A lightweight design method for wing structures based on machine learning

Abstract

The present invention discloses a lightweight design method for a wing structure based on machine learning, comprising: (1) importing loads and boundary constraints to obtain weight and stiffness indicators of the wing structure, and deriving a corresponding mathematical optimization model; (2) constructing an optimized population considering space filling characteristics; (3) evaluating the feasibility status of the population, and designing a subpopulation evolution operation to generate candidate individuals; (4) constructing a global or local radial basis machine learning prediction model based on the population update rate; (5) designing two screening strategies according to the feasibility of the parent individual; (6) evaluating the selected best candidate individual using a wing structure stiffness and weight simulation model, updating the population and going to step (3) until the optimized structure meets the requirements. The present invention dynamically allocates evolutionary strategies, adaptively models the prediction model, and reasonably selects the screening strategy according to the information fed back during the optimization process, thereby improving the optimization efficiency for the lightweight design problem of the wing structure.

Description

Technical Field

[0001] The present invention relates to the fields of general artificial intelligence technology and swarm intelligence, and in particular to a lightweight design method for a wing structure based on machine learning. Background Art

[0002] The lightweight design of wing structures is a key technology in the aerospace field, which aims to reduce the weight of aircraft, thereby improving their fuel efficiency, range and load capacity, while maintaining their structural strength and performance. Commonly used evolutionary algorithms include genetic algorithms, particle swarm algorithms, etc. Although these algorithms have very good global exploration capabilities, they usually require a lot of computing resources and time for population evolution and fitness evaluation, and may require multiple generations of evolution to approach the global optimal solution. The lightweight design of wing structures often requires time-consuming simulation calculations, which makes traditional evolutionary algorithms not efficient enough in the lightweight design of wing structures. Summary of the invention

[0003] In view of the technical problem that traditional evolutionary algorithms are not efficient enough in the lightweight design of wing structures, the present invention proposes a lightweight design method for wing structures based on machine learning. Based on the characteristics of the time-consuming stiffness simulation model and the lightweight design requirements involved in the optimization design of wing structures, a machine learning design method that fully utilizes the feedback information in the optimization process is studied and designed. First, compared with traditional evolutionary algorithms, machine learning design methods can learn and summarize complex patterns and optimization trends in structural lightweight design from a large amount of historical design data and simulation results through a data-driven approach. To this end, the present invention guides the entire structural optimization design process by constructing a machine learning model for the stiffness simulation model and the complex geometric model of the wing structure. Part of the time-consuming simulation calculations are replaced by the machine learning model, which can give full play to the global exploration ability of the evolutionary algorithm within a limited design cycle. Secondly, considering that most algorithms currently ignore feedback information during the optimization process, including population feasibility rate, population update rate and various individual information, and the selection of evolutionary strategy, the modeling method of the prediction model, and the reasonable use of the screening strategy have a significant impact on the performance of the algorithm, for this reason, the present invention considers making full use of population state information and individual information in the algorithm optimization process to dynamically allocate evolutionary strategies, adaptively model prediction models, and select appropriate screening strategies, and apply them to the lightweight design of wing structures. In short, the present invention not only has stronger robustness, but also improves the optimization efficiency for the lightweight problem of wing structures.

[0004] To achieve the above object, the present invention provides a lightweight design method for a wing structure based on machine learning, which is applicable to the weight optimization problem of a wing structure, and includes:

[0005] Step (1) constructing a simulation model of the stiffness and weight of the wing structure in Abaqus according to the load and boundary constraints, and deriving a mathematical optimization model for the lightweight design problem of the wing structure with the center coordinates and thickness of each member of the wing structure as the optimization design parameters, the weight of the wing structure as the optimization target, and the stiffness of the wing structure as the optimization constraint;

[0006] Step (2) according to the assembly requirements of the wing-shaped structure, the value range of the center coordinates and thickness optimization design parameters of each member of the wing-shaped structure is obtained, and a design space composed of the center coordinates and thickness optimization design parameters of each member of the wing-shaped structure is constructed, and an optimization population is generated within the design space considering the space filling characteristics between individuals, and the stiffness and weight simulation model of the wing-shaped structure is used in Abaqus to respectively evaluate the stiffness and weight value of each individual vector in the optimization population, and all the individual vectors of the population and their stiffness and weight values ​​are saved in a database;

[0007] Step (3) dividing the optimized population into infeasible, semi-feasible or fully feasible states according to population feasibility, and dividing sub-populations according to individual information, and designing sub-population evolution operations within the design space composed of the center coordinates of each member of the wing-shaped structure and the thickness optimization design parameters to generate multiple candidate offspring individual vectors composed of the center coordinates of each member of the wing-shaped structure and the thickness optimization design parameters;

[0008] Step (4) calculating the update rate of the optimized population in the previous generation, and comparing the set update rate threshold with the calculated update rate to construct a global or local radial basis machine learning prediction model;

[0009] Step (5) Design feasibility rules and improved e The mechanism of using the constraint method and obtaining the best candidate individual vector consisting of the center coordinates and thickness optimization design parameters of each member of the wing structure through the screening strategy;

[0010] Step (6) uses the wing structure stiffness and weight simulation model to evaluate the best candidate individual vector, uses the feasibility rule to update the optimization population and other iterative information, and determines whether the wing structure corresponding to the current optimal individual vector meets the weight and stiffness requirements. If so, output the wing structure corresponding to the current optimal individual vector; otherwise, go to step (3) until the wing structure corresponding to the current optimal individual vector meets the weight and stiffness requirements.

[0011] Furthermore, the mathematical optimization model of the lightweight design problem of the wing structure in step (1) is specifically expressed as follows:

[0012] ,

[0013] In the above formula, is the weight of the wing structure, is the stiffness of the wing structure, M is the optimized design parameter vector in the lightweight design problem of the wing structure, M 1 , M 2 as well as M n is the optimized design parameter vector in the lightweight design problem of wing structure, T represents the transpose, are the center coordinates and thickness of each member of the wing structure, the number of optimized design parameters, f and t are the Neumann boundary Γ t The body force density on the surface and the preset surface traction, is the Heaviside function, is the topological description function of the wing structure, u is the displacement field, V ad is the permissible set of virtual displacement vectors v, is the wing structure material density, is the random variable of the wing structure volume, is the wing structure displacement random variable, The center coordinates and thickness of each member of the wing structure are the upper and lower limits of the optimization design parameters. is the lower limit of the stiffness of the wing structure, Find is to find a set of center coordinates and thickness optimization design parameters of each member of the wing structure that meet the weight and stiffness requirements, Min is to minimize the weight of the wing structure, and St is the constraint to be satisfied.

[0014] Furthermore, the specific steps of step (2) are as follows:

[0015] The first step is to determine the number of individual vectors that need to be sampled NP As well as the value range of the center coordinates and thickness optimization design parameters of each member of the wing-shaped structure, and construct a design space composed of the center coordinates and thickness optimization design parameters of each member of the wing-shaped structure;

[0016] The second step is to divide the value range of the center coordinates and thickness optimization design parameters of each member of the wing structure into NP non-overlapping intervals, and the center coordinates and thickness optimization design parameters of each member of the wing structure are NP The intervals are randomly arranged, and the center coordinates and thickness optimization design parameters of each member of the wing structure are NP A sampling point is randomly generated in each interval, and the random sampling points of the center coordinates and thickness optimization design parameters of each member of the wing structure are combined to form NP indivual n Sampling points in dimensional space;

[0017] The third step is to calculate the Euclidean distance matrix between all sampling points;

[0018] The fourth step is to locate the minimum distance point pair in the current Euclidean distance matrix and increase the minimum distance between sampling points by exchanging sampling point pairs in different dimensions;

[0019] Step 5: Repeat step 3 and step 4 until the set iteration limit is reached to obtain the optimized population.

[0020] In the sixth step, the wing structure stiffness and weight simulation model is used in Abaqus to evaluate the wing structure stiffness and weight value of each individual vector in the optimized population, and all population individual vectors and their stiffness and weight data are saved in the database.

[0021] Furthermore, the specific steps of step (3) are as follows:

[0022] According to the feasibility of the individuals in the population, the optimized population is divided into infeasible, semi-feasible or fully feasible states. When all individuals in the optimized population are feasible individuals, the optimized population is in a fully feasible state; when only some individuals in the optimized population are feasible individuals, the optimized population is in a semi-feasible state; when all individuals in the optimized population are infeasible individuals, the optimized population is in an infeasible state; infeasible individuals are individuals that violate the stiffness constraints of the wing structure, and feasible individuals are individuals that satisfy the stiffness constraints of the wing structure;

[0023] When the optimized population is in a completely feasible state, the individuals successfully updated in the previous generation are divided into subpopulations U , and the individuals that failed to update successfully in the previous generation are divided into subpopulations Q ; Subpopulation U Evolutionary operations that emphasize development are performed, subpopulations Q Evolutionary operations that emphasize exploration were performed;

[0024] When the optimized population is in a semi-feasible state, feasible individuals are divided into subpopulations U The remaining individuals are sorted using a non-dominated sorting with wing structure weight, wing structure stiffness constraint violation value and nearest neighbor distance as three objectives. The individuals in the first half of the sorting are divided into sub-populations. U , the individuals ranked in the second half are classified into subpopulations Q ; Subpopulation U Evolutionary operations that emphasize development are performed, subpopulations Q Evolutionary operations that emphasize exploration were performed;

[0025] When the state of the optimized population is infeasible, the optimized population is sorted based on the wing structure stiffness constraint violation value, and the individuals in the first half of the sorting are divided into sub-populations Q , the individuals ranked in the second half are classified into the subpopulation W ; SubpopulationQ Evolutionary operations that emphasize development are performed, subpopulations W Evolutionary operations that emphasize exploration were performed;

[0026] Among them, the evolutionary operations that focus on development are DE / rand / 1, DE / rand / 2, and DE / current-to-rand / 1, and the evolutionary operations that focus on exploration are DE / rand / 1, DE / rand / 2, and DE / random-to-random / 1. Each mutation operation generates the same number of offspring individual vectors. The expressions of the four mutation operations are as follows:

[0027] DE / rand / 1: ,

[0028] DE / rand / 2: ,

[0029] DE / random-to-random / 1: ,

[0030] DE / current-to-rand / 1: ,

[0031] In the above formula, DE stands for differential evolution, rand and random represent random individuals, current represents the current parent individual, to represents the direction of mutation, 1 and 2 represent the number of random perturbations, and x rand 、x r1 、x r2 、x r3 、x r4 and x r5 are 6 individual vectors randomly selected from the parent generation, consisting of the center coordinates of each member of the wing structure and the thickness optimization design parameters, x cur is the parent individual vector composed of the center coordinates of each member of the wing structure and the thickness optimization design parameters, F , F 1 and F 2 is the scaling factor that determines the amplitude of the mutation, and I is the individual vector obtained after the mutation;

[0032] The wing structure stiffness constraint violation value can be calculated by the following formula:

[0033] ,

[0034] In the above formula, c is an individual vector composed of the center coordinates of each member of the wing structure and the thickness optimization design parameters. S ( c)yes c The corresponding wing structure stiffness constraint violation value, max is the maximum output value, s ( c )yes c The wing structure stiffness constraint value obtained by evaluating the wing structure stiffness and weight simulation model, is the lower limit of the wing structure stiffness;

[0035] The nearest neighbor distance can be calculated as follows:

[0036] ,

[0037] In the above formula, d is the nearest neighbor distance, and are two individual vectors in the design space composed of the center coordinates of each member of the wing structure and the thickness optimization design parameters. and Representation vector and vector In the The coordinates on the dimension, n is the dimension of the individual vector, q j Is removed from the database p Other than j individual vectors, min is the minimum output value.

[0038] Furthermore, the specific steps of step (4) are as follows:

[0039] The first step is to calculate the update rate of the optimized population in the previous generation. The mathematical expression is as follows:

[0040] ,

[0041] In the above formula, UR is to optimize the population's update rate in the previous generation, NS is the number of wing structure individual vectors successfully updated in the previous generation, NP is the size of the optimized population;

[0042] In the second step, when the calculated update rate is less than the set update rate threshold of 0.1, the stiffness and weight values ​​of all population individual vectors evaluated in the current database are used to build a global radial basis function machine learning prediction model; when the calculated update rate is greater than the set update rate threshold of 0.1, the parent individual is found in the database adjacent to it. K individual vectors, and through the K The stiffness and weight values ​​of each individual vector are used to construct a local radial basis function machine learning prediction model;

[0043] For stiffness and weight values, the mathematical expression for constructing a radial basis function machine learning prediction model with a first-order polynomial is:

[0044] ,

[0045] In the above formula, It is a radial basis function machine learning prediction model constructed based on the stiffness and weight values ​​of the wing structure. For the Wing structure individual vector The corresponding weight parameter, Indicates Wing structure individual vector The basis function of It is expressed as a first-order polynomial, and x represents the offspring individual vector composed of the center coordinates of each member of the wing structure and the thickness optimization design parameters.

[0046] Furthermore, the specific steps of step (5) are as follows:

[0047] The first step is to use the constructed radial basis machine learning prediction model to predict the stiffness and weight values ​​of the offspring individual vectors;

[0048] The second step is to determine the feasibility of the individuals in the parent population. The individuals that meet the wing structure stiffness constraint are feasible individuals, and the individuals that violate the wing structure stiffness constraint are infeasible individuals.

[0049] The third step is to apply the feasibility rule to the offspring of feasible individuals in the parent population, and to apply the improved e Constraint method, select the best candidate individual vector composed of the center coordinates of each member of the wing structure and the thickness optimization design parameters;

[0050] based on e The constraint method determines that the formula for individual vector x is better than individual vector y is as follows:

[0051] ,

[0052] In the above formula, x and y are the child individual vectors composed of the center coordinates of each member of the wing structure and the thickness optimization design parameters. it is the current iteration number, f (x) is the wing structure weight of the offspring individual vector x predicted by the radial basis machine learning prediction model, f (y) is the wing structure weight of the offspring individual vector y predicted by the radial basis machine learning prediction model, G (x) is the wing structure stiffness constraint violation value of the offspring individual vector x predicted by the radial basis machine learning prediction model, G(y) is the wing structure stiffness constraint violation value of the offspring individual vector y predicted by the radial basis machine learning prediction model, e ( it ) is the number of iterations equal to it The relaxed constraint violation value when ;

[0053] Improved e The constraint method value formula is as follows:

[0054] ,

[0055] In the above formula, represents the relaxation constraint violation value calculation function, The initial value is , G (x θ ) represents the ranking of the wing structure stiffness constraint violation values ​​in ascending order i The wing structure stiffness constraint violation value of individual vectors, it is the current iteration number, IT It is a setting update e The final number of iterations of the value, tf Yes e A constant that plays a key role in the downward trend of its value.

[0056] Furthermore, in step (6), the wing structure weight and stiffness simulation model is used to evaluate the best candidate individual vector, and the feasibility rule is used to update the optimized population and other iterative information. The specific steps are as follows:

[0057] The weight and stiffness values ​​of the best candidate individual vectors are evaluated using the wing structure weight and stiffness simulation model in Abaqus;

[0058] The wing structure stiffness and weight values ​​of the best candidate evaluated are stored in a database;

[0059] Update and optimize the population based on feasibility rules;

[0060] Update the current number of iterations and the optimal individual consisting of the center coordinates of each member of the wing structure and the thickness optimization design parameters to prepare for the next generation.

[0061] In summary, compared with the prior art, the above technical solution conceived by the present invention provides a lightweight design method for wing structures based on machine learning, which mainly has the following beneficial effects:

[0062] 1. Considering the space filling characteristics to initialize the population individuals, it ensures the uniformity of individual distribution and lays a good foundation for subsequent optimization;

[0063] 2. By evaluating the feasibility of the population and dividing sub-populations according to individual information, and designing sub-population evolution strategies, dynamic resource allocation is achieved while keeping computing resources unchanged, balancing the development and exploration of sub-population areas, and improving the robustness of the overall optimization of the algorithm;

[0064] 3. Using the population update rate to dynamically build a global or local radial basis function machine learning prediction model, effectively improving the prediction ability of the prediction model and improving the efficiency of lightweight design of wing structures;

[0065] 4. Feasibility rules and improvements based on individual feasibility e The constraint method is used appropriately; in addition, the improved e Constraint methods are easier to control e The downward trend of the market will not converge prematurely;

[0066] 5. The present invention can perform complex optimization on time-consuming simulation models, thereby improving optimization efficiency. It is suitable for design optimization of lightweight wing structures and is conducive to popularization and application. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 A simplified flow chart of a wing structure lightweight design method based on machine learning provided by the present invention. DETAILED DESCRIPTION

[0068] In order to make the purpose, technical scheme and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0069] See also Figure 1 The present invention provides a wing structure lightweight design method based on machine learning, which is applicable to the wing structure weight optimization problem. Specifically, the method mainly includes steps (1) to (6).

[0070] Step (1) According to the load and boundary constraints, a simulation model of the stiffness and weight of the wing structure is constructed in Abaqus, and a mathematical optimization model of the lightweight design problem of the wing structure is derived with the center coordinates and thickness of each member of the wing structure as the optimization design parameters, the weight of the wing structure as the optimization target, and the stiffness of the wing structure as the optimization constraint.

[0071] The mathematical optimization model of the lightweight design problem of the wing structure in step (1) is specifically expressed as follows:

[0072] ,

[0073] In the above formula, is the weight of the wing structure, is the stiffness of the wing structure, M is the optimized design parameter vector in the lightweight design problem of the wing structure, M 1 , M 2 as well as M n is the optimized design parameter vector in the lightweight design problem of wing structure, T represents the transpose, are the center coordinates and thickness of each member of the wing structure, the number of optimized design parameters, f and t are the Neumann boundary Γ t The body force density on the surface and the preset surface traction, is the Heaviside function, is the topological description function of the wing structure, u is the displacement field, V ad is the permissible set of virtual displacement vectors v, is the wing structure material density, is the random variable of the wing structure volume, is the wing structure displacement random variable, The center coordinates and thickness of each member of the wing structure are the upper and lower limits of the optimization design parameters. is the lower limit of the stiffness of the wing structure, Find is to find a set of center coordinates and thickness optimization design parameters of each member of the wing structure that meet the weight and stiffness requirements, Min is to minimize the weight of the wing structure, and St is the constraint to be satisfied.

[0074] Step (2) obtains the value range of the center coordinates and thickness optimization design parameters of each member of the wing structure according to the assembly requirements of the wing structure, and constructs a design space composed of the center coordinates and thickness optimization design parameters of each member of the wing structure. Considering the space filling characteristics between individuals, an optimization population is generated within the design space. The stiffness and weight simulation model of the wing structure is used in Abaqus to evaluate the stiffness and weight value of each individual vector in the optimization population, and all population individual vectors and their stiffness and weight values ​​are saved in the database.

[0075] The specific steps of step (2) are as follows:

[0076] The first step is to determine the number of individual vectors that need to be sampled NP As well as the value range of the center coordinates and thickness optimization design parameters of each member of the wing-shaped structure, and construct a design space composed of the center coordinates and thickness optimization design parameters of each member of the wing-shaped structure;

[0077] The second step is to divide the value range of the center coordinates and thickness optimization design parameters of each member of the wing structure into NP non-overlapping intervals, and the center coordinates and thickness optimization design parameters of each member of the wing structure are NP The intervals are randomly arranged, and the center coordinates and thickness optimization design parameters of each member of the wing structure are NP A sampling point is randomly generated in each interval, and the random sampling points of the center coordinates and thickness optimization design parameters of each member of the wing structure are combined to form NP indivual n Sampling points in dimensional space;

[0078] The third step is to calculate the Euclidean distance matrix between all sampling points;

[0079] The fourth step is to locate the minimum distance point pair in the current Euclidean distance matrix and increase the minimum distance between sampling points by exchanging sampling point pairs in different dimensions;

[0080] Step 5: Repeat step 3 and step 4 until the set iteration limit is reached to obtain the optimized population.

[0081] In the sixth step, the wing structure stiffness and weight simulation model is used in Abaqus to evaluate the wing structure stiffness and weight value of each individual vector in the optimized population, and all population individual vectors and their stiffness and weight data are saved in the database.

[0082] Step (3) divides the optimized population into infeasible, semi-feasible or fully feasible states according to the population feasibility, and divides the sub-population according to the individual information, and designs the sub-population evolution operation within the design space composed of the center coordinates of each member of the wing-shaped structure and the thickness optimization design parameters to generate multiple candidate offspring individual vectors composed of the center coordinates of each member of the wing-shaped structure and the thickness optimization design parameters.

[0083] The specific steps of step (3) are as follows:

[0084] According to the feasibility of the individuals in the population, the optimized population is divided into infeasible, semi-feasible or fully feasible states. When all individuals in the optimized population are feasible individuals, the optimized population is in a fully feasible state; when only some individuals in the optimized population are feasible individuals, the optimized population is in a semi-feasible state; when all individuals in the optimized population are infeasible individuals, the optimized population is in an infeasible state; infeasible individuals are individuals that violate the stiffness constraints of the wing structure, and feasible individuals are individuals that satisfy the stiffness constraints of the wing structure;

[0085] When the optimized population is in a completely feasible state, the individuals successfully updated in the previous generation are divided into subpopulations U , and the individuals that failed to update successfully in the previous generation are divided into subpopulations Q ; Subpopulation UEvolutionary operations that emphasize development are performed, subpopulations Q Evolutionary operations that emphasize exploration were performed;

[0086] When the optimized population is in a semi-feasible state, feasible individuals are divided into subpopulations U The remaining individuals are sorted using a non-dominated sorting with wing structure weight, wing structure stiffness constraint violation value and nearest neighbor distance as three objectives. The individuals in the first half of the sorting are divided into sub-populations. U , the individuals ranked in the second half are classified into the subpopulation Q ; Subpopulation U Evolutionary operations that emphasize development are performed, subpopulations Q Evolutionary operations that emphasize exploration were performed;

[0087] When the state of the optimized population is infeasible, the optimized population is sorted based on the wing structure stiffness constraint violation value, and the individuals in the first half of the sorting are divided into sub-populations Q , the individuals ranked in the second half are classified into the subpopulation W ; Subpopulation Q Evolutionary operations that emphasize development are performed, subpopulations W Evolutionary operations that emphasize exploration were performed;

[0088] Among them, the evolutionary operations that focus on development are DE / rand / 1, DE / rand / 2, and DE / current-to-rand / 1, and the evolutionary operations that focus on exploration are DE / rand / 1, DE / rand / 2, and DE / random-to-random / 1. Each mutation operation generates the same number of offspring individual vectors. The expressions of the four mutation operations are as follows:

[0089] DE / rand / 1: ,

[0090] DE / rand / 2: ,

[0091] DE / random-to-random / 1: ,

[0092] DE / current-to-rand / 1: ,

[0093] In the above formula, DE stands for differential evolution, rand and random represent random individuals, current represents the current parent individual, to represents the direction of mutation, 1 and 2 represent the number of random perturbations, and x rand 、x r1 、x r2 、xr3 、x r4 and x r5 are 6 individual vectors randomly selected from the parent generation, consisting of the center coordinates of each member of the wing structure and the thickness optimization design parameters, x cur is the parent individual vector composed of the center coordinates of each member of the wing structure and the thickness optimization design parameters, F , F 1 and F 2 is the scaling factor that determines the amplitude of the mutation, and I is the individual vector obtained after the mutation;

[0094] The wing structure stiffness constraint violation value can be calculated by the following formula:

[0095] ,

[0096] In the above formula, c is an individual vector composed of the center coordinates of each member of the wing structure and the thickness optimization design parameters. S ( c )yes c The corresponding wing structure stiffness constraint violation value, max is the maximum output value, s ( c )yes c The wing structure stiffness constraint value obtained by evaluating the wing structure stiffness and weight simulation model, is the lower limit of the wing structure stiffness;

[0097] The nearest neighbor distance can be calculated as follows:

[0098] ,

[0099] In the above formula, d is the nearest neighbor distance, and are two individual vectors in the design space composed of the center coordinates of each member of the wing structure and the thickness optimization design parameters. and Representation vector and vector In the The coordinates on the dimension, n is the dimension of the individual vector, q j Is removed from the database p Other than j individual vectors, min is the minimum output value.

[0100] Step (4) calculates the update rate of the optimized population in the previous generation, and compares the set update rate threshold with the calculated update rate to build a global or local radial basis machine learning prediction model.

[0101] The specific steps of step (4) are as follows:

[0102] The first step is to calculate the update rate of the optimized population in the previous generation. The mathematical expression is as follows:

[0103] ,

[0104] In the above formula, UR is to optimize the population's update rate in the previous generation, NS is the number of wing structure individual vectors successfully updated in the previous generation, NP is the size of the optimized population;

[0105] In the second step, when the calculated update rate is less than the set update rate threshold of 0.1, the stiffness and weight values ​​of all population individual vectors evaluated in the current database are used to build a global radial basis function machine learning prediction model; when the calculated update rate is greater than the set update rate threshold of 0.1, the parent individual is found in the database adjacent to it. K individual vectors, and through the K The stiffness and weight values ​​of each individual vector are used to construct a local radial basis function machine learning prediction model;

[0106] For stiffness and weight values, the mathematical expression for constructing a radial basis function machine learning prediction model with a first-order polynomial is:

[0107] ,

[0108] In the above formula, It is a radial basis function machine learning prediction model constructed based on the stiffness and weight values ​​of the wing structure. For the Wing structure individual vector The corresponding weight parameter, Indicates Wing structure individual vector The basis function of It is expressed as a first-order polynomial, and x represents the offspring individual vector composed of the center coordinates of each member of the wing structure and the thickness optimization design parameters.

[0109] Step (5) Design feasibility rules and improved e The mechanism of using the constraint method is proposed, and the best candidate individual vector consisting of the center coordinates and thickness optimization design parameters of each member of the wing structure is obtained through the screening strategy.

[0110] The specific steps of step (5) are as follows:

[0111] The first step is to use the constructed radial basis machine learning prediction model to predict the stiffness and weight values ​​of the offspring individual vectors;

[0112] The second step is to determine the feasibility of the individuals in the parent population. The individuals that meet the wing structure stiffness constraint are feasible individuals, and the individuals that violate the wing structure stiffness constraint are infeasible individuals.

[0113] The third step is to apply the feasibility rule to the offspring of feasible individuals in the parent population, and to apply the improved e Constraint method, select the best candidate individual vector composed of the center coordinates of each member of the wing structure and the thickness optimization design parameters;

[0114] based on e The constraint method determines that the formula for individual vector x is better than individual vector y is as follows:

[0115] ,

[0116] In the above formula, x and y are the child individual vectors composed of the center coordinates of each member of the wing structure and the thickness optimization design parameters. it is the current iteration number, f (x) is the wing structure weight of the offspring individual vector x predicted by the radial basis machine learning prediction model, f (y) is the wing structure weight of the offspring individual vector y predicted by the radial basis machine learning prediction model, G (x) is the wing structure stiffness constraint violation value of the offspring individual vector x predicted by the radial basis machine learning prediction model, G (y) is the wing structure stiffness constraint violation value of the offspring individual vector y predicted by the radial basis machine learning prediction model, e ( it ) is the number of iterations equal to it The relaxed constraint violation value when ;

[0117] Improved e The constraint method value formula is as follows:

[0118] ,

[0119] In the above formula, represents the relaxation constraint violation value calculation function, The initial value is , G (x θ ) represents the ranking of the wing structure stiffness constraint violation values ​​in ascending order i The wing structure stiffness constraint violation value of individual vectors, it is the current iteration number, ITIt is a setting update e The final number of iterations of the value, tf Yes e A constant that plays a key role in the downward trend of its value.

[0120] Applying the feasibility rule to the offspring of feasible individuals is beneficial to maintaining the feasibility of the parent population; applying the feasibility rule to the offspring of infeasible individuals is beneficial to maintaining the feasibility of the parent population. e The constraint method relaxes the stiffness constraint of the wing structure, which is beneficial for the method to deal with nonlinear constraints.

[0121] Step (6) uses the wing structure stiffness and weight simulation model to evaluate the best candidate individual vector, uses the feasibility rule to update the optimization population and other iterative information, and determines whether the wing structure corresponding to the current optimal individual vector meets the weight and stiffness requirements. If so, output the wing structure corresponding to the current optimal individual vector; otherwise, go to step (3) until the wing structure corresponding to the current optimal individual vector meets the weight and stiffness requirements.

[0122] Among them, in step (6), the wing structure weight and stiffness simulation model is used to evaluate the best candidate individual vector, and the feasibility rule is used to update the optimization population and other iterative information. The specific steps are as follows:

[0123] The weight and stiffness values ​​of the best candidate individual vectors are evaluated using the wing structure weight and stiffness simulation model in Abaqus;

[0124] The wing structure stiffness and weight values ​​of the best candidate evaluated are stored in a database;

[0125] Update and optimize the population based on feasibility rules;

[0126] Update the current number of iterations and the optimal individual consisting of the center coordinates of each member of the wing structure and the thickness optimization design parameters to prepare for the next generation.

[0127] Example

[0128] This embodiment uses a benchmark test function to illustrate the optimization performance of a wing structure lightweight design method based on machine learning provided by the present invention. The expression of the benchmark test function is as follows:

[0129]

[0130] In this embodiment, f (x) is the objective function, g (x) is the constraint function, x j The value range is [-100,100] 10 The design variables on jThe value of each dimension, Min is the minimization of the objective function, and St is the constraint that needs to be satisfied.

[0131] The above-mentioned benchmark test function is processed respectively through steps (1) to (6) of a wing structure lightweight design method based on machine learning provided by the present invention to obtain experimental results.

[0132] In order to further illustrate the present embodiment, a lightweight design method for wing structures based on machine learning in the present embodiment is compared with another algorithm MPMLS, and the maximum number of simulation evaluations in the present embodiment is set to 3000. The experimental results are shown in Table 1. Under the same number of simulation samples, the method in the present embodiment obtains an effect close to the global optimal solution, and is better than MPMLS, which reflects the optimization efficiency of the lightweight design method for wing structures based on machine learning of the present invention. It can be considered that the method in the present embodiment has good performance in the lightweight design problem of wing structures.

[0133] Table 1 Comparison of optimization results of different algorithms

[0134]

[0135] The present invention provides a lightweight design method for wing structures based on machine learning. The method makes full use of the information fed back during the optimization process to dynamically allocate evolutionary strategies, adaptive modeling prediction models, and reasonably select screening strategies, thereby providing a systematic solution for the lightweight design of wing structures.

[0136] It will be easily understood by those skilled in the art that the above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A lightweight design method for wing structures based on machine learning, characterized in that: The method is applicable to the weight optimization problem of wing structures, including: Step (1) constructing a simulation model of the stiffness and weight of the wing structure in Abaqus according to the load and boundary constraints, and deriving a mathematical optimization model for the lightweight design problem of the wing structure with the center coordinates and thickness of each member of the wing structure as the optimization design parameters, the weight of the wing structure as the optimization target, and the stiffness of the wing structure as the optimization constraint; Step (2) according to the assembly requirements of the wing-shaped structure, the value range of the center coordinates and thickness optimization design parameters of each member of the wing-shaped structure is obtained, and a design space composed of the center coordinates and thickness optimization design parameters of each member of the wing-shaped structure is constructed, and an optimization population is generated within the design space considering the space filling characteristics between individuals, and the stiffness and weight simulation model of the wing-shaped structure is used in Abaqus to respectively evaluate the stiffness and weight value of each individual vector in the optimization population, and all the individual vectors of the population and their stiffness and weight values ​​are saved in a database; Step (3) dividing the optimized population into infeasible, semi-feasible or fully feasible states according to population feasibility, and dividing sub-populations according to individual information, and designing sub-population evolution operations within the design space composed of the center coordinates of each member of the wing-shaped structure and the thickness optimization design parameters to generate multiple candidate offspring individual vectors composed of the center coordinates of each member of the wing-shaped structure and the thickness optimization design parameters; Step (4) calculating the update rate of the optimized population in the previous generation, and comparing the set update rate threshold with the calculated update rate to construct a global or local radial basis machine learning prediction model; wherein the constructed radial basis machine learning prediction model is used to predict the stiffness and weight values ​​of the offspring individual vectors; Step (5) Design feasibility rules and improved ε The mechanism of using the constraint method is used, and the best candidate individual vector composed of the center coordinates of each member of the wing structure and the thickness optimization design parameters is obtained through the screening strategy; among them, the individuals that meet the stiffness constraint of the wing structure are feasible individuals, and the individuals that violate the stiffness constraint of the wing structure are infeasible individuals; the improved ε constraint method is applied to the offspring of the infeasible individuals in the parent population to select the best candidate individual vector; Step (6) uses the wing structure stiffness and weight simulation model to evaluate the best candidate individual vector, uses the feasibility rule to update the optimization population and other iterative information, and determines whether the wing structure corresponding to the current optimal individual vector meets the weight and stiffness requirements. If so, output the wing structure corresponding to the current optimal individual vector; otherwise, go to step (3) until the wing structure corresponding to the current optimal individual vector meets the weight and stiffness requirements.

2. The method according to claim 1, characterized in that The mathematical optimization model of the lightweight design problem of the wing structure in step (1) is specifically expressed as follows: ， In the above formula, is the weight of the wing structure, is the stiffness of the wing structure, M is the optimized design parameter vector in the lightweight design problem of the wing structure, M 1 , M 2 as well as M n is the optimized design parameter vector in the lightweight design problem of wing structure, T represents the transpose, are the center coordinates and thickness of each member of the wing structure, the number of optimized design parameters, f and t are the Neumann boundary Γ t The body force density on the surface and the preset surface traction, is the Heaviside function, is the topological description function of the wing structure, u is the displacement field, V ad is the permissible set of virtual displacement vectors v, is the wing structure material density, is the random variable of the wing structure volume, is the wing structure displacement random variable, The center coordinates and thickness of each member of the wing structure are the upper and lower limits of the optimization design parameters. is the lower limit of the stiffness of the wing structure, Find is to find a set of center coordinates and thickness optimization design parameters of each member of the wing structure that meet the weight and stiffness requirements, Min is to minimize the weight of the wing structure, and St is the constraint to be satisfied.

3. The method according to claim 1, characterized in that The specific steps of step (2) are as follows: The first step is to determine the number of individual vectors that need to be sampled NP As well as the value range of the center coordinates and thickness optimization design parameters of each member of the wing-shaped structure, and construct a design space composed of the center coordinates and thickness optimization design parameters of each member of the wing-shaped structure; The second step is to divide the value range of the center coordinates and thickness optimization design parameters of each member of the wing structure into NP non-overlapping intervals, and the center coordinates and thickness optimization design parameters of each member of the wing structure are NP The intervals are randomly arranged, and the center coordinates and thickness optimization design parameters of each member of the wing structure are NP A sampling point is randomly generated in each interval, and the random sampling points of the center coordinates and thickness optimization design parameters of each member of the wing structure are combined to form NP indivual n Sampling points in dimensional space; The third step is to calculate the Euclidean distance matrix between all sampling points; The fourth step is to locate the minimum distance point pair in the current Euclidean distance matrix and increase the minimum distance between sampling points by exchanging sampling point pairs in different dimensions; Step 5: Repeat step 3 and step 4 until the set iteration limit is reached to obtain the optimized population. In the sixth step, the wing structure stiffness and weight simulation model is used in Abaqus to evaluate the wing structure stiffness and weight value of each individual vector in the optimized population, and all population individual vectors and their stiffness and weight data are saved in the database.

4. The method according to claim 1, characterized in that: The specific steps of step (3) are as follows: According to the feasibility of the individuals in the population, the optimized population is divided into infeasible, semi-feasible or fully feasible states. When all individuals in the optimized population are feasible individuals, the optimized population is in a fully feasible state; when only some individuals in the optimized population are feasible individuals, the optimized population is in a semi-feasible state; when all individuals in the optimized population are infeasible individuals, the optimized population is in an infeasible state; infeasible individuals are individuals that violate the stiffness constraints of the wing structure, and feasible individuals are individuals that satisfy the stiffness constraints of the wing structure; When the optimized population is in a completely feasible state, the individuals successfully updated in the previous generation are divided into subpopulations U , and the individuals that failed to update successfully in the previous generation are divided into subpopulations Q ; Subpopulation U Evolutionary operations that emphasize development are performed, subpopulations Q Evolutionary operations that emphasize exploration were performed; When the optimized population is in a semi-feasible state, feasible individuals are divided into subpopulations U The remaining individuals are sorted using a non-dominated sorting with wing structure weight, wing structure stiffness constraint violation value and nearest neighbor distance as three objectives. The individuals in the first half of the sorting are divided into sub-populations. U , the individuals ranked in the second half are classified into the subpopulation Q ; Subpopulation U Evolutionary operations that emphasize development are performed, subpopulations Q Evolutionary operations that emphasize exploration were performed; When the state of the optimized population is infeasible, the optimized population is sorted based on the wing structure stiffness constraint violation value, and the individuals in the first half of the sorting are divided into sub-populations Q , the individuals ranked in the second half are classified into the subpopulation W ; Subpopulation Q Evolutionary operations that emphasize development are performed, subpopulations W Evolutionary operations that emphasize exploration were performed; Among them, the evolutionary operations that focus on development are DE / rand / 1, DE / rand / 2, and DE / current-to-rand / 1, and the evolutionary operations that focus on exploration are DE / rand / 1, DE / rand / 2, and DE / random-to-random / 1. Each mutation operation generates the same number of offspring individual vectors. The expressions of the four mutation operations are as follows: DE / row / 1: , DE / row / 2: , DE / random-to-random / 1: , DE / current-to-rand / 1: , In the above formula, DE stands for differential evolution, rand and random represent random individuals, current represents the current parent individual, to represents the direction of mutation, 1 and 2 represent the number of random perturbations, and x rand 、x r1 、x r2 、x r3 、x r4 and x r5 are 6 individual vectors randomly selected from the parent generation, consisting of the center coordinates of each member of the wing structure and the thickness optimization design parameters, x cur is the parent individual vector composed of the center coordinates of each member of the wing structure and the thickness optimization design parameters, F , F 1 and F 2 is the scaling factor that determines the amplitude during mutation, and I is the individual vector obtained after mutation; The wing structure stiffness constraint violation value can be calculated by the following formula: ， In the above formula, c is an individual vector composed of the center coordinates of each member of the wing structure and the thickness optimization design parameters. S ( c )yes c The corresponding wing structure stiffness constraint violation value, max is the maximum output value, s ( c )yes c The wing structure stiffness constraint value obtained by evaluating the wing structure stiffness and weight simulation model, is the lower limit of the wing structure stiffness; The nearest neighbor distance can be calculated as follows: ， In the above formula, d is the nearest neighbor distance, and are two individual vectors in the design space composed of the center coordinates of each member of the wing structure and the thickness optimization design parameters. and Representation vector and vector In the The coordinates on the dimension, n is the dimension of the individual vector, q j Is removed from the database p Other than j individual vectors, min is the minimum output value.

5. The method according to claim 1, characterized in that The specific steps of step (4) are as follows: The first step is to calculate the update rate of the optimized population in the previous generation. The mathematical expression is as follows: ， In the above formula, UR is to optimize the population's update rate in the previous generation, NS is the number of wing structure individual vectors successfully updated in the previous generation, NP is the size of the optimized population; In the second step, when the calculated update rate is less than the set update rate threshold of 0.1, the stiffness and weight values ​​of all population individual vectors evaluated in the current database are used to build a global radial basis function machine learning prediction model; when the calculated update rate is greater than the set update rate threshold of 0.1, the parent individual is found in the database adjacent to it. K individual vectors, and through the K The stiffness and weight values ​​of each individual vector are used to construct a local radial basis function machine learning prediction model; For stiffness and weight values, the mathematical expression for constructing a radial basis function machine learning prediction model with a first-order polynomial is: ， In the above formula, It is a radial basis function machine learning prediction model constructed by the stiffness and weight values ​​of the wing structure. For the Wing structure individual vector The corresponding weight parameter, Indicates Wing structure individual vector The basis function of It is expressed as a first-order polynomial, and x represents the offspring individual vector composed of the center coordinates of each member of the wing structure and the thickness optimization design parameters.

6. The method according to claim 1, characterized in that The specific steps of step (5) are as follows: The first step is to use the constructed radial basis machine learning prediction model to predict the stiffness and weight values ​​of the offspring individual vectors; The second step is to determine the feasibility of the individuals in the parent population. The individuals that meet the wing structure stiffness constraint are feasible individuals, and the individuals that violate the wing structure stiffness constraint are infeasible individuals. The third step is to apply the feasibility rule to the offspring of feasible individuals in the parent population, and to apply the improved ε Constraint method, select the best candidate individual vector composed of the center coordinates of each member of the wing structure and the thickness optimization design parameters; based on ε The constraint method determines that the formula for individual vector x is better than individual vector y is as follows: ， In the above formula, x and y are the child individual vectors composed of the center coordinates of each member of the wing structure and the thickness optimization design parameters. it is the current iteration number, f (x) is the wing structure weight of the offspring individual vector x predicted by the radial basis machine learning prediction model, f (y) is the wing structure weight of the offspring individual vector y predicted by the radial basis machine learning prediction model, G (x) is the wing structure stiffness constraint violation value of the offspring individual vector x predicted by the radial basis machine learning prediction model, G (y) is the wing structure stiffness constraint violation value of the offspring individual vector y predicted by the radial basis machine learning prediction model, ε ( it ) is the number of iterations equal to it The relaxed constraint violation value when ; Improved ε The constraint method value formula is as follows: ， In the above formula, represents the relaxation constraint violation value calculation function, The initial value is , G (x θ ) represents the ranking of the wing structure stiffness constraint violation values ​​in ascending order θ The wing structure stiffness constraint violation value of individual vectors, it is the current iteration number, IT It is an update of settings ε The final number of iterations of the value, tf Yes ε A constant that plays a key role in the downward trend of its value.

7. The method according to claim 1, characterized in that In step (6), the wing structure weight and stiffness simulation model is used to evaluate the best candidate individual vector, and the feasibility rule is used to update the optimization population and other iterative information. The specific steps are as follows: The weight and stiffness values ​​of the best candidate individual vectors are evaluated using the wing structure weight and stiffness simulation model in Abaqus; The wing structure stiffness and weight values ​​of the best candidate evaluated are stored in a database; Update and optimize the population based on feasibility rules; Update the current number of iterations and the optimal individual consisting of the center coordinates of each member of the wing structure and the thickness optimization design parameters to prepare for the next generation.

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