Layer design criterion mining method based on generative and interpretable artificial intelligence

Abstract

The invention provides a generative and interpretable artificial intelligence-based layering design criterion mining method. The method mainly comprises the following steps of: (1) generating a training data set through a finite element method; (2) establishing and training a generative model; (3) establishing and training a symbol regression model; and (4) summarizing a layering design criterion. According to the method, through a data driving thought, a comprehensive composite material layer design rule aiming at a specific design target is mined from big data meeting design requirements.

Description

Technical Field

[0001] The present invention relates to the technical field of intelligent composite materials, and particularly relates to a method for mining ply design criteria based on generative and interpretable artificial intelligence. Background Art

[0002] After nearly 60 years of development, carbon fiber composite materials, known as "black gold", have not only been limited to high-precision and sophisticated technology industries such as aerospace with the continuous progress of manufacturing and design levels, but have also been widely used in new energy vehicle industries, railway track transportation, large-scale wind power generation industries, energy chemical industries, modern municipal construction and other fields. At the same time, under the development trend of carbon neutrality, countries around the world have formulated industrial policy goals in the field of carbon fiber, which has played a role in driving the development of the composite material industry. At present, China's composite materials are in a stage of rapid development. In the new energy vehicle industry alone, the market scale of carbon fiber composite materials is expected to exceed 50 billion yuan in the next 5 years. However, the application of composite materials in most industries is still in the initial exploration stage and has not yet achieved a complete iteration of composite materials for traditional metals. Different from the isotropic and plastic characteristics of metal materials, composite materials have obvious anisotropic and brittle characteristics, making their designability stronger and the design method different from that of traditional metal materials. The main problem faced in the structural design of composite materials is ply design, and its main difficulty comes from its large design space and the coupling effect brought by anisotropy, resulting in the ply design of composite materials being an optimization design problem of multiple parameters under multi-objective constraint conditions.

[0003] In structural design, forward prediction of mechanical properties and reverse optimization are required to design ply and constituent material selection schemes that meet performance requirements such as load-bearing and deformation. To reduce the design difficulty of composite material plies, a series of traditional design criteria are adopted in actual engineering applications for engineers to refer to. These classical criteria include: (1) selection from 4 traditional angle libraries (0°, 90°, ±45°); (2) the principle of balanced and symmetric ply design; (3) no more than 4 layers of continuous same ply angles, etc. The above criteria help narrow the design space of composite material design, thus reducing the design difficulty of composite material plies. However, despite this, in actual applications, finding the optimal solution for composite material ply design is still not an easy task, so quasi-isotropic plies are widely used. The above ply design criteria are usually based on long-term aviation structure design experience. On the one hand, more scientific methods are needed to verify and propose composite material ply design criteria. On the other hand, when facing different working conditions and considering different design constraints, traditional design criteria may not cover them, and new criteria still need to be explored to guide ply design under specific conditions. Therefore, how to effectively explore composite material ply design criteria and simplify and reduce the cost of the analysis and design problems of composite material structures is the key to expanding its application in the field of people's livelihood in the future.

[0004] Different from traditional composite material ply design work, composite material ply design criteria are the common characteristics of a type of ply method. Its purpose is not to find a specific optimal ply result, but to summarize the regularity of ply design under specific constraints and comprehensively guide the design of composite material plies. Therefore, the data-driven method of exploring physical laws from big data will surely play an important role in it. Summary of the Invention

[0005] Aiming at the problems of insufficient coverage of traditional composite material design criteria under different design constraints in the above background technology, and relying on experience and lacking theoretical support, etc., the present invention proposes a ply design criterion mining method based on generative and interpretable artificial intelligence. Through a data-driven idea, it mines comprehensive composite material ply design laws for specific design goals from big data that meet design requirements, can be applied to any aspect of design requirements, can be effectively extended to multi-objective optimization design problems, and ensures the computational solution efficiency of the same scale.

[0006] To solve the above technical problems, a ply design criterion mining method based on generative and interpretable artificial intelligence provided by the present invention mainly includes the following steps:

[0007] (1) Generate a training data set by the finite element method;

[0008] (2) Establish and train a generative model;

[0009] (3) Establishment and training of the symbolic regression model;

[0010] (4) Summary of the ply design criteria.

[0011] The ply design criteria mining method based on generative and interpretable artificial intelligence, wherein the specific process of the step (1) is as follows:

[0012] (1.1) Establish a random ply generation method

[0013] First, according to the design scenario, determine the number of composite material plies and the selection range of ply angles; then, generate random numbers through the random module in python; by setting the relationship between the random numbers, the number of plies, and the ply angles, determine the randomly generated ply design scheme;

[0014] (1.2) Establish a finite element model for parametric modeling of plies

[0015] Utilize the secondary development function of the finite element software Abaqus to convert the ply definition of the composite material into the form of a parametric script; then, assign the ply design randomly generated by the random module in python as a variable to each ply of the laminated plate finite element model; then, sequentially complete the functions of mesh generation, element property setting, boundary condition and load setting, solver setting, and calculation result output and saving in the finite element software Abaqus to obtain the analysis result;

[0016] (1.3) Establish a training data set

[0017] Perform a loop on the above steps (1.1)-(1.2), save the randomly generated ply design and its corresponding target performance each time, and obtain a large number of training data sets.

[0018] The ply design criteria mining method based on generative and interpretable artificial intelligence, wherein: the number of plies in the step (1.1) can cover any number of plies in the actual composite structure;

[0019] The selection range of ply angles in the step (1.1) is -90° to 90°.

[0020] The ply design criteria mining method based on generative and interpretable artificial intelligence, wherein the specific process of the step (2) is as follows:

[0021] (2.1) Establish a generative model under multi-objective constraints

[0022] A generative model under multi-objective constraints is established with a generative adversarial network as the basic framework; the generative model includes a generator network and a discriminator network; the generator network is used to output a ply design scheme from a random parameter input; the discriminator network has two functions, one is to judge the rationality of the generated ply design scheme, and the other is to obtain the performance index of the objective function corresponding to the generated composite ply; the input of the generator is a random variable, and the output is the ply angle design; the input of the discriminator is the ply angle, and the output is the rationality judgment of the ply scheme and the objective function value corresponding to the angle;

[0023] (2.2) Initialize the neural network parameters of the generative model

[0024] The neural network parameters are the number of hidden layers, the number of neurons, the activation function, and the loss function; the loss function of the generator is the distance between the objective function value and the design target value, and this distance realizes positive deviation through the ReLU function. The loss function for realizing positive deviation is Loss1, that is, when the predicted value is greater than the target value, the loss function value is 0; the form of the ReLU function is as follows:

[0025]

[0026] The loss function of the discriminator is the error between the performance prediction value and the true value of the ply, and the ply design rationality index;

[0027] The loss function of the generator is a combination of Loss1 and Loss2, where y target is the design target value, y pred is the model output result, y true is the true value of the rationality index; the loss function of the discriminator is a combination of Loss2 and Loss3;

[0028] Loss1 = ReLU(y target - y pred ) (1);

[0029] Loss2 = cross_entropy(y true , y pred ) (2);

[0030] Loss3 = mean_absolute_error(y true , y pred ) (3);

[0031] In the above formulas (1)-(3), Loss1 is the distance between the objective function value and the design target value, Loss2 is the rationality of the ply design, and Loss3 is the error between the performance prediction value and the true value of the ply;

[0032] (2.3) Generative model training

[0033] First, initialize the training parameters of the generative model, that is, set the number of training rounds, the optimization algorithm, and the batch sample size; the training process is as follows:

[0034] (2.3.1) Fix the parameters of the generator network and train the predictive ability of the discriminator's objective function; the training dataset is the training dataset generated in step (1) above.

[0035] (2.3.2) Fix the network parameters of the part of the discriminator's predictive objective function.

[0036] (2.3.3) Start the loop of training rounds. First, fix the generator network and train the discriminator's ability to predict the rationality of the layup; the training data is: in the dataset, the true layup angle is true, and the layup angle generated by the generator network is false; after training the discriminator several times, fix the discriminator parameters and release the training of the generator parameters; train the overall model composed of the generator and the fixator to optimize the network parameters of the generator part; the training data is: random Gaussian variable input, and the layup objective function value in the dataset is the output.

[0037] (2.3.4) Repeat the process of step (2.3.3) according to the set number of training rounds to complete the reciprocating training of the discriminator and the generator until the number of training rounds is reached.

[0038] (2.4) Generation of layup design schemes

[0039] After saving the generator network in the trained generative model, using a random variable as the input, a layup design scheme that meets the design constraint conditions can be obtained; by setting a loop of several random variables, a large number of layup design schemes are generated, and the distribution diagrams of each layup angle are drawn for subsequent regularity mining.

[0040] For the layup design criterion mining method based on generative and interpretable artificial intelligence, the specific process of step (3) is as follows:

[0041] (3.1) Establish a symbolic regression model between each layup angle based on the genetic programming algorithm

[0042] (3.2) Initialize the parameters of the symbolic regression model.

[0043] (3.3) Train the symbolic regression model.

[0044] The method for mining ply design criteria based on generative and interpretable artificial intelligence, wherein: in step (3.1), the symbolic regression model is established according to the Symbolic Regressor function in the open-source symbolic regression library GPlearn. Its basic steps are successively setting the population size, setting the number of iterative optimizations, the iteration termination condition, the cross-shift mutation coefficient, the proportion of verification samples, defining the formula length penalty factor, and setting the operator set.

[0045] The method for mining ply design criteria based on generative and interpretable artificial intelligence, wherein the basic process of establishing a symbolic regression model according to the Symbolic Regressor function in the open-source symbolic regression library GPlearn is as follows:

[0046] (3.1.1) Initialize the population

[0047] Randomly generate the initial population, and each individual is a mathematical expression tree;

[0048] (3.1.2) Fitness evaluation

[0049] Calculate the fitness for each individual to measure the fitting degree of the expression to the training data;

[0050] (3.1.3) Termination condition check

[0051] If the condition is met, stop; otherwise, enter iterative optimization;

[0052] (3.1.4) Selection operation

[0053] Select parent individuals according to the fitness and retain excellent individuals;

[0054] (3.1.5) Genetic operation

[0055] Crossover: Randomly select two parent individuals and exchange subtrees to generate new individuals; Mutation: Randomly modify the subtrees in an individual; Shift: Randomly permute the positions of subtrees within an individual;

[0056] (3.1.6) Generate a new population

[0057] Merge the parent and offspring individuals, screen out a new population according to the fitness; Update the number of iterations and return to step (3.1.2);

[0058] (3.1.7) Output the optimal solution

[0059] Return the expression tree with the highest fitness as the final symbolic regression model.

[0060] The method for mining ply design criteria based on generative and interpretable artificial intelligence, wherein step (3.2) initializes the symbolic regression model, and the set parameters include the population initialization parameters related to the genetic optimization process in model establishment according to the Symbolic Regressor function in the open-source symbolic regression library GPlearn, namely the population size and the set operator set, the genetic process parameters, namely the cross-shift mutation coefficient, the formula length penalty factor, and the validation sample ratio, and the result control parameters, namely the number of iterative optimizations and the iterative termination condition.

[0061] The method for mining ply design criteria based on generative and interpretable artificial intelligence, wherein the specific process of step (3.3) is as follows:

[0062] (3.3.1) Using the laying angle θ2 as the output and the laying angle θ1 as the variable to train the symbolic regression model, and obtaining the regression coefficients;

[0063] (3.3.2) Using the laying angle θ3 as the output and (θ1, θ2) as the variables to train the symbolic regression model, and obtaining the regression coefficients;

[0064] (3.3.3) Sequentially using the laying angle θ k as the output and (θ1, θ2,... θ k-1 ) as the variables to train the symbolic regression model, and obtaining the regression coefficients.

[0065] The method for mining ply design criteria based on generative and interpretable artificial intelligence, wherein the specific process of step (4) is as follows: Taking the rule with the regression coefficient R 2 above 0.7 as the significant quantitative relationship, constructing the quantitative formula relationship of the composite material ply angle, and summarizing the ply design criteria for the corresponding design problem according to the quantitative formula relationship.

[0066] Adopting the above technical solution, the present invention has the following beneficial effects:

[0067] The method for mining ply design criteria based on generative and interpretable artificial intelligence of the present invention is reasonably conceived. Through a data-driven approach, it mines the comprehensive composite material ply design rules for specific design objectives from the big data that meets the design requirements, and has the following characteristics and advantages compared with the prior art:

[0068] (1) The existing ply design criteria originate from engineering experience and are applicable to the general situation of ply design, while the mining of ply design criteria of the present invention is based on the analysis data of laminate theory and can be applied to the design scenarios under specific working conditions and specific design constraints;

[0069] (2) Most of the existing ply design criteria only target the design requirements for mechanical properties. In contrast, the method of the present invention is essentially a data-driven approach that can be applied to design requirements in any aspect, such as thermal conductivity requirements, electromagnetic property requirements, cost requirements, structural size constraints, and so on.

[0070] (3) Existing composite ply design methods are all for the optimal ply design under specific working conditions and it is difficult to form a summary of guiding ply design rules. The method of the present invention targets the comprehensive excavation of ply design rules, and the formed criteria are more universal and can provide more references in practical engineering applications. The obtained ply design criteria can further combine with theoretical analysis to obtain the relevant physical mechanisms of composites.

[0071] (4) As an optimal design, existing composite ply design methods are prone to falling into local optimal solutions rather than global optimal solutions. The generative artificial intelligence method provided by the present invention evaluates based on the ply performance in the overall dataset, avoiding the problem of local optimal solutions.

[0072] (5) Due to the complexity of the multi-objective optimization model, existing composite ply design methods face problems of solution accuracy and efficiency for the high-dimensional composite ply design variables and optimization problems with more than three objective functions. The method of the present invention uses a generative artificial intelligence method to integrate multi-objective constraints into the training loss function, which can effectively be extended to design problems of multi-objective optimization and ensure the computational solution efficiency of the same scale. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the description of the specific embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0074] Figure 1 It is the specific flowchart of the composite ply design criteria of the present invention;

[0075] Figure 2 It is the generative artificial intelligence model framework;

[0076] Figure 3 It is the ply angle distribution diagram in the method example of the present invention;

[0077] Figure 4 It is the formula tree model of symbolic regression in the method example of the present invention;

[0078] Figure 5This is the quantitative layup angle rule in the method example of the present invention. Detailed implementation manners

[0079] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0080] The present invention will be further explained and described below in conjunction with specific implementation manners.

[0081] As Figure 1 shown, the composite material layup design criterion mining method provided in this embodiment mainly includes 4 steps in specific implementation manners. Combining Figure 1 , the specific implementation steps are as follows:

[0082] S100. Generate a training data set through finite element or laminate theory.

[0083] S101. Establish a random layup generation method

[0084] First, according to the design scenario, determine the number of composite material layups (the number of layups can cover any number of layups in the actual composite structure) and the range of layup angle selection (usually from -90 degrees to 90 degrees); then, generate random numbers through the random module in python; by setting the relationship between the random numbers and the number of layups and layup angles (for example, using the random module to randomly take an integer within the range of [0,3] for a, if a = 0, select a 0° layup, if a = 0, select a 90° layup, if a = 0, select a -45° layup, if a = 0, select a 45° layup, so as to determine the randomly generated layup design scheme).

[0085] S102. Establish a finite element or theoretical model for parametric modeling of layups

[0086] Taking the finite element calculation process as an example, using the secondary development function of finite element software such as Abaqus, convert the layup definition of the composite material into the form of a parametric script; then, assign the layup design randomly generated by the random module in python to the finite element model as a variable; then, in the finite element software Abaqus, complete the functions of mesh generation, element property setting, boundary condition and load setting, solver setting, and calculation result output and saving in sequence.

[0087] S103. Establish a training data set

[0088] Perform the above steps S101 - S102 in several loops, save the randomly generated layup designs obtained each time and their corresponding target performances, and obtain a large amount of training data sets.

[0089] S200. Establishment and training of a generative model

[0090] S210. Establish a generative model under multi - objective constraints

[0091] Establish a generative model under multi - objective constraints with the Generative Adversary Nets as the basic framework (the basic framework of this generative model is the Generative Adversary Nets, which is a commonly used deep - learning structure in the field of AI; the main system structure in the present invention consists of two neural networks, namely the generator network and the discriminator network, and can be constructed using the open - source deep - learning library Keras). The corresponding model principle is as Figure 2 shown. This model mainly includes two network modules, namely the generator network and the discriminator network. The generator network is used to output a layup design scheme from random parameter inputs. The discriminator network has two main functions. One is to judge whether the layup design of the generated layup design scheme is reasonable, and the other is to obtain the performance index of the objective function corresponding to the generated composite material layup. The input of the generator is a random variable (typical example: a Python script generates a 50 - dimensional Gaussian random number), and the output is the layup angle design (typical example: for an 8 - layer composite material design, it is 8 fiber angles [θ1, θ2, θ3, θ4, θ5, θ6, θ7, θ8]). The input of the discriminator is the layup angle, and the output is the rationality judgment (0 or 1) of the layup scheme and the objective function value corresponding to the angle.

[0092] S220. Initialize the network parameters of the generative model

[0093] The initialization parameters of the neural network are the number of hidden layers, the number of neurons, the activation function, and the loss function. Among them, the loss function of the generator is the distance between the objective function value and the design target value (realizing positive deviation through the ReLU function). The form of the ReLU function is as follows, and the loss function realizing positive deviation is Loss1 in Equation (1), that is, when the predicted value is greater than the target value, the loss function value is 0;

[0094]

[0095] The loss function of the discriminator is the error between the performance predicted value and the true value of the layup (usually using the mean absolute error MAE function), and the layup design rationality index (true or false in the traditional generative adversarial network); the form of the MAE function is: represents the mean absolute error between the predicted value and the true value on n training data.

[0096] The loss function of the generator (the combined model of the generator + discriminator) is a combination of Loss1 and Loss2, where y target is the design target value, y pred is the model output result, and y true is the true value of the rationality index; the loss function of the discriminator is a combination of Loss2 and Loss3;

[0097] Loss1 = ReLU(y target - y pred ) (1);

[0098] Loss2 = cross_entropy(y true , y pred ) (2);

[0099] Loss3 = mean_absolute_error(y true , y pred ) (3);

[0100] In the above formulas (1)-(3), Loss1 is the distance between the objective function value and the design target value, Loss2 is the rationality of the ply design, and Loss3 is the error between the predicted value and the true value of the ply performance;

[0101] S230. Generative model training

[0102] First, initialize the training parameters of the generative model; set the number of training epochs, the optimization algorithm, and the batch sample size; the training process is as follows:

[0103] S231. Fix the network parameters of the generator and train the target function prediction ability of the discriminator. The training dataset is the training dataset generated in the above step S100;

[0104] S232. Fix the network parameters of the part of the discriminator that predicts the target function;

[0105] S233. Start the loop of training rounds. First, fix the generator network and train the discriminator's ability to predict the rationality of the ply layup (the training process is a standard process in machine learning. After defining the training data, loss function, and network parameters, the Adam training algorithm is used); the training data is as follows: in the dataset, the true ply angle is true, and the ply angle generated by the generator network is false. After training the discriminator several times, fix the discriminator parameters and release the training of the generator parameters. Then train the overall model composed of the generator and the fixer (the training process is a standard process in machine learning. After defining the training data, loss function, and network parameters, the Adam training algorithm is used; specifically, the module of Keras in the open-source deep learning library is called) to optimize the network parameters of the generator part. The training data is the input of random Gaussian variables and the output of the ply objective function value in the dataset.

[0106] S234. Repeat the process of step S233 according to the set number of training rounds to complete the reciprocating training of the discriminator and the generator until the number of training rounds is reached.

[0107] S240. Generation of ply layup design scheme

[0108] After saving the generator network in the trained generative model, using random variables as the input, a ply layup design scheme that meets the design constraint conditions can be obtained. By setting the loop of several random variables, a large number of ply layup design schemes are generated, and the distribution diagrams of each ply angle are drawn for subsequent regularity mining.

[0109] S300. Establishment and training of the symbolic regression model

[0110] S310. Establish a symbolic regression model between each ply angle based on the genetic programming algorithm

[0111] Establish a symbolic regression model based on the genetic programming algorithm. That is, in the form of a tree model, the quantitative formula relationship is expressed using operators such as addition, subtraction, multiplication, and division, as well as constants and variables. Then, the genetic algorithm of inheritance, crossover, and mutation is used for the optimal design of the symbolic formula (the construction of the symbolic regression model is based on the Symbolic Regressor function in the open-source symbolic regression library GPlearn. The specific steps are to set the population size, the number of iterative optimizations, the iteration termination condition, the crossover shift mutation coefficient, the proportion of validation samples, define the formula length penalty factor, and set the operator set);a formula tree model in this solution example is as Figure 4 shown;

[0112] The basic process of symbolic regression modeling based on the Symbolic Regressor function in the open-source symbolic regression library GPlearn is as follows:

[0113] (3.1.1) Initialize the population

[0114] Randomly generate the initial population, where each individual is a mathematical expression tree;

[0115] (3.1.2) Fitness evaluation

[0116] Calculate the fitness for each individual to measure the fitting degree of the expression to the training data;

[0117] (3.1.3) Termination condition check

[0118] Stop if the conditions are met (maximum number of iterations, fitness threshold), otherwise enter iterative optimization;

[0119] (3.1.4) Selection operation

[0120] Select parent individuals according to fitness and retain excellent individuals;

[0121] (3.1.5) Genetic operations

[0122] Crossover: Randomly select two parent individuals and exchange subtrees to generate new individuals; Mutation: Randomly modify subtrees in an individual; Shift: Randomly permute the positions of subtrees within an individual;

[0123] (3.1.6) Generate a new population

[0124] Merge the parent and offspring individuals, and screen out a new population according to fitness. Update the number of iterations and return to step (3.1.2);

[0125] (3.1.7) Output the optimal solution

[0126] Return the expression tree with the highest fitness as the final symbolic regression model.

[0127] S320. Initialize the parameters of the symbolic regression model

[0128] Initialize the symbolic regression model. Taking the typical gplearn library as an example, the parameters to be set include the population initialization parameters, genetic process parameters, and result control parameters related to the genetic optimization process; among them, the population initialization parameters include the population size and the set of operators; the genetic process parameters include the crossover shift mutation coefficient, formula length penalty factor, and validation sample ratio; the result control parameters include the number of iterative optimizations and the iterative termination conditions.

[0129] S330. Train the symbolic regression model

[0130] Taking the 8-layer composite material design [θ1, θ2, θ3, θ4, θ5, θ6, θ7, θ8] as an example, the process of training the symbolic regression model is as follows:

[0131] S331. Use the ply angle θ2 as the output, and use θ1 as the variable to train the symbolic regression model to obtain the regression coefficients;

[0132] S332. Use the ply angle θ3 as the output, and use (θ1, θ2) as the variables to train the symbolic regression model to obtain the regression coefficients;

[0133] S333. Successively use the ply angle θ k as the output, and use (θ1, θ2,... θ k-1 ) as the variables to train the symbolic regression model to obtain the regression coefficients; until using θ8 as the output and using (θ1, θ2, θ3, θ4, θ5, θ6, θ7) as the variables to train the symbolic regression model to obtain the regression coefficients.

[0134] S400. Summary of Ply Design Criteria

[0135] Take the rule with the regression coefficient R 2 above 0.7 as the significant quantitative relationship. This embodiment is illustrated by taking the laminate uniformity design goal as an example. The objective function of the laminate uniformity is shown in the following formula (4):

[0136]

[0137] In the above formula (4), [A*] is the laminate normalized tensile stiffness matrix; [D*] is the normalized bending stiffness matrix; [B*] is the normalized coupling matrix; A 16 , A 26 , D 16 , D 26 are the stiffness matrix components related to the coupling effect.

[0138] The quantitative formula relationship of the ply angles of the 8-layer composite material with the goal of homogenization design is as follows (typical results are as Figure 5 shown):

[0139] ① θ8 = -θ1 (the regression coefficient R 2 is 0.72);

[0140] ② θ7 = -θ2 (the regression coefficient R 2 is 0.71);

[0141] ③ θ6 = -θ3 (the regression coefficient R 2 is 0.83);

[0142] ④ θ5 = -θ4 (the regression coefficient R 2 is 0.82);

[0143] According to the quantitative formula relationships ①-④ obtained by symbolic regression, the ply design criteria for the corresponding design problems can be summarized; for this example, the ply layup method of should be followed.

[0144] Through a data-driven approach, the present invention mines the comprehensive composite material ply design rules for specific design objectives from the big data that meets the design requirements, can be applied to the design requirements in any aspect, can be effectively extended to the design problems of multi-objective optimization, and ensures the computational solution efficiency of the same scale.

[0145] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for mining ply design criteria based on generative and interpretable artificial intelligence, characterized in that It mainly includes the following steps: (1) Generate a training dataset through the finite element method; (2) Establish and train a generative model; (3) Establish and train a symbolic regression model; (4) Summarize the ply design criteria.

2. The method for mining ply design criteria based on generative and interpretable artificial intelligence according to claim 1, wherein The specific process of step (1) is as follows: (1.1) Establish a random ply generation method First, according to the design scenario, determine the number of composite material plies and the selection range of ply angles; then, generate random numbers through the random module in python; by setting the relationship between the random numbers, the number of plies, and the ply angles, determine the randomly generated ply design scheme; (1.2) Establish a finite element model for ply parametric modeling Utilize the secondary development function of the finite element software Abaqus to convert the ply definition of the composite material into the form of a parametric script; then, assign the ply design randomly generated by the random module in python as a variable to each ply of the laminated plate finite element model; then, sequentially complete the functions of mesh generation, element property setting, boundary condition and load setting, solver setting, and calculation result output and saving in the finite element software Abaqus to obtain the analysis result; (1.3) Establish a training dataset Loop through the above steps (1.1)-(1.2), save each randomly generated ply design and its corresponding target performance, and obtain a large number of training datasets.

3. The layup design criterion mining method based on generative and interpretable artificial intelligence according to claim 1, characterized in that: The number of plies in step (1.1) can cover any number of plies in the actual composite structure; The selection range of ply angles in step (1.1) is -90° to 90°.

4. The method for mining ply design criteria based on generative and interpretable artificial intelligence according to claim 1, characterized in that, The specific process of step (2) is as follows: (2.1) Establish a generative model under multi-objective constraints Establish a generative model under multi-objective constraints with a generative adversarial network as the basic framework; the generative model includes a generator network and a discriminator network; the generator network is used to output a ply design scheme from a random parameter input; the discriminator network has two functions, one is to judge the rationality of the generated ply design scheme, and the other is to obtain the performance index of the objective function corresponding to the generated composite material ply; the input of the generator is a random variable, and the output is the ply angle design; the input of the discriminator is the ply angle, and the output is the rationality judgment of the ply scheme and the objective function value corresponding to the angle; (2.2) Initialize the neural network parameters of the generative model The neural network parameters are the number of hidden layers, the number of neurons, the activation function, and the loss function; the loss function of the generator is the distance between the objective function value and the design target value, and this distance realizes positive deviation through the ReLU function. The loss function for realizing positive deviation is Loss1, that is, when the predicted value is greater than the target value, the loss function value is 0; the form of the ReLU function is as follows: The loss function of the discriminator is the error between the performance predicted value and the true value of the ply, and the ply design rationality index; The loss function of the generator is a combination of Loss1 and Loss2, where y target is the design target value, y pred is the model output result, y true is the true value of the rationality index; the loss function of the discriminator is a combination of Loss2 and Loss3; Loss1 = ReLU(y target -y pred )(1); Loss2 = cross_entropy(y true , y pred )(2); Loss3 = mean_absolute_error(y true , y pred )(3); In the above formulas (1)-(3), Loss1 is the distance between the objective function value and the design target value, Loss2 is the rationality of the ply design, and Loss3 is the error between the performance predicted value and the true value of the ply; (2.3) Train the generative model First, initialize the training parameters of the generative model, that is, set the number of training epochs, the optimization algorithm, and the batch sample size; the training process is as follows: (2.3.1) Fix the network parameters of the generator, and train the prediction ability of the discriminator's objective function; the training dataset is the training dataset generated in the above step (1); (2.3.2) Fix the network parameters of the part of the discriminator that predicts the objective function; (2.3.3) Start the loop of training epochs. First, fix the generator network and train the discriminator's ability to predict the rationality of the layup; the training data is: in the dataset, the true layup angle is true, and the layup angle generated by the generator network is false; after training the discriminator several times, fix the discriminator parameters and release the training of the generator parameters; train the overall model composed of the generator and the fixer to optimize the network parameters of the generator part; the training data is: the input is a random Gaussian variable, and the output is the layup objective function value in the dataset; (2.3.4) Repeat the process in the above step (2.3.3) according to the set number of training epochs to complete the reciprocating training of the discriminator and the generator until the number of training epochs is reached; (2.4) Generation of layup design scheme After saving the generator network in the trained generative model, using a random variable as the input, a layup design scheme that meets the design constraint conditions can be obtained; by setting a loop of several random variables, a large number of layup design schemes are generated, and the distribution diagrams of each layup angle are drawn for subsequent regularity mining.

5. The layup design criterion mining method based on generative and interpretable artificial intelligence according to claim 1, characterized in that The specific process of the above step (3) is as follows: (3.1) Establish a symbolic regression model between each layup angle based on the genetic programming algorithm (3.2) Initialize the parameters of the symbolic regression model; (3.3) Train the symbolic regression model.

6. The method for mining ply design criteria based on generative and interpretable artificial intelligence according to claim 5, wherein: In the above step (3.1), the symbolic regression model is established according to the SymbolicRegressor function in the open-source symbolic regression library GPlearn. Its basic steps are to set the population size, the number of iterative optimizations, the iteration termination condition, the cross-shift mutation coefficient, the proportion of validation samples, define the formula length penalty factor, and set the operator set in sequence.

7. The method for mining ply design criteria based on generative and interpretable artificial intelligence according to claim 6, characterized in that, The basic process of establishing a symbolic regression model according to the Symbolic Regressor function in the open-source symbolic regression library GPlearn is as follows: (3.1.1) Initialize the population Randomly generate an initial population, and each individual is a mathematical expression tree; (3.1.2) Fitness evaluation Calculate the fitness for each individual to measure the fitting degree of the expression to the training data; (3.1.3) Termination condition check If the condition is met, stop; otherwise, enter iterative optimization; (3.1.4) Selection operation Select parent individuals according to the fitness and retain excellent individuals; (3.1.5) Genetic operations Crossover, randomly select two parent individuals and exchange subtrees to generate new individuals; Mutation, randomly modify the subtrees in the individual; Shift, randomly permute the positions of the subtrees within the individual; (3.1.6) Generate a new population Merge the parent and offspring individuals, screen out a new population according to the fitness; update the number of iterations and return to step (3.1.2); (3.1.7) Output the optimal solution Return the expression tree with the highest fitness as the final symbolic regression model.

8. The method for mining ply design criteria based on generative and interpretable artificial intelligence according to claim 5, wherein The step (3.2) is to initialize the symbolic regression model, and the set parameters include the population initialization parameters related to the genetic optimization process in the model establishment according to the Symbolic Regressor function in the open-source symbolic regression library GPlearn, namely the population size and the set operator set, the genetic process parameters, namely the cross-shift mutation coefficient, the formula length penalty factor, and the validation sample ratio, and the result control parameters, namely the number of iterative optimizations and the iterative termination condition.

9. The ply design criterion mining method based on generative and interpretable artificial intelligence according to claim 5, characterized in that, The specific process of the step (3.3) is as follows: (3.3.1) Use the laying angle θ2 as the output, and use the laying angle θ1 as the variable to train the symbolic regression model, and obtain the regression coefficients; (3.3.2) Use the laying angle θ3 as the output, and use (θ1, θ2) as the variables to train the symbolic regression model, and obtain the regression coefficients; (3.3.3) In sequence, with the laying angle θ k as the output, using (θ1, θ2,... θ k-1 ) as variables to train the symbolic regression model and obtain the regression coefficients.

10. The layup design criterion mining method based on generative and interpretable artificial intelligence according to claim 1, characterized in that, The specific process of the step (4) is as follows: Regarding the rule that the regression coefficient R 2 is above 0.7 as a significant quantitative relationship, constructing a quantitative formula relationship for the ply angle of the composite material, and summarizing the ply design criteria for the corresponding design problems according to the quantitative formula relationship.

Images