A multi-objective optimization method for a carbon fiber reinforced epoxy resin-based curing system

Abstract

The present invention discloses a multi-objective optimization method for a carbon fiber reinforced epoxy resin-based curing system. The optimization method includes: generating a sample set; constructing a data set; performing normalization processing on the data set; selecting initial values of Gaussian model parameters and hyperparameters; constructing a regression model based on the normalized data set; using the regression model for prediction and comparing with experimental samples; establishing a full-factor network data set of variables to be optimized; performing regression prediction through a Gaussian process regression model to obtain a full-factor prediction data set; selecting appropriate weight factors to obtain multi-objective optimal performance, thereby obtaining corresponding optimal process parameter solutions. The present invention realizes accurate prediction of a small sample data set through the Gaussian process regression algorithm, and can effectively reduce the experimental data volume by more than 90% compared with the full-factor experiment method, effectively balancing development and exploration; at the same time, the present invention can specifically develop and utilize the required properties of the material, and realize targeted enhancement and optimization of single or multiple properties of the material.

Description

Technical Field

[0001] The invention relates to a multi-objective optimization method, in particular to a multi-objective optimization method for a carbon fiber reinforced epoxy resin-based curing system. Background Art

[0002] Epoxy resin (EP) is a kind of high molecular organic compound containing two or more epoxy groups in its molecular structure. It is widely used as a matrix resin in composite materials due to its good adhesion. It is a thermosetting polymer with excellent comprehensive performance. It is widely used in the fields of machinery, coatings, aerospace and advanced composite materials. However, due to the defects of EP after curing, such as brittleness, poor impact resistance, easy cracking, poor toughness, and strength to be improved, the application scope of EP is limited. In order to improve the performance of EP, researchers in the industry have proposed many methods of toughening and modifying EP. Among them, the study of modifying EP with fiber has become the current research focus. Carbon fiber has excellent properties such as light weight, high specific strength, high specific modulus (tensile, bending, torsion), heat transfer, fatigue resistance, and super strong environmental adaptability and strong resistance to chemical corrosion. Therefore, carbon fiber reinforced resin-based composite materials with excellent performance have been widely studied in recent years.

[0003] However, most current research is still dominated by process factors, rather than considering material optimization based on engineering performance requirements. In addition, the optimization subject is generally multivariate single-objective optimization, which fails to fully consider the collaborative optimization enhancement between conflicting objectives. Therefore, when the enhancement processes of multiple target performances to be optimized conflict with each other, it is difficult to make reasonable trade-offs and optimizations.

[0004] At the same time, the optimization of epoxy curing system performance is essentially to find the best process parameters in the epoxy resin curing process, and the combination of such process parameters is endless, which greatly increases the experimental cost and difficulty of the epoxy resin curing process. Therefore, it is very important to find a method that can quickly search for the optimal process parameters based on the target strength requirements and then improve the performance of epoxy curing materials. This can carry out the performance development of new materials in a targeted manner, greatly reduce the experimental cost, and improve the experimental efficiency. Summary of the invention

[0005] Purpose of the invention: The present invention aims to provide a multi-objective optimization method for a carbon fiber reinforced epoxy resin-based curing system to overcome the defects in the prior art that the performance of the new epoxy resin curing system cannot be quickly and effectively optimized and multiple conflicting objectives cannot be synergistically optimized, resulting in increased experimental costs and reduced efficiency.

[0006] Technical solution: A multi-objective optimization method for a carbon fiber reinforced epoxy resin-based curing system of the present invention comprises:

[0007] Step S1: Determine the value ranges of N (N is a positive integer) variables to be optimized according to the curing process;

[0008] Step S2: Generate n groups of sample parameters using the value ranges of the N variables to be optimized to form a sample set;

[0009] Step S3: Cure the epoxy resin using all the sample parameters in the sample set and test its performance to obtain the measured performance values, and construct a data set with a one-to-one correspondence between "the sample parameters and the measured performance values";

[0010] Step S4: Perform normalization processing on the measured performance value data based on the data set;

[0011] Step S5: Determine the Gaussian process regression (GPR) prior model, select the kernel function, and determine the initial values of the hyperparameters;

[0012] Step S6: Construct a regression model based on the normalized data set;

[0013] Step S7: Use the regression model for prediction and compare it with the experimental samples to determine whether the regression model meets the accuracy requirements. If the accuracy does not meet the requirements, repeat Step S5 to re-determine the initial values of the hyperparameters;

[0014] Step S8: Evenly divide the value ranges of the N variables to be optimized into t levels, and establish a full-factor mesh data set of the variables to be optimized;

[0015] Step S9: Perform regression prediction on the full-factor mesh data set of the variables to be optimized through the Gaussian process regression model to obtain a full-factor prediction data set;

[0016] Step S10: Select a suitable weight factor to obtain the optimal solution for multi-objective performance optimization in the full-factor prediction data set, so as to obtain the corresponding optimal process parameter solution.

[0017] In the present invention, the epoxy resin may include conventional epoxy resins in the art, such as E51 epoxy resin.

[0018] In the present invention, the carbon fiber is a commercial micron-sized chopped carbon fiber, preferably a T700 micron-sized chopped carbon fiber, without external treatment of the curing process.

[0019] In Step S1, the N variables to be optimized are variables that have a relatively obvious influence on the performance during the entire curing process.

[0020] In Step S1, the N can be any integer and can be selected according to actual needs. Preferably, the N is 4, and the carbon fiber percentage content (Cf), the secondary curing temperature (T), the secondary curing time (t), and the concentration of the silane coupling agent solution (Si) are determined as the variables to be optimized.

[0021] Among them, preferably, the range values of Cf, T, t, and Si can be obtained through preliminary experiments and combined with conventional experience in the art.

[0022] The range values of Cf, T, t, and Si can be 1% ≤ Cf ≤ 8%, 60°C ≤ T ≤ 130°C, 0 h ≤ t ≤ 5 h, and 0% ≤ Si ≤ 10% respectively.

[0023] In step S2, the value ranges of N variables to be optimized are input into Matlab software, and then n groups of sample parameters are generated using the Latin hypercube sampling method. Among them, the Latin hypercube sampling (LHS) method generally refers to dividing the sampling units into different layers according to a certain characteristic or rule, and then independently and randomly extracting samples from different layers, so as to ensure that the structure of the samples is similar to that of the population, thereby improving the accuracy of estimation. In addition, the sample points generated by the LHS method can evenly fill the entire design optimization space, the sample points are scattered evenly, and have good spatial representativeness.

[0024] In step S2, for the "n groups of sample parameters", the value of n should be greater than 2N + 1.

[0025] In step S3, the measured performance values include one or more of mechanical property values, viscosity values, elongation at break values, tensile modulus values, and compression modulus values.

[0026] In step S4, the purpose of the "normalization process" is to eliminate the dimensional influence between multiple indicators and make each indicator at the same order of magnitude.

[0027] In step S5, the GPR uses a Gaussian process as a prior, that is, it is assumed that the learning samples are samples of a Gaussian process, so its estimation result is closely related to the kernel function.

[0028] In step S5, preferably, the rational quadratic covariance function (RQ) is selected as the kernel function.

[0029] Among them, the rational quadratic covariance function (RQ) model is:

[0030]

[0031] In step S5, preferably, the initial values of the hyperparameters are selected as the mean of 0, the covariance of [-1 -1 -1], and the Gaussian likelihood function of -3.

[0032] In step S6, the "construction of the regression model" is a Gaussian model.

[0033] In step S7, the performance evaluation of the model is judged according to the following formula:

[0034]

[0035] t is the number of sample parameters, and y i is the measured performance value; is the predicted performance value of the surrogate model; is the average value of the measured performance values; When R 2 is closer to 1, the construction of the surrogate model is better.

[0036] In step S7, there is an optimization of the initial values of the hyperparameters in the Gaussian process regression algorithm model, and the change of the iterative values can be used to evaluate whether the model is better.

[0037] In step S8, the "t level" can be selected according to actual needs. A larger t level can obtain more full-factor data sets of process parameters. Preferably, t is 30.

[0038] In step S9, the "Gaussian process regression model" is the regression model established in step S6.

[0039] In step S10, the weight factor is the weight obtained by weight distribution through the subjective weighting method.

[0040] Among them, the subjective weighting method can divide the primary and secondary importance according to the subjective requirements of the target performance to obtain the corresponding weights.

[0041] In an embodiment of a set of preferred parameters in the present invention:

[0042] Step S1: Determine the carbon fiber percentage content (Cf), the secondary curing temperature (T), the secondary curing time, and the concentration of the silane coupling agent solution (Si) as variables to be optimized according to the epoxy resin curing process, and determine the value ranges of the variables to be optimized according to experiments and experience in the art;

[0043] Step S2: Use the Cf range value, the T range value, the t range value, and the Si range value to generate n > 2N + 1 sets of curing process sample parameters to form a sample set;

[0044] Step S3: Cure the epoxy resin with all the sample parameters in the sample set and test its performance to obtain the measured performance values, and construct a data set that is in one-to-one correspondence between "the sample parameters and the measured performance values";

[0045] Step S4: Perform normalization processing on the measured performance value data based on the data set described in step S3;

[0046] Step S5: Determine the Gaussian process regression (GPR) prior model, select the rational quadratic covariance function (RQ) as the kernel function, and determine the initial values of the hyperparameters;

[0047] Step S6: Construct a Gaussian process regression prediction model based on the normalized data set and the model parameters selected in Step S5;

[0048] Step S7: Use the regression model for prediction and compare it with the experimental samples to determine whether the regression model meets the accuracy requirements. If the accuracy does not meet the requirements, repeat Step S5 to re-determine the initial values of the hyperparameters;

[0049] Step S8: Evenly divide the value ranges of N variables to be optimized into t levels, and establish a full-factor mesh data set of the variables to be optimized;

[0050] Step S9: Perform regression prediction on the full-factor mesh data set of the variables to be optimized through the Gaussian process regression model to obtain a full-factor prediction data set;

[0051] Step S10: Obtain weights through the subjective weighting method according to the target strength of the material requirements, and obtain the optimal solution of multi-objective optimization in the full-factor prediction data set through these weights, so as to obtain the corresponding optimal process parameter solution.

[0052] Beneficial effects: Compared with the prior art, the present invention has the following remarkable advantages: The present invention uses the Gaussian process regression algorithm to obtain a relatively accurate full-factor prediction data set of the properties of carbon fiber reinforced epoxy resin matrix composites from a small sample data set. Compared with the full-factor experiment method, it can effectively reduce the experimental data volume by more than 90%, greatly reducing the experimental cost and time cost, effectively balancing development and exploration, and having great guiding significance for space exploratory experiments; at the same time, the present invention obtains a suitable weight factor through the target performance requirements, and obtains the optimal multi-objective optimization scheme through weight allocation. Compared with the current optimization methods mainly based on multiple single objectives, it fully considers the synergistic optimization effects between conflicting objectives, and can develop and utilize the material demand performance in a targeted manner, realizing the targeted enhancement and optimization of single or multiple properties of the material. The optimization method proposed by the present invention is simple to operate, meets process feasibility, and can also be developed and applied in many other material exploration fields. Description of the Drawings

[0053] Figure 1 It is a flowchart of the multi-objective optimization method for the carbon fiber reinforced epoxy resin curing system of the present invention.

[0054] Figure 2 It is a model iteration convergence diagram of the Gaussian process regression algorithm. Detailed Embodiments

[0055] The present invention will be further described below by way of examples, but the present invention is not limited to the scope of the described examples. The experimental methods without specific conditions in the following examples are carried out according to conventional methods and conditions, or selected according to the product specifications.

[0056] Example: Multi-objective Optimization Method for the Performance of Carbon Fiber Reinforced Epoxy Resin Curing System

[0057] This example provides a multi-objective optimization method for a carbon fiber reinforced epoxy resin curing system. As Figure 1 shown, this optimization method includes:

[0058] Step S1: Determine the carbon fiber percentage content (Cf), secondary curing temperature (T), secondary curing time (t), and silane coupling agent solution concentration (Si) as variables to be optimized according to the curing process of carbon fiber reinforced epoxy resin composites. According to preliminary experiments and industry experience, select the ranges of curing process parameters for carbon fiber reinforced epoxy resin composites as the Cf range value, T range value, t range value, and Si range value, which are 1% ≤ Cf ≤ 8%, 60°C ≤ T ≤ 130°C, 0 h ≤ t ≤ 5 h, and 0 ≤ Si ≤ 10% respectively;

[0059] Step S2: Generate a sample set; use the MBC toolbox of Matlab software to input the value ranges of Cf, T, t, and Si into the software. As shown in Table 1, use Latin Hypercube Sampling (LHS) to generate a set of sample parameters, set the number of sample parameters. In this example, set the number of sample parameters to 23 to generate a sample set consisting of 23 groups of sample parameters;

[0060] Table 1: Process Parameters to be Optimized and Their Ranges

[0061]

[0062] Step S3: Cure the epoxy resin with 23 groups of sample parameters in the sample set, conduct tensile and compressive property tests, repeat each test 3 times, and take the average value; obtain the measured values of the tensile strength, tensile modulus, compressive strength, and compressive modulus of the carbon fiber reinforced epoxy resin composite. Construct a data set based on the curing process parameters and the measured values of the material test performance, and construct a one-to-one corresponding data set between the "curing process parameters and material test performance", as shown in Table 2;

[0063] Table 2: Experimental Data of Material Test Performance Corresponding to Latin Hypercube Sampling Parameter Points

[0064]

[0065]

[0066] Step S4: Normalize the process parameters and measured performance value data based on the data set described in Step S3;

[0067] Step S5: Determine the Gaussian process regression (GPR) prior model, select the rational quadratic covariance function (RQ) as the kernel function, and determine the initial values of the hyperparameters. The selected mean is 0, the covariance is [-1 -1 -1], and the Gaussian likelihood function is -3;

[0068] Step S6: Based on the normalized data set and the model parameters selected in Step S5, construct a Gaussian process regression prediction model;

[0069] Step S7: Use the regression model for prediction and compare it with the experimental samples to determine whether the regression model meets the accuracy requirements. If the accuracy does not meet the requirements, repeat Step S5 to re-determine the initial values of the hyperparameters; as Figure 2 As shown, after 120 algorithm iterations, the model values tend to be unchanged and gradually converge. At this time, a regression model with higher regression accuracy optimized based on the initial values of the hyperparameters is obtained.

[0070] Step S8: Evenly divide the value ranges of the 4 variables to be optimized into 30 levels, and establish a full-factor mesh data set of 810,000 data parameters for the variables to be optimized;

[0071] Step S9: Through the Gaussian process regression model, perform regression prediction on the full-factor mesh data set of the variables to be optimized to obtain a full-factor prediction data set;

[0072] Step S10: Regarding the compressive strength as the most important factor for the target strength of the material, the importance order is compressive strength (Ts), tensile strength (Tm), compressive modulus (Cs), and tensile modulus (Cm). Therefore, according to the subjective weighting method, the weights are Tm: Ts: Cs: Cm = 0.3: 0.1: 0.4: 0.2. The optimal solution for multi-objective optimization performance in the full-factor prediction data set is Tm = 48.5 MPa, Ts = 1560 MPa, Cs = 88.8 MPa, and Cm = 1400 MPa. Thus, the corresponding optimal process parameter solution is that the carbon fiber percentage content (Cf) is 1%, the secondary curing temperature (T) is 110 °C, the secondary curing time (t) is 3.6 h, and the concentration of the silane coupling agent solution (Si) is 8%.

Claims

1. A multi-objective optimization method for a carbon fiber reinforced epoxy resin-based curing system, characterized in that The optimization method includes the following: Step S1: Determine the value ranges of N variables to be optimized according to the curing process, where N is a positive integer; the variables to be optimized include the carbon fiber percentage content (Cf), the secondary curing temperature (T), the secondary curing time, and the concentration of the silane coupling agent solution (Si); Step S2: Generate n sets of sample parameters using the value ranges of the N variables to be optimized to form a sample set; Step S3: Cure the epoxy resin using all the sample parameters in the sample set and test its performance to obtain the measured performance values, and construct a data set that is in one-to-one correspondence between "the sample parameters and the measured performance values"; the measured performance values include one or more of the mechanical property values, viscosity values, elongation at break values, tensile modulus values, and compression modulus values; Step S4: Perform normalization processing on the measured performance value data based on the data set; Step S5: Determine the Gaussian process regression (GPR) prior model, select the kernel function, and determine the initial values of the hyperparameters; Step S6: Construct a regression model based on the normalized data set; Step S7: Use the regression model for prediction and compare it with the experimental samples to determine whether the regression model meets the accuracy requirements. If the accuracy does not meet the requirements, repeat Step S5 to re-determine the initial values of the hyperparameters; Step S8: Equally divide the value ranges of the N variables to be optimized into t levels to establish a full-factor mesh data set of the variables to be optimized; Step S9: Perform regression prediction on the full-factor mesh data set of the variables to be optimized through the Gaussian process regression model to obtain a full-factor prediction data set; Step S10: Select an appropriate weight factor to obtain the optimal solution for multi-objective performance optimization in the full-factor prediction data set, so as to obtain the corresponding optimal process parameter solution.

2. The multi-objective optimization method for a carbon fiber-reinforced epoxy resin-based curing system as described in claim 1, wherein In Step S1, the variables to be optimized can be determined according to the curing process, and the quantity N is not limited.

3. The multi-objective optimization method of the carbon fiber reinforced epoxy resin-based curing system according to claim 2, wherein In Step S1, the variables to be optimized are one or more variables that have a relatively obvious impact on the performance during the full curing process.

4. The multi-objective optimization method for a carbon fiber-reinforced epoxy resin-based curing system as described in claim 1 or 2, wherein In Step S1, N is 4, and the carbon fiber percentage content (Cf), the secondary curing temperature (T), the secondary curing time (t), and the concentration of the silane coupling agent solution (Si) are determined as the variables to be optimized.

5. The multi-objective optimization method for a carbon fiber-reinforced epoxy resin-based curing system as described in claim 4, wherein In Step S1, first obtain the Cf range value, T range value, t range value, and Si range value through preliminary experiments and in combination with the conventional experience in the art.

6. The multi-objective optimization method of the carbon fiber reinforced epoxy resin-based curing system according to claim 5, characterized in that, The Cf range value, the T range value, the t range value, and the Si range value are respectively 0% < Cf ≤ 8%, 60°C ≤ T ≤ 130°C, 0 h < t ≤ 5 h, and 0% ≤ Si ≤ 10%.

7. The multi-objective optimization method for a carbon fiber-reinforced epoxy resin-based curing system as described in claim 1, wherein In step S2, the value ranges of N variables to be optimized are input into Matlab software, and then n groups of sample parameters are generated by using the Latin hypercube sampling method.

8. The multi-objective optimization method for a carbon fiber reinforced epoxy resin-based curing system according to claim 2, characterized in that In step S2, when N is 4 and the carbon fiber percentage content (Cf), the secondary curing temperature (T), the secondary curing time, and the concentration of the silane coupling agent solution (Si) are determined as parameters, 23 sample parameters are generated by using the range values of the carbon fiber percentage content, the range values of the secondary curing temperature, the range values of the secondary curing time, and the range values of the concentration of the silane coupling agent solution to form a sample set.

9. The multi-objective optimization method for a carbon fiber reinforced epoxy resin-based curing system according to claim 1, characterized in that The epoxy resin includes conventional epoxy resin E44 epoxy resin and E51 epoxy resin; And / or, in steps S5 and S6, the model is a Gaussian model; And / or, the carbon fiber is T700 micron-level short-cut carbon fiber.

10. The multi-objective optimization method for a carbon fiber reinforced epoxy resin-based curing system according to claim 1, characterized in that Step S1: Determine the carbon fiber percentage content (Cf), the secondary curing temperature (T), the secondary curing time, and the concentration of the silane coupling agent solution (Si) as variables to be optimized; determine the value ranges of the variables to be optimized according to preliminary tests and the experience in the field; Step S2: Generate 23 groups of sample parameters by using the value ranges of the carbon fiber percentage content (Cf), the secondary curing temperature (T), the secondary curing time, and the concentration of the silane coupling agent solution (Si) to form a sample set; Step S3: Cure the epoxy resin by using all the sample parameters in the sample set and test its performance to obtain the measured performance values, and construct a data set that corresponds one-to-one between the "curing process parameters and material test performance"; Step S4: Perform data normalization processing on the curing process parameters and the material test performance based on the data set; Step S5: Determine the Gaussian process regression (GPR) prior model, select the rational quadratic covariance function (RQ) as the kernel function, and determine the initial values of the hyperparameters; Step S6: Construct a regression model based on the normalized data set; Step S7: Use the regression model to make predictions and compare with the experimental samples to determine whether the regression model meets the accuracy requirements. If the accuracy does not meet the requirements, repeat step S5 to re-determine the initial values of the hyperparameters; Step S8: Equally divide the value ranges of the 4 variables to be optimized into 30 levels, and establish a full-factor mesh data set of the variables to be optimized; Step S9: Perform regression prediction on the full-factor mesh data set of the variables to be optimized through the Gaussian process regression model to obtain a full-factor prediction data set; Step S10: Select an appropriate weight factor according to the target performance requirements, and obtain the optimal solution of the multi-objective performance optimization in the full-factor prediction data set, so as to obtain the corresponding optimal process parameter solution.

Images