,>an mth objective function value representing an ith-1 mixed population of individuals;
s25, selecting individuals of the mixed population layer by layer according to non-dominant sorting:
sorting the crowds of the individuals on each non-dominant layer, when the number of the individuals of the population allocated to the first non-dominant layer is larger than the number of the individuals required by the preset population, selecting the individuals of the population allocated to the first non-dominant layer according to the numerical sorting from small crowds to large crowds until the number of the individuals of the selected population reaches the number of the individuals required by the preset population, entering the next iteration, and returning to the step S22;
if the number of the population individuals distributed to the first non-dominant layer is smaller than the preset population number, all the population individuals distributed to the first non-dominant layer are placed into the preset population, and layer-by-layer accumulation is carried out from the population individuals distributed to the second non-dominant layer until the accumulated population individual number reaches the preset population required individual number, the next iteration is carried out, and the step S22 is returned;
s26, when the iteration times reach the maximum value or the optimal solution sets of the mixed population of two adjacent iterations are the same, ending the iteration; and taking the individuals with the highest non-dominant level in the mixed population of the last iteration as Pareto optimal solutions.
An electronic device, comprising:
a memory for storing a computer program;
a processor for implementing steps of the method as multi-objective optimization when executing the computer program.
A computer readable storage medium having stored thereon a computer program which when executed by a processor performs steps of a method such as multi-objective optimization.
Compared with the prior art, the invention has the remarkable advantages that: the deformation strategy of the missile wing and the attack angle change of the rocket projectile are considered at the same time, and the deformation strategy and the attack angle change of the rocket projectile are incorporated into the trajectory optimization calculation process. In order to achieve the optimization goal of improving the range and the tail end speed of the rocket projectile to the greatest extent, a multi-objective genetic algorithm is adopted as an optimization algorithm to obtain a group of Pareto optimal solutions, and a plurality of pairs of different range and tail end speed combinations are obtained, so that the far range is obtained, and meanwhile, the high tail end striking speed is obtained, and the performance of the swept wing guided rocket projectile is further improved.
Drawings
FIG. 1 is a schematic illustration of the geometry of a swept wing guided rocket missile wing with a swept angle of 0 degrees in an embodiment of the present invention;
FIG. 2 is a schematic illustration of the geometry of a swept wing guided rocket missile wing with a swept angle of 20 degrees in an embodiment of the present invention;
FIG. 3 is a schematic illustration of the geometry of a swept wing guided rocket missile wing with a swept angle of 40 degrees in an embodiment of the present invention;
FIG. 4 is a schematic illustration of the geometry of a swept wing guided rocket missile wing with a swept angle of 60 degrees in an embodiment of the present invention;
FIG. 5 is a schematic representation of the path of a swept wing guided rocket projectile flight trajectory in an embodiment of the present invention;
FIG. 6 is a schematic representation of a glide segment trajectory in an embodiment of the present invention;
FIG. 7 is a graph showing velocity versus time for a glide segment in accordance with one embodiment of the invention;
FIG. 8 is a graph of glide segment trajectory tilt angle versus time for one embodiment of the present invention;
FIG. 9 is a graph showing angle of attack versus time for a glide segment in accordance with one embodiment of the present invention;
FIG. 10 is a schematic illustration of a sweep angle versus time curve of a glide segment-changing sweep wing rocket projectile in accordance with an embodiment of the present invention;
FIG. 11 is a graph illustrating the results of a range-end-of-range speed multi-objective optimization in accordance with one embodiment of the present invention.
Detailed Description
For the purpose of making apparent the objects, technical solutions and advantages of the present invention, the present invention will be further described in detail with reference to the following examples and the accompanying drawings, wherein the exemplary embodiments of the present invention and the descriptions thereof are for illustrating the present invention only and are not to be construed as limiting the present invention.
A method for optimizing multiple targets of a sweep-changing wing guided rocket projectile trajectory, comprising the following steps:
based on the instant balance assumption, taking the sweep angle of the missile wing into consideration, constructing a longitudinal plane ballistic motion equation of the guided rocket with the variable sweep wing;
adopting a sweep-changing wing and glide range-increasing technology, and constructing a sweep-changing wing guided rocket projectile trajectory multi-target optimization model by taking a sweep-back angle and an attack angle of a missile wing as control variables for a glide segment trajectory;
and solving the multi-target optimization model of the trajectory of the variable sweep wing guided rocket projectile by adopting a multi-target genetic algorithm.
The following describes the operation procedure of the multi-objective optimization method in detail in connection with the specific application scenario of the present invention.
Firstly, designing the geometric shape of a guided rocket projectile with a variable swept wing; the guided rocket projectile with the variable sweepback wings is used for adjusting sweepback angles of the missile wings to adapt to different flight conditions when in subsonic and transonic flight under the premise of meeting stability and operability, so that the overall flight performance is improved.
As shown in fig. 1-4, the geometry of the swept wing guided rocket projectile according to the embodiment of the present invention includes: the rocket projectile has a bullet length of 400mm, a blunt end and a tangential oval shape, a cylindrical body, a length of 2594mm and an aspect ratio of 21.3. The tail part adopts a small stern design and is provided with 6 foldable tail wings. When the engine does not work, the tail fin is folded outside the spray pipe due to compression of the torsion spring, and after the engine works, the rocket flies out of the muzzle, and then the torsion spring is sprung to enable the fin to be unfolded.
In order to ensure aerodynamic characteristics, structural strength, maneuvering performance and stability, the swept-back wing guided rocket projectile is selected from trapezoidal control surfaces with larger root tip ratio, and adopts a duck-type layout. The middle part of the projectile body adopts deformable projectile wings arranged in a straight line. In order to enable the rocket to have good flight performance under supersonic speed, a double-wedge wing type is selected. In consideration of the structural strength of the missile wing and the index limiting requirement, the sweepback angle of the missile wing ranges from 0 degrees to 60 degrees.
As shown in fig. 5, in order to raise the range of the guided rocket projectile with variable swept wings, the invention adopts the technology of variable swept wings and glide range increase, and the longitudinal plane flight process of the guided rocket projectile with variable swept wings is as follows:
the tail is folded and retracted before the swept wing guided rocket projectile is launched; when the guided rocket projectile with the swept back wing is launched at a certain speed, the tail wing opens immediately to ensure the stable flight of the rocket projectile. And then the small rocket booster engine is ignited to push the rocket to climb the flying height.
When the engine works, the guided rocket projectile with the changed sweepback wings can continue to ascend, ascend to a certain position, start the work of the ballistic parameter detection system, and open the rudders and the deformable wings near the vertex of the trajectory. The rudder piece deflects to enter a gliding flight stage, and at the moment, the missile wing changes along with the change of the flight state, so that the guided rocket projectile with the changed swept wing can keep better aerodynamic flight, and finally the range of the guided rocket projectile with the changed swept wing is greatly improved.
Based on instantaneous balance, the flying motion process in the longitudinal plane is optimized by taking the swept wing guided rocket projectile as a mass point, and the calculation formula of the flying motion process is as follows:
in the formula (1): v represents the velocity of the rocket projectile; θ represents the ballistic dip; s represents the range; h represents the shooting height; p represents engine thrust; g represents gravitational acceleration; alpha represents the angle of attack; m represents the mass of the rocket projectile; m is m s Representing mass flow rate; d represents air resistance; l represents lift;
wherein: the calculation formula of the air resistance and the lift force is as follows:
in the formula (2): s represents a reference area; ρ represents the air density; ma represents the flight Mach number; χ represents the sweep angle of the missile wing; c (C) D (Ma, alpha, X) and C L (Ma, α, χ) represents the drag coefficient and the lift coefficient, respectively;
in the formula (3), C Dα2 (Ma,χ)、C Dα (Ma,χ)、C D0 (Ma,χ)、C Lα (Ma,χ)、C L0 (Ma, χ) represents the fitting coefficients for the sweep χ and Mach number Ma of the missile wing.
Specifically, in the embodiment of the invention, the multi-objective optimization problem of the sweep-changing wing guided rocket projectile is actually an optimal control problem, and under the condition that the state variables meet all constraint conditions, the control variables are searched, so that the objective function J= [ J ] 1 ,J 2 ]Maximum is reached, wherein: objective function J 1 Representing the firing range of the rocket, the objective function J 2 Representing the end attack speed of the rocket projectile, the state variable x (t) = [ V, θ, s, h] T Control variable u (t) = [ α, χ ]] T The method comprises the steps of carrying out a first treatment on the surface of the The mathematical expression of the optimal control problem is:
wherein: j represents an objective function, and consists of an objective function phi related to end point constraint and an integral objective function C; x epsilon R n Representing state variables of the system, u.epsilon.R r Representing a control variable of the system, t representing a time variable of the system,representing the system state equation, ψ represents the boundary constraints, and g represents the system parameter inequality constraints.
The constraint conditions include:
1) Initial state constraints: starting from the starting point of a gliding trajectory, the sweep-wing-changing guided rocket projectile opens the sweep wings and rudder pieces at the trajectory vertex, controls are implemented, and the initial state variables of the system are constrained as follows:
x 0 ＝[V 0 ,θ 0 ,s 0 ,h 0 ] T
wherein: x is x 0 Representing an initial limit value of the state variable x (t), V 0 Represents an initial flight speed limit value, θ 0 Representing the initial ballistic dip limit value s 0 Represents an initial range limit value, h 0 Representing an initial fly-height limit value;
2) End state constraints: to ensure the killing power of the guided rocket projectile with the variable sweep wings at the end point, the velocity V of the end point is controlled f And ballistic inclination angle theta f Constraint is carried out, specifically expressed as:
wherein: h (t) f )、V(t f )、θ(t f ) Respectively representing the tail end height, the tail end flying speed and the tail end trajectory dip angle; t is t f Indicating the attack moment of the end, h f Representing the end height limit value, V f Represents the limit value of the terminal flying speed, theta f Representing the terminal ballistic dip limit;
3) Process constraints: dynamic pressure affects the aerodynamic force of rocket projectile in the flying process, and has important influence on the stability and control of rocket projectile attitude, and dynamic pressure needs to be limited. To ensure that the load carrying capacity of equipment and a projectile body structure carried on the projectile cannot be exceeded during flight of the projectile, normal overload is restrained:
wherein: q represents dynamic pressure, q max Represents the maximum dynamic pressure, n y Indicating normal overload, n ymax Indicating a maximum normal overload;
4) Control variable constraints: adding deformation strategy of sweep-wing guided rocket projectile into ballistic multipleIn the target optimization model, the attack angle alpha and the sweepback angle χ of the missile wing are selected as double control variables u= [ alpha, χ ]] T . In order to ensure smooth trajectory and good flying performance of the swept wing guided rocket projectile, the range of attack and sweep angle capabilities are constrained in consideration of the characteristics and target mission requirements.
Wherein: alpha min 、α max Respectively represent the minimum value and the maximum value of the attack angle alpha, χ min 、χ max Representing the minimum and maximum values of the sweep χ of the missile wing, respectively.
Then, adopting bivariate control of attack angle alpha and missile wing backswept angle χ to realize trajectory optimization of the sliding section of the variable sweep wing guided rocket projectile, determining the capability boundary of the variable sweep wing guided rocket projectile and carrying out comparison analysis with the result of the fixed wing rocket projectile trajectory optimization; wherein: the control constraint alpha epsilon [ -10 degrees, 10 degrees ], χ epsilon [0 degrees, 60 degrees ].
Specifically, the start and end state parameter constraint settings are shown in Table 1.
TABLE 1 start-end State parameters
| Parameter name | Numerical value |
| Initial point velocity V 0 | 353.6m/s |
| Initial point trajectory inclination angle theta 0 | 0° |
| Initial point height h 0 | 13606.7m |
| End speed V f | ≥200m/s |
| Inclination angle theta of end trajectory f | ≤-60° |
| Height h f | 0m |
In order to determine the range boundary of the variable sweep wing rocket projectile, the superiority of the variable sweep wing rocket projectile compared with the fixed wing rocket projectile is proved, the fixed wing with different sweep angles and the variable sweep wing rocket projectile trajectory are respectively subjected to range single-target optimization, and the terminal speed is limited; and comparing the calculation results, and obtaining the optimal deformation rule of the grazing wing rocket projectile when the grazing wing rocket projectile is in optimal range as shown in figures 6-10. And (3) specifically analyzing and calculating the result:
as shown in figure 6, the range of the swept-wing rocket projectile is improved by 10.8-34.6% compared with the fixed-wing rocket projectiles with different sweep angles of the missile wings. As shown in fig. 9, the swept wing guided rocket projectile achieves a longer range by controlling a smaller angle of attack than the fixed wing, and can avoid the problem of rocket projectile stall caused by an excessive angle of attack. Meanwhile, as shown in fig. 10, the optimal deformation rule of the rocket projectile in flight also shows the superiority of the rocket projectile with the sweep wings in the elasticity.
Then, optimizing two targets of the range and the tail end speed of the variable sweep wing guided rocket projectile, wherein the invention adopts a multi-target genetic algorithm to solve, and the specific solving flow is as follows:
s1, using a direct targeting method to control the variable in a time interval [ t ] 0 ,t f ]Discretizing, and converting the ballistic optimization problem solved by the continuous sweep-changing wing guided rocket projectile trajectory multi-target optimization model into a nonlinear gaugeDrawing a problem; time interval t 0 ,t f ]The method is divided into N time periods, and is specifically expressed as follows: t is t 0 ＜t 1 ＜t 2 ＜…＜t N-1 ＜t N ＝t f Wherein: t is t 0 Is the initial firing time of the rocket projectile, t f The striking time of the tail end of the rocket projectile;
the control variables are discretized into:
u(t)＝(u 1 ,u 2 ,…u N )
s2, solving a nonlinear programming problem by adopting a non-dominant ordering multi-objective genetic algorithm NSGA-II with elite strategy. Discrete control variable [ u ] 1 ,u 2 ,…u N ]As optimization variables of population individuals, the specific solving process is as follows:
s21, randomly generating an initial population in the constraint of meeting the upper limit and the lower limit of the control variable;
s22, intersecting and mutating individuals in the initial population to generate new offspring;
s23, combining the newly generated offspring with the selected father to form a mixed population; non-dominated sorting is carried out on the mixed population, wherein the non-dominated sorting is carried out according to the optimized performance of the mixed population individuals in the variable sweep wing guided rocket projectile trajectory multi-target optimization model, and all the mixed population individuals are distributed into all non-dominated layers;
s24, evaluating the degree of density of solutions around the individuals of the mixed population, and calculating the degree of congestion of the individuals of each mixed population in each non-dominant layer;
i distance ＝1/(Δd i +1)
wherein Δd i Indicating the crowding distance, i, of the ith mixed population individual distance Represents the crowding degree of the ith mixed population individual, M is the total number of objective functions,for individual i+1Mth objective function value,>an mth objective function value representing an ith-1 mixed population of individuals;
s25, for reserving individuals with the best mixed population in the generation, directly transmitting the individuals to the next generation, and preventing the Pareto optimal solution from being lost; the individuals with the non-dominant layers and higher ranks are selected preferentially, and the individuals with the mixed population with lower crowding degree are selected from the same non-dominant layer, so that the species diversity can be preserved;
selecting individuals of the mixed population layer by layer according to non-dominant ranking:
sorting the crowds of the individuals on each non-dominant layer, when the number of the individuals of the population allocated to the first non-dominant layer is larger than the number of the individuals required by the preset population, selecting the individuals of the population allocated to the first non-dominant layer according to the numerical sorting from small crowds to large crowds until the number of the individuals of the selected population reaches the number of the individuals required by the preset population, entering the next iteration, and returning to the step S22;
if the number of the population individuals distributed to the first non-dominant layer is smaller than the preset population number, all the population individuals distributed to the first non-dominant layer are placed into the preset population, and layer-by-layer accumulation is carried out from the population individuals distributed to the second non-dominant layer until the accumulated population individual number reaches the preset population required individual number, the next iteration is carried out, and the step S22 is returned;
s26, when the iteration times reach the maximum value or the optimal solution sets of the mixed population of two adjacent iterations are the same, ending the iteration; and taking the individuals with the highest non-dominant level in the mixed population of the last iteration as Pareto optimal solutions.
As shown in fig. 11, the tail end speed and the range of the Pareto front of the multi-objective optimization find that the range obtained by the adopted multi-objective optimization method is 41.3 km-54.3 km according to the optimization result, and the tail end speed is 230.8 m/s-322.2 m/s; when the range is 54.3km, the terminal speed is 230.8m/s, the feasibility of the multi-target optimization algorithm applied to the sweep-wing rocket projectile trajectory optimization is verified, the rocket projectile range and the terminal speed can be weighed, a plurality of groups of combinations of the range and the terminal speed are obtained, and the long range is obtained while the large speed is achieved.
In conclusion, the multi-target optimization method for the trajectory of the variable sweep wing guided rocket projectile provided by the invention builds a multi-target trajectory optimization model. And solving the ballistic optimization problem of two optimization targets of the variable sweep wing rocket projectile firing range and the terminal striking speed by adopting a multi-target genetic algorithm to obtain the Pareto front with optimal terminal speed and firing range. And the advantage of the variable sweep wing rocket projectile in flight compared with the fixed wing rocket projectile is verified, and the remote striking capacity of the variable sweep wing guided rocket projectile is effectively improved.
It should be noted that: the foregoing sequence of the embodiments of the present application is only for describing, and does not represent the advantages and disadvantages of the embodiments. And the foregoing description has been directed to specific embodiments of this application. Other embodiments are within the scope of the following claims. In some cases, the actions or steps recited in the claims can be performed in a different order than in the embodiments and still achieve desirable results. In addition, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results. In certain embodiments: multitasking and parallel processing are also possible or may be advantageous.
All embodiments in the application are described in a progressive manner, and identical and similar parts of all embodiments are mutually referred, so that each embodiment mainly describes differences from other embodiments. In particular, for apparatus, devices and storage medium embodiments, the description is relatively simple as it is substantially similar to method embodiments, with reference to the description of method embodiments in part.
Those skilled in the art will appreciate that implementing all or part of the above-described methods may be accomplished by way of a computer program, which may be stored on a non-transitory computer readable storage medium and which, when executed, may comprise the steps of the above-described embodiments of the methods. Any reference to memory, storage, database, or other medium used in the various embodiments provided herein may include non-volatile and/or volatile memory. The nonvolatile memory can include Read Only Memory (ROM), programmable ROM (PROM), electrically Programmable ROM (EPROM), electrically Erasable Programmable ROM (EEPROM), or flash memory. Volatile memory can include Random Access Memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms such as Static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double Data Rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous Link DRAM (SLDRAM), memory bus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), among others.
The above examples merely represent a few embodiments of the present application, which are described in more detail and are not to be construed as limiting the scope of the invention. It should be noted that it would be apparent to those skilled in the art that various modifications and improvements could be made without departing from the spirit of the present application, which would be within the scope of the present application. Accordingly, the scope of protection of the present application is to be determined by the claims appended hereto.
Claims (8)
1. A method for optimizing the trajectory of a swept-wing guided rocket projectile by multiple targets is characterized by comprising the following steps of: the multi-objective optimization method comprises the following steps:
based on the instant balance assumption, taking the sweep angle of the missile wing into consideration, constructing a longitudinal plane ballistic motion equation of the guided rocket with the variable sweep wing;
adopting a sweep-changing wing and glide range-increasing technology, and constructing a sweep-changing wing guided rocket projectile trajectory multi-target optimization model by taking a sweep-back angle and an attack angle of a missile wing as control variables for a glide segment trajectory;
and solving the variable sweep wing guided rocket projectile trajectory multi-target optimization model by adopting a multi-target genetic algorithm.
2. The method for optimizing the trajectory of a swept wing guided rocket projectile according to claim 1, wherein: the longitudinal plane ballistic motion equation of the sweep-changing wing guided rocket projectile is as follows:
in the formula (1): v represents the velocity of the rocket projectile; θ represents the ballistic dip; s represents the range; h represents the shooting height; p represents engine thrust; g represents gravitational acceleration; alpha represents the angle of attack; m represents the mass of the rocket projectile; m is m s Representing mass flow rate; d represents air resistance; l represents lift;
the calculation formula of the resistance and the lift force is as follows:
in the formula (2): s represents a reference area; ρ represents the air density; ma represents the flight Mach number; χ represents the sweep angle of the missile wing; c (C) D (Ma, alpha, X) and C L (Ma, α, χ) represents the drag coefficient and the lift coefficient, respectively;
in the formula (3), C Dα2 (Ma,χ)、C Dα (Ma,χ)、C D0 (Ma,χ)、C Lα (Ma,χ)、C L0 (Ma, χ) represents the fitting coefficients for the sweep χ and Mach number Ma of the missile wing.
3. The method for optimizing the trajectory of a swept wing guided rocket projectile according to claim 1, wherein: the sweep-changing wing guided rocket projectile trajectory multi-target optimization model specifically comprises the following steps:
when the state variable satisfies the ballistic constraint, an optimal control variable is sought such that the objective function j= [ J ] 1 ,J 2 ]Taking the maximum value; wherein the objective function J 1 Representing the firing range of the rocket, the objective function J 2 Representing the end attack speed of the rocket projectile;
the state variable x (t) = [ V, θ, s, h] T The control variable u (t) = [ α, χ ]] T 。
4. The method for optimizing the trajectory of a swept wing guided rocket projectile according to claim 1, wherein: the ballistic constraint conditions are specifically:
(1) Initial state constraints:
x 0 ＝[V 0 ,θ 0 ,s 0 ,h 0 ] T ；
wherein: x is x 0 Representing an initial limit value of the state variable x (t), V 0 Represents an initial flight speed limit value, θ 0 Representing the initial ballistic dip limit value s 0 Represents an initial range limit value, h 0 Representing an initial fly-height limit value;
(2) End state constraints:
wherein: h (t) f )、V(t f )、θ(t f ) Respectively representing the tail end height, the tail end flying speed and the tail end trajectory dip angle; t is t f Indicating the attack moment of the end, h f Representing the end height limit value, V f Represents the limit value of the terminal flying speed, theta f Representing the terminal ballistic dip limit;
(3) Process constraints:
wherein: q represents dynamic pressure, q max Represents the maximum dynamic pressure, n y Indicating normal overload, n ymax Indicating a maximum normal overload;
(4) Control variable constraints:
wherein: alpha min 、α max Respectively represent the minimum value and the maximum value of the attack angle alpha, χ min 、χ max Representing the minimum and maximum values of the sweep χ of the missile wing, respectively.
5. The method for optimizing the trajectory of a swept wing guided rocket projectile according to claim 1, wherein: the multi-objective genetic algorithm is solved, and the specific solving flow is as follows:
s1, using a direct targeting method to control the variable in a time interval [ t ] 0 ,t f ]Discretizing, and converting the ballistic optimization problem solved by the continuous variable sweep wing guided rocket projectile trajectory multi-target optimization model into a nonlinear programming problem; wherein t is 0 Representing the initial firing time, t, of the rocket projectile f Representing the end striking time of the rocket projectile;
s2, solving a nonlinear programming problem by adopting a non-dominant ordering multi-objective genetic algorithm NSGA-II with elite strategy.
6. The method for optimizing the trajectory of a swept wing guided rocket projectile according to claim 5, wherein: the non-dominant ordering multi-objective genetic algorithm NSGA-II with elite strategy is adopted to solve the nonlinear programming problem, and the specific solving flow is as follows;
s21, randomly generating an initial population in the constraint of meeting the upper limit and the lower limit of the control variable;
s22, intersecting and mutating individuals in the initial population to generate new offspring;
s23, combining the newly generated offspring with the selected father to form a mixed population; non-dominated sorting is carried out on the mixed population, wherein the non-dominated sorting is carried out according to the optimized performance of the mixed population individuals in the variable sweep wing guided rocket projectile trajectory multi-target optimization model, and all the mixed population individuals are distributed into all non-dominated layers;
s24, evaluating the degree of density of solutions around the individuals of the mixed population, and calculating the degree of congestion of the individuals of each mixed population in each non-dominant layer;
i distance ＝1/(Δd i +1)
wherein Δd i Indicating the crowding distance, i, of the ith mixed population individual distance Represents the crowding degree of the ith mixed population individual, M is the total number of objective functions,an mth objective function value for individual i+1,>an mth objective function value representing an ith-1 mixed population of individuals;
s25, selecting individuals of the mixed population layer by layer according to non-dominant sorting:
sorting the crowds of the individuals on each non-dominant layer, when the number of the individuals of the population allocated to the first non-dominant layer is larger than the number of the individuals required by the preset population, selecting the individuals of the population allocated to the first non-dominant layer according to the numerical sorting from small crowds to large crowds until the number of the individuals of the selected population reaches the number of the individuals required by the preset population, entering the next iteration, and returning to the step S22;
if the number of the population individuals distributed to the first non-dominant layer is smaller than the preset population number, all the population individuals distributed to the first non-dominant layer are placed into the preset population, and layer-by-layer accumulation is carried out from the population individuals distributed to the second non-dominant layer until the accumulated population individual number reaches the preset population required individual number, the next iteration is carried out, and the step S22 is returned;
s26, when the iteration times reach the maximum value or the optimal solution sets of the mixed population of two adjacent iterations are the same, ending the iteration; and taking the individuals with the highest non-dominant level in the mixed population of the last iteration as Pareto optimal solutions.
7. An electronic device, characterized in that: comprising the following steps:
a memory for storing a computer program;
a processor for implementing the steps of the multi-objective optimization method according to any one of claims 1 to 6 when executing said computer program.
8. A computer-readable storage medium, characterized by: the computer readable storage medium has stored thereon a computer program which, when executed by a processor, implements the steps of the multi-objective optimization method according to any of claims 1 to 6.
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