CN105975651B - Guided missile Parameters design based on Genetic Particle Swarm algorithms for multidisciplinary design optimization - Google Patents

Abstract

Guided missile Parameters design based on Genetic Particle Swarm algorithms for multidisciplinary design optimization, is related to guided missile Parameters design.The present invention is not suitable for the case where multidisciplinary lower design parameter is more and there are Coupled Variable phenomenons to solve the existing guided missile Parameters design based on intelligent optimization algorithm.The present invention chooses engine larynx diameter, engine combustion face area, motor charge meat thickness, guided missile outer diameter, engine/motor specific impulse, engine quality, fuel mass, missile wing root chord length, empennage root tip length, empennage tip chord length as design parameter：Then utilize genetic algorithm to three control parameters w, c in standard particle group's algorithm₁、c₂It carries out preferably, genetic idea being introduced population position updating process when optimizing for particle cluster algorithm during preferred with design parameter.The present invention is suitable for guided missile parameter designing field.

Description

Missile parameter design method based on genetic particle swarm multidisciplinary design optimization algorithm

technical field

The invention relates to a missile parameter design method.

Background technique

Many disciplines are involved in the design of aircraft. From the perspective of the overall system, there must be a certain degree of interaction and coupling effect among the various subsystems. Since the subsystems have their own independent analysis and design tools, the traditional sequential design often cannot be considered comprehensively, thus failing to fully consider the coupling factors between the various systems. Applying multidisciplinary design optimization to solve the design problems of the above-mentioned overall system not only improves the design efficiency, but also improves the performance of the product.

Missile weapon design requires comprehensive knowledge of multiple disciplines such as aerodynamics, ballistics, and power. With the development of the design level, it is necessary to carry out multidisciplinary comprehensive design in the design process of such complex systems, and to find the global optimal design scheme on the basis of considering the interaction of various disciplines. However, some existing missile design methods are based on the design of missile parameters in another discipline under the limited conditions of a certain discipline (such as ballistic discipline). This design method has poor overall performance of the designed missile; The method is to combine multidisciplinary parameters to design, but this design method is not suitable for the situation where there are many design parameters in different disciplines and there are multivariate coupling phenomena.

Nowadays, intelligent optimization algorithms have brought many conveniences to many fields, and some scholars have introduced intelligent optimization algorithms into the field of missile design, but the general missile parameter design based on intelligent optimization algorithms is suitable for situations with fewer parameters. Under the multi-parameter design method, the general intelligent optimization algorithm cannot converge and can not achieve better design results.

Contents of the invention

The invention aims to solve the problem that the existing missile parameter design method based on the intelligent optimization algorithm is not applicable to the situation that there are many design parameters and variable coupling phenomenon under multidisciplinary conditions.

The missile parameter design method based on the genetic particle swarm multidisciplinary design optimization algorithm includes the following steps:

Step 1. Select the following design variables as design parameters:

Engine throat diameter x ₁ , engine combustion surface area x ₂ , engine charge flesh thickness x ₃ , missile outer diameter x ₄ , engine specific impulse x ₅ , engine mass x ₆ , fuel mass x ₇ , root chord length of the projectile wing x ₈ , root tip length of empennage x ₉ , chord length of empennage tip x ₁₀ ;

Combining the subjects of aerodynamics, dynamics and ballistics, according to the limit of fuel weight x ₇ , the motion equation of the missile in the horizontal plane is integrated to obtain the total range of the missile trajectory, which is the objective function F(X _i );

The following design constraints exist:

(1) Select the missile end-of-flight speed Ma=1.4 as the termination condition, reduce the overload requirement at this time, and set the available overload to be greater than or equal to 8g;

(2) The ratio of the outlet pressure of the nozzle nozzle to the external pressure satisfies: p _e /p _a >0.3;

(3) The working pressure of the combustion chamber is higher than the critical pressure of fuel combustion, and meets the upper limit constraint: 2MP<p _c <30MP;

(4) The volume filling factor of the engine charge satisfies: η _v <0.95;

Step 2. Using the genetic algorithm to optimize the three control parameters w, c ₁ , c ₂ and the design parameters in the standard particle swarm optimization algorithm:

Step 2.1. Select the genetic population size n _p , the crossover rate p _c and the mutation rate p _m , and the maximum evolution algebra T for a given problem;

Step 2.2: Randomly generate the initialization population of the genetic algorithm;

Step 2.3: Calculate the individual fitness value of genetic algorithm, the specific process is as follows:

Step 2.3.1: Select the population size m of the particle swarm optimization algorithm, and determine the maximum number of iterations;

Step 2.3.2: Initialize particle swarm velocity and position v ₀ and x ₀ randomly;

Step 2.3.3: Calculate the fitness value F(X _i ) of each particle;

Step 2.3.4: Compare the fitness value of each particle, record its own optimal value p _i and group optimal particle label g;

Step 2.3.5: Apply the following formula to update the velocity and position of the particle;

The meaning of each parameter is: in an n=10-dimensional search space, a population X={x ₁ ,..., _xi ,...,x _m } composed of m particles, where the i-th particle The position of x _i ={x _i1 ,x _i2 ,...,x _in } ^T , that is, x _i ={x _i1 ,x _i2 ,...,x _i10 } ^T , and its velocity is v _i ={v _i1 ,v _i2 ,...,v _in } ^T ; the individual extremum value of the i-th particle is p _i ={p _i1 ,p _i2 ,...,p _i10 } ^T , and the global extremum value of the population is p _g ＝{p _g1 ,p _g2 ,...,p _g10 } ^T ; d=1,2,...,n, i=1,2,...,m, t is the current evolution algebra, r ₁ and r ₂ is a random number distributed between [0, 1], c ₁ and c ₂ are acceleration constants;

Step 2.3.6: Introduce the genetic idea into the particle swarm position update process,

The positions of any two particles in the particle swarm are genetically updated, and the new positions are calculated by the following formula:

x ₁ ′(t)=rand()*x ₁ (t)+(1-rand())*x ₂ (t)

x ₂ ′(t)=rand()*x ₂ (t)+(1-rand())*x ₁ (t)

Among them, x ₁ ′(t) and x ₂ ′(t) represent the updated positions respectively; rand() represents randomly selecting a certain position for cross operation;

Step 2.3.7: Check whether the termination condition of the algorithm is satisfied, if not, go to step 2.3.3; if so, find the optimal value;

Step 2.3.8: The optimal value found by the particle swarm optimization algorithm is the fitness value of the genetic algorithm individual;

Step 2.4: Calculate the selection probability of each individual according to the individual fitness value of the genetic algorithm, usually calculated by linear ranking;

Step 2.5: Execute selection, crossover and mutation operators to generate a new generation of population;

Step 2.6: Check whether the termination condition of the genetic algorithm is satisfied, if not, go to step 2.3; if yes, find the optimal solution, which is the value of the design parameters.

The present invention has the following effects:

The present invention is aimed at engine throat diameter, engine combustion surface area, engine charge meat thickness, missile outer diameter, engine specific impulse, engine mass, fuel mass, wing root chord length, empennage root under the subject of aerodynamics, dynamics and ballistics. The multidisciplinary optimization design based on the intelligent algorithm based on the tip length and tail tip chord length can not only converge the design, but also introduce genetic ideas into the particle swarm position update process during the optimization process of the particle swarm optimization algorithm, avoiding being trapped in the local optimization process. best case. Using the invention for design can achieve better design effect. Compared with the MDF design method, the range of the missile designed by the invention can be increased by more than 2.41‰.

Moreover, the invention can solve the subsystem coupling problem in the traditional design method; reduce repeated design links in the overall design process of the missile weapon, thereby improving design efficiency; reduce the total design time of the missile weapon system, and further reduce the development cost. At the same time, the invention can also improve the design precision of the missile weapon and shorten the development time of the overall system.

Description of drawings

Figure 1 shows the information exchange between various disciplines as follows;

Fig. 2 is the schematic diagram of data flow after dividing in the embodiment;

Fig. 3 is a graph of the fitness degree of the objective function of the present invention.

Detailed ways

Specific implementation mode one:

The missile parameter design method based on the genetic particle swarm multidisciplinary design optimization algorithm includes the following steps:

Step 1. Select the following design variables as design parameters:

Engine throat diameter x ₁ , engine combustion surface area x ₂ , engine charge meat thickness x ₃ , missile outer diameter x ₄ , engine specific impulse x ₅ , engine mass x ₆ , fuel mass x ₇ , root chord length of the projectile wing x ₈ , root tip length of empennage x ₉ , chord length of empennage tip x ₁₀ ;

Combining the subjects of aerodynamics, dynamics and ballistics, according to the limit of fuel weight x ₇ , the motion equation of the missile in the horizontal plane is integrated to obtain the total range of the missile trajectory, which is the objective function F(X _i );

The following design constraints exist:

(1) Select the missile end-of-flight speed Ma=1.4 as the termination condition, reduce the overload requirement at this time, and set the available overload to be greater than or equal to 8g;

(2) The ratio of the outlet pressure of the nozzle nozzle to the external pressure satisfies: p _e /p _a >0.3;

(3) The working pressure of the combustion chamber is higher than the critical pressure of fuel combustion, and meets the upper limit constraint: 2MP<p _c <30MP;

(4) The volume filling factor of the engine charge satisfies: η _v <0.95;

Step 2. Using the genetic algorithm to optimize the three control parameters w, c ₁ , c ₂ and the design parameters in the standard particle swarm optimization algorithm:

Step 2.1. Select the genetic population size n _p , the crossover rate p _c and the mutation rate p _m , and the maximum evolution algebra T for a given problem;

Step 2.2: Randomly generate the initialization population of the genetic algorithm;

Step 2.3: Calculate the individual fitness value of genetic algorithm, the specific process is as follows:

Step 2.3.1: Select the population size m of the particle swarm optimization algorithm, and determine the maximum number of iterations;

Step 2.3.2: Initialize particle swarm velocity and position v ₀ and x ₀ randomly;

Step 2.3.3: Calculate the fitness value F(X _i ) of each particle;

Step 2.3.4: Compare the fitness value of each particle, record its own optimal value p _i and group optimal particle label g;

Step 2.3.5: Apply the following formula to update the velocity and position of the particle;

The meaning of each parameter is: in an n=10-dimensional search space, a population X={x ₁ ,..., _xi ,...,x _m } composed of m particles, where the i-th particle The position of x _i ={x _i1 ,x _i2 ,...,x _in } ^T , that is, x _i ={x _i1 ,x _i2 ,...,x _i10 } ^T , and its velocity is v _i ={v _i1 ,v _i2 ,...,v _in } ^T ; the individual extremum value of the i-th particle is p _i ={p _i1 ,p _i2 ,...,p _i10 } ^T , and the global extremum value of the population is p _g ＝{p _g1 ,p _g2 ,...,p _g10 } ^T ; d=1,2,...,n, i=1,2,...,m, t is the current evolution algebra, r ₁ and r ₂ is a random number distributed between [0, 1], c ₁ and c ₂ are acceleration constants;

Step 2.3.6: Introduce the genetic idea into the particle swarm position update process,

The positions of any two particles in the particle swarm are genetically updated, and the new positions are calculated by the following formula:

x ₁ ′(t)=rand()*x ₁ (t)+(1-rand())*x ₂ (t)

x ₂ ′(t)=rand()*x ₂ (t)+(1-rand())*x ₁ (t)

Among them, x ₁ ′(t) and x ₂ ′(t) represent the updated positions respectively; rand() represents randomly selecting a certain position for cross operation;

Step 2.3.7: Check whether the termination condition of the algorithm is satisfied, if not, go to step 2.3.3; if so, find the optimal value;

Step 2.3.8: The optimal value found by the particle swarm optimization algorithm is the fitness value of the genetic algorithm individual;

Step 2.4: Calculate the selection probability of each individual according to the individual fitness value of the genetic algorithm, usually calculated by linear ranking;

Step 2.5: Execute selection, crossover and mutation operators to generate a new generation of population;

Step 2.6: Check whether the termination condition of the genetic algorithm is satisfied, if not, go to step 2.3; if yes, find the optimal solution, which is the value of the design parameters.

Specific implementation mode two:

The specific process of integrating the equation of motion of the missile in the horizontal plane to obtain the total range of the missile trajectory according to the fuel weight x ₇ limit described in step 1 of the present embodiment is as follows:

Step 1.1, pneumatic calculation:

The total lift coefficient of the projectile is:

C _y =C _yW +C _yT +C _yB

In the formula, C _yW is the lift coefficient of the missile wing; C _yT is the lift coefficient of the missile body acting on the empennage; C _yB is the lift coefficient of the missile body;

Step 1.2, power calculation:

The zero-dimensional internal ballistic differential equation of solid rocket motor used for internal ballistic calculation is:

Among them, ρ _c is the average density of combustion chamber gas; t' represents time, V _c is the free volume of the combustion chamber; ρ _p is the propellant density; S is the burning surface area, that is, x ₂ ; r is the propellant burning velocity; Γ is the function of specific impulse, that is, x ₅ ; p _c is the working pressure of the combustion chamber; A _t is the throat area of the nozzle, which is _Tc is the average temperature; R is the gas constant;

According to the finite element analysis method, the thickness E of the charge and the area of the burning surface can be obtained, and the thickness E of the charge is _x3 ;

The relationship between the burning surface area is:

Among them, V _e is the charge volume after burnt out, ΔV _j is the charge volume in the finite volume element, subscripts e, e-Δe respectively represent the state of solid fuel at the combustion moment and the previous moment; n′ represents the number of finite elements;

Corresponding simplifications and calculations are made to the above formulas in the power calculation, and the thrust P in the steady working section of the engine can be obtained as:

In the above formula, is the mass flow rate of the nozzle, pe _is the outlet pressure of the nozzle mouth, pa is the external pressure, ε _A is the expansion ratio of the nozzle, ε _p is the expansion ratio of the nozzle, and k is the specific heat ratio of _the gas;

Step 1.3, ballistic calculation:

The movement of the missile in the horizontal plane is mainly considered, and the equation of motion of the missile in the horizontal plane is given below:

mg=Pα+Y

In the above formula, V is the instantaneous flight speed of the missile, x and z are the coordinate components of the axial direction and the vertical direction of the projectile in the horizontal plane respectively; g is the acceleration of gravity, m is the mass of the missile, and _x6 is the main influencing factor of m; P Y, Z are lift force and sideslip force respectively; V is flight speed; α is missile flight angle of attack; φ _v is track deflection angle; _β is sideslip angle; m _c is limited by x ₇ ;

According to the limitation of fuel weight x ₇ , the total range of the missile trajectory can be obtained by integrating the above motion equation, which is the objective function F(X _i ).

Other steps and parameters are the same as those in Embodiment 1.

Specific implementation mode three:

The calculation process of C _yW , C _yT , and C _yB described in step 1.1 of this embodiment is as follows:

Among them, K _W , K _T , and K _B are the interference factors of the wing, empennage, and body, respectively, and the relevant values can be obtained from empirical formulas; S _W , S _T , and S _B are the references of the wing, tail, and body, respectively. area.

Other steps and parameters are the same as in the second embodiment.

Specific implementation mode four:

The calculation process of S _W , S _T , and S _B described in step 1.1 of this embodiment is as follows:

S _W ＝x ₈ ·l _W

S _T ＝(x ₉ +x ₁₀ )·l _T /2

S _B ＝S _W +S _T +π(x ₄ /2) ² l _B

Among them, l _W , l _T , and l _B represent the lengths of the wing, empennage, and body, respectively.

Other structures and parameters are the same as those in the third embodiment.

Example

In the design process of the present invention, information exchange between each subject is as shown in Figure 1, according to the information exchange figure between the subject as shown in Figure 1, in conjunction with genetic particle swarm algorithm, the missile design problem under the multidisciplinary environment The design variables are divided, and the following figure is a schematic diagram of the data flow after division, as shown in Figure 2;

The simulation experiment was carried out according to Embodiment 4, and the optimization results of the present invention are shown in Table 1 as follows; at the same time, in order to verify the present invention, a multidisciplinary method (MDF) method was used for comparison. The optimization results are shown in Table 1 below, and the fitness curve of the objective function of the present invention is shown in FIG. 3 .

Table 1

Claims (4)

1. The missile parameter design method based on genetic particle swarm multidisciplinary design optimization algorithm is characterized in that comprising the steps: Step 1. Select the following design variables as design parameters: Engine throat diameter x ₁ , engine combustion surface area x ₂ , engine charge flesh thickness x ₃ , missile outer diameter x ₄ , engine specific impulse x ₅ , engine mass x ₆ , fuel mass x ₇ , root chord length of the projectile wing x ₈ , root tip length of empennage x ₉ , chord length of empennage tip x ₁₀ ; According to the limitation of fuel weight x ₇ , the motion equation of the missile in the horizontal plane is integrated to obtain the total range of the missile trajectory, which is the objective function F(X _i ); The following design constraints exist: (1) Select the missile end-of-flight speed Ma=1.4 as the termination condition, and set the available overload to be greater than or equal to 8g; (2) The ratio of the outlet pressure of the nozzle nozzle to the external pressure satisfies: p _e /p _a >0.3; (3) The working pressure of the combustion chamber is higher than the critical pressure of fuel combustion, and meets the upper limit constraint: 2MP<p _c <30MP; (4) The volume filling factor of the engine charge satisfies: η _v <0.95; Step 2. Using the genetic algorithm to optimize the three control parameters w, c ₁ , c ₂ and the design parameters in the standard particle swarm optimization algorithm: Step 2.1. Select the genetic population size n _p , the crossover rate p _c and the mutation rate p _m , and the maximum evolution algebra T for a given problem; Step 2.2: Randomly generate the initialization population of the genetic algorithm; Step 2.3: Calculate the individual fitness value of genetic algorithm, the specific process is as follows: Step 2.3.1: Select the population size m of the particle swarm optimization algorithm, and determine the maximum number of iterations; Step 2.3.2: Initialize particle swarm velocity and position v ₀ and x ₀ randomly; Step 2.3.3: Calculate the fitness value F(X _i ) of each particle; Step 2.3.4: Compare the fitness value of each particle, record its own optimal value p _i and group optimal particle label g; Step 2.3.5: Apply the following formula to update the velocity and position of the particle; The meaning of each parameter is: in an n=10-dimensional search space, a population X={x ₁ ,..., _xi ,...,x _m } composed of m particles, where the i-th particle The position of x _i ={x _i1 ,x _i2 ,...,x _in } ^T , that is, x _i ={x _i1 ,x _i2 ,...,x _i10 } ^T , and its velocity is v _i ={v _i1 ,v _i2 ,...,v _in } ^T ; the individual extremum value of the i-th particle is p _i ={p _i1 ,p _i2 ,...,p _i10 } ^T , and the global extremum value of the population is p _g ＝{p _g1 ,p _g2 ,...,p _g10 } ^T ; d=1,2,...,n, i=1,2,...,m, t is the current evolution algebra, r ₁ and r ₂ is a random number distributed between [0, 1], c ₁ and c ₂ are acceleration constants; Step 2.3.6: Genetically update the positions of any two particles in the particle swarm, and the new position is calculated by the following formula: x ₁ ′(t)=rand()*x ₁ (t)+(1-rand())*x ₂ (t) x ₂ ′(t)=rand()*x ₂ (t)+(1-rand())*x ₁ (t) Among them, x ₁ ′(t) and x ₂ ′(t) represent the updated positions respectively; rand() represents randomly selecting a certain position for cross operation; Step 2.3.7: Check whether the termination condition of the algorithm is satisfied, if not, go to step 2.3.3; if so, find the optimal value; Step 2.3.8: The optimal value found by the particle swarm optimization algorithm is the fitness value of the genetic algorithm individual; Step 2.4: Calculate the selection probability of each individual according to the individual fitness value of the genetic algorithm, and calculate according to the linear ranking; Step 2.5: Execute selection, crossover and mutation operators to generate a new generation of population; Step 2.6: Check whether the termination condition of the genetic algorithm is satisfied, if not, go to step 2.3; if yes, find the optimal solution, which is the value of the design parameters. 2. the missile parameter design method based on the genetic particle swarm multidisciplinary design optimization algorithm according to claim 1, is characterized in that according to fuel weight x ₇ limit described in step 1, the equation of motion of the missile in the horizontal plane is integrated to obtain the missile The specific process of the ballistic total voyage is as follows: Step 1.1, pneumatic calculation: The total lift coefficient of the projectile is: C _y =C _yW +C _yT +C _yB In the formula, C _yW is the lift coefficient of the missile wing; C _yT is the lift coefficient of the missile body acting on the empennage; C _yB is the lift coefficient of the missile body; Step 1.2, power calculation: The zero-dimensional internal ballistic differential equation of solid rocket motor used for internal ballistic calculation is: Among them, ρ _c is the average density of combustion chamber gas; t' represents time, V _c is the free volume of the combustion chamber; ρ _p is the propellant density; S is the burning surface area, that is, x ₂ ; r is the propellant burning velocity; Γ is the function of specific impulse, that is, x ₅ ; p _c is the working pressure of the combustion chamber; A _t is the throat area of the nozzle, which is _Tc is the average temperature; R is the gas constant; According to the finite element analysis method, the thickness E of the charge and the area of the burning surface can be obtained, and the thickness E of the charge is _x3 ; The relationship between the burning surface area is: Among them, V _e is the charge volume after burnt out, ΔV _j is the charge volume in the finite volume element, subscripts e, e-Δe respectively represent the state of solid fuel at the combustion moment and the previous moment; n′ represents the number of finite elements; Corresponding simplification and calculation of the above formulas in the power calculation, the thrust P in the steady working section of the engine is: In the above formula, is the mass flow rate of the nozzle, pe _is the outlet pressure of the nozzle mouth, pa is the external pressure, ε _A is the expansion ratio of the nozzle, ε _p is the expansion ratio of the nozzle, and k is the specific heat ratio of _the gas; Step 1.3, ballistic calculation: Considering the motion of the missile in the horizontal plane, the equation of motion of the missile in the horizontal plane is given below: mg=Pα+Y In the above formula, V is the instantaneous flight speed of the missile, x and z are the coordinate components of the axial direction and the vertical direction of the projectile in the horizontal plane respectively; g is the acceleration of gravity, m is the mass of the missile, and _x6 is the main influencing factor of m; P Y, Z are the lift force and sideslip force respectively; V is the flight speed; α is the missile flight angle of attack; _φv is the track deflection angle; _β is the sideslip angle; m _c is limited by x ₇ ; According to the limitation of fuel weight x ₇ , the total range of the missile trajectory can be obtained by integrating the above motion equation, which is the objective function F(X _i ). 3. the missile parameter design method based on genetic particle swarm multidisciplinary design optimization algorithm according to claim 2, is characterized in that the calculation process of C _yW , C _yT , C _yB described in step 1.1 is as follows: Among them, K _W , K _T , _KB are the interference factors of the wing, tail and body respectively; S _W , S _T , S _B are the reference areas of the wing, tail and body respectively. 4. the missile parameter design method based on genetic particle swarm multidisciplinary design optimization algorithm according to claim 3, is characterized in that the _SW described in step 1.1, _ST , the calculation process of S _B is as follows: S _W ＝x ₈ ·l _W S _T ＝(x ₉ +x ₁₀ )·l _T /2 S _B ＝S _W +S _T +π(x ₄ /2) ² l _B Among them, l _W , l _T , and l _B represent the lengths of the wing, empennage, and body, respectively.