Carbon fiber carbonization parameter optimization method based on two-stage robust optimization algorithm

Abstract

The invention provides a carbon fiber carbonization parameter optimization method based on a two-stage robust optimization algorithm, and the method comprises the steps: building a robust multi-target GP model of a carbon fiber carbonization process based on data parameters in the carbon fiber carbonization process as decision variables and tensile strength and Young modulus as targets; and on the basis of a two-stage robust multi-objective evolutionary algorithm, solving the GP model to obtain process parameters of the carbonization process, and selecting an optimal mechanical property value from the process parameters. According to the method, the problems of high mechanism model construction difficulty, complicated calculation, limited experimental data and uncertainty in the production process are avoided, and the actual requirements of modeling in the carbon fiber production process are better met. Optimization is pursued without considering disturbance in the early stage, disturbance is increased in the later stage to optimize robustness, the optimality and robustness of the solution are effectively balanced, waste of computing resources is reduced, guarantee is provided for stable and efficient production of the carbonization process technology, and improvement of the mechanical property and quality of carbon fibers is facilitated.

Description

Technical Field

[0001] The invention belongs to the technical field of carbon fiber production, and in particular relates to a carbon fiber carbonization parameter optimization method based on a two-stage robust optimization algorithm. Background Art

[0002] Composite materials made of carbon fiber have excellent mechanical properties and can produce significant enhancement and weight reduction effects. They have been widely used in many fields, such as wind turbine blades, high-pressure storage tanks and other new energy industries, forming an irreplaceable value contribution. Taking PAN-based carbon fiber as an example, PAN precursor is formed into PAN-based carbon fiber through four stages of spinning, pre-oxidation, carbonization and graphitization. Among them, the process conditions of the carbonization process have a direct impact on the mechanical properties of the final carbon fiber, and they are quite sensitive. Slower carbonization speed helps to form larger graphite crystallites and high modulus, but also introduces more crystallite defects and pores, resulting in reduced strength. On the contrary, faster carbonization speed can increase strength, but will sacrifice some modulus. In addition, the carbonization process is a gradual heating process, and the physical, chemical and structural changes in each temperature stage are different. Applying different tensions at different temperature stages is very beneficial to the optimization of fiber structure and performance improvement. Therefore, setting reasonable parameters for carbonization speed, low temperature and high temperature carbonization tensions during carbonization is of great significance for improving the mechanical properties of carbon fiber.

[0003] At present, most of the research on process optimization of carbon fiber is about the drawing, solidification and pre-oxidation processes, and less about the parameter optimization of the carbonization process. Moreover, most of the research on the optimization of process parameters of the carbonization process does not consider the influence of uncertainty, which has certain limitations in practical applications. In addition, most robust optimization algorithms consider the robustness of the solution from the initial exploration of the decision space, but there is no robust solution in some areas with poor fitness. Measuring the robustness of the solutions in these areas will waste a lot of computing resources.

[0004] Carbon fiber production is extremely expensive and time-consuming, so the industry typically tries to minimize the number of process runs during data collection. Limited experimental data and high uncertainty limit the use of modeling methods. Although methods such as nonlinear multivariate regression and neural network algorithms have been used to optimize the modulus of carbon fiber, they do not take into account the variability of mechanical properties. GP modeling can effectively handle noise and autocorrelation, does not require a preset relationship between input and output, and provides a separate fitting error for each prediction point. This makes GP a robust and accurate tool for complex data modeling and optimization in carbon fiber production. Summary of the invention

[0005] The purpose of the present invention is to provide a method for optimizing carbon fiber carbonization process parameters based on a two-stage robust optimization algorithm for the purpose of comprehensive optimization of fiber mechanical properties.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] A carbon fiber carbonization parameter optimization method based on a two-stage robust optimization algorithm comprises the following steps:

[0008] Step 1: Based on the carbonization speed, low-temperature carbonization tension and high-temperature carbonization tension in the carbon fiber carbonization process as decision variables, and tensile strength and Young's modulus as targets, a robust multi-objective GP model of the carbon fiber carbonization process is constructed;

[0009] Step 2: Based on a two-stage robust multi-objective evolutionary algorithm, the robust multi-objective GP model is solved to obtain the process parameters of the carbonization process and select the optimal value of the mechanical properties.

[0010] Preferably, the method for constructing the robust multi-objective GP model in step 1 is as follows:

[0011] Step 1.1: Data collection and preprocessing: collect experimental data related to the carbonization process of carbon fiber, including carbonization speed, low-temperature carbonization tension and high-temperature carbonization tension process parameters, as well as the corresponding tensile strength and Young's modulus performance indicators of carbon fiber; preprocess the data, remove outliers and perform normalization;

[0012] Step 1.2: Select a suitable kernel function;

[0013] Step 1.3: Use the method of maximizing the log-marginal likelihood function to optimize the model's hyperparameters;

[0014] Step 1.4: Based on the processed data, the GP model is used to train and verify the data;

[0015] Step 1.5: Denormalize the prediction results and calculate the error and performance indicators;

[0016] Step 1.6: Calculate the confidence interval;

[0017] Step 1.7: Analyze the residuals and evaluate the performance and reliability of the model.

[0018] Preferably, the Gaussian process model of carbon fiber carbonization process used in selecting a suitable kernel function in step 1.2 is composed of a constant mean function and a square exponential (SE) covariance function, which is defined as:

[0019] m(x)=c

[0020]

[0021] Preferably, the decision variables of the carbonization speed, low-temperature carbonization tension and high-temperature carbonization tension in step 1 correspond to the process boundaries of the model as follows:

[0022] The range of the carbonization speed is: 2≤x1(m / h)≤40;

[0023] The tension range of the low temperature carbonization stage is: 80≤x2(cN)≤350;

[0024] The tension range of the high temperature carbonization stage is: 180≤x3(cN)≤500.

[0025] Preferably, in step S2, the robust multi-objective GP model is used as an optimization objective function, and a two-stage robust multi-objective evolutionary algorithm (TRMEA) is applied to solve the model, and the steps are as follows:

[0026] Phase 1: Regional Detection Phase

[0027] Step 2.1: Initialize the subpopulation and determine the number, upper and lower limits of decision variables;

[0028] Step 2.2: Update subpopulation information, including: number of subpopulations, size, and grouping sequence number;

[0029] Step 2.3: Perform non-dominated sorting on the individuals in each subpopulation;

[0030] Step 2.4: Subpopulation optimization includes subpopulation independent evolution and subpopulation cooperative evolution, which are used to update the local optimal solution and the global optimal solution;

[0031] Step 2.5: Periodically update the feature weight vector;

[0032] Step 2.6: If the recombination conditions are met, the sub-populations are recombined;

[0033] Step 2.7: Repeat steps 2.2 to 2.6 until the switching condition is met. If the switching condition is met, the second stage is entered;

[0034] Phase 2: Robust Optimization Phase

[0035] Step 2.8: Divide the sub-population into high robustness archives and low robustness archives;

[0036] Step 2.9: Perform non-dominated sorting on the individuals in the two archives;

[0037] Step 2.10: Evolution of two archives. The high-robustness archive does not consider perturbations and only focuses on optimality. The low-robustness archive considers perturbations and performs robust optimization.

[0038] Step 2.11: Repeat steps 2.9 to 2.10 until the maximum number of iterations is reached, and output all individuals in the archive.

[0039] Preferably, the subpopulation evolution in step 2.4 uses a random number q to determine the subpopulation evolution method;

[0040] When the random number q is greater than the set value, an intra-group crossover is performed, and the parent generation is selected from the respective sub-populations using a binary bidding competition;

[0041] When the random number q is less than or equal to the set value, inter-group crossover is performed, which uses binary bidding to select parents from their respective sub-populations, and also randomly selects parents from the remaining sub-populations.

[0042] Preferably, the specific steps of periodically updating the feature weight vector in step 2.5 are as follows:

[0043] First, all solutions are regarded as features, and the average feature Fmean of individuals in each subpopulation is calculated; then, K-means clustering is performed on the average feature Fmean of each subpopulation to obtain the index idx of the subpopulation cluster; then, the cluster number FID of each feature (i.e., each solution) is further obtained; secondly, the Spearman rank correlation coefficient ρ between the population feature F and the feature cluster number FID is calculated; finally, ρ is processed to obtain the feature weight vector w.

[0044] The value of w varies in the range of 0 to 1, and the crossover probability of each dimension of the decision variable can be controlled by the feature weight; w plays the role of the crossover probability in the crossover operation;

[0045] The value of w represents the correlation between the dimensional feature and the cluster sequence number. The closer it is to 1, the weaker the correlation is. This dimensional feature is used to distinguish individuals in different groups, and the probability of cross-learning between them becomes smaller. The closer it is to 0, the stronger the correlation is. This dimensional feature needs to be cross-learned, and the cross-probability is higher.

[0046] Preferably, the recombination methods of the recombinant subpopulations in step 2.6 include two methods: one is to reallocate the subpopulations with the worst non-dominated levels of individuals; the other is to periodically and forcibly merge the two subpopulations with the shortest inter-group distance.

[0047] Preferably, the switching condition in step 2.7 is achieved by judging whether the current population has found the characteristics of different optimal solutions and presents a convergence trend;

[0048] The characteristics of the optimal solution include characteristics that distinguish different PS segments, and the specific steps are as follows:

[0049] First, the standard deviation of the decision variables of one quarter of the individuals in the contemporary population is calculated; when the standard deviation value of a decision variable in a certain dimension is less than or equal to the threshold, the decision variable in this dimension is confirmed to have good convergence. At this time, multiple optimal solutions to the optimization problem are also found, and the contemporary population enters the robust optimization stage.

[0050] Preferably, the partitioning of the archive in step 2.8 is performed based on the overall sensitivity of the solutions within the subpopulation to disturbances;

[0051] When the solutions within a subpopulation are collectively insensitive or highly sensitive to perturbations on the variables, the subpopulation is classified as a high-robustness or low-robustness archive.

[0052] Preferably, the evolution of the two archives in step 2.10 includes binary tournament selection, crossover mutation, and environmental selection using non-dominated sorting and crowding distance;

[0053] The optimization of the high-robustness archive does not consider disturbances, but only considers the optimal evolution of the original objective function within the archive itself; the low-robustness archive will first learn from the high-robustness archive by constructing a mating pool containing individuals in the high-robustness archive;

[0054] Secondly, the impact of perturbations on the solution needs to be considered, and the new objective function values ​​are sorted instead of the original ones in the non-dominated sorting process;

[0055] The new objective function value is taken as the original objective value plus the standard deviation of the difference between the perturbed solution and the original solution relative to the origin in the objective space.

[0056] Compared with the prior art, the present invention has the following beneficial effects:

[0057] 1. The present invention constructs a GP model to predict the mechanical properties of the carbonization process in carbon fiber production, avoiding the problems of difficulty and complex calculation in constructing a mechanism model, limited experimental data, and uncertainty in the production process, and is more in line with the actual needs of carbon fiber production process modeling.

[0058] 2. The present invention effectively balances the optimality and robustness of the solution by pursuing the optimum without considering disturbances in the early stage, and then adding disturbances in the later stage to optimize robustness, and reduces unnecessary waste of computing resources, thereby providing a guarantee for the stable and efficient production of the carbonization process, which is beneficial to improving the mechanical properties and quality of carbon fiber. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 A schematic flow chart of a method for optimizing carbon fiber carbonization parameters based on a two-stage robust optimization algorithm is provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0060] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0061] like Figure 1 As shown, a carbon fiber carbonization parameter optimization method based on a two-stage robust optimization algorithm disclosed in the present invention comprises the following steps:

[0062] Step 1: Based on the carbonization speed, low-temperature carbonization tension and high-temperature carbonization tension in the carbon fiber carbonization process as decision variables, and tensile strength and Young's modulus as targets, a robust multi-objective GP model of the carbon fiber carbonization process is constructed.

[0063] The construction method of the robust multi-objective GP model is as follows:

[0064] Step 1.1: Data collection and preprocessing, collect experimental data related to the carbonization process of carbon fiber, including carbonization speed, low-temperature carbonization tension and high-temperature carbonization tension process parameters, as well as the corresponding tensile strength and Young's modulus performance indicators of carbon fiber; preprocess the data, remove outliers and perform normalization.

[0065] The decision variables of carbonization speed, low-temperature carbonization tension, and high-temperature carbonization tension correspond to the process boundaries of the model as follows:

[0066] The range of carbonization speed is: 2≤x1(m / h)≤40;

[0067] The tension range in the low-temperature carbonization stage is: 80≤x2(cN)≤350;

[0068] The tension range in the high temperature carbonization stage is: 180≤x3(cN)≤500.

[0069] Step 1.2: Select a suitable kernel function. The Gaussian process model of carbon fiber carbonization process adopted is composed of a constant mean function and a square exponential (SE) covariance function, which is defined as:

[0070] m(x)=c

[0071]

[0072] Step 1.3: Use the method of maximizing the log-marginal likelihood function to optimize the model's hyperparameters (signal variance Characteristic length scale l and noise variance );

[0073] Step 1.4: Based on the processed data, the GP model is used to train and verify the data;

[0074] Step 1.5: Denormalize the prediction results and calculate the error and performance indicators;

[0075] Step 1.6: Calculate the confidence interval;

[0076] Step 1.7: Analyze the residuals and evaluate the performance and reliability of the model.

[0077] Step 2: Based on the two-stage robust multi-objective evolutionary algorithm, the robust multi-objective GP model is solved to obtain the process parameters of the carbonization process and select the optimal values ​​of the mechanical properties.

[0078] In step S2, the robust multi-objective GP model is used as the optimization objective function, and the model is solved by applying a two-stage robust multi-objective evolutionary algorithm (TRMEA), and the steps are as follows:

[0079] Phase 1: Regional Detection Phase

[0080] Step 2.1: Initialize the subpopulation and determine the number, upper and lower limits of decision variables.

[0081] Step 2.2: Update subpopulation information, including the number of subpopulations, size, and grouping sequence number.

[0082] Step 2.3: Perform non-dominated sorting on the individuals in each subpopulation.

[0083] Step 2.4: Subpopulation optimization includes subpopulation independent evolution and subpopulation cooperative evolution, which are used to update local optimal and global optimal solutions.

[0084] The subpopulation evolution in step 2.4 uses a random number q to determine the subpopulation evolution method.

[0085] When the random number q is greater than the set value, intra-group crossover is performed, and the parent generation is selected from the respective sub-populations using a binary bidding competition.

[0086] When the random number q is less than or equal to the set value, inter-group crossover is performed, which uses binary bidding to select parents from their respective sub-populations, and also randomly selects parents from the remaining sub-populations.

[0087] Step 2.5: Periodically update the feature weight vector. The specific steps are as follows:

[0088] First, all solutions are regarded as features, and the average feature Fmean of individuals in each subpopulation is calculated; then, K-means clustering is performed on the average feature Fmean of each subpopulation to obtain the index idx of the subpopulation cluster; then, the cluster number FID of each feature (i.e., each solution) is further obtained; secondly, the Spearman rank correlation coefficient ρ between the population feature F and the feature cluster number FID is calculated; finally, ρ is processed to obtain the feature weight vector w.

[0089] The value of w varies from 0 to 1. The crossover probability of each dimension of the decision variable can be controlled by the feature weight; w plays the role of crossover probability in the crossover operation;

[0090] The value of w represents the correlation between the dimension feature and the cluster sequence number. The closer it is to 1, the weaker the correlation is. This dimension feature is used to distinguish individuals in different groups, and the probability of cross-learning between them becomes smaller. The closer it is to 0, the stronger the correlation is. This dimension feature needs to be cross-learned, and the cross-probability is higher.

[0091] Step 2.6: If the recombination conditions are met, the subpopulations are reorganized. There are two methods for reorganizing the subpopulations: one is to reallocate the subpopulations with the worst non-dominated levels of the individuals; the other is to periodically force the merger of the two subpopulations with the closest distance between the groups.

[0092] Step 2.7: Repeat steps 2.2 to 2.6 until the switching condition is met. If the switching condition is met, the second stage is entered. The switching condition is achieved by judging whether the current population has found the characteristics of different optimal solutions and shows a convergence trend; the characteristics of the optimal solution include the characteristics that distinguish different PS segments. The specific steps are as follows: First, calculate the standard deviation of the decision variables of one quarter of the individuals in the contemporary population; when the standard deviation value of a decision variable in a certain dimension is less than or equal to the threshold, the decision variable in this dimension is confirmed to have good convergence. At this time, multiple optimal solutions to the optimization problem are also found, and the contemporary population enters the robust optimization stage.

[0093] Phase 2: Robust Optimization Phase

[0094] Step 2.8: Divide the subpopulation into high robustness archives and low robustness archives according to the overall sensitivity of the solutions in the subpopulation to disturbances. The archives are divided according to the overall sensitivity of the solutions in the subpopulation to disturbances; when the solutions in the subpopulation are insensitive or highly sensitive to disturbances on the variables as a whole, the subpopulation is divided into high robustness or low robustness archives.

[0095] Step 2.9: Perform non-dominated sorting on the individuals in the two archives.

[0096] Step 2.10: Evolution of two archives. The high-robustness archive does not consider perturbations and only focuses on optimality. The low-robustness archive considers perturbations and performs robust optimization.

[0097] Both archive evolutions include binary tournament selection, crossover mutation, and environmental selection using nondominated sorting and crowding distance;

[0098] The optimization of the high-robustness archive does not consider disturbances, but only considers the optimal evolution of the original objective function within its own archive; the low-robustness archive will first learn from the high-robustness archive by building a mating pool containing individuals in the high-robustness archive;

[0099] Secondly, the impact of perturbations on the solution needs to be considered, and the new objective function values ​​are sorted instead of the original ones in the non-dominated sorting process;

[0100] The new objective function value is taken as the original objective value plus the standard deviation of the difference between the perturbed solution and the original solution relative to the origin in the objective space.

[0101] Step 2.11: Repeat steps 2.9 to 2.10 until the maximum number of iterations is reached, and output all individuals in the archive.

[0102] Step 3: This embodiment studies the effects of three process parameters on the mechanical properties of carbon fiber (tensile strength f1 and Young's modulus f2). The algorithm used in the present invention is compared with other advanced algorithms to verify the effectiveness of the algorithm. Other algorithms include but are not limited to NSGA-II-DTI, CNSDE-DVC and RMOEA-DVA algorithms.

[0103] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", "clockwise", "counterclockwise" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the referred device or element must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on the present invention.

[0104] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, the meaning of "plurality" is two or more, unless otherwise clearly and specifically defined.

[0105] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A carbon fiber carbonization parameter optimization method based on a two-stage robust optimization algorithm, characterized in that: The steps include: Step 1: Based on the carbonization speed, low-temperature carbonization tension and high-temperature carbonization tension in the carbon fiber carbonization process as decision variables, and tensile strength and Young's modulus as targets, a robust multi-objective GP model of the carbon fiber carbonization process is constructed; Step 2: Based on a two-stage robust multi-objective evolutionary algorithm, the robust multi-objective GP model is solved to obtain the process parameters of the carbonization process and select the optimal value of the mechanical properties.

2. The carbon fiber carbonization parameter optimization method based on the two-stage robust optimization algorithm according to claim 1 is characterized in that: The method for constructing the robust multi-objective GP model in step 1 is as follows: Step 1.1: Data collection and preprocessing: collect experimental data related to the carbonization process of carbon fiber, including carbonization speed, low-temperature carbonization tension and high-temperature carbonization tension process parameters, as well as the corresponding tensile strength and Young's modulus performance indicators of carbon fiber; preprocess the data, remove outliers and perform normalization; Step 1.2: Select a suitable kernel function; Step 1.3: Use the method of maximizing the log-marginal likelihood function to optimize the model's hyperparameters; Step 1.4: Based on the processed data, the GP model is used to train and verify the data; Step 1.5: Denormalize the prediction results and calculate the error and performance indicators; Step 1.6: Calculate the confidence interval; Step 1.7: Analyze the residuals and evaluate the performance and reliability of the model.

3. The carbon fiber carbonization parameter optimization method based on the two-stage robust optimization algorithm according to claim 2 is characterized in that: The Gaussian process model of carbon fiber carbonization process used in selecting a suitable kernel function in step 1.2 is composed of a constant mean function and a square exponential (SE) covariance function, which is defined as: m(x)=c The decision variables of the carbonization speed, low-temperature carbonization tension and high-temperature carbonization tension correspond to the process boundaries of the model as follows: The range of the carbonization speed is: 2≤x1(m / h)≤40; The tension range of the low temperature carbonization stage is: 80≤x2(cN)≤350; The tension range of the high temperature carbonization stage is: 180≤x3(cN)≤500.

4. The carbon fiber carbonization parameter optimization method based on the two-stage robust optimization algorithm according to claim 1, characterized in that: In step S2, the robust multi-objective GP model is used as the optimization objective function, and a two-stage robust multi-objective evolutionary algorithm (TRMEA) is used to solve the model, and the steps are as follows: Phase 1: Regional Detection Phase Step 2.1: Initialize the subpopulation and determine the number, upper and lower limits of decision variables; Step 2.2: Update subpopulation information, including: number of subpopulations, size, and grouping sequence number; Step 2.3: Perform non-dominated sorting on the individuals in each subpopulation; Step 2.4: Subpopulation optimization includes subpopulation independent evolution and subpopulation cooperative evolution, which are used to update the local optimal solution and the global optimal solution; Step 2.5: Periodically update the feature weight vector; Step 2.6: If the recombination conditions are met, the sub-populations are recombined; Step 2.7: Repeat steps 2.2 to 2.6 until the switching condition is met. If the switching condition is met, the second stage is entered; Phase 2: Robust Optimization Phase Step 2.8: Divide the sub-population into high robustness archives and low robustness archives; Step 2.9: Perform non-dominated sorting on the individuals in the two archives; Step 2.10: Evolution of two archives. The high-robustness archive does not consider perturbations and only focuses on optimality. The low-robustness archive considers perturbations and performs robust optimization. Step 2.11: Repeat steps 2.9 to 2.10 until the maximum number of iterations is reached, and output all individuals in the archive.

5. The carbon fiber carbonization parameter optimization method based on the two-stage robust optimization algorithm according to claim 5, characterized in that: The subpopulation evolution in step 2.4 uses the size of a random number q to determine the subpopulation evolution method; When the random number q is greater than the set value, an intra-group crossover is performed, and the parent generation is selected from the respective sub-populations using a binary bidding competition; When the random number q is less than or equal to the set value, inter-group crossover is performed, which uses binary bidding to select parents from their respective sub-populations, and also randomly selects parents from the remaining sub-populations.

6. The carbon fiber carbon parameter optimization method based on the two-stage robust optimization algorithm according to claim 5, characterized in that: The specific steps of periodically updating the feature weight vector in step 2.5 are as follows: First, all solutions are treated as features, and the average feature Fmean of individuals in each subpopulation is calculated; then, K-means clustering is performed on the average feature Fmean of each subpopulation to obtain the index idx of the subpopulation cluster; then, the cluster number FID of each feature (i.e., each solution) is further obtained; secondly, the Spearman rank correlation coefficient ρ between the population feature F and the feature cluster number FID is calculated; finally, ρ is processed to obtain the feature weight vector w. The value of w varies from 0 to 1, and the crossover probability of each dimensional decision variable can be controlled by the feature weight; w plays the role of crossover probability in the crossover operation; The value of w represents the correlation between the dimensional feature and the cluster sequence number. The closer it is to 1, the weaker the correlation is. This dimensional feature is used to distinguish individuals in different groups, and the probability of cross-learning between them becomes smaller. The closer it is to 0, the stronger the correlation is. This dimensional feature needs to be cross-learned, and the cross-probability is higher.

7. The carbon fiber carbonization parameter optimization method based on the two-stage robust optimization algorithm according to claim 5, characterized in that: There are two methods for recombining the recombinant subpopulations in step 2.6: one is to reallocate the subpopulations with the worst non-dominated levels of individuals; the other is to periodically and forcibly merge the two subpopulations with the closest inter-group distances.

8. The carbon fiber carbonization parameter optimization method based on the two-stage robust optimization algorithm according to claim 5, characterized in that: The switching condition in step 2.7 is achieved by judging whether the current population has found the characteristics of different optimal solutions and shows a convergence trend; The characteristics of the optimal solution include characteristics that distinguish different PS segments, and the specific steps are as follows: First, the standard deviation of the decision variables of one quarter of the individuals in the contemporary population is calculated; when the standard deviation value of a decision variable in a certain dimension is less than or equal to the threshold, the decision variable in this dimension is confirmed to have good convergence. At this time, multiple optimal solutions to the optimization problem are also found, and the contemporary population enters the robust optimization stage.

9. The carbon fiber carbonization parameter optimization method based on the two-stage robust optimization algorithm according to claim 5, characterized in that: The partitioning of the archive in step 2.8 is based on the overall sensitivity of the solutions within the subpopulation to disturbances; When the solutions within a subpopulation are collectively insensitive or highly sensitive to perturbations on the variables, the subpopulation is classified as a high-robustness or low-robustness archive.

10. The carbon fiber carbonization parameter optimization method based on the two-stage robust optimization algorithm according to claim 5, characterized in that: The evolution of both archives in step 2.10 includes binary tournament selection, crossover mutation, and environmental selection using non-dominated sorting and crowding distance; The optimization of the high-robustness archive does not consider disturbances, but only considers the optimal evolution of the original objective function within the archive itself; the low-robustness archive will first learn from the high-robustness archive by constructing a mating pool containing individuals in the high-robustness archive; Secondly, the impact of perturbations on the solution needs to be considered, and the new objective function values ​​are sorted instead of the original objective function values ​​in the non-dominated sorting process; The new objective function value is taken as the original objective value plus the standard deviation of the difference between the perturbed solution and the original solution relative to the origin in the objective space.

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