Machine learning based epoxy curing process constraint optimization method and system

Abstract

The application relates to the technical field of material process optimization, and discloses an epoxy resin curing process constraint optimization method and system based on machine learning. The method comprises the following steps: acquiring an initial parameter vector by constructing multiple optimization parameters in an epoxy resin curing whole process, combining random block design and diversity indexes to determine a target population, and establishing a database containing process parameters and corresponding curing performance; calculating constraint information values of each parameter vector of the population and sorting and dividing a sub-population, executing constraint information guided classification evolution to generate a process parameter candidate set; predicting optimization targets and constraint values of the candidate set by using a heterogeneous machine learning model, screening an optimal parameter vector based on a constraint dominance criterion; respectively evaluating and verifying the optimal parameter performance, updating the population and the database, and outputting optimal process parameters when design requirements are met; the method effectively balances constraint satisfaction and multi-objective optimization, improves multi-objective prediction accuracy and constraint screening efficiency, and can obtain a process parameter combination considering multiple curing performances.

Description

[0001] This application relates to the field of materials and process optimization technology, and in particular to a method and system for constrained optimization of epoxy resin curing process based on machine learning. Background Technology

[0002] The optimal combination of epoxy resin curing process parameters is a crucial factor in determining curing performance. Furthermore, various curing properties of epoxy resin are mutually exclusive and must meet the threshold values ​​of key performance indicators under equipment operating conditions. Therefore, optimizing epoxy resin curing process parameters to improve curing performance is one of the important research directions for achieving optimal epoxy resin curing.

[0003] In related technologies, the optimization of epoxy resin curing process is often carried out by constructing an initial dataset through physical experiments, using a surrogate model to predict the curing performance corresponding to the process parameters, then using the EGO algorithm to calculate the expected gain and select the optimal sample for verification, and iteratively updating the dataset until the requirements are met. However, this method is limited to the temperature and time parameters of the curing stage. The curing performance of epoxy resin is related to the curing process parameters of epoxy resin with multiple curing properties. Therefore, the existing method cannot meet the curing performance requirements. At the same time, it ignores the strong coupling relationship between multiple optimization parameters. Since there is a mutual exclusion relationship between various curing properties of epoxy resin, the prediction accuracy of multiple objectives is low. Furthermore, the algorithm used is essentially a single-objective optimization and lacks a constraint-guided evolutionary mechanism. It is prone to premature convergence to local optima, which makes it impossible to balance the high accuracy of the optimization objective prediction with the high efficiency of constraint condition screening. Summary of the Invention

[0004] Based on this, this application provides a machine learning-based method and system for constrained optimization of epoxy resin curing process, aiming to solve the technical problems in related technologies where the epoxy resin curing process constraint optimization method cannot obtain a combination of epoxy resin curing process parameter values ​​that can simultaneously take into account multiple curing properties. At the same time, it lacks a constraint-guided optimization mechanism, making it difficult to balance constraint satisfaction and target optimization, resulting in low optimization accuracy and efficiency.

[0005] In a first aspect, embodiments of this application provide a machine learning-based method for optimizing epoxy resin curing process constraints, including: Step S10: Obtain multiple optimization parameters during the epoxy resin curing process to construct an initial parameter vector. Use a randomized block design method and diversity index on the initial parameter vector to determine the target population, which includes the initial parameter vector, optimization objective, and optimization constraints. Construct a database based on the target population. Step S20: Based on the target population, calculate the constraint information values ​​of all parameter vectors in the population, sort the constraint information values ​​to construct at least two subpopulations, and randomly select corresponding parameter vectors from the two subpopulations to perform constraint information-guided classification evolution to obtain a candidate set of parameter vectors for the epoxy resin curing process. Step S30: Input the parameter vector candidate set into a preset heterogeneous machine learning model to predict the optimization objective and optimization constraints of the parameter vector candidate set respectively, and determine the optimal parameter vector based on the constraint dominance criterion; Step S40: Evaluate the optimization objective and optimization constraint values ​​corresponding to the optimal parameter vector respectively, and update the target population and database accordingly. If the evaluation results meet the design requirements, output the target parameter vector of the epoxy resin curing process.

[0006] In some embodiments, in step S10, the initial parameter vector includes the ingredient ratio, stirring speed, stirring time, heating rate, curing temperature, holding time, and mold pressure parameters; the optimization objectives include tensile strength, flexural strength, curing shrinkage rate, and total curing cycle; and the optimization constraints include impact strength.

[0007] In some embodiments, in step S10, a randomized block design method and a diversity index are applied to the initial parameter vector to determine the target population, which includes the optimization parameter vector, the optimization objective, and the optimization constraints, including: The randomized block design method is executed cyclically to generate multiple temporary populations, each of which consists of multiple parameter vectors of the epoxy resin curing process. The diversity score of each temporary population is assessed based on diversity indicators, where the expression for calculating the diversity score is:

[0008] In the formula, In order to target the temporary population The calculated diversity score, For indexing temporary populations, For the index of the parameter vector in the temporary population, This refers to the index of the specific optimization parameter in the parameter vector of the temporary population. For the first The first parameter vector One optimization parameter, For the first The first parameter vector One optimization parameter; Based on the diversity score, a temporary population with the highest diversity score is selected as the target population. The database is constructed based on all parameter vectors in the target population and their corresponding tensile strength, flexural strength, impact strength, curing shrinkage rate, and total curing cycle.

[0009] In some embodiments, step S20 involves calculating constraint information values ​​for all parameter vectors in the target population based on the target population, and sorting the constraint information values ​​to construct at least two sub-populations, including: The constraint information value is calculated based on the impact intensity values ​​of all parameter vectors in the target population; The constraint information values ​​are sorted from smallest to largest. The parameter vectors in the first half of the sorting are used to construct the first subpopulation, and the parameter vectors in the second half of the sorting are used to construct the second subpopulation.

[0010] In some embodiments, in step S20, corresponding parameter vectors are randomly selected from two subpopulations for constraint-guided classification evolution to obtain a candidate set of parameter vectors for the epoxy resin curing process, including: Based on the aforementioned optimization objective, the simplex method is used to determine the uniformly distributed weight vector; Construct the Chebyshev aggregation function corresponding to the weight vector to transform the multi-objective constrained optimization problem into multiple uniformly distributed single-objective constrained optimization problems; For each single-objective constrained optimization problem, calculate the vertical distance between the corresponding weight vector and all parameter vectors in the population, and associate the parameter vector with the smallest vertical distance with the weight vector. If the parameter vector associated with its corresponding weight vector is in the first subpopulation, then the corresponding constraint-guided classification evolution operation is as follows:

[0011] In the formula, For the first A temporary child parameter vector; For the first A parameter vector corresponding to a single-objective constrained optimization problem; and These are two parameter vectors randomly selected from the first subpopulation. and These are the indices for random selection; The parameter vector is randomly selected from the second subpopulation. For indexing when selecting randomly; and These are scaling factors; If the parameter vector associated with its corresponding weight vector is in the second subpopulation, then the corresponding constraint-guided classification evolution operation is as follows:

[0012] In the formula, and These are two parameter vectors randomly selected from the second subpopulation. and These are the indices for random selection; The parameter vector is randomly selected from the first subpopulation. This is the index for random selection.

[0013] In some embodiments, in step S30, the heterogeneous machine learning model includes a Gaussian process machine learning model and a radial basis function machine learning model, wherein the construction of the heterogeneous machine learning model includes: Using all parameter vectors in the database as input data and the four optimization objective values ​​corresponding to all parameter vectors as output response values, four corresponding Gaussian process machine learning models are constructed. Using all parameter vectors in the database as input data and the optimization constraint values ​​corresponding to all parameter vectors in the database as output response values, a corresponding radial basis function machine learning model is constructed.

[0014] In some embodiments, step S30, determining the optimal parameter vector based on the constraint dominance criterion, includes: Determine the constraint information values ​​of all child parameter vectors in the candidate parameter vector set; If the minimum constraint information value of all child parameter vectors is equal to zero, then all child parameter vectors with constraint information values ​​equal to zero are used to construct a set of feasible parameter vectors, and the parameter vector with the minimum Chebyshev aggregation function value in the set of feasible parameter vectors is selected as the optimal parameter vector. If the minimum constraint information value of all child parameter vectors is greater than zero, then the child parameter vector with the minimum constraint information value is taken as the optimal parameter vector.

[0015] Compared with the prior art, the technical solution provided in the first aspect of this application includes at least the following beneficial effects or advantages: The epoxy resin curing process constraint optimization method provided in this application generates a target population and constructs a database through randomized block design combined with diversity indicators to cover all key parameters affecting curing performance. This ensures that the initial population is evenly distributed within the design space. Based on constraint information values, multiple subpopulations are divided and constraint-guided classification evolution is performed. During the evolution process, the relationship between constraint satisfaction and target optimization is simultaneously balanced, preventing the algorithm from prematurely converging to local optima and generating a broader set of process parameter candidates. On this basis, heterogeneous machine learning models are used to predict the optimization target and constraints separately, which can adapt to the prediction needs of different performance indicators, improve the accuracy of simultaneous prediction of multiple targets and the efficiency of constraint condition screening. Then, the optimal parameters are screened through constraint dominance criteria to ensure that the output process parameters meet the requirements of epoxy resin curing process. At the same time, through experimental verification and continuous updating of the population and database, the model and evolution direction can be continuously iterated and optimized, ultimately obtaining a combination of process parameters that can simultaneously take into account multiple curing performances.

[0016] Secondly, embodiments of this application also provide a machine learning-based epoxy resin curing process constraint optimization system, comprising: The database construction module is configured to acquire multiple optimization parameters during the epoxy resin curing process to construct an initial parameter vector, apply a randomized block design method and a diversity index to the initial parameter vector to determine a target population including the initial parameter vector, optimization objective and optimization constraints, and construct a database based on the target population; The candidate set determination module is configured to calculate the constraint information values ​​of all parameter vectors in the target population based on the target population, sort the constraint information values ​​to construct at least two subpopulations, and randomly select corresponding parameter vectors from the two subpopulations to perform constraint information-guided classification evolution to obtain a candidate set of parameter vectors for the epoxy resin curing process. The optimal parameter determination module is configured to input the parameter vector candidate set into a preset heterogeneous machine learning model to predict the optimization objective and optimization constraints of the parameter vector candidate set respectively, and determine the optimal parameter vector based on the constraint dominance criterion. The iterative output module is configured to evaluate the optimization objective and optimization constraint values ​​corresponding to the optimal parameter vector respectively, and update the target population and database accordingly. If the evaluation results meet the design requirements, the target parameter vector of the epoxy resin curing process is output.

[0017] Thirdly, embodiments of this application also provide an electronic device, including: At least one processor; and A memory communicatively connected to the at least one processor; wherein, The memory stores instructions executable by the at least one processor, which, when executed by the at least one processor, enables the at least one processor to perform the steps of a machine learning-based epoxy resin curing process constraint optimization method as described in any of the first aspects above.

[0018] Fourthly, embodiments of this application also provide a computer-readable storage medium storing computer program instructions thereon, characterized in that, when the computer program instructions are executed by a processor, they implement the steps of a machine learning-based epoxy resin curing process constraint optimization method as described in any of the first aspects above.

[0019] It is understood that the beneficial effects of the technical solutions provided in the second, third and fourth aspects mentioned above can be found in the relevant descriptions in the first aspect mentioned above, and will not be repeated here.

[0020] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application. Attached Figure Description

[0021] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 A flowchart of a machine learning-based epoxy resin curing process constraint optimization method provided in an embodiment of this application; Figure 2 A structural block diagram of a machine learning-based epoxy resin curing process constraint optimization system provided in this application embodiment; Figure 3 This is a structural block diagram of an electronic device provided in an embodiment of this application. Detailed Implementation

[0023] To facilitate understanding of this application, a more complete description will be provided below with reference to the accompanying drawings, which illustrate several embodiments of the present application. However, the present application can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided so that the disclosure of this application will be thorough and complete.

[0024] It should be noted that, unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0025] Please see Figure 1 This embodiment provides a machine learning-based method for optimizing the constraints of epoxy resin curing process, specifically including steps S10 to S40.

[0026] Step S10: Obtain multiple optimization parameters during the epoxy resin curing process to construct an initial parameter vector. Use a randomized block design method and diversity index on the initial parameter vector to determine the target population, which includes the initial parameter vector, optimization objective, and optimization constraints. Construct a database based on the target population. In some embodiments, the initial parameter vector (parameters to be optimized) for the epoxy resin curing process includes the mixing ratio, stirring speed, stirring time, heating rate, curing temperature, holding time, and mold pressure parameters. These parameters can be acquired using existing data acquisition equipment. Optimization objectives include tensile strength, flexural strength, curing shrinkage rate, and total curing cycle. Optimization constraints include impact strength. To integrate these parameters and quantify the epoxy resin curing process optimization, a calculation expression corresponding to the epoxy resin curing process optimization can be constructed. The specific expression is as follows:

[0027] In the formula, This is the initial parameter vector to be optimized for the epoxy resin curing process, which contains seven parameters to be optimized. For ingredient ratios, This refers to the stirring speed. This refers to the stirring time. For the heating rate, This is the curing temperature. For heat preservation time, For mold pressure, , , and Based on the optimized parameter vector The expressions for tensile strength, flexural strength, impact strength, and curing shrinkage rate are obtained. and These represent the optimization parameter vectors respectively. The calculated negative values ​​of tensile strength and flexural strength , as well as These represent the optimization parameter vectors respectively. The calculated impact strength, curing shrinkage rate, and total curing cycle are as follows: The threshold value for impact strength. The upper and lower bounds of the optimization parameters are represented. Find represents finding the optimal optimization parameter vector for the mathematical optimization problem corresponding to the epoxy resin curing process. Min represents minimizing each performance index of the epoxy resin curing process. St represents the constraints that need to be satisfied.

[0028] Furthermore, the design space is determined based on the value ranges of each optimized parameter in the initial parameter vector. A population is generated and a database is established by combining the randomized block design method with diversity indicators. The parameters in the initial parameter vector, the value ranges of each optimized parameter, and the design space can be determined based on prior knowledge of the epoxy resin curing process or historical experience data of the epoxy resin curing process. The database construction specifically includes: iteratively executing the randomized block design method to generate... Each temporary population consists of [number] species. The parameters of an epoxy resin curing process are composed of a vector. The diversity score of each temporary population is assessed based on diversity indicators, where the expression for calculating the diversity score is:

[0029] In the formula, In order to target the temporary population The calculated diversity score, For indexing temporary populations, For the index of the parameter vector in the temporary population, This refers to the index of the specific optimization parameter in the parameter vector of the temporary population. For the first The first parameter vector One optimization parameter, For the first The first parameter vector One optimization parameter; After obtaining multiple diversity scores, a temporary population with the highest diversity score is selected as the target population; and the database is constructed based on all parameter vectors in the target population and their corresponding tensile strength, flexural strength, impact strength, curing shrinkage rate and total curing period.

[0030] In one example, the tensile strength, flexural strength, impact strength, curing shrinkage, and total curing period can be obtained by: using mechanical property testing equipment such as an electronic universal testing machine to test the tensile and flexural strength corresponding to each parameter vector in the target population; using mechanical property testing equipment such as a cantilever beam impact testing machine to test the impact strength corresponding to each parameter vector in the target population; using a laser displacement sensor to test the curing shrinkage corresponding to each parameter vector in the target population; and using an infrared thermal imager to test the total curing period corresponding to each parameter vector in the target population; and then using all parameter vectors in the target population, along with their corresponding tensile strength, flexural strength, impact strength, curing shrinkage, and total curing period, to construct a database.

[0031] Step S20: Based on the target population, calculate the constraint information values ​​of all parameter vectors in the population, sort the constraint information values ​​to construct at least two subpopulations, and randomly select corresponding parameter vectors from the two subpopulations to perform constraint information-guided classification evolution to obtain a candidate set of parameter vectors for the epoxy resin curing process. In some embodiments, considering that the mathematical optimization problem corresponding to the epoxy resin curing process optimization is a multi-objective constrained optimization problem with four optimization objectives and optimization constraints, this embodiment constructs a multi-objective evolutionary algorithm based on decomposition (MOEA / D) architecture for the four optimization objectives. Specifically, this includes: generating a set of uniformly distributed weight vectors in the objective space composed of the four optimization objectives using the simplex method; and designing a Chebyshev aggregation function based on the weight vectors to transform the multi-objective constrained optimization problem into... This is a uniformly distributed single-objective constrained optimization problem. It needs to be explained that the objective space is a multi-dimensional geometric space spanned by all performance indices to be optimized as independent coordinate axes; in this application, it is a four-dimensional numerical space composed of four optimization objectives: tensile strength, flexural strength, curing shrinkage rate, and total curing period; any point in the objective space uniquely corresponds to the comprehensive performance of a set of epoxy resin curing process parameters; the simplex method is a classic algorithm in the field of linear programming, its function is to find the global optimal solution of the linear objective function under constraints; the core function of the Chebyshev aggregation function is to transform a multi-dimensional multi-objective optimization problem into multiple independent single-objective subproblems.

[0032] Furthermore, the constraint information value is calculated based on the impact intensity values ​​of all parameter vectors in the population, such as for the first... A parameter vector, the specific formula is as follows: ; In the formula, The threshold value for impact strength. Indicates the first in the population The constraint information value of each parameter vector. Indicates the first in the population A parameter vector; Furthermore, after obtaining multiple constraint information values, the constraint information values ​​in the target population are sorted from smallest to largest. The parameter vectors in the first half of the sorted values ​​are used to construct the first subpopulation, and the parameter vectors in the second half of the sorted values ​​are used to construct the second subpopulation. Then, for each single-objective constraint optimization problem under the MOEA / D architecture, the vertical distance between the weight vector corresponding to the single-objective constraint optimization problem and all parameter vectors in the population is calculated, and the parameter vector with the smallest vertical distance is associated with the weight vector.

[0033] Specifically, for each single-objective constrained optimization problem under the MOEA / D architecture, if the parameter vector associated with its corresponding weight vector is in the first subpopulation, the corresponding constraint-guided classification evolution operation is as follows: ; In the above formula, For the first Each child parameter vector ,and Each child parameter vector constitutes a candidate set of parameter vectors; For the first A single-objective constrained optimization problem corresponds to a parameter vector associated with a weight vector; and These are two parameter vectors randomly selected from the first subpopulation, where... and These are the indices for random selection; Let be a parameter vector randomly selected from the second subpopulation, where For indexing when selecting randomly; and These are scaling factors.

[0034] Furthermore, to drive each temporary child parameter vector toward the optimal optimization objective value, an evolutionary operation is designed based on the gradient information of the optimization objective function to generate child parameter vectors in the direction of the fastest convergence of the optimization objective gradient, as follows:

[0035] In the formula, For the first Each child parameter vector ,and Each child parameter vector constitutes a candidate set of parameter vectors; Indicating targeting The optimization objective gradient; Let be a parameter vector randomly selected from the first subpopulation, where For indexing when selecting randomly; This represents a normally distributed random number with a mean of 0 and a standard deviation of 1, to provide diverse evolutionary trajectories in the direction of the constraint gradient; This means that the mean is Furthermore, random numbers generated from a normal distribution with a standard deviation of 1 evolve in a diversified manner towards high-potential individuals; express L1 norm; express The L2 norm; This is the scaling factor; In some embodiments, for each single-objective constrained optimization problem under the MOEA / D architecture, if the parameter vector associated with its corresponding weight vector is in the second subpopulation, the corresponding constraint-guided classification evolution operation is as follows: ; In the above formula, and These are two parameter vectors randomly selected from the second subpopulation, where... and These are the indices for random selection; Let be a parameter vector randomly selected from the first subpopulation, where This is the index for random selection.

[0036] Furthermore, to drive each temporary offspring parameter vector toward the feasible region, an evolutionary operation is designed incorporating constraint gradient information to generate offspring parameter vectors that meet the constraints, as follows:

[0037] In the formula, For the first Each child parameter vector ,and Each child parameter vector constitutes a candidate set of parameter vectors; Indicating targeting The constraint information gradient; Let be a parameter vector randomly selected from the first subpopulation, where For indexing when selecting randomly; This represents a normally distributed random number with a mean of 0 and a standard deviation of 1, to provide diverse evolutionary trajectories in the direction of the constraint gradient; This indicates that the mean is Furthermore, random numbers generated from a normal distribution with a standard deviation of 1 evolve in a diversified manner towards high-potential individuals; express L1 norm; express The L2 norm.

[0038] It should be noted that in this embodiment, a decomposition-based multi-objective evolutionary algorithm architecture is constructed to address the four-objective constrained optimization characteristics of the epoxy resin curing process. The simplex method is used to generate uniformly distributed weight vectors, ensuring that the decomposed single-objective sub-problems are uniformly covered in the objective space, laying the foundation for obtaining a uniformly distributed optimal solution set. The original multi-objective constrained optimization problem is transformed into multiple single-objective constrained optimization problems through Chebyshev aggregation functions, enabling parallel solving of the multi-objective problem. The constraint information values ​​of the parameter vectors are calculated based on impact strength and divided into two subpopulations according to their magnitude, clearly distinguishing the feasible region. By associating individuals within the infeasible region with the nearest parameter vector for each single-objective subproblem, a precise correspondence between the subproblem and the population individuals is established, ensuring the targeted nature of the evolutionary direction. Differentiated classification and evolutionary operations are applied to different subpopulations to which the associated individuals belong, which can guide individuals within the feasible region to evolve toward the multi-objective optimal direction, while simultaneously driving individuals within the infeasible region to converge rapidly toward the feasible region boundary. This effectively balances the relationship between constraint satisfaction and multi-objective optimization, preventing the algorithm from converging to a local optimum too early, and improving the quality of the candidate set of process parameters and the efficiency of the global search.

[0039] Step S30: Input the parameter vector candidate set into a preset heterogeneous machine learning model to predict the optimization objective and optimization constraints of the parameter vector candidate set respectively, and determine the optimal parameter vector based on the constraint dominance criterion; In some embodiments, the heterogeneous machine learning model includes a Gaussian process machine learning model constructed for the optimization objective and a radial basis function machine learning model constructed for the optimization constraints. The construction of the Gaussian process machine learning model and the radial basis function machine learning model includes: using all parameter vectors in the database as input data and the four optimization objective values ​​corresponding to all parameter vectors as output response values ​​to construct four corresponding Gaussian process machine learning models; and using all parameter vectors in the database as input data and the optimization constraint values ​​corresponding to all parameter vectors in the database as output response values ​​to construct a corresponding radial basis function machine learning model.

[0040] In one example, the Gaussian process machine learning model includes an input module, a hyperparameter optimization module, and a prediction module. Specifically, the input module mainly takes all parameter vectors from the database and four optimization target values ​​corresponding to the parameter vectors as input, and performs Gaussian normalization on these data to eliminate dimensional differences. The hyperparameter optimization module mainly takes the initial hyperparameter values ​​as input and all data after Gaussian normalization in the input module, and calls optimization operators such as differential evolution or gradient algorithms to determine the optimal hyperparameter values. The prediction module mainly takes the optimal parameter vector and offspring parameter vectors generated by the algorithm during the evolution process as input to obtain the predicted optimization target values ​​corresponding to these parameter vectors. In one example, the radial basis function machine learning model includes an input module, a model parameter determination module, and a prediction module. Specifically, the input module mainly takes all parameter vectors in the database and the corresponding optimization constraint values ​​as input, and performs maximum-minimum normalization on these data to eliminate dimensional differences. In the model parameter determination module, based on all the data in the input module after maximum-minimum normalization, the least squares method is used to determine the model parameter values. In the prediction module, the optimal parameter vector and the offspring parameter vector are mainly input to obtain the predicted optimization constraint values ​​corresponding to these parameter vectors. In some embodiments, determining the optimal parameter vector based on the constraint dominance criterion specifically includes: determining the constraint information values ​​of all child parameter vectors in the parameter vector candidate set; if the minimum constraint information value of all child parameter vectors is equal to zero, then using all child parameter vectors with constraint information values ​​equal to zero to construct a feasible parameter vector set, and selecting the parameter vector with the minimum Chebyshev aggregation function value in the feasible parameter vector set as the optimal parameter vector; if the minimum constraint information value of all child parameter vectors is greater than zero, then using the child parameter vector with the minimum constraint information value as the optimal parameter vector.

[0041] In this embodiment, a Gaussian process machine learning model is constructed to independently fit the four optimization objectives, thereby obtaining the nonlinear coupling relationship between various performance indicators in the epoxy resin curing process. This improves the accuracy and reliability of simultaneous prediction of multiple objectives. At the same time, a radial basis function machine learning model is used to model the optimization constraints, enabling rapid evaluation and screening of the constraints. Based on this, a phased constraint dominance criterion is used to screen the optimal parameter vector, prioritizing the selection of feasible parameter vectors that meet the constraints and choosing the individual with the best overall performance. This allows for better overall curing performance while ensuring that the process parameters meet the usage requirements.

[0042] In some embodiments, an adaptive heterogeneous machine learning model is established that integrates coupling information of multiple optimization objectives and constraint satisfaction information to address the nonlinear coupling relationships (such as the positive correlation between tensile and bending strength, and the negative correlation between curing period and mechanical properties) between various optimization objectives that cannot be learned by independently training machine learning models for each optimization objective. First, all optimization objectives are standardized to eliminate dimensional differences between different optimization objectives. Specifically, tensile strength and bending strength are inversely standardized, and the algorithm expression is as follows: ; In the formula, This represents the m-th standardized optimization objective value corresponding to the i-th parameter vector in the database. Let m be the m-th optimization target value corresponding to the i-th parameter vector in the database, where m=1 represents tensile strength and m=2 represents bending strength; and These are the maximum and minimum values ​​of the i-th optimization objective value corresponding to all parameter vectors in the database, respectively; For precision parameters, to avoid and When they are equal, they cannot be divided. The algorithm for positively standardizing the curing shrinkage rate and total curing cycle is as follows: ; In the formula, This represents the m-th standardized optimization objective value corresponding to the i-th parameter vector in the database. Let m be the m-th optimization target value corresponding to the i-th parameter vector in the database, where m=3 represents the curing shrinkage rate and m=4 represents the total curing cycle; Finally, based on all the data in the standardized database, heterogeneous machine learning models are established for the optimization objective and optimization constraints respectively. Specifically, a Gaussian process machine learning model is constructed for the optimization objective, and a radial basis function machine learning model is constructed for the optimization constraints.

[0043] Step S40: Evaluate the optimization objective and optimization constraint values ​​corresponding to the optimal parameter vector respectively, and update the target population and database accordingly. If the evaluation results meet the design requirements, output the target parameter vector of the epoxy resin curing process.

[0044] In this step, the evaluation of the optimization objective and optimization constraint value corresponding to the optimal parameter vector can be achieved based on physical experimental evaluation. For example, mechanical performance testing equipment such as an electronic universal testing machine is used to test the tensile strength and flexural strength corresponding to the optimal parameter vector; mechanical performance testing equipment such as a cantilever beam impact testing machine is used to test the impact strength corresponding to the optimal parameter vector; a laser displacement sensor is used to test the curing shrinkage rate corresponding to the optimal parameter vector; and an infrared thermal imager is used to test the total curing cycle corresponding to the optimal parameter vector.

[0045] After evaluation, according to the constraint dominance criterion, the worst parameter vector in the population is replaced by the optimal parameter vector to achieve population update. It should be noted that the constraint dominance criterion is the core rule used to judge the quality of parameter vectors in constrained multi-objective optimization. Its principle is to first judge the degree of constraint satisfaction, and then compare the target performance to ensure that the optimization process always converges to the feasible region. If the optimal result corresponding to the optimal parameter vector meets the design requirements, the target parameter vector of the epoxy resin curing process is output; otherwise, the process returns to step S20 above until the optimal result meets the design requirements.

[0046] In the aforementioned steps of the epoxy resin curing process constraint optimization method, a target population is generated and a database is constructed by combining randomized block design with diversity indicators to cover all key parameters affecting curing performance. This ensures that the initial population is evenly distributed within the design space, providing a comprehensive process performance mapping basis for subsequent optimization. Based on constraint information values, multiple subpopulations are divided and constraint-guided classification evolution is performed. During the evolution process, the relationship between constraint satisfaction and target optimization is simultaneously balanced, preventing the algorithm from prematurely converging to local optima and generating a broader set of process parameter candidates. On this basis, heterogeneous machine learning models are used to predict the optimization target and constraints respectively, which can adapt to the prediction needs of different performance indicators, improve the accuracy of simultaneous prediction of multiple targets and the efficiency of constraint condition screening. Then, the optimal parameters are screened through constraint dominance criteria to ensure that the output process parameters meet the requirements of epoxy resin curing process. At the same time, physical experiments are used to verify and the population and database are continuously updated, which can continuously iterate and optimize the model and evolution direction, ultimately obtaining a combination of process parameters that can simultaneously take into account multiple curing performances.

[0047] In some embodiments, a benchmark function is provided to illustrate the optimization performance of the machine learning-based epoxy resin curing process constraint optimization method provided in the above embodiments. The expression of the benchmark function is as follows:

[0048] In the above formula, , , and These represent four optimization objectives. This represents the optimization constraint. and It is a function with two coefficients. Represents a parameter vector. Indicates the index of the optimization parameter. This represents the i-th optimization parameter. Indicates minimization. This indicates the constraints that need to be satisfied.

[0049] The benchmark function was processed through the steps of the machine learning-based epoxy resin curing process constraint optimization method provided in the above embodiments to obtain experimental results. To further illustrate this embodiment, the machine learning-based epoxy resin curing process constraint optimization method of this embodiment was compared with the NSGA-II algorithm. The maximum number of evaluations for each optimization objective and constraint in this embodiment was set to 800. The experimental results are shown in Table 1.

[0050] Table 1 Comparison of optimization results of different methods

[0051] As shown in Table 1, under the same optimization objective and number of optimization constraint evaluations, the IGD index value obtained by the method in this embodiment is smaller than that of the comparative NSGA-II algorithm. It should be explained that the IGD index calculates the average of the minimum distances from each point on the true Pareto front to the generated approximate Pareto front. The smaller the IGD index value, the better the performance. Therefore, the optimization efficiency of the machine learning-based epoxy resin curing process constraint optimization design method in this embodiment is higher. The method in this embodiment has good performance in the epoxy resin curing process parameter optimization problem. It has better performance in terms of convergence accuracy, solution set distribution uniformity and coverage in multi-objective optimization, and can more efficiently obtain epoxy resin curing process parameter combinations that take into account multiple curing properties.

[0052] Please see Figure 2 , Figure 2 This embodiment illustrates a machine learning-based epoxy resin curing process constraint optimization system. In this embodiment, the machine learning-based epoxy resin curing process constraint optimization system is used to perform the above-mentioned... Figure 1 The steps in the corresponding embodiments. Please refer to the details. Figure 1 as well as Figure 1 The relevant descriptions in the corresponding embodiments are shown below. For ease of explanation, only the parts relevant to this embodiment are shown. See also... Figure 2 The machine learning-based epoxy resin curing process constraint optimization system 200 includes: The database construction module 210 is configured to acquire multiple optimization parameters during the epoxy resin curing process to construct an initial parameter vector, apply a randomized block design method and a diversity index to the initial parameter vector, determine a target population including the initial parameter vector, optimization objective and optimization constraints, and construct a database based on the target population; The candidate set determination module 220 is configured to calculate the constraint information values ​​of all parameter vectors in the target population based on the target population, sort the constraint information values ​​to construct at least two sub-populations, and randomly select corresponding parameter vectors from the two sub-populations to perform constraint information-guided classification evolution to obtain a parameter vector candidate set for the epoxy resin curing process. The optimal parameter determination module 230 is configured to input the parameter vector candidate set into a preset heterogeneous machine learning model to predict the optimization objective and optimization constraints of the parameter vector candidate set respectively, and determine the optimal parameter vector based on the constraint dominance criterion. The iterative output module 240 is configured to evaluate the optimization objective and optimization constraint values ​​corresponding to the optimal parameter vector respectively, and update the target population and database accordingly. If the evaluation results meet the design requirements, the target parameter vector of the epoxy resin curing process is output.

[0053] The machine learning-based epoxy resin curing process constraint optimization system provided in this embodiment generates a target population and constructs a database through randomized block design combined with diversity indicators to cover all key parameters affecting curing performance. This ensures that the initial population is evenly distributed within the design space, providing a comprehensive process performance mapping foundation for subsequent optimization. Based on constraint information values, multiple subpopulations are divided and constraint-guided classification evolution is performed. During the evolution process, the relationship between constraint satisfaction and target optimization is simultaneously balanced, preventing the algorithm from prematurely converging to local optima and generating a broader set of process parameter candidates. On this basis, heterogeneous machine learning models are used to predict the optimization target and constraints separately, adapting to the prediction needs of different performance indicators and improving the accuracy of simultaneous multi-target prediction and the efficiency of constraint selection. The optimal parameters are then selected through constraint dominance criteria, ensuring that the output process parameters meet the requirements of epoxy resin curing processes. Simultaneously, physical experiments are used to verify and continuously update the population and database, enabling iterative optimization of the model and evolution direction, ultimately obtaining a combination of process parameters that can simultaneously consider multiple curing performances.

[0054] It should be understood that the modules in the system provided in this embodiment are used to execute... Figure 1 The steps in the corresponding embodiments, and for Figure 1 The steps in the corresponding embodiments have been explained in detail in the above embodiments. Please refer to them for details. Figure 1 as well as Figure 1 The relevant descriptions in the corresponding embodiments will not be repeated here.

[0055] Figure 3 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Figure 3 As shown, the electronic device 90 provided in this embodiment includes at least one processor 901 and a memory 902. Optionally, the electronic device 90 further includes a communication component 903. The processor 901, memory 902, and communication component 903 are connected via a bus 904. In the specific implementation process, at least one processor 901 executes computer execution instructions stored in memory 902, causing at least one processor 901 to execute the above-mentioned machine learning-based epoxy resin curing process constraint optimization method.

[0056] The specific implementation process of processor 901 can be found in the above method embodiments, and its implementation principle and technical effect are similar. It will not be repeated here.

[0057] In the above embodiments, it should be understood that the processor 901 may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or any conventional processor.

[0058] The memory 902 can be an internal storage unit of the electronic device 90, such as a hard drive or memory in a server. The memory 902 can also be an external storage terminal device of the electronic device 90, such as a plug-in hard drive, smart media card (SMC), secure digital (SD) card, flash card, etc. equipped on the electronic device 90.

[0059] Furthermore, the memory 902 may include both internal storage units of the electronic device 90 and external storage terminal devices. The memory 902 is used to store computer programs and other programs and data required by the turntable terminal device. The memory 902 can also be used to temporarily store data that has been output or will be output.

[0060] Bus 904 can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of illustration, the buses shown in the accompanying drawings are not limited to a single bus or a single type of bus.

[0061] Those skilled in the art will understand that Figure 3 This is merely an example of electronic device 90 and does not constitute a limitation on electronic device 90. It may include more or fewer components than shown, or combine certain components, or different components. For example, a turntable terminal device may also include input / output terminal devices, network access terminal devices, etc.

[0062] In one embodiment, a computer-readable storage medium is also provided, the computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the machine learning-based epoxy resin curing process constraint optimization method as described in the above embodiments.

[0063] The aforementioned readable storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The readable storage medium can be any available medium accessible to a general-purpose or special-purpose computer.

[0064] An exemplary readable storage medium is coupled to a processor, enabling the processor to read information from and write information to the readable storage medium. Of course, the readable storage medium can also be a component of the processor. The processor and the readable storage medium can reside in application-specific integrated circuits (ASICs). Alternatively, the processor and the readable storage medium can exist as discrete components in the device.

[0065] The division of units is merely a logical functional division; in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be indirect coupling or communication connection through some interfaces, devices, or units, and may be electrical, mechanical, or other forms.

[0066] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0067] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. The computer-readable storage medium can be non-volatile or volatile. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable storage medium can include: any entity or device capable of carrying computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc.

[0068] The terms "first," "second," "third," etc., in the specification, claims, and accompanying drawings of this application are used to distinguish different objects and not to describe a particular order. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, it may include a series of steps or units, or optionally, steps or units not listed, or other steps or units inherent to these processes, methods, products, or devices.

[0069] The accompanying drawings show only the portions relevant to this application, not all of them. Before discussing exemplary embodiments in more detail, it should be noted that some exemplary embodiments are described as processes or methods depicted as flowcharts. Although the flowcharts describe operations (or steps) as sequential processes, many of these operations may be performed in parallel, concurrently, or simultaneously. Furthermore, the order of the operations may be rearranged. The process may be terminated when its operation is completed, but may also have additional steps not included in the drawings. The process may correspond to a method, function, procedure, subroutine, subprogram, etc.

[0070] The terms “component,” “module,” “system,” “unit,” etc., used in this specification are used to refer to computer-related entities, hardware, firmware, combinations of hardware and software, software, or software in execution. For example, a unit can be, but is not limited to, a process running on a processor, a processor, an object, an executable file, a thread of execution, a program, and / or distributed between two or more computers. Furthermore, these units can be executed from various computer-readable media on which various data structures are stored. Units can communicate, for example, via local and / or remote processes based on signals having one or more data packets (e.g., data from a second unit interacting with another unit between a local system, a distributed system, and / or a network; for example, the Internet interacting with other systems via signals).

[0071] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "illustrative embodiment," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example.

[0072] Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. The reference to "embodiment" herein means that a specific feature, structure, or characteristic described in connection with an embodiment can be included in at least one embodiment of this application. The appearance of this phrase in various places in the specification does not necessarily indicate the same embodiment, nor is it an independent or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

Claims

1. A machine learning-based method for constrained optimization of epoxy resin curing process, characterized in that, include: Step S10: Obtain multiple optimization parameters during the epoxy resin curing process to construct an initial parameter vector. Use a randomized block design method and diversity index on the initial parameter vector to determine the target population, which includes the initial parameter vector, optimization objective, and optimization constraints. Construct a database based on the target population. Step S20: Based on the target population, calculate the constraint information values ​​of all parameter vectors in the population, sort the constraint information values ​​to construct at least two subpopulations, and randomly select corresponding parameter vectors from the two subpopulations to perform constraint information-guided classification evolution to obtain a candidate set of parameter vectors for the epoxy resin curing process. Step S30: Input the parameter vector candidate set into a preset heterogeneous machine learning model to predict the optimization objective and optimization constraints of the parameter vector candidate set respectively, and determine the optimal parameter vector based on the constraint dominance criterion; Step S40: Evaluate the optimization objective and optimization constraint values ​​corresponding to the optimal parameter vector respectively, and update the target population and database accordingly. If the evaluation results meet the design requirements, output the target parameter vector of the epoxy resin curing process.

2. The machine learning-based constrained optimization method for epoxy resin curing process according to claim 1, characterized in that, In step S10, the initial parameter vector includes the ingredient ratio, stirring speed, stirring time, heating rate, curing temperature, holding time, and mold pressure parameters; the optimization objectives include tensile strength, flexural strength, curing shrinkage rate, and total curing cycle; and the optimization constraints include impact strength.

3. The machine learning-based constrained optimization method for epoxy resin curing process according to claim 2, characterized in that, In step S10, a randomized block design method and a diversity index are used to determine the target population, including the optimization parameter vector, the optimization objective, and the optimization constraints, based on the initial parameter vector. The randomized block design method is executed cyclically to generate multiple temporary populations, each of which consists of multiple parameter vectors of the epoxy resin curing process. The diversity score of each temporary population is assessed based on diversity indicators, where the expression for calculating the diversity score is: In the formula, In order to target the temporary population The calculated diversity score, For indexing temporary populations, For the index of the parameter vector in the temporary population, This refers to the index of the specific optimization parameter in the parameter vector of the temporary population. For the first The first parameter vector One optimization parameter, For the first The first parameter vector One optimization parameter; Based on the diversity score, a temporary population with the highest diversity score is selected as the target population. The database is constructed based on all parameter vectors in the target population and their corresponding tensile strength, flexural strength, impact strength, curing shrinkage rate, and total curing cycle.

4. The machine learning-based constrained optimization method for epoxy resin curing process according to claim 2, characterized in that, In step S20, based on the target population, constraint information values ​​of all parameter vectors in the population are calculated, and the constraint information values ​​are sorted to construct at least two sub-populations, including: The constraint information value is calculated based on the impact intensity values ​​of all parameter vectors in the target population; The constraint information values ​​are sorted from smallest to largest. The parameter vectors in the first half of the sorting are used to construct the first subpopulation, and the parameter vectors in the second half of the sorting are used to construct the second subpopulation.

5. The machine learning-based constrained optimization method for epoxy resin curing process according to claim 4, characterized in that, In step S20, corresponding parameter vectors are randomly selected from the two subpopulations for constraint-guided classification evolution to obtain a candidate set of parameter vectors for the epoxy resin curing process, including: Based on the aforementioned optimization objective, the simplex method is used to determine the uniformly distributed weight vector; Construct the Chebyshev aggregation function corresponding to the weight vector to transform the multi-objective constrained optimization problem into multiple uniformly distributed single-objective constrained optimization problems; For each single-objective constrained optimization problem, calculate the vertical distance between the corresponding weight vector and all parameter vectors in the population, and associate the parameter vector with the smallest vertical distance with the weight vector. If the parameter vector associated with its corresponding weight vector is in the first subpopulation, then the corresponding constraint-guided classification evolution operation is as follows: In the formula, For the first A temporary child parameter vector; For the first A parameter vector corresponding to a single-objective constrained optimization problem; and These are two parameter vectors randomly selected from the first subpopulation. and These are the indices for random selection; The parameter vector is randomly selected from the second subpopulation. For indexing when selecting randomly; and These are scaling factors; If the parameter vector associated with its corresponding weight vector is in the second subpopulation, then the corresponding constraint-guided classification evolution operation is as follows: In the formula, and These are two parameter vectors randomly selected from the second subpopulation. and These are the indices for random selection; The parameter vector is randomly selected from the first subpopulation. This is the index for random selection.

6. The machine learning-based constrained optimization method for epoxy resin curing process according to claim 2, characterized in that, In step S30, the heterogeneous machine learning model includes a Gaussian process machine learning model and a radial basis function machine learning model, wherein the construction of the heterogeneous machine learning model includes: Using all parameter vectors in the database as input data and the four optimization objective values ​​corresponding to all parameter vectors as output response values, four corresponding Gaussian process machine learning models are constructed. Using all parameter vectors in the database as input data and the optimization constraint values ​​corresponding to all parameter vectors in the database as output response values, a corresponding radial basis function machine learning model is constructed.

7. The machine learning-based constrained optimization method for epoxy resin curing process according to claim 6, characterized in that, In step S30, determining the optimal parameter vector based on the constraint dominance criterion includes: Determine the constraint information values ​​of all child parameter vectors in the candidate parameter vector set; If the minimum constraint information value of all child parameter vectors is equal to zero, then all child parameter vectors with constraint information values ​​equal to zero are used to construct a set of feasible parameter vectors, and the parameter vector with the minimum Chebyshev aggregation function value in the set of feasible parameter vectors is selected as the optimal parameter vector. If the minimum constraint information value of all child parameter vectors is greater than zero, then the child parameter vector with the minimum constraint information value is taken as the optimal parameter vector.

8. A machine learning-based constrained optimization system for epoxy resin curing processes, characterized in that, include: The database construction module is configured to acquire multiple optimization parameters during the epoxy resin curing process to construct an initial parameter vector, apply a randomized block design method and a diversity index to the initial parameter vector to determine a target population including the initial parameter vector, optimization objective and optimization constraints, and construct a database based on the target population; The candidate set determination module is configured to calculate the constraint information values ​​of all parameter vectors in the target population based on the target population, sort the constraint information values ​​to construct at least two subpopulations, and randomly select corresponding parameter vectors from the two subpopulations to perform constraint information-guided classification evolution to obtain a candidate set of parameter vectors for the epoxy resin curing process. The optimal parameter determination module is configured to input the parameter vector candidate set into a preset heterogeneous machine learning model to predict the optimization objective and optimization constraints of the parameter vector candidate set respectively, and determine the optimal parameter vector based on the constraint dominance criterion. The iterative output module is configured to evaluate the optimization objective and optimization constraint values ​​corresponding to the optimal parameter vector respectively, and update the target population and database accordingly. If the evaluation results meet the design requirements, the target parameter vector of the epoxy resin curing process is output.

9. An electronic device, characterized in that, include: At least one processor; as well as A memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the steps of the machine learning-based epoxy resin curing process constraint optimization method according to any one of claims 1-7.

10. A computer-readable storage medium having computer program instructions stored thereon, characterized in that, When the computer program instructions are executed by the processor, they implement the steps of the machine learning-based epoxy resin curing process constraint optimization method according to any one of claims 1-7.

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