An adaptive PSO-based overall optimization design method for aerial dispenser

Abstract

The application discloses an adaptive PSO-based overall optimization design method of an aerial dispenser, and belongs to the technical field of aerial dispenser design. In order to improve the feasibility and optimality of an overall scheme, an engine model, a dynamics model and an aerodynamic shape model of the aerial dispenser are constructed; an adaptive mutation updating-based PSO overall optimization method of the aerial dispenser is constructed, including elitist learning strategy design, weight parameter adaptive updating and mutation factor updating; overall optimization design variables are defined, constraint conditions of the optimization design variables are established, and an index function of the overall optimization design variables is established; the overall optimization design variables are taken as state values of PSO particles in the adaptive mutation updating-based PSO overall optimization method of the aerial dispenser, initial values of the overall optimization design variables are given, and the adaptive mutation updating-based PSO overall optimization method of the aerial dispenser is used for optimizing the overall optimization design variables. The application has high calculation efficiency.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of aerial dispenser design, and particularly relates to an aerial dispenser overall optimization design method based on adaptive PSO. BACKGROUND

[0002] The overall system design of an aerial dispenser is a system process involving multiple disciplines, multiple fields and multiple specialties. In traditional design, each discipline of the aerial dispenser design is managed separately, and after the overall system requirements are given, each discipline completes iteration in turn, and the design results are passed to the next discipline, and through repeated iteration optimization, an overall design scheme meeting the tactical index requirements is obtained. The traditional overall design scheme is independent of each other between disciplines, and the coupling relationship between disciplines is ignored, thereby affecting the feasibility and optimality of the overall scheme.

[0003] In order to overcome the defects of independent design of each discipline and further improve the overall performance of the aerial dispenser, the mutual coupling relationship in the design process of each discipline is considered, and the overall design is performed in the mode of multidisciplinary optimization. In order to improve the optimal characteristics of the overall multidisciplinary optimization design, the particle swarm optimization (PSO) optimization algorithm is often used to solve the optimal overall performance index, and since the PSO algorithm needs to perform random wide-area search in the overall design space, there are disadvantages such as low search precision, easy to fall into local optimum, and large error in solving discrete variable optimization problems. SUMMARY

[0004] The problem to be solved by the application is to improve the feasibility and optimality of the overall scheme, and an overall optimization design method of an aerial dispenser based on adaptive PSO is proposed.

[0005] To achieve the above object, the application realizes the following technical scheme:

[0006] An overall optimization design method of an aerial dispenser based on adaptive PSO, comprising the following steps:

[0007] S1. Constructing an engine model, a dynamics model and an aerodynamic shape model of the aerial dispenser;

[0008] S2. Constructing an overall optimization method of the aerial dispenser PSO based on adaptive mutation update, including elitist learning strategy design, weight parameter adaptive update and mutation factor update;

[0009] S3. Based on the engine model, the dynamics model and the aerodynamic shape model constructed in step S1, defining overall optimization design variables, establishing constraint conditions of the optimization design variables, and defining an index function of the overall optimization design variables;

[0010] S4. Taking the overall optimization design variables designed in step S3 as the state values of the PSO particles in the PSO overall optimization method for the aerial dispenser based on adaptive mutation update, giving the initial value of the overall optimization design variables, the PSO overall optimization method for the aerial dispenser based on adaptive mutation update constructed in step S2 is used to optimize the overall optimization design variables, the optimization target is to maximize the index function of the overall optimization design variables, and the optimized overall optimization design variables and index are output.

[0011] Further, the specific implementation method of step S1 includes the following steps:

[0012] S1.1. Constructing an engine model of the aerial dispenser, main parameters of the engine of the aerial dispenser including engine diameter, nozzle diameter, nozzle outlet diameter, propellant mass, and engine working time, and constructing the following engine model:

[0013] The outer diameter of the grain:

[0014] d0=d c -2δ (1)

[0015] Wherein, d0 is the outer diameter of the grain, d c is the engine outer diameter; δ is the thickness including the shell, bushing and inner and outer thermal insulation layer;

[0016] The combustion chamber volume:

[0017]

[0018] Wherein, V c is the combustion chamber volume, l c is the grain length;

[0019] The propellant mass:

[0020] M p =V p ρ p (3)

[0021] Wherein, M p is the propellant mass, ρ p is the density of the propellant, and V p is the propellant volume;

[0022] The fuel filling factor η:

[0023] η=V p / V c ; (4)

[0024] The total mass of the engine: the shell adopts graphite fiber winding, and the total mass M of the engine is:

[0025] M=Mp / 0.9; (5)

[0026] Propellant passage area A p :

[0027]

[0028] Initial nozzle throat diameter d t0 :

[0029]

[0030] where J is the throat passage ratio;

[0031] Considering the ablative effect, the throat diameter d td after engine operation is:

[0032] d td = d t0 + 2r b t b (8)

[0033] where r b is the ablation radius, and t b is the engine operation time;

[0034] Average throat diameter

[0035]

[0036] Average nozzle area

[0037]

[0038] Initial nozzle area A t0 :

[0039]

[0040] Outlet diameter d e :

[0041]

[0042] where A e / A t0 is the nozzle expansion ratio;

[0043] Propellant consumption q m :

[0044] q m = M p / t b ; (13)

[0045] Average pressure in the combustion chamber

[0046]

[0047] Where, η c For combustion chamber efficiency, c th The theoretical characteristic velocity of the propellant;

[0048] Engine thrust F:

[0049] F = I s q m (15)

[0050] Among them, I s For engine specific impulse;

[0051] S1.2. Constructing the dynamic model of the aircraft dispenser:

[0052] The equation of motion of an airborne dispenser in an inertial coordinate system is expressed as follows:

[0053]

[0054] Where r and v are the position vector and velocity vector, respectively. The derivative of the position vector, Let g(r) be the derivative of the velocity vector, g(r) be the gravitational acceleration of the position vector, T be the current thrust magnitude, and the total engine thrust be aligned with the longitudinal axis of the aircraft dispenser. Vectors A and N are the longitudinal and normal aerodynamic forces of the aircraft dispenser, respectively. b is the unit vector along the vertical axis of the air dispenser, and m(t) is the mass at the current time; T represents the rate of change of mass over the current time. vac It is the full vacuum thrust amplitude, η represents the engine throttle position, g0 is the gravitational acceleration at the Earth's surface, and I sp This refers to the engine's specific impulse.

[0055] The dimensionless equation of motion for equation (16) is as follows:

[0056]

[0057] Where r′ and v′ are the derivatives of the position vector and velocity vector, respectively; vector A g and N g These are the longitudinal and normal aerodynamic accelerations, respectively, in units of g0 and T. g It is the magnitude of the acceleration produced by the thrust, in g0.

[0058]

[0059] T g= [T vac -S exit p(r)] / m(t)g0 (20)

[0060] where p0 is the atmospheric density at sea level, R0 is the radius of the earth at the equator, q is the dynamic pressure, S ref is the characteristic area, C A is the axial force coefficient, Mach is the Mach number, a is the angle of attack, C N is the normal force coefficient, S exit is the area at the exit of the engine nozzle, p(r) is the ambient atmospheric pressure at r; the axial force coefficient C A and the normal force coefficient C N are functions of the angle of attack a and the Mach number Mach;

[0061]

[0062] where p(r) is the air density at r, v r = ||v r ||;

[0063] The maximum lift-drag ratio L / D max glide is used as the flight control scheme of the dispenser, and the constant dynamic pressure flight can be converted into the flight trajectory angle. The flight trajectory angle is used as a variable to control the flight dynamic pressure, and the flight trajectory angle command expression is:

[0064] γ c = γ ODP + Δγ (22)

[0065] where γ c is the command angle, γ ODP is the flight trajectory angle corresponding to the optimal dynamic pressure with the maximum lift-drag ratio, and Δγ is the compensated flight trajectory angle, which is used to adjust the flight dynamic pressure or compensate for the uncertain error and steady-state tracking error; the flight trajectory angle command is used as the criterion dynamics integral to generate the range;

[0066] S1.3. Constructing the aerodynamic shape model of the aerial dispenser: the aerodynamic engineering software is used to construct the aerodynamic shape model of the aerial dispenser, and the aerodynamic parameters of the aerial dispenser are calculated, including the projectile body radius D, the projectile body length L, the projectile wing span D l , the projectile wing chord D c

[0067] Further, the specific implementation method of step S2 includes the following steps:

[0068] S2.1. Set based on the standard PSO algorithm, each particle represents a solution of the overall optimization problem of the aerial dispenser, and a group of particles explore and utilize the solution space to find the optimal solution of the overall system of the aerial dispenser, and the expression is:

[0069]

[0070] where, is the velocity of particle i for variable j, is the position of particle i for variable j, is the best position found so far by particle i for variable j, is the best position in the swarm for variable j, ω is the inertia weight that keeps the original velocity, c1 is the particle weight coefficient that keeps the historical best position, c2 is the particle weight coefficient that tracks the swarm best position, ξ and η are independent random weight coefficients between 0 and 1, d is the constriction factor;

[0071] S2.2. Design an elitist learning strategy based on the standard PSO algorithm of step S2.1, define the elite set as the set of pbest whose cost value is not significantly higher than the cost of gbest, the elite set at iteration t is denoted as E t , which is defined as follows:

[0072]

[0073] where, c e is the coefficient that determines the threshold value considered as elite, cs represents the cost value of the hypothetical particle;

[0074] S2.3. Construct the inertia weight, self-cognition coefficient and social influence coefficient in the PSO algorithm of the elitist learning strategy;

[0075] S2.3.1. Set the expression of inertia weight as:

[0076]

[0077] where, is the inertia weight at iteration t, w max and w min are the maximum and minimum values of inertia weight, t max represents the maximum number of iterations allowed for the PSO algorithm to run;

[0078] S2.3.2. Set the self-cognition coefficient to determine the contribution of each elite pbest to update the particle position, then the self-cognition coefficient vector where, represents the self-cognition coefficient of the nth particle at iteration t.

[0079]

[0080] where, F t is the relative fitness at iteration t, Rt is a non-negative random matrix at iteration t;

[0081]

[0082] wherein, represents the relative fitness size of the nth elite particle at iteration t, expressed as:

[0083]

[0084] C1 t each element in contains the elite self-awareness coefficient of which takes the following values:

[0085]

[0086] wherein, ne t represents the number of elite particles at iteration t, represents the self-awareness coefficient of the nth elite particle at iteration t;

[0087] S2.3.3. Set the social influence coefficient for determining the degree of influence of the global best value on the position of each selected particle, using the maximum element of C1 t as the social influence coefficient, the social influence coefficient is defined as:

[0088]

[0089] Based on the constructed parameter update scheme, the formula for updating the speed of each selected particle p i , expressed as:

[0090]

[0091] wherein, V i t+1 is the speed of the ith particle at t+1, the matrix EM t is the extension of the elite particle E t is the extension of

[0092] S2.4. Construct the index mutation operator with two components, the first component is the mutation probability of the selected particle p i , the second component is the mutation dimension of the selected particle p i

[0093] ​​​​ The calculation method is as follows:

[0094]

[0095] in, This represents the overall mutation probability at time t, which decreases continuously as the iteration progresses; It is the mutation probability of the i-th particle;

[0096] The calculation formula is as follows:

[0097]

[0098] Where NSIi represents the selected particle p i The number of stalled iterations, NIt represents the number of iterations that give the particle the opportunity to take advantage of its surroundings, and λm is the particle mutation probability adjustment parameter;

[0099] The calculation formula is as follows:

[0100]

[0101] Where D is the dimension mutation parameter.

[0102] Furthermore, the specific implementation method of step S3 includes the following steps:

[0103] S3.1. Based on the engine model, dynamics model, and aerodynamic shape model constructed in step S1, define the overall optimization design variable X as a vector, with the expression:

[0104] X = [d c d t0 d e M p t b L / D max DLD l D c ] T (36)

[0105] S3.2. Establish constraints for the optimization design variables;

[0106] The constraints for setting the engine model include: the engine mass ratio must satisfy μ at each stage. Fmin ≤μ F The requirement is that the difference in nozzle expansion half-angle between the initial and exit points satisfies Δα ≤ Δα at each stage. max The requirement is that the ratio of the nozzle outlet diameter to the body diameter is μ. dD ≤μ dDmax The takeoff ratio of thrust to weight satisfies N01min ≤N 01 ≤N 01max , the ratio of the nozzle outlet pressure and the external pressure satisfies k p*min ≤k p ;

[0107] The dynamic model constraint conditions include maximum overload and maximum attack angle.

[0108] The aerodynamic shape model constraints include that the ratio of the blunt radius and the base radius satisfies μ bD ≤μ bDmax , and the half-cone angle and the air distribution device slenderness ratio satisfy the size boundary requirements.

[0109] The constraint of each discipline model is uniformly expressed in the form of g i ≤0, such as g1=μ Fmin -μ F ≤0.

[0110] g(X)=[g1 g2…g n ] T ≤0 (37)

[0111] Wherein, g(X) represents a constraint function, and g n represents the constraint of each subsystem.

[0112] S3.3. Establish the index function of the overall optimization design variable, and the expression is:

[0113]

[0114] Wherein, X min and X max are the lower limit and the upper limit of the optimization design variable X respectively.

[0115] Further, the optimization target is set to the farthest range in step S4.

[0116] The beneficial effects of the present application are:

[0117] The overall optimization design method of the air distribution device based on the adaptive PSO provided by the present application firstly establishes each discipline optimization design model including the engine discipline, the dynamics discipline and the aerodynamic shape discipline; the elitist learning strategy is adopted to prevent low-quality particles from guiding the overall optimization direction and improve the overall system optimization efficiency; the exponential mutation operator is applied to the population to prevent the overall optimization design from falling into a local optimal value; and the overall coupled optimization design system is constructed in combination with the coupled design variables of each discipline. Finally, the superiority of the algorithm provided by the present application is verified through comparison and analysis with the traditional algorithm; and the optimization time is greatly shortened on the premise of ensuring the multi-discipline optimization accuracy. BRIEF DESCRIPTION OF DRAWINGS

[0118] Figure 1 A flow chart of an overall optimization design method of an aerial dispenser based on adaptive PSO according to the present application;

[0119] Figure 2 A flow chart of a comprehensive design according to the present application;

[0120] Figure 3 A logic block diagram of PSO-ELPM optimization design according to the present application;

[0121] Figure 4 A curve of an overall optimization design method of an aerial dispenser based on adaptive PSO according to the present application, which is optimized with a performance index function of maximum range;

[0122] Figure 5 A curve of a comparative example according to the present application, which is optimized with a performance index function of maximum range by SQP separated serial multidisciplinary optimization. DETAILED DESCRIPTION

[0123] In order to make the objectives, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application, that is, the specific embodiments described herein are only a part of the embodiments of the present application, but not all the specific embodiments. The components of the specific embodiments of the present application described and shown in the accompanying drawings can be arranged and designed in various different configurations, and the present application can also have other embodiments.

[0124] Therefore, the detailed description of the specific embodiments of the present application provided in the accompanying drawings below is not intended to limit the scope of the claimed present application, but only represents selected specific embodiments of the present application. Based on the specific embodiments of the present application, all other specific embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0125] In order to further understand the inventive content, characteristics and effects of the present application, the following specific embodiments are exemplified, and the accompanying drawings are Figure 1 - the accompanying drawings Figure 5 The detailed description is as follows: Specific embodiment one:

[0127] An overall optimization design method of an aerial dispenser based on adaptive PSO, comprising the following steps:

[0128] S1. Constructing an engine model, a dynamics model and an aerodynamic shape model of the aerial dispenser;

[0129] Further, the specific implementation method of step S1 includes the following steps:

[0130] S1.1. Constructing an engine model of the aerial dispenser, the main parameters of the engine of the aerial dispenser including engine diameter, nozzle diameter, nozzle outlet diameter, propellant mass, engine working time, and constructing the following engine model:

[0131] The outer diameter of the grain:

[0132] d0=d c -2δ (1)

[0133] Wherein, d0 is the outer diameter of the grain, d c is the engine outer diameter; δ is the thickness including the shell, bushing and inner and outer thermal insulation layer;

[0134] The combustion chamber volume:

[0135]

[0136] Wherein, V c is the combustion chamber volume, l c is the grain length;

[0137] Propellant mass:

[0138] M p =V p ρ p (3)

[0139] Wherein, M p is the propellant mass, ρ p is the density of the propellant, and V p is the propellant volume;

[0140] Fuel filling factor η:

[0141] η=V p / V c ; (4)

[0142] The total mass of the engine: the shell adopts graphite fiber winding, and the total mass M of the engine is:

[0143] M=M p / 0.9; (5)

[0144] Propellant channel area A p :

[0145]

[0146] Nozzle initial throat diameter d t0 :

[0147]

[0148] where J is the throat ratio;

[0149] Considering the ablation effect, the throat diameter d td after engine operation is:

[0150] d td = d t0 + 2r b t b (8)

[0151] where r b is the ablation radius, and t b is the engine operation time;

[0152] Average throat diameter

[0153]

[0154] Average throat area

[0155]

[0156] Initial throat area A t0 : A

[0157]

[0158] Exit diameter d e : d

[0159]

[0160] where A e / A t0 is the nozzle expansion ratio;

[0161] Propellant consumption q m : q

[0162] q m = M p / t b ; (13)

[0163] Average combustion chamber pressure

[0164]

[0165] where η c is the combustion chamber efficiency, and c th is the theoretical characteristic velocity of propellant;

[0166] Engine thrust F:

[0167] F = I s q m (15)

[0168] where I s is the specific impulse of the engine;

[0169] S1.2. Constructing the dynamics model of aerial dispenser:

[0170] The expression of the aerial dispenser's motion equation in the inertial coordinate system is:

[0171]

[0172] where r and v are the position vector and velocity vector, respectively, is the derivative of the position vector, is the derivative of the velocity vector, g(r) is the gravitational acceleration of the position vector, T is the current thrust size, based on the engine total thrust and the aerial dispenser's longitudinal axis alignment, vectors A and N are the longitudinal aerodynamic force and normal aerodynamic force of the aerial dispenser, respectively, I b is the unit vector of the aerial dispenser's longitudinal axis, m(t) is the mass at the current time; is the current time mass change rate, T vac is the full vacuum thrust amplitude, η represents the engine throttle size, g0 is the gravitational acceleration of the earth's surface, I sp is the specific impulse of the engine;

[0173] The dimensionless motion equation of equation (16) is as follows:

[0174]

[0175] where r' and v' are the derivatives of the position vector and velocity vector, respectively; vectors A g and N g are the longitudinal and normal aerodynamic accelerations, respectively, with the unit of g0; T g is the size of the thrust generated acceleration, with the unit of g0;

[0176]

[0177] T g = [T vac -S exit p(r)] / m(t)g0 (20)

[0178] where p0 is the atmospheric density at sea level, R0 is the radius of the earth at the equator, q is the dynamic pressure, S ref is the characteristic area, C A is the axial force coefficient, Mach is the Mach number, a is the attack angle, C Nis the normal force coefficient, S exit is the area at the engine nozzle exit, p(r) is the ambient atmospheric pressure at r; axial force coefficient C A and normal force coefficient C N is a function of the angle of attack a and Mach number Mach;

[0179]

[0180] where p(r) is the air density at r, v r =||v r ||;

[0181] The maximum lift-drag ratio L / D max is used as the flight control scheme of the dispenser, and the constant dynamic pressure flight can be converted into the flight trajectory angle. The flight trajectory angle is used as a variable to control the flight dynamic pressure. The flight trajectory angle command expression is:

[0182] γ c =γ ODP +Δγ (22)

[0183] where γ c is the command angle, γ ODP is the flight trajectory angle corresponding to the optimal dynamic pressure with the maximum lift-drag ratio, and Δγ is the compensated flight trajectory angle, which is used to adjust the flight dynamic pressure or compensate for the uncertain error and steady-state tracking error. The flight trajectory angle command is used as the criterion dynamics integral to generate the range.

[0184] S1.3. Constructing the aerodynamic shape model of the aerial dispenser: the aerodynamic shape model of the aerial dispenser is constructed by using the aerodynamic engineering software, and the aerodynamic parameters of the aerial dispenser are calculated, including the body radius D, body length L, wing span D l , wing chord D c

[0185] Further, first, the input parameter list is constructed according to the body radius D, body length L, wing span D l , wing chord D c and other aerodynamic shape construction input parameters of the aerial dispenser;

[0186] Then, the angle of attack, Mach number, height, reference area, reference length and other related data will be written into the “input.dat” file for the subroutine to read;

[0187] Finally, the executable program “misdat.exe” is used to calculate the aerodynamic parameters, and the results are saved in an aerodynamic parameter output file for calling in the overall optimization design solution.

[0188] S2. Constructing an aerial dispenser PSO overall optimization method based on adaptive mutation update, including the design of elitist learning strategy, adaptive update of weight parameters, and mutation factor update;

[0189] As an intelligent optimization algorithm, the PSO algorithm can handle multiple particles simultaneously and search in parallel. Due to its significant advantages of simplicity and ease of implementation, the PSO algorithm has been widely explored. Compared with genetic algorithms and simulated annealing algorithms, the PSO algorithm can eliminate crossover and mutation and show fast convergence speed and strong search balance ability of the global and local. However, the standard PSO optimization algorithm has the disadvantages of low search precision, easy to fall into local optimum, large error in solving discrete variable optimization problems, etc. In order to overcome these shortcomings of the standard PSO, the patent adopts an aerial dispenser overall optimization algorithm based on adaptive mutation, which ensures global optimization rather than local optimization during search and has a high optimization convergence speed.

[0190] In the standard PSO algorithm, a group of particles explores and utilizes the solution space to find the optimal solution of the aerial dispenser overall system, and each particle represents a solution of the aerial dispenser overall optimization problem, so it corresponds to a position in the D-dimensional solution space. In addition, it searches the solution space at a certain speed. Each particle will consider its current position, its own experience and the experience of the group, so as to adjust its speed and search in the direction of the global optimum of the aerial dispenser overall system.

[0191] Further, the specific implementation method of step S2 includes the following steps:

[0192] S2.1. Set based on the standard PSO algorithm, each particle represents a solution of the aerial dispenser overall optimization problem, a group of particles explores and utilizes the solution space to find the optimal solution of the aerial dispenser overall system, expressed as:

[0193]

[0194] wherein, is the speed of particle i for variable j, is the position of particle i for variable j, is the best position found so far by particle i for variable j, is the best position in the group for variable j, ω is the inertia weight that keeps the original speed, c1 is the particle weight coefficient that keeps the historical best position, c2 is the particle weight coefficient that tracks the best position of the population, ξ and η are independent random weight coefficients between 0 and 1, and d is the constraint factor;

[0195] S2.2. Design elite learning strategy based on the standard PSO algorithm of step S2.1, define elite set as the set of pbest whose cost value is not significantly higher than the cost of gbest, the elite set at iteration t is denoted as E t , which is defined as follows:

[0196]

[0197] where c e is the coefficient that determines the threshold value considered as elite, cs represents the cost value of the hypothetical particle;

[0198] Further, the elite learning strategy is adopted to prevent low-quality particles from guiding the overall optimization direction and improve the overall system optimization efficiency. The exponential mutation operator is applied to the population to prevent the overall optimization design from falling into a local optimal value. Therefore, a self-adaptive mutation updating PSO overall optimization algorithm PSO-ELPM (PSO with elite learning, enhanced parameter updating, and exponential mutation operator) for aerial dispenser is designed. The elite is defined as the set of pbest whose cost value is not significantly higher than the cost of gbest. Unlike previous algorithms, the number of elites in the population will change according to the quality of the particles. This strategy avoids unnecessary calculations for low-quality particles when most pbests perform poorly relative to gbest, while ensuring that all high-performance particles are included when the quality of pbests relative to gbest is satisfactory. The elite set of the population at iteration t is denoted as E t .

[0199] S2.3. Construct the inertia weight, self-cognition coefficient, and social influence coefficient in the PSO algorithm of the elite learning strategy;

[0200] Further, the main parameters of the particle swarm algorithm are the inertia weight, self-cognition coefficient, and social influence coefficient. This parameter controls the balance between exploration and exploitation in the PSO algorithm. A higher inertia weight means that particles will move to new neighborhoods more frequently, thereby increasing exploration. On the other hand, a smaller inertia weight allows particles to remain around the same neighborhood and find the optimal solution therein.

[0201] S2.3.1. Set the expression of the inertia weight as:

[0202]

[0203] where, is the inertia weight at iteration t, w max and w minis the maximum and minimum value of the inertial weight, t max denotes the maximum number of iterations allowed for the PSO algorithm to run;

[0204] S2.3.2. Setting the self-awareness coefficient for determining the contribution of each elite pbest to update the particle position, then the self-awareness coefficient vector where, denotes the self-awareness coefficient of the ne-th particle at iteration t;

[0205]

[0206] where, F t is the relative fitness at iteration t, R t is a non-negative random matrix at iteration t;

[0207]

[0208] where, denotes the relative fitness of the ne-th particle at iteration t, expressed as:

[0209]

[0210] Each element in contains the self-awareness coefficient of the elite with the following values:

[0211]

[0212] where, ne t denotes the number of elite particles at iteration t, denotes the self-awareness coefficient of the ne-th elite particle at iteration t;

[0213] Further, the self-awareness coefficient: this parameter determines the contribution of each elite pbest to update the particle position, which should depend on the knowledge discovered by that elite pbest, such that the elite pbest with higher quality has higher contribution. The self-awareness coefficient is calculated with matrix multiplication of a vector representing the relative fitness of different elites and a non-negative random matrix R of size ne t × ne t The relative fitness of elite particles is calculated using the following formula, where the contribution of each elite particle is inversely proportional to the cube root of its cost value.

[0214] S2.3.3. Setting the social influence coefficient for determining the degree of influence of the global best value on the position of each selected particle, using C1 tThe largest element is used as the social influence coefficient. Defined as:

[0215]

[0216] Based on the constructed parameter update scheme, it is used to update each selected particle p. i The formula for the velocity is:

[0217]

[0218] Among them, V i t+1 It is the velocity of the i-th particle at time t+1, and the matrix EM t It is elite particle E t extension yes expansion

[0219] Furthermore, matrix EM t Contains elite particles, and by... Copy to line j to form. Additionally, it has ne. t Row matrix By copying in each line To form.

[0220] S2.4. Constructing an exponential mutation operator has two components. The first component is the selected particle p. i mutation probability The second component is the selected particle p i mutation dimension

[0221] The calculation method is as follows:

[0222]

[0223] in, This represents the overall mutation probability at time t, which decreases continuously as the iteration progresses; It is the mutation probability of the i-th particle;

[0224] The calculation formula is as follows:

[0225]

[0226] Where NSIi represents the selected particle p i The number of stalled iterations, NIt represents the number of iterations that give the particle the opportunity to take advantage of its surroundings, and λm is the particle mutation probability adjustment parameter;

[0227] The formula for the calculation is as follows:

[0228]

[0229] where D is the dimension mutation parameter.

[0230] Further, the mutation operator is applied to particles trapped in local minima, which randomly changes some dimensions of the selected particle in an attempt to find a higher quality solution. First, the mutation probability should decrease over time to improve the convergence accuracy; second, for particles whose pbest has not been updated in the last iterations, the probability should increase; finally, both parameters are considered to determine the mutation dimension. Thus, the proposed mutation operator has two components, the first one is the mutation probability per particle p i This probability is influenced by two factors. First, the overall mutation probability of the algorithm decreases over time to improve the convergence accuracy; second, the mutation probability of a particle is increased for the last iterations. This is achieved by introducing an exponential factor based on the history of the particle p i . This parameter is controlled by the number of iterations without improvement . The second component of the mutation operator is to determine the dimension to be mutated for the selected particle p i , called This parameter is calculated according to the configuration of the algorithm and the problem setup. The parameter NIt represents the number of iterations given to the particle to take advantage of its surroundings. If the particle p i has recently improved, then NSIi becomes smaller than NIt. Thus, will have a value smaller than 1 and decreases. This state gives the particle a greater chance of staying in its neighborhood, which helps to avoid the problem of losing promising neighborhoods in the early stages of the PSO algorithm. On the other hand, if has not improved, then NSIi becomes greater than NIt. As a result, becomes greater than 1, which helps the exploration ability of the algorithm. This strategy ensures that the mutation probability increases if the quality of the particle has not improved, regardless of the current iteration in which the algorithm is. As a result of the combination of the two proposed control parameters, is influenced by the quality of the particle and the current iteration in which the algorithm is executing. Thus, particles flying in acceptable directions require less modification. Moreover, the exploration ability of the algorithm decreases as the algorithm progresses. The second contribution is to determine the dimension to be mutated for a certain particle by the mutation operator, considering the parameters of the problem. The following equation is introduced to use the parameters D, NSIi and​ to calculate the mutation dimension of particle p i According to the equation, increases by increasing D, because a space with more dimensions requires more mutation dimensions to ensure acceptable changes in particle positions. Another important factor is the phase of the algorithm's execution. Later iterations must involve lower exploration, which requires fewer mutation genes. Therefore, is contained in the following formula. Finally, if the mass of the particle does not improve, it needs to be mutated more aggressively to increase the chances of finding a good solution.

[0231] S3. Constructing the engine model, the dynamics model, and the aerodynamic configuration model based on step S1, defining the overall optimization design variables, establishing the constraint conditions of the optimization design variables, and defining the index function of the overall optimization design variables;

[0232] Further, the specific implementation method of step S3 includes the following steps:

[0233] S3.1. Constructing the engine model, the dynamics model, and the aerodynamic configuration model based on step S1, defining the overall optimization design variables X represented in the form of a vector, and the expression is:

[0234] X = [d c d t0 d e M p t b L / D max D L D l D c ] T ; (36)

[0235] Further, the design variables X contained in formula (36) are selected as the state values of the PSO particles, corresponding to the positions of the particles in formula (25). On the basis of engineering experience, the initial values (classical values of the design variables) of the particles are given, and the PSO-ELPM optimization algorithm designed in this paper is used to optimize the design variables to maximize the range.

[0236] S3.2. Establishing the constraint conditions of the optimization design variables;

[0237] Setting the engine model constraint conditions includes: the engine mass ratio satisfies the requirements of each stage μ Fmin ≤μ F , the difference between the initial and the outlet nozzle expansion half-angle satisfies the requirements of each stage Δα≤Δα max , the ratio of the nozzle outlet diameter to the body diameter is μ dD ≤μ dDmax , the takeoff ratio of thrust to weight satisfies N 01min ≤N 01≤N 01max , the ratio of the nozzle exit pressure to the external pressure satisfies k p*min ≤k p ;

[0238] The dynamic model constraint conditions include maximum overload and maximum attack angle;

[0239] The aerodynamic shape model constraint includes that the ratio of the blunt radius to the base radius satisfies μ bD ≤μ bDmax , the half-cone angle and the air distribution device slenderness ratio satisfy the size boundary requirements;

[0240] The constraint of each discipline model is uniformly expressed in the form of g i ≤0, such as g1=μ Fmin -μ F ≤0;

[0241] g(X)=[g1 g2 … g n ] T ≤0 (37)

[0242] Wherein, g(X) represents the constraint function, and g n represents the constraint of each subsystem;

[0243] S3.3. Establish the index function of the overall optimization design variable, and the expression is:

[0244]

[0245] Wherein, X min and X max are the lower limit and upper limit of the optimization design variable X respectively.

[0246] S4. The overall optimization design variable designed in step S3 is taken as the state value of the PSO particle in the air distribution device PSO overall optimization method based on adaptive mutation update, the initial value of the overall optimization design variable is given, and the air distribution device PSO overall optimization method based on adaptive mutation update is constructed based on step S2. The overall optimization design variable is optimized, and the optimization target is that the index function of the overall optimization design variable reaches the maximum, and the optimized overall optimization design variable and index are output.

[0247] Further, the optimization target in step S4 is set as the farthest range.

[0248] Further, the optimization is carried out in the computer performance environment as follows:

[0249] Table 1 Computer performance environment

[0250]

[0251] The overall multidisciplinary optimization design process of the aerial dispenser based on the adaptive PSO is carried out by constructing the engine model, the dynamics model and the aerodynamic shape model. The feasibility of the multidisciplinary overall optimization algorithm of the patent is verified by taking the typical aerial dispenser flight process as an example. The overall performance parameters obtained through the system and overall requirements are set as follows by analyzing the correlation of the input variables of each model and selecting the input variables with higher correlation:

[0252] In the multidisciplinary overall optimization problem of the aerial dispenser, the design variables of each discipline are as follows:

[0253] The design variables of the engine model include the engine diameter d c , the nozzle diameter d t0 , the nozzle exit diameter d e , the propellant mass M p , and the engine working time t b .

[0254] The design variables of the dynamics model include the maximum lift-drag ratio L / D max .

[0255] The design variables of the aerodynamic shape model include the body radius D, the body length L, the wing span D l , and the wing chord length D c . The above optimization design variables can be expressed in the form of a vector, as shown in Table 2:

[0256] Table 2: Parameter table for overall optimization design of aerial dispenser

[0257]

[0258] The system optimization process is constrained by setting the constraint parameters of each model. The optimization constraint variable parameter settings are shown in Table 3:

[0259] Table 3: Optimization constraint parameter table based on aerial dispenser

[0260]

[0261] The following optimization indexes are set by Table 4:

[0262] Table 4: Optimization target based on aerial dispenser

[0263]

[0264] As Figure 4As shown, the adaptive PSO-based aerial dispenser overall multidisciplinary optimization algorithm proposed in this embodiment obtains the farthest optimization result of 104.63 km after 2.3 h of optimization calculation. Through two rounds of re-iteration optimization by designing different initial conditions, the final results are consistent, and thus the optimization ends. By using the multidisciplinary serial optimization process, the same optimization design variables and optimization constraint variables are set, and the sequential quadratic programming method (SQP) is used for optimization calculation for comparison. As shown in Table 5 and Table 5: Figure 5 and Table 5:

[0265] Table 5 Optimization Result Comparison

[0266]

[0267] Compared with the multidisciplinary serial optimization process, the same optimization design variables and optimization constraint variables are set, and the sequential quadratic programming method (SQP) is used for optimization calculation, and the final maximum range optimization result is 102.78 km after 4.4 h. Compared with the adaptive PSO-based aerial dispenser overall multidisciplinary optimization algorithm of the present patent, the maximum range optimization result is 104.63 km, and the traditional multidisciplinary optimization algorithm result is reduced by 1.85 km compared with the optimal range result of the present patent algorithm, and the optimization time is increased by 2.1 h. Therefore, the adaptive PSO-based aerial dispenser overall multidisciplinary optimization algorithm proposed in this embodiment greatly shortens the optimization time on the premise of ensuring the accuracy of multidisciplinary optimization.

[0268] It should be noted that the relational terms, such as "first" and "second", and the like are used solely to distinguish one from another entity or action, without necessarily requiring or implying any such actual relationship or order between such entities or actions. Moreover, the terms "comprises", "comprising", or any other variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but can include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without more limitations, an element defined by the statement "comprising a" does not exclude the existence of additional identical elements in the process, method, article, or apparatus including the element.

[0269] Although the present application has been described with reference to the specific embodiments thereof, it should be understood by those skilled in the art that various changes can be made and equivalents can be substituted for elements thereof without departing from the scope of the present application. In particular, various features and aspects of the present application can be used individually or in any combination depending on the specific application and implementation. Therefore, it is expressly intended that the specific embodiments of the present application both as set forth and including any equivalents thereof should not limit the present application or scope of the claims herein, but rather the overall scope of pertaining solely to the methods and the articles of manufacture specifically recited in the following claims.

Claims

1. A method for overall optimization design of aircraft dispensers based on adaptive PSO, characterized in that, Includes the following steps: S1. Construct the engine model, dynamics model, and aerodynamic shape model of the aircraft dispenser; S2. Construct an overall optimization method for airborne dispenser PSO based on adaptive mutation update, including elitist learning strategy design, adaptive update of weight parameters, and update of mutation factors; The specific implementation method of step S2 includes the following steps: S2.

1. Based on the standard PSO algorithm, each particle represents a solution to the overall optimization problem of the airborne dispenser. A group of particles explores and utilizes the solution space to find the optimal solution for the overall airborne dispenser system. The expression is: ； ； in, It is a particle For variables speed, It is a particle For variables Location, It is a particle So far for variables The best location found It is the group for variables The best location It is the inertial weight that maintains the original velocity. These are particle weighting coefficients that maintain the best historical position. These are the particle weight coefficients that track the optimal position of the population. and These are independent random weight coefficients between 0 and 1. It is a constraint factor; S2.

2. Based on the standard PSO algorithm in step S2.1, design an elitist learning strategy, defining the elite set as those whose cost value is not significantly higher than [the standard PSO algorithm]. Cost The set, in iteration The elite set at a location is represented as The definition is as follows: ； in, It is a coefficient that determines the threshold for being considered elite, and cs represents the cost value of the hypothetical particle; S2.

3. Constructing the inertia weight, self-awareness coefficient, and social influence coefficient in the PSO algorithm for elitist learning strategies; S2.3.

1. The expression for setting the inertia weight is: ； in, It is iteration Inertial weight at the location, and These are the maximum and minimum values ​​of inertial weight. This indicates the maximum number of iterations allowed for the PSO algorithm to run; S2.3.

2. Set a self-awareness coefficient to determine each elite The contribution to updating the particle's position is then expressed as the self-awareness coefficient vector. ,in, Representing the The particles iterate to Self-awareness coefficient at the time of the event; ； in, It is iteration Relative fitness at that location It is iteration A nonnegative random matrix at the location; ； in, Representing the The particles iterate to The relative fitness at any given time is expressed as: ； Each element in contains elites Self-awareness coefficient Its values ​​are as follows: ； in, Indicates that the elite particles iterate to The number of hours, Representing the Elite particles iterate to Self-awareness coefficient at the time of the event; S2.3.

3. Set the social impact coefficient to determine the degree of influence of the global optimum on the position of each selected particle. The largest element is used as the social influence coefficient. Defined as: ； Based on the constructed parameter update scheme, it is used to update each selected particle. The formula for the velocity is: ； in, It is the first Individual particles The speed at time, matrix Elite particles extension , yes expansion ; S2.

4. Constructing an exponential mutation operator has two components; the first component is the selected particle. mutation probability The second component is the selected particle. mutation dimension ; The calculation method is as follows: ； in, represent The overall mutation probability at any given time decreases continuously as the iteration progresses; It is the first The mutation probability of each particle; The calculation formula is as follows: ； in, Indicates selected particle The number of stalled iterations, λm represents the number of iterations that give a particle the opportunity to utilize its surrounding environment, and is the particle mutation probability adjustment parameter. The calculation formula is as follows: ； Where D is the dimension mutation parameter; S3. Based on the engine model, dynamics model, and aerodynamic shape model constructed in step S1, define the overall optimization design variables, establish the constraints of the optimization design variables, and the index function of the overall optimization design variables; S4. Using the overall optimization design variables designed in step S3 as the state values ​​of PSO particles in the overall optimization method of PSO for airborne dispensers based on adaptive mutation update, given the initial values ​​of the overall optimization design variables, the overall optimization design variables are optimized based on the overall optimization method of PSO for airborne dispensers based on adaptive mutation update constructed in step S2. The optimization objective is to maximize the index function of the overall optimization design variables, and the optimized overall optimization design variables and index are output.

2. The overall optimization design method for an airborne dispenser based on adaptive PSO as described in claim 1, characterized in that, The specific implementation method of step S1 includes the following steps: S1.

1. Construct an aircraft dispenser engine model. The main parameters of the aircraft dispenser engine include engine diameter, nozzle diameter, nozzle exit diameter, propellant mass, and engine operating time. Construct the following engine model: outer diameter of the propellant column: ； in, The outer diameter of the medicine column. The outer diameter of the engine; The thickness includes the shell, bushing, and inner and outer insulation layers; Combustion chamber volume: ； in, The volume of the combustion chamber. This refers to the length of the propellant charge; Propellant quality: ； in, For propellant quality, For the density of the propellant, For propellant volume; Fuel loading factor : ； Engine total mass: With the casing made of graphite fiber winding and considering the external heat dissipation protection layer, the engine's total mass is... for: ； Propellant channel area : ； Initial throat diameter : ； in, For throat patency ratio; Considering the effects of ablation, the throat diameter after engine operation for: ； in, Where is the ablation radius, Engine operating time; Average larynx diameter : ； Average throat area : ； Initial throat area : ； outlet diameter : ； in, This refers to the nozzle expansion ratio; Propellant consumption per second : ； Average pressure in the combustion chamber : ； in, For combustion chamber efficiency, The theoretical characteristic velocity of the propellant; Engine thrust : ； in, For engine specific impulse; S1.

2. Constructing a dynamic model of an aircraft dispenser: The equation of motion for an airborne dispenser in an inertial coordinate system is expressed as follows: ； in, and These are the position vector and the velocity vector, respectively. The derivative of the position vector, The derivative of the velocity vector. It is the position vector of gravitational acceleration. This is the current thrust magnitude, based on the total engine thrust aligned with the longitudinal axis of the aircraft dispenser, and is a vector. and These are the longitudinal and normal aerodynamic forces of an aircraft dispenser. The unit vector along the longitudinal axis of the aircraft dispenser. The quality of the current time; The rate of change of quality at the current time. It is the full vacuum thrust amplitude. Represents the engine throttle position. It is the gravitational acceleration at the Earth's surface. This refers to the engine's specific impulse. The dimensionless equation of motion for equation (16) is as follows: ； in, and These are the derivatives of the position vector and the velocity vector, respectively; vector and These are the longitudinal and normal aerodynamic accelerations, respectively, in units of: ; It is the magnitude of the acceleration produced by the thrust, in units of: ; ； ； ； in, The atmospheric density at sea level. The radius at the Earth's equator. For dynamic pressure, For the characteristic area, This is the axial force coefficient. Mach number, For the angle of attack, Normal force coefficient, This represents the area at the engine nozzle exit point. for Atmospheric pressure at the location; axial force coefficient and normal force coefficient It is an angle of attack and Mach number The function; (21)； in, for air density at that location, ; Using the maximum lift-to-drag ratio Gliding, as a flight control scheme for dispensers, can be converted into a flight trajectory angle since constant dynamic pressure flight can be used as a variable to control flight dynamic pressure. The expression for the flight trajectory angle command is as follows: ； in, For command angle, The flight path angle corresponding to the optimal dynamic pressure that maximizes the lift-to-drag ratio. The compensated flight trajectory angle is used to adjust flight pressure or compensate for uncertainties and steady-state tracking errors; the flight trajectory angle command is used as the criterion for dynamic integration to generate the range. S1.

3. Constructing the aerodynamic shape model of the aircraft dispenser: An aerodynamic shape model of the aircraft dispenser was constructed using aerodynamic engineering software, and the aerodynamic parameters of the aircraft dispenser, including the projectile radius, were calculated. Projectile length Wingspan of the missile wing chord length .

3. The overall optimization design method for an airborne dispenser based on adaptive PSO as described in claim 2, characterized in that, The specific implementation method of step S3 includes the following steps: S3.

1. Based on the engine model, dynamics model, and aerodynamic shape model constructed in step S1, define the overall optimization design variables. Represented as a vector, the expression is: ； S3.

2. Establish constraints for the optimized design variables; The constraints for setting the engine model include: ensuring the engine mass ratio meets the requirements of each stage. The requirements, the difference between the initial and outlet nozzle expansion half-angle, meet the requirements of each stage. The requirement is that the ratio of the nozzle outlet diameter to the body diameter is [value missing]. The thrust-to-weight takeoff ratio satisfies The ratio of nozzle outlet pressure to external pressure satisfies ; The constraints of the dynamic model include maximum overload and maximum angle of attack; Aerodynamic shape model constraints include satisfying the ratio of blunt radius to bottom diameter. The semi-cone angle and the slenderness ratio of the aircraft dispenser meet the size boundary requirements; The constraints of each subject model are uniformly represented as follows: Form, such as ; ； in, Represents the constraint function. Constraints representing each subsystem; S3.

3. Establish the index function for the overall optimization design variables, with the following expression: ； in, and These are the optimization design variables. The lower and upper limits.

4. The overall optimization design method for an airborne dispenser based on adaptive PSO as described in claim 3, characterized in that, In step S4, the optimization target is set to the longest range.

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