Aircraft high ballistic coefficient multi-objective optimization method considering complex coupling constraints

Abstract

The application belongs to the technical field of aircraft overall design, and discloses a kind of aircraft high trajectory coefficient multi-objective optimization method considering complex coupling constraint, comprising: setting the design variable vector of aircraft and determining constraint condition, constructing multi-objective optimization mathematical model;Improved multi-objective particle swarm algorithm is used to solve, through particle coding and population initialization, fitness evaluation and constraint processing, non-dominated sorting and crowded distance calculation, individual optimal solution and global optimal solution selection, velocity vector and position update, external file maintenance and iterative convergence, output pareto optimal solution set;From it, the particle that satisfies all constraint conditions and realizes balanced improvement on all optimization objectives is selected as the final design scheme.The application can balance multiple optimization objectives under complex coupling constraint.

Description

Technical Field

[0001] This invention belongs to the field of aircraft overall design technology, specifically relating to a multi-objective optimization method for high ballistic coefficients of aircraft that considers complex coupling constraints. Background Technology

[0002] In the overall design of aircraft (such as commercial launch vehicles), the ballistic coefficient is a core parameter characterizing the rocket's ability to overcome aerodynamic drag. A high ballistic coefficient helps reduce velocity loss and improve range and payload efficiency. However, the pursuit of a high ballistic coefficient often creates sharp conflicts with external envelope constraints, overload constraints, and stability constraints. External envelope constraints require sufficient clearance between the aircraft and the launch tube / transport container, limiting large aspect ratios or large wing dimensions. Overload constraints require that axial and normal overloads throughout flight do not exceed the allowable values ​​for the structure and equipment, but a high ballistic coefficient is usually accompanied by high dynamic pressure flight, which can easily lead to excessive overload. Stability constraints require that the center of pressure and center of mass maintain an appropriate distance, which conflicts with the pursuit of drag reduction in the shape design. In the traditional design model, each constraint is analyzed independently by different disciplines: the aerodynamics discipline focuses on improving the ballistic coefficient, the structural discipline checks overload and loading, and the control discipline evaluates stability. There is a lack of coordination among them, and all constraints are often barely met by increasing the safety factor or repeated trial and error, resulting in design results that deviate significantly from the global optimal solution and low overall rocket performance.

[0003] Traditional performance-oriented optimization methods typically treat single performance indicators such as range and payload capacity as objectives, while considering overload, loading capacity, and stability as boundary constraints. When dealing with multi-objective problems, weighted summation methods are often used to merge multiple objectives into a single objective, or to transform secondary objectives into constraints. However, there is a non-linear competitive relationship between high ballistic coefficient, peak overload, and volumetric efficiency: increasing the ballistic coefficient may cause the peak overload to exceed the limit, while reducing the overload requires sacrificing the ballistic coefficient; increasing the volumetric efficiency often requires a slender aircraft, but this increases drag and reduces the ballistic coefficient. Weighted summation methods struggle to set appropriate weighting coefficients, easily losing equilibrium solutions in the Pareto front. The resulting solutions either have too low a ballistic coefficient leading to excessive cost, or exceed the overload limit and fail to meet mission requirements. Therefore, traditional methods cannot find the truly optimal trade-off solution under complex coupled constraints.

[0004] Furthermore, the design variables involved in high ballistic coefficient optimization span multiple disciplines, including aerodynamic shape (slenderness ratio, nose shape, wing parameters), structural parameters, and mass distribution. External envelope constraints involve the spatial geometric matching of the aircraft and launch device; overload constraints are strongly correlated with the flight angle of attack profile and structural stiffness; and stability constraints depend on the relative positions of the center of pressure and center of mass. The analytical models of each discipline are computationally expensive and interconnected. Incorporating all variables into a single-layer, single-objective framework leads to convergence difficulties, complex constraint handling, and the inability to obtain multi-objective trade-off solutions. Therefore, there is an urgent need to develop an efficient algorithm that can uniformly handle multi-disciplinary coupling and perform Pareto optimization among multiple competing objectives, in order to comprehensively optimize indicators such as high ballistic coefficient and volumetric efficiency while satisfying complex constraints such as loading, overload, and stability. Summary of the Invention

[0005] The purpose of this invention is to provide a multi-objective optimization method for high ballistic coefficients of aircraft that considers complex coupling constraints, in order to solve the problem that traditional single-objective weighted methods are prone to losing Pareto front equilibrium solutions.

[0006] To achieve the above objectives, the present invention employs the following technical solution: Define the design variable vector of the aircraft and determine the constraints, then construct a multi-objective optimization mathematical model; An improved multi-objective particle swarm optimization algorithm is used to solve the multi-objective optimization mathematical model. Through particle encoding and population initialization, fitness evaluation and constraint handling, non-dominated sorting and crowding distance calculation, selection of individual and global optimal solutions, velocity vector and position updates, external archive maintenance, and iterative convergence judgment, a Pareto optimal solution set is finally output. In the velocity vector and position updates, an adaptive linearly decreasing inertia weight is used. The global optimal solution is selected from the external archive to guide the population to explore sparse regions, and crowding distance is used to maintain the external archive to preserve the uniformity of the Pareto front distribution. The final design scheme is determined by selecting the particle that satisfies all constraints and has the best overall performance from the Pareto optimal solution set.

[0007] Furthermore, the design variable vector includes five design variables: aircraft aspect ratio, wing aspect ratio, total wing area, structural wall thickness coefficient, and center of mass position adjustment. The constraints include external envelope constraints, overload constraints, and stability constraints. The multi-objective optimization mathematical model aims to maximize the ballistic coefficient, minimize the peak value of the synthetic overload in the full ballistic normal direction, and maximize the volume ratio.

[0008] Furthermore, the constraint function of the external envelope constraint is: ,in This is the minimum clearance between the widest part of the aircraft and the inner wall of the launch tube. Allowable gap; The constraint function for the overload constraint is: ,in For permitted overload, The peak value of the combined overload along the entire ballistic normal. The constraint function for the stability constraint is: Among them, static stability , This is the core position. The location of the center of mass. The total length of the aircraft This represents the minimum allowable static stability.

[0009] Furthermore, the solution of the constraint functions and constraint conditions is achieved through an integrated aerodynamic characteristic analysis module, mass characteristic analysis module, and ballistic characteristic analysis module, which are automatically called in a chain, wherein: The aerodynamic characteristics analysis module estimates the drag coefficient, center of gravity position, and theoretical outer envelope volume of the entire aircraft through a surrogate model; the mass characteristics analysis module provides the takeoff mass, center of gravity position, and available propellant volume of the aircraft through a parameterized model of the aircraft; and the ballistic characteristics analysis module obtains the peak value of the synthetic overload in the normal direction of the entire ballistic trajectory through three-degree-of-freedom mass simulation.

[0010] Furthermore, the particle encoding and population initialization include: Real number encoding is used to map the position vector of each particle to a set of design variable values; the value range of each design variable is set, and the upper and lower limits of the value range of all design variables together constitute the design space; the design space is then normalized. During population initialization, the initial position of each particle is randomly generated within the normalized design space, and then the initial position is mapped back to the value range of each design variable to obtain the specific design variable value represented by the particle. The velocity vector of each particle is randomly initialized, and its velocity components are randomly selected within a preset multiple of the normalization interval length corresponding to each design variable.

[0011] Furthermore, the fitness evaluation and constraint processing includes: Calculate the ballistic coefficients for the design variables corresponding to each particle. , Peak normal overload of the entire ballistic trajectory Floor area ratio and the constraint function of the outer envelope constraint. Overload constraint function constraint functions for stability constraints Define the total constraint violation degree. :

[0012] in Indicates the first One constraint function; This indicates the operation of retrieving the maximum value; Transform the optimization objective into a minimization problem: make , , ,in , , These are the three target values ​​after transformation; a penalty is applied to the transformed target values: when At that time, the particles , , Each with a penalty factor Total constraint violation The product of these factors yields the target value after penalty treatment; the penalty factor... The value of is greater than 0; when hour, , , It remains unchanged.

[0013] Furthermore, the non-dominated sorting and crowding distance calculation includes: Particles with a total constraint violation degree of zero are selected as feasible solutions. Only feasible solutions are subjected to fast non-dominated sorting and classified into Pareto levels. Within the same Pareto level, the crowding distance of each particle is calculated. For each optimization objective, sort the corresponding objective values ​​in ascending order to determine the boundary particles and internal particles; where the crowding distance of the boundary particles is set to infinity; the... Crowding distance of internal particles According to the The maximum value of the target value after penalizing all particles on the optimization objective. and minimum value To confirm: when hour: ; in, and The first The internal particles in the first The target value after penalty treatment of two adjacent particles in the optimization objective; when At that time, the crowding distance .

[0014] Furthermore, the selection of the individual optimal solution and the global optimal solution includes: Each particle maintains an individual historical optimal solution. In each iteration, the dominance relationship between the target value corresponding to the new position of the particle and the target value corresponding to the individual historical optimal solution is compared to determine whether to update the individual historical optimal solution. Two non-dominated feasible solutions are randomly selected from external archives using the tournament method, and the one with the larger crowding distance is taken as the global optimal solution. The adaptive linearly decreasing inertia weight is represented as follows: ; in, For inertial weights, As the initial inertia weight, To terminate the inertia weight, For the maximum number of iterations, This represents the current iteration number; The particle velocity vector and position are updated by utilizing inertial weights and combining them with the particle velocity vector and position update formula.

[0015] Furthermore, the external file maintenance includes: storing all non-dominated feasible solutions in the population as new particles in the external file, removing particles in the external file that are dominated by the new particles, and if the size of the external file exceeds the preset maximum capacity, calculating the crowding distance of all particles and deleting the one with the smallest distance.

[0016] A terminal device includes a processor, a memory, and a computer program stored in the memory; when the processor executes the computer program, it implements the multi-objective optimization method for high ballistic coefficients of aircraft that considers complex coupling constraints.

[0017] A computer-readable storage medium storing a computer program; when executed by a processor, the computer program implements the multi-objective optimization method for high ballistic coefficients of aircraft considering complex coupling constraints.

[0018] Compared with the prior art, the present invention has the following technical features: The method of this invention can effectively coordinate the contradiction between high ballistic coefficient, low overload and high volumetric efficiency. Under the premise of strictly meeting the coupling constraints of loading, overload and stability, it presents designers with a complete Pareto optimal solution frontier. It is particularly suitable for small solid launch vehicles or launch vehicles with tight loading requirements, strict overload limits and static stability requirements, and supports the engineering trade-offs and decisions of the overall scheme of commercial launch vehicles. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating the method of the present invention. Detailed Implementation

[0020] This invention discloses a multi-objective optimization method for high ballistic coefficient aircraft considering complex coupling constraints. This method addresses the problem where external envelope constraints, overload constraints, and stability constraints are coupled and compete with objectives such as high ballistic coefficient and volumetric efficiency. It establishes a mathematical model with optimization objectives of maximizing ballistic coefficient, minimizing peak overload, and maximizing volumetric efficiency. The model adaptively adjusts the weight distribution of these objectives, using external envelope, static stability, and structural strength as hard constraints. It simultaneously optimizes the three competing objectives of ballistic coefficient, peak overload, and volumetric efficiency, and outputs a Pareto optimal solution set through a multi-objective particle swarm optimization (MOPSO) algorithm. This invention can efficiently balance multiple optimization objectives under complex coupling constraints, outputting the optimal overall design scheme that meets engineering requirements, and significantly improving the overall performance and economy of the aircraft. The specific steps of this invention are as follows: Step 1: Define the design variable vector of the aircraft and determine the constraints, and construct a multi-objective optimization mathematical model.

[0021] (1-1) Define design variables.

[0022] The design variable vector is The superscript T indicates transpose, and the same applies below; the design variable vector contains a total of five design variables: The aspect ratio of an aircraft, i.e., the length of the aircraft. Compared with reference diameter The ratio; For the aspect ratio of the wing surface; The total wing surface area is expressed in square meters. This is the structural wall thickness coefficient, which is a multiple of the reference wall thickness. It is the adjustment amount of the center of mass position, that is, the proportion of the adjustment amount of the center of mass position relative to the reference center of mass to the total length of the aircraft.

[0023] The value range of each of the above design variables is set based on the design experience or design requirements of the actual model.

[0024] (1-2) Set constraints.

[0025] Three types of hard constraints are defined and all are treated as The form; where the subscript These represent the external envelope constraint, overload constraint, and stability constraint, respectively, and their specific forms are as follows: The constraint function for the outer envelope constraint is: ,in This is the minimum clearance between the widest part of the aircraft and the inner wall of the launch tube. This is the allowable gap.

[0026] The constraint function for overload constraints is: ,in For permitted overload, The peak value of the combined overload in the normal direction of the entire ballistic trajectory.

[0027] The constraint function for stability constraints is: Among them, static stability , This is the core position. The location of the center of mass. The total length of the aircraft This represents the minimum allowable static stability.

[0028] (1-3) Multi-objective optimization mathematical model.

[0029] The optimization objectives of this scheme are to simultaneously maximize the ballistic coefficient, minimize the peak value of the combined overload in the full ballistic normal direction, and maximize the volumetric efficiency. These three objectives are non-linearly competitive. The specific mathematical model for the multi-objective optimization is as follows: Maximize ballistic coefficient: ,in For ballistic coefficients, For the takeoff mass of the aircraft, The drag coefficient of the entire aircraft. For reference area, the maximum cross-sectional area of ​​the aircraft is taken.

[0030] Minimize the peak value of the synthesized overload in the entire ballistic normal direction: .

[0031] Maximize floor area ratio: ,in For floor area ratio, The volume of available propellant. This refers to the theoretical outer envelope volume of the aircraft.

[0032] The calculation of the above constraint functions and constraints depends on the aerodynamic characteristic analysis module, mass characteristic analysis module, and ballistic characteristic analysis module. Specifically: The calculation requires the aircraft's takeoff mass. (Provided by the mass characteristic analysis module), overall aircraft drag coefficient (Provided by the aerodynamic characteristics analysis module) and reference area For input; The trajectory characteristics analysis module outputs the results directly through ascent phase trajectory simulation. The calculation requires the available propellant volume (Provided by the mass characteristic analysis module) and the theoretical outer envelope volume of the aircraft. (Provided by the aerodynamic characteristics analysis module) as input.

[0033] Regarding constraints: external envelope constraints middle Provided by the aerodynamic characteristics analysis module; overload constraints middle Provided by the ballistic characteristics analysis module; stability constraints Static stability The calculation requires the position of the pressure core. (Provided by the aerodynamic characteristics analysis module) and center of mass position (The input is the quality characteristic analysis module).

[0034] The aerodynamic characteristic analysis module rapidly estimates performance using surrogate models based on engineering accuracy methods (such as Kriging models, support vector regression models, or radial basis function networks). , and The mass characteristic analysis module provides the following results through the parametric model of the aircraft: , and The ballistic characteristics analysis module obtains data through three-degree-of-freedom mass simulation. .

[0035] In this scheme, the aerodynamic characteristic analysis module, mass characteristic analysis module, and ballistic characteristic analysis module have been integrated into an automatic call chain, and the analysis time for a single particle is less than 0.3 s.

[0036] Step two involves solving the multi-objective optimization mathematical model using an improved multi-objective particle swarm optimization algorithm. This involves particle encoding and population initialization, fitness evaluation and constraint handling, non-dominated sorting and crowding distance calculation, selection of individual optimal solutions and global optimal solutions, velocity vector and position updates, external archive maintenance, and iterative convergence judgment. The final output is a Pareto optimal solution set. In the velocity vector and position updates, an adaptive linearly decreasing inertia weight is used. The global optimal solution is selected from the external archive to guide the population to explore sparse regions, and the crowding distance is used to maintain the external archive to keep the distribution uniformity of the Pareto front.

[0037] This step uses an improved multi-objective particle swarm optimization algorithm to solve the multi-objective optimization mathematical model; compared with the standard multi-objective particle swarm optimization algorithm, this algorithm uses adaptive linearly decreasing inertia weights.

[0038] (2-1) Particle encoding and population initialization.

[0039] Real-number encoding is used to map the position vector of each particle to a set of design variable values. First, the value range of each design variable in step one is set, and the upper and lower limits of the value range of all design variables constitute the design space. In order to eliminate the influence of the differences in the dimensions and scales of each design variable on the optimization algorithm, the design space is normalized: the value range of each design variable is uniformly mapped to the interval [0,1] to form the normalized design space.

[0040] During population initialization, populations are randomly generated within the normalized design space. There are several points, each representing the initial position of a particle. By mapping the particle's position coordinates back to the value range of each design variable, we can obtain a set of specific design variable values ​​represented by the particle.

[0041] The velocity vector of each particle is randomly initialized, and its velocity components are randomly selected within ±0.1 times the length of the normalized interval (the normalized result of the upper and lower limits of the value range) corresponding to each design variable. The population size is denoted as... External archives Initially an empty set, it is used to store non-dominated feasible solutions generated during the iteration process.

[0042] (2-2) Fitness assessment and constraint treatment.

[0043] For each particle, the aerodynamic characteristic analysis module, mass characteristic analysis module, and ballistic characteristic analysis module are invoked to calculate the ballistic coefficients corresponding to the design variable values ​​of the particle. , Peak normal overload of the entire ballistic trajectory Floor area ratio and the constraint functions corresponding to each constraint condition , and Define the total constraint violation degree. : ; because and To maximize the problem, and To minimize the problem, and since the dominance relationship comparison in the multi-objective particle swarm optimization algorithm needs to be unified based on minimization, the three optimization objectives are uniformly transformed into a minimization problem: make , , ,in , , These are the three target values ​​after transformation; a penalty is applied to the transformed target values: when At that time, , , Each with a penalty factor Total constraint violation The product; when hour, , , The target values ​​remain unchanged; the target values ​​after penalty processing are denoted as follows: , , ,Right now: ; in, This is a preset penalty factor, and its value is greater than 0.

[0044] when At that time, the particle's , , All because of the addition As the value increases, in subsequent comparisons of dominance relations based on minimization, the particle will arbitrarily satisfy all three types of hard constraints. Dominated by particles of ); when At that time, the target value of the particle remains unchanged, that is , , They are respectively equal to , , Directly involved in the comparison of dominance relationships.

[0045] (2-3) Non-dominated sorting and crowding distance calculation.

[0046] After penalizing all particles in step (2-2), the total constraint violation rate is selected. The particles, which are the feasible solutions that satisfy all three types of hard constraints; only for these feasible solutions (i.e. The particles are subjected to fast non-dominated sorting and Pareto ordering.

[0047] Within the same Pareto level, to maintain the distribution of the solution set, the crowding distance of each particle is calculated; for each optimization objective, the particles are sorted in ascending order according to their corresponding objective values ​​to determine the boundary particles (particles at the beginning and end of the sorted sequence) and the internal particles (particles between boundary particles); the crowding distance of the boundary particles is set to infinity, and the crowding distance of the internal particles is determined according to the... The maximum value of the target value after penalizing all particles on the optimization objective. and minimum value To confirm: when At that time, the first Crowding distance of internal particles This is the sum of the normalized differences between the two adjacent particles before and after this internal particle on the three optimization objectives, i.e.: ; in, and The first The internal particles in the first The target value after penalty treatment for two adjacent particles in the optimization objective is such that the larger the crowding distance, the sparser the distribution of the particles on the Pareto front.

[0048] when At that time, it is considered that the first Each internal particle has no distinguishing effect on the particle distribution; its corresponding crowding distance .

[0049] (2-4) Selection of individual optimal solution and global optimal solution.

[0050] Each particle maintains an individual historical optimal position during the search process, denoted as the individual historical optimal solution. , which represents the position where the particle has so far achieved the best performance on the target value after penalty treatment.

[0051] In each iteration, after the particle moves to a new position, the target value after penalty processing corresponding to that new position is calculated. , , Compare the target value corresponding to the new position with the individual historical best solution of the particle. Compare the dominance relationships of the corresponding target values: if the new position dominates... Then the particle's Update to this new location; if If it dominates a new position, then the particle's Keep it unchanged; if the new position is the same as If they do not dominate each other, then they will be in a new position and One is randomly selected from the middle as the updated particle. .

[0052] Global optimal solution From external archives The tournament method is used for selection: two non-dominated feasible solutions from two external archives are randomly selected, and the one with the larger crowding distance is chosen. This guides the population to explore sparsely distributed areas on the Pareto front.

[0053] Individual historical optimal solution Update rule: If the new position is within the target value after penalty processing , , Dominate If, then replace; if If a player takes control of a new position, that position remains; otherwise, one position is randomly retained.

[0054] Global optimal solution From external archives The tournament method is used for selection: Two non-dominated solutions from two external archives are randomly selected, and the one with the larger crowding distance is chosen. This guides the population to converge toward a sparse, real Pareto frontier.

[0055] (2-5) Velocity vector and position update.

[0056] Adaptive linearly decreasing inertial weights and standard particle swarm velocity-displacement formulas are used; inertial weights Decreases linearly with the number of iterations: ; in, As the initial inertia weight, To terminate the inertia weight, For the maximum number of iterations, This represents the current iteration number.

[0057] The formula for updating the particle velocity vector and position is: ; ; in, and The first The particle in the first The velocity vector and position of the vector. , As a learning factor, , The values ​​are uniformly random numbers within the range [0,1]. To prevent out-of-bounds operations, the velocity components are limited, and boundary absorbing processing is applied to out-of-bounds locations.

[0058] (2-6) External file maintenance.

[0059] During the external archive maintenance process, each generation will include all non-dominated feasible solutions (Pareto level 1 and...) in the population. The particles were stored as new particles in the external archive. And remove particles from external archives that are dominated by the new particles; if the size of the external archive exceeds the maximum capacity. Then, calculate the crowding distance of all particles and remove the one with the smallest distance, so as to keep the Pareto front distribution uniform and the external archive size stable.

[0060] (2-7) Iterative convergence judgment.

[0061] Repeat steps (2-2) to (2-6) until the preset maximum number of iterations is reached, and finally output the external file. This is the Pareto optimal solution set.

[0062] Step 3: Select the particle that satisfies all constraints and has the best overall performance from the Pareto optimal solution set, thereby determining the final design scheme.

[0063] From the Pareto optimal solution set, particles that simultaneously satisfy three types of hard constraints—external envelope constraint, overload constraint, and stability constraint—are selected. Then, from these particles, the particle with the best overall performance is chosen. Specifically: The particle that achieves balanced improvement in all three optimization objectives (as evaluated by experts and designers) is selected, and its corresponding design variable value is taken as the final design scheme. See the comprehensive equilibrium solution in Table 2 of the example.

[0064] Example

[0065] This embodiment uses the overall parameter optimization of a small commercial solid-propellant launch vehicle as an example for illustration. The spacecraft employs a cold launch method using a launch tube, with an inner diameter of [missing information]. The main feature of the baseline scheme is that the diameter of the cylindrical section of the aircraft is... (i.e., reference diameter) The length-to-slenderness ratio of the aircraft is... The wing surface is a flat wing with a cross-shaped layout, and the total wing surface area is... wing aspect ratio The structural wall thickness coefficient is centroid position adjustment amount The mission requires a minimum clearance between the widest point of the spacecraft and the inner wall of the launch tube. Not less than the allowable gap The peak value of the combined normal overload in the entire ballistic trajectory does not exceed 10g, and the static stability is... The minimum requirement is 5%. Although the baseline scheme can initially meet the hard constraints, its ballistic coefficient is low (approximately 5200 kg / m²) and its volume ratio is only about 0.55, leaving considerable room for improvement in carrying efficiency and economy.

[0066] In this embodiment, the design variable vector is constructed as follows: Table 1: Value range of the five design variables.

[0067]

[0068] When implementing the multi-objective particle swarm optimization algorithm, the population size is... External archives Maximum capacity Punishment factor Initial inertia weights Termination of inertial weights Learning factor , Uniformly distributed random numbers within [0,1]; Maximum number of iterations After 200 iterations, a well-distributed three-dimensional Pareto front was obtained.

[0069] This embodiment yielded a well-distributed three-dimensional Pareto front. Pursuing a higher ballistic coefficient inevitably leads to an increase in the peak value of the synthetic overload in the full ballistic normal direction, while excessive overload suppression causes the ballistic coefficient to drop rapidly. The volumetric ratio target exhibits a high-middle-low characteristic on the front, but the overall fluctuation range is relatively small. Three typical schemes are extracted and listed in Table 2.

[0070] Table 2: Three typical schemes obtained in the embodiments.

[0071]

[0072] The comprehensive equilibrium solution improves the ballistic coefficient by 44.6% compared to the baseline scheme, with a safety margin of 8.5g (g is the acceleration due to gravity) in the full ballistic normal direction, an increase in volumetric efficiency from 0.55 to 0.64, a minimum clearance of 6.2mm, and a static stability of 5.7%. It fully meets the hard constraints and achieves multi-objective equilibrium optimization; therefore, this comprehensive equilibrium solution is selected as the final design scheme.

[0073] To illustrate the superiority of this invention, the traditional weighted summation method is used to optimize the problem of this invention, employing linear weighting. For a single objective, the weights were selected after multiple trials. The constraints are handled using the penalty function method; under the same computational resources, the optimal solution obtained is: , , , , Its performance includes: ballistic coefficient Peak value of synthetic overload in the full ballistic normal direction Floor area ratio The minimum gap is only Static stability Therefore, it is evident that the optimal solution obtained by the traditional weighted summation method not only fails to meet the hard constraints in terms of minimum gap and static stability, making it unsuitable for direct application, but also results in a peak value of synthetic overload in the full ballistic normal direction that is extremely close to the limit, and a ballistic coefficient that is significantly lower than the Pareto solution of this invention. Even with weight adjustments, the traditional weighted summation method struggles to find an equilibrium solution that satisfies all hard constraints among multiple conflicting targets, thus verifying the significant advantages of the Pareto optimization method based on multi-target particle swarm optimization in handling complex coupled constraints.

[0074] The method of this invention can effectively coordinate the contradiction between high ballistic coefficient, low overload and high volumetric efficiency. Under the premise of strictly meeting the coupling constraints of loading, overload and stability, it presents designers with a complete Pareto optimal solution frontier, supporting the engineering trade-offs and decisions of the overall scheme of commercial launch vehicles.

[0075] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A multi-objective optimization method for high ballistic coefficients of aircraft considering complex coupling constraints, characterized in that, include: Define the design variable vector of the aircraft and determine the constraints, then construct a multi-objective optimization mathematical model; An improved multi-objective particle swarm optimization algorithm is used to solve the multi-objective optimization mathematical model. Through particle encoding and population initialization, fitness evaluation and constraint handling, non-dominated sorting and crowding distance calculation, selection of individual and global optimal solutions, velocity vector and position updates, external archive maintenance, and iterative convergence judgment, a Pareto optimal solution set is finally output. In the velocity vector and position updates, an adaptive linearly decreasing inertia weight is used. The global optimal solution is selected from the external archive to guide the population to explore sparse regions, and crowding distance is used to maintain the external archive to preserve the uniformity of the Pareto front distribution. The final design scheme is determined by selecting the particle that satisfies all constraints and has the best overall performance from the Pareto optimal solution set.

2. The multi-objective optimization method for high ballistic coefficient of aircraft considering complex coupling constraints as described in claim 1, characterized in that, The design variable vector includes five design variables: aircraft aspect ratio, wing aspect ratio, total wing area, structural wall thickness coefficient, and center of mass position adjustment. The constraints include external envelope constraints, overload constraints, and stability constraints. The multi-objective optimization mathematical model aims to maximize the ballistic coefficient, minimize the peak value of the synthetic overload in the full ballistic normal direction, and maximize the volume ratio.

3. The multi-objective optimization method for high ballistic coefficients of aircraft considering complex coupling constraints as described in claim 2, characterized in that, The constraint function of the external envelope constraint is: ,in This is the minimum clearance between the widest part of the aircraft and the inner wall of the launch tube. Allowable gap; The constraint function for the overload constraint is: ,in For permitted overload, The peak value of the combined overload along the entire ballistic normal. The constraint function of the stability constraint is: Among them, static stability , This is the core position. The location of the center of mass. The total length of the aircraft This represents the minimum allowable static stability.

4. The multi-objective optimization method for high ballistic coefficients of aircraft considering complex coupling constraints according to claim 3, characterized in that, The solution of the constraint functions and constraint conditions is achieved through an integrated aerodynamic characteristic analysis module, mass characteristic analysis module, and ballistic characteristic analysis module, which are automatically called in a chain. The aerodynamic characteristics analysis module estimates the drag coefficient, center of gravity position, and theoretical outer envelope volume of the entire aircraft through a surrogate model; the mass characteristics analysis module provides the takeoff mass, center of gravity position, and available propellant volume of the aircraft through a parameterized model of the aircraft; and the ballistic characteristics analysis module obtains the peak value of the synthetic overload in the normal direction of the entire ballistic trajectory through three-degree-of-freedom mass simulation.

5. The multi-objective optimization method for high ballistic coefficient of aircraft considering complex coupling constraints according to claim 1, characterized in that, The particle encoding and population initialization include: Real number encoding is used to map the position vector of each particle to a set of design variable values; the value range of each design variable is set, and the upper and lower limits of the value range of all design variables together constitute the design space; the design space is then normalized. During population initialization, the initial position of each particle is randomly generated within the normalized design space, and then the initial position is mapped back to the value range of each design variable to obtain the specific design variable value represented by the particle. The velocity vector of each particle is randomly initialized, and its velocity components are randomly selected within a preset multiple of the normalization interval length corresponding to each design variable.

6. The multi-objective optimization method for high ballistic coefficient of aircraft considering complex coupling constraints according to claim 2, characterized in that, The fitness evaluation and constraint processing include: Calculate the ballistic coefficients for the design variables corresponding to each particle. , peak value of combined overload in the normal direction of the entire ballistic trajectory Floor area ratio and the constraint function of the outer envelope constraint. Overload constraint function constraint functions for stability constraints Define the total constraint violation degree. : in Indicates the first One constraint function; This indicates the operation of retrieving the maximum value; Transform the optimization objective into a minimization problem: make , , ,in , , These are the three target values ​​after transformation; a penalty is applied to the transformed target values: when At that time, the particles , , Each with a penalty factor Total constraint violation The product of these factors yields the target value after penalty treatment; the penalty factor... The value of is greater than 0; when hour, , , It remains unchanged.

7. The multi-objective optimization method for high ballistic coefficient of aircraft considering complex coupling constraints according to claim 6, characterized in that, The non-dominated sorting and crowd distance calculation includes: Particles with a total constraint violation degree of zero are selected as feasible solutions. Only feasible solutions are subjected to fast non-dominated sorting and classified into Pareto levels. Within the same Pareto level, the crowding distance of each particle is calculated. For each optimization objective, sort the corresponding objective values ​​in ascending order to determine the boundary particles and internal particles; where the crowding distance of the boundary particles is set to infinity; the... Crowding distance of internal particles According to the The maximum value of the target value after penalizing all particles on the optimization objective. and minimum value To confirm: when hour: ； in, and The first The internal particles in the first The target value after penalty treatment of two adjacent particles in the optimization objective; when At that time, the crowding distance .

8. The multi-objective optimization method for high ballistic coefficients of aircraft considering complex coupling constraints according to claim 1, characterized in that, The selection of the individual optimal solution and the global optimal solution includes: Each particle maintains an individual historical optimal solution. In each iteration, the dominance relationship between the target value corresponding to the new position of the particle and the target value corresponding to the individual historical optimal solution is compared to determine whether to update the individual historical optimal solution. Two non-dominated feasible solutions are randomly selected from external archives using the tournament method, and the one with the larger crowding distance is taken as the global optimal solution. The adaptive linearly decreasing inertia weight is represented as follows: ； in, For inertial weights, As the initial inertia weight, To terminate the inertia weight, For the maximum number of iterations, This represents the current iteration number; The particle velocity vector and position are updated by utilizing inertial weights and combining them with the particle velocity vector and position update formula.

9. The multi-objective optimization method for high ballistic coefficients of aircraft considering complex coupling constraints according to claim 7, characterized in that, The external file maintenance includes: storing all non-dominated feasible solutions in the population as new particles in the external file, removing particles in the external file that are dominated by the new particles, and if the size of the external file exceeds the preset maximum capacity, calculating the crowding distance of all particles and deleting the one with the smallest distance.

10. A terminal device, comprising a processor, a memory, and a computer program stored in the memory; when the processor executes the computer program, it implements the multi-objective optimization method for high ballistic coefficients of an aircraft considering complex coupling constraints as described in any one of claims 1-9.

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