A method for predicting modulus of fiber glass based on optimization of makishima-mackenzie formula

Abstract

The application discloses a kind of based on optimization Makishima-Mackenzie formula's fiber glass modulus prediction method.The application first establishes an oxide dissociation energy optimization model based on differentiating weight coefficient, by introducing independent optimization coefficient, the difference of different oxides in glass network structure to modulus contribution can be optimized, compared with the prediction error of traditional MM formula on high modulus glass modulus is greatly reduced;At the same time, the clear physical image based on dissociation energy and component is retained, the internal relationship between glass microstructure and macro modulus can be revealed, and the "black box" problem of pure machine learning method is avoided.In addition, the modulus prediction can be completed only by oxide dissociation energy, molar volume and other basic parameters easy to obtain, the calculation efficiency is improved by more than 100 times, and high-performance computing resources are not needed, which significantly reduces the time cost and technical threshold of high-performance glass fiber research and development.

Description

Technical Field

[0001] This invention belongs to the field of glass fiber technology, and in particular to a method for predicting the modulus of fiber glass based on an optimized Makishima-Mackenzie formula. Background Technology

[0002] Glass fiber, as an important reinforcing material, has wide applications in aerospace, wind power generation, and civil engineering. Particularly in the field of clean energy equipment, high-modulus glass fiber is a key basic material for wind turbine blade manufacturing. With the global energy structure transformation and the rapid development of the wind power industry, the size of wind turbine blades is constantly increasing, placing higher demands on the mechanical properties of glass fiber, especially its elastic modulus. High-modulus glass fiber can significantly improve the stiffness and load-bearing capacity of blades, extend their service life, and reduce total life cycle costs. Therefore, developing glass fiber materials with higher modulus has become an urgent need for industry development.

[0003] However, traditional glass fiber formulation design mainly relies on trial and error, that is, by producing glass samples with different component ratios through numerous experiments, testing their performance, and then gradually optimizing the formulation. This method has obvious drawbacks: on the one hand, it requires a large number of melting experiments, which consumes a lot of time, manpower, and raw material costs; on the other hand, it lacks theoretical guidance, resulting in low optimization efficiency and difficulty in systematically exploring the composition-performance relationship, which seriously restricts the research and development process of new high-modulus glass fibers.

[0004] In recent years, with the development of artificial intelligence technology, machine learning methods have been introduced into the field of glass material performance prediction, accelerating material design by establishing big data-driven predictive models. However, machine learning methods also have inherent limitations: their prediction accuracy is highly dependent on the quality and quantity of training data, and for new systems or specific component ranges with scarce data, the generalization ability and reliability of the model are often insufficient; at the same time, machine learning models lack physical interpretability, making it difficult to reveal the intrinsic relationship between the microstructure and macroscopic properties of glass, which is not conducive to a deeper understanding of the modulus strengthening mechanism.

[0005] Quantitative structure-property relationship (QSPR) analysis based on theoretical models provides another approach to predicting the modulus of glass. This method establishes descriptors to correlate the microstructural parameters of glass with macroscopic properties, combining computational efficiency with physical significance. For example, patent (CN11623001A) and the literature "Yan J, Zhang Y, Wang F, et al. Electronegativity-Based QSPR Analysis for Understanding Structure–PropertyRelationships of Glass Materials. The Journal of Physical Chemistry B. 2025;129:5033-46." report QSPR models based on oxide formation energy and coordination number. However, existing theoretical models have significant errors in predicting the modulus of fiber-reinforced glasses, especially MgO-containing systems. Currently, the mainstream system for high-modulus glass fibers is the SiO2-Al2O3-MgO ternary system, and existing models lack sufficient accuracy in calculating this system, limiting its application in practical formulation design. In addition, the QSPR model relies on molecular dynamics simulations to calculate structural parameters such as coordination number. This process is computationally intensive and time-consuming, which can reduce the efficiency of glass fiber research and development.

[0006] Besides the QSPR model, the Makishima-Mackenzie (MM) formula is another classic method for predicting the glass modulus. Based on the theory of glass packing density, the MM formula establishes the relationship between the modulus and the glass composition and dissociation energy:

[0007]

[0008] In the formula, E is Young's modulus, and V t C is the packing density factor. i G represents the mole fraction of the i-th oxide. i This refers to the dissociation energy. The advantages of the MM formula are its clear physical meaning and ease of calculation, but it also has significant limitations: on the one hand, for high-modulus fiber glass systems, the MM formula's prediction accuracy is insufficient, and the calculated modulus is often significantly smaller than the actual glass modulus; on the other hand, the calculation of the packing density factor requires the actual density of the glass, and when designing or predicting glass systems of unknown origin, it is difficult to obtain the accurate density of the glass, which also leads to a decrease in the accuracy of the predicted glass modulus.

[0009] Therefore, there is an urgent need to develop a new theoretical calculation model that can accurately predict the elastic modulus of high-modulus glass fibers in the SiO2-Al2O3-MgO system, while simplifying the calculation process and improving calculation efficiency, so as to provide an effective tool for the rapid design of high-performance glass fibers. Summary of the Invention

[0010] The purpose of this invention is to address the problems existing in the prior art by providing a method for analyzing the modulus of glass fiber materials based on oxide dissociation energy and molar volume. This method, through the construction of a novel descriptor model, can accurately predict the elastic modulus of high-modulus glass fibers in the SiO2-Al2O3-MgO system without molecular dynamics simulations, significantly improving computational efficiency and providing theoretical guidance and technical support for the formulation design of high-performance glass fibers.

[0011] The technical solution to achieve the objective of this invention is: a method for predicting the modulus of fiber glass based on an optimized Makishima-Mackenzie formula, the method comprising the following steps:

[0012] Step 1: Collect composition and Young's modulus data of glass fibers of different systems from publicly available glass performance databases to form a dataset, which includes data of the SiO2-Al2O3-MgO ternary system and its extended systems; and establish corresponding glass molecular models for the composition of glass fibers of different systems.

[0013] Step 2: Calculate the total number of atoms and the total number of different cations in each glass molecule model;

[0014] Step 3: Based on the total number of atoms, the total number of different cations, the dissociation energy of different oxides, and the molar volume, construct a correlation model between the composition of glass fiber and its Young's modulus.

[0015] Step 4: Based on the dataset, optimize the association model using a genetic algorithm to minimize the root mean square error between the predicted modulus and the experimental modulus;

[0016] Step 5: Based on the dataset, select data from different Young's modulus intervals to verify the generalization of the association model, and adjust it according to the verification results to obtain the final association model.

[0017] Step 6: For the glass fiber to be predicted, input its composition into the final correlation model and output the corresponding Young's modulus result.

[0018] Furthermore, the correlation model between the composition of the glass fiber and its Young's modulus constructed in step 3 is as follows:

[0019]

[0020] In the formula, F represents the modulus-related parameter, N represents the total number of atoms in the model, and i represents the type of oxide. Let i be the molar ratio of the components of the i-th oxide. Let be the dissociation energy of the i-th oxide. Let be the optimization coefficient for the dissociation energy of the i-th oxide. Let i be the molar volume of the i-th oxide. This indicates the total number of oxide types.

[0021] Furthermore, in step 4, the NGAS-II algorithm is used to optimize the association model.

[0022] Furthermore, step 4 optimizes the association model using the NGAS-II algorithm, specifically including:

[0023] Step 4-1: Divide the dataset from Step 1 into a training set, a test set, and a validation set;

[0024] Step 4-2, construct the optimization objective function:

[0025]

[0026] In the formula, n is the number of training samples, and E pred,j Let E be the predicted Young's modulus for the j-th sample. exp,j The corresponding experimental Young's modulus measurement value; the optimization objective is to minimize the root mean square error (RMSE) value;

[0027] Step 4-3: Set the initial range of values ​​for the dissociation energy coefficient δᵢ of each oxide, and generate an initial solution set with a population size of Q, where each individual represents a complete combination of dissociation energy coefficients.

[0028] Step 4-4: For each individual in the population, i.e., a set of dissociation energy coefficient combinations, perform the following operations:

[0029] ① Substitute this set of dissociation energy coefficients into the correlation model established in step 3;

[0030] ② Calculate the modulus-related parameter F for all glass fibers in the training set;

[0031] ③ Establish the modulus-related parameter F and the experimental Young's modulus E. exp Linear regression relationship between them:

[0032] E exp = a·F + b

[0033] The coefficients a and b are determined using the least squares method;

[0034] ④ Calculate the RMSE value corresponding to the set of dissociation energy coefficient combinations as a fitness index. The smaller the RMSE, the higher the fitness.

[0035] Steps 4-5 involve genetic manipulation, including:

[0036] The selection process is carried out by randomly selecting m individuals each time using the tournament selection method. The individual with the highest fitness is selected to enter the next generation. This process is repeated until a number of individuals equal to the population size are selected.

[0037] Perform crossover operation with probability P c Selected individuals are paired, and offspring are generated using a simulated binary crossover method; for each parent pair ( , The formula for calculating the offspring coefficient is:

[0038]

[0039] in, Let be the dissociation energy coefficient of the i-th oxide in the first parent generation. Let be the dissociation energy coefficient of the i-th oxide of the second parent generation. Let be the dissociation energy coefficient of the i-th oxide in the first offspring. β is the dissociation energy coefficient of the i-th oxide of the second offspring, and β is the cross-distribution parameter;

[0040] Perform a mutation operation with probability P m The individuals are mutated using a polynomial mutation method, specifically the dissociation energy coefficient of the selected individuals. The perturbation is performed according to the following formula:

[0041]

[0042] In the formula, The dissociation energy coefficient of the i-th oxide after the mutation. The dissociation energy coefficient of the i-th oxide before the mutation. Let be the maximum value of the dissociation energy coefficient of oxide i. This represents the minimum value of the dissociation energy coefficient of the i-th oxide. A random number within the range [-0.1, 0.1];

[0043] Steps 4-6 involve iterative optimization, using the new population generated through selection, crossover, and mutation operations as the next generation population. The optimal fitness value and corresponding dissociation energy coefficient combination are recorded for each generation. The iteration terminates when any of the following conditions are met:

[0044]

[0045] In the formula, the units of the second preset threshold and the third preset threshold are both... ;

[0046] Steps 4-7 output the final optimized dissociation energy coefficients of each oxide. The optimal value is obtained by outputting the optimal set of dissociation energy coefficients, thereby obtaining the optimized correlation model.

[0047] Furthermore, the verification process in step 5 includes:

[0048] Using the optimized association model from step 4, perform Young's modulus prediction on the validation set data outside the training set, and calculate the prediction error of the validation set.

[0049] If the prediction error of the validation set is greater than the error of the training set and the difference exceeds the preset threshold, then the genetic algorithm parameters are adjusted or the training set is expanded, and then the process returns to step 4 to re-optimize the association model.

[0050] On the other hand, a fiber glass modulus prediction system is provided, the system comprising:

[0051] The first module is used to: collect composition and Young's modulus data of glass fibers of different systems from publicly available glass performance databases to form a dataset, which includes data of the SiO2-Al2O3-MgO ternary system and its extended systems; and establish corresponding glass molecular models for the composition of glass fibers of different systems.

[0052] The second module is used to calculate the total number of atoms and the total number of different cations in each glass molecule model.

[0053] The third module is used to realize: based on the total number of atoms, the total number of different cations, the dissociation energy of different oxides and molar volume, construct a correlation model between the composition of glass fiber and its Young's modulus;

[0054] The fourth module is used to: optimize the association model based on the dataset using a genetic algorithm to minimize the root mean square error between the predicted modulus and the experimental modulus;

[0055] The fifth module is used to: verify the generalization of the association model by selecting data from different Young's modulus ranges based on the dataset, and adjust it according to the verification results to obtain the final association model;

[0056] The sixth module is used to: input the composition of the glass fiber to be predicted into the final correlation model and output the corresponding Young's modulus result.

[0057] On the other hand, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the fiber glass modulus prediction method based on the optimized Makishima-Mackenzie formula.

[0058] On the other hand, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the fiber glass modulus prediction method based on the optimized Makishima-Mackenzie formula.

[0059] Compared with the prior art, the significant advantages of this invention are:

[0060] (1) This invention establishes an oxide dissociation energy optimization model based on differential weight coefficients. By introducing independent optimization coefficients, it can optimize the difference in the contribution of different oxides to the modulus in the glass network structure. Compared with the traditional Makishima-Mackenzie formula, the prediction error of the modulus of high modulus glass is greatly reduced.

[0061] (2) This invention makes innovative improvements on the physical framework of the classic Makishima-Mackenzie formula, retains a clear physical picture based on dissociation energy and composition, and each parameter has a clear physical meaning. It can reveal the intrinsic connection between the microstructure of glass and the macro modulus, provide an effective research means for a deeper understanding of the modulus strengthening mechanism, and avoid the "black box" problem of pure machine learning methods.

[0062] (3) The glass modulus prediction method proposed in this invention abandons the complex process of calculating coordination number through molecular dynamics simulation in the QSPR analysis method. The modulus prediction can be completed using only basic parameters that are easy to obtain, such as oxide dissociation energy and molar volume. The calculation efficiency is improved by more than 100 times, and no high-performance computing resources are required, which significantly reduces the time cost and technical threshold of high-performance glass fiber research and development.

[0063] (4) Compared with existing similar technologies, the glass modulus calculation method proposed in this invention has significantly improved the accuracy of modulus prediction for MgO-containing glass systems. It is applicable to different glass systems containing multi-component oxides such as CaO, Na2O, K2O, Fe2O3, and CeO2. The parameter optimization strategy of the genetic algorithm has good adaptability and can be quickly extended to the modulus prediction of new glass materials.

[0064] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0065] Figure 1 This is a flowchart of a fiber glass modulus prediction method based on an optimized Makishima-Mackenzie formula in one embodiment.

[0066] Figure 2 This is a schematic diagram illustrating the verification results of the glass modulus calculation method model generated by the present invention and the glass data of the SiO2-Al2O3-MgO system in one embodiment.

[0067] Figure 3 This is a schematic diagram illustrating the verification results of a glass modulus calculation method model based on the melting enthalpy of atomic pairs and glass data of the SiO2-Al2O3-MgO system in one embodiment.

[0068] Figure 4 This is a schematic diagram illustrating the verification results of a glass modulus calculation method model based on oxide formation energy and glass data of the SiO2-Al2O3-MgO system in one embodiment. Detailed Implementation

[0069] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0070] It should be noted that if the embodiments of the present invention involve descriptions such as "first" and "second," these descriptions are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first" and "second" may explicitly or implicitly include at least one of those features. Furthermore, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or impossible to implement, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0071] In one embodiment, combined Figure 1 This paper provides a method for predicting the modulus of fiber glass based on an optimized Makishima-Mackenzie formula. The method includes the following steps:

[0072] Step 1: Collect composition and Young's modulus data of glass fibers of different systems from publicly available glass performance databases to form a dataset, which includes data of the SiO2-Al2O3-MgO ternary system and its extended systems; and establish corresponding glass molecular models for the composition of glass fibers of different systems.

[0073] Preferably, data from the INTERGLAD glass performance database is used, and the data covers a variety of glass systems, including the currently mainstream high-modulus SiO2-Al2O3-MgO system.

[0074] Step 2: Calculate the total number of atoms and the total number of different cations in each glass molecule model;

[0075] Specifically, this involves calculating the total number of atoms per mole for each type of glass data, including cations and oxygen atoms from different oxides.

[0076] Step 3: Based on the total number of atoms, the total number of different cations, the dissociation energy of different oxides, and the molar volume, construct a correlation model between the composition of glass fiber and its Young's modulus.

[0077] Step 4: Based on the dataset, optimize the association model using a genetic algorithm to minimize the root mean square error between the predicted modulus and the experimental modulus;

[0078] Step 5: Based on the dataset, select data from different Young's modulus intervals to verify the generalization of the association model, and adjust it according to the verification results to obtain the final association model.

[0079] Step 6: For the glass fiber to be predicted, input its composition into the final correlation model and output the corresponding Young's modulus result.

[0080] Furthermore, in one embodiment, the correlation model between the glass fiber composition and its Young's modulus constructed in step 3 is specifically as follows:

[0081]

[0082] In the formula, F represents the modulus-related parameter, N represents the total number of atoms in the model, and i represents the type of oxide. Let i be the molar ratio of the components of the i-th oxide. Let be the dissociation energy of the i-th oxide. Let be the optimization coefficient for the dissociation energy of the i-th oxide. Let i be the molar volume of the i-th oxide. This indicates the total number of oxide types.

[0083] Furthermore, in one embodiment, step 4 employs the NGAS-II algorithm to optimize the association model, specifically including:

[0084] Step 4-1: Divide the dataset from Step 1 into a training set, a test set, and a validation set;

[0085] Step 4-2, construct the optimization objective function:

[0086]

[0087] In the formula, n is the number of training samples, and E pred,j Let E be the predicted Young's modulus for the j-th sample. exp,j The corresponding experimental Young's modulus measurement value; the optimization objective is to minimize the root mean square error (RMSE) value;

[0088] Here, to evaluate different dissociation energy coefficients The prediction accuracy of the combined model is defined by the objective function as the root mean square error (RMSE) between the predicted modulus and the experimental modulus.

[0089] Step 4-3: Set the initial range of values ​​for the dissociation energy coefficient δᵢ of each oxide, and generate an initial solution set with a population size of Q, where each individual represents a complete combination of dissociation energy coefficients.

[0090] Here, the initial value range needs to ensure the rationality of the parameters while also providing sufficient search space.

[0091] Preferably, the initial value range is set to [0.5, 2.0].

[0092] Preferably, Q is set to 100.

[0093] Step 4-4: For each individual in the population, i.e., a set of dissociation energy coefficient combinations, perform the following operations:

[0094] ① Substitute this set of dissociation energy coefficients into the correlation model established in step 3;

[0095] ② Calculate the modulus-related parameter F for all glass fibers in the training set;

[0096] ③ Establish the modulus-related parameter F and the experimental Young's modulus E. exp Linear regression relationship between them:

[0097] E exp = a·F + b

[0098] The coefficients a and b are determined using the least squares method;

[0099] ④ Calculate the RMSE value corresponding to the set of dissociation energy coefficient combinations as a fitness index. The smaller the RMSE, the higher the fitness.

[0100] Steps 4-5 involve genetic manipulation, including:

[0101] The selection process is carried out by randomly selecting m individuals each time using the tournament selection method. The individual with the highest fitness is selected to enter the next generation. This process is repeated until a number of individuals equal to the population size are selected.

[0102] Perform crossover operation with probability P c Selected individuals are paired, and offspring are generated using the simulated binary crossover (SBX) method; for each parent pair ( , The formula for calculating the offspring coefficient is:

[0103]

[0104] in, Let be the dissociation energy coefficient of the i-th oxide in the first parent generation. Let be the dissociation energy coefficient of the i-th oxide of the second parent generation. Let be the dissociation energy coefficient of the i-th oxide in the first offspring. β is the dissociation energy coefficient of the i-th oxide of the second offspring, and β is the cross-distribution parameter;

[0105] Perform a mutation operation with probability P m The individuals are mutated using a polynomial mutation method, specifically the dissociation energy coefficient of the selected individuals. The perturbation is performed according to the following formula:

[0106]

[0107] In the formula, The dissociation energy coefficient of the i-th oxide after the mutation. The dissociation energy coefficient of the i-th oxide before the mutation. Let be the maximum value of the dissociation energy coefficient of oxide i. This represents the minimum value of the dissociation energy coefficient of the i-th oxide. A random number within the range [-0.1, 0.1];

[0108] Preferably, P c =0.8, P m =0.1.

[0109] Steps 4-6 involve iterative optimization, using the new population generated through selection, crossover, and mutation operations as the next generation population. The optimal fitness value and corresponding dissociation energy coefficient combination are recorded for each generation. The iteration terminates when any of the following conditions are met:

[0110]

[0111] In the formula, the units of the second preset threshold and the third preset threshold are both... ;

[0112] Preferably, the first preset threshold is set to 500, and the second preset threshold is set to 0.01. The third preset threshold value is 0.5. .

[0113] Steps 4-7 output the final optimized dissociation energy coefficients of each oxide. The optimal value is obtained by outputting the optimal set of dissociation energy coefficients, thereby obtaining the optimized correlation model.

[0114] Furthermore, in one embodiment, the verification process in step 5 includes:

[0115] Using the optimized association model from step 4, perform Young's modulus prediction on the validation set data outside the training set, and calculate the prediction error of the validation set.

[0116] If the prediction error of the validation set is greater than the error of the training set and the difference exceeds the preset threshold, then the genetic algorithm parameters are adjusted or the training set is expanded, and then the process returns to step 4 to re-optimize the association model.

[0117] In one embodiment, a fiber glass modulus prediction system based on an optimized Makishima-Mackenzie formula is provided, the system comprising:

[0118] The first module is used to: collect composition and Young's modulus data of glass fibers of different systems from publicly available glass performance databases to form a dataset, which includes data of the SiO2-Al2O3-MgO ternary system and its extended systems; and establish corresponding glass molecular models for the composition of glass fibers of different systems.

[0119] The second module is used to calculate the total number of atoms and the total number of different cations in each glass molecule model.

[0120] The third module is used to realize: based on the total number of atoms, the total number of different cations, the dissociation energy of different oxides and molar volume, construct a correlation model between the composition of glass fiber and its Young's modulus;

[0121] The fourth module is used to: optimize the association model based on the dataset using a genetic algorithm to minimize the root mean square error between the predicted modulus and the experimental modulus;

[0122] The fifth module is used to: verify the generalization of the association model by selecting data from different Young's modulus ranges based on the dataset, and adjust it according to the verification results to obtain the final association model;

[0123] The sixth module is used to: input the composition of the glass fiber to be predicted into the final correlation model and output the corresponding Young's modulus result.

[0124] Specific limitations regarding the fiber glass modulus prediction system based on the optimized Makishima-Mackenzie formula can be found in the limitations of the fiber glass modulus prediction method based on the optimized Makishima-Mackenzie formula mentioned above, and will not be repeated here. Each module in the aforementioned fiber glass modulus prediction system based on the optimized Makishima-Mackenzie formula can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the corresponding operations of each module.

[0125] In one embodiment, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements:

[0126] Step 1: Collect composition and Young's modulus data of glass fibers of different systems from publicly available glass performance databases to form a dataset, which includes data of the SiO2-Al2O3-MgO ternary system and its extended systems; and establish corresponding glass molecular models for the composition of glass fibers of different systems.

[0127] Step 2: Calculate the total number of atoms and the total number of different cations in each glass molecule model;

[0128] Step 3: Based on the total number of atoms, the total number of different cations, the dissociation energy of different oxides, and the molar volume, construct a correlation model between the composition of glass fiber and its Young's modulus.

[0129] Step 4: Based on the dataset, optimize the association model using a genetic algorithm to minimize the root mean square error between the predicted modulus and the experimental modulus;

[0130] Step 5: Based on the dataset, select data from different Young's modulus intervals to verify the generalization of the association model, and adjust it according to the verification results to obtain the final association model.

[0131] Step 6: For the glass fiber to be predicted, input its composition into the final correlation model and output the corresponding Young's modulus result.

[0132] For specific limitations on each step, please refer to the limitations on the fiber glass modulus prediction method based on the optimized Makishima-Mackenzie formula mentioned above, which will not be repeated here.

[0133] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, the computer program being implemented when executed by a processor:

[0134] Step 1: Collect composition and Young's modulus data of glass fibers of different systems from publicly available glass performance databases to form a dataset, which includes data of the SiO2-Al2O3-MgO ternary system and its extended systems; and establish corresponding glass molecular models for the composition of glass fibers of different systems.

[0135] Step 2: Calculate the total number of atoms and the total number of different cations in each glass molecule model;

[0136] Step 3: Based on the total number of atoms, the total number of different cations, the dissociation energy of different oxides, and the molar volume, construct a correlation model between the composition of glass fiber and its Young's modulus.

[0137] Step 4: Based on the dataset, optimize the association model using a genetic algorithm to minimize the root mean square error between the predicted modulus and the experimental modulus;

[0138] Step 5: Based on the dataset, select data from different Young's modulus intervals to verify the generalization of the association model, and adjust it according to the verification results to obtain the final association model.

[0139] Step 6: For the glass fiber to be predicted, input its composition into the final correlation model and output the corresponding Young's modulus result.

[0140] For specific limitations on each step, please refer to the limitations on the fiber glass modulus prediction method based on the optimized Makishima-Mackenzie formula mentioned above, which will not be repeated here.

[0141] As a specific example, the invention will be further verified and illustrated in one embodiment.

[0142] This embodiment implements the fiber glass modulus prediction method proposed in this invention, specifically including:

[0143] (1) Collect the composition and Young's modulus data of the 16-element glass material, in which the 16-element oxides are the types required for conventional high modulus glass fibers, including SiO2, B2O3, Al2O3, MgO, CaO, Li2O, Na2O, K2O, Fe2O3, TiO2, ZrO2, ZnO, CeO2, Y2O3, La2O3 and SrO.

[0144] (2) Based on the glass composition in the collected data, calculate the total number of atoms per mole in each glass data, including cations and oxygen atoms of different oxides.

[0145] (3) Based on the total number of atoms, the number of cations, the dissociation energy of different oxides, and the molar volume, a correlation model between glass composition and its modulus is constructed:

[0146]

[0147] In the formula, F is the modulus correlation parameter, N is the total number of atoms in the model, i is the type of oxide, and C i Let G be the molar ratio of the components of the i-th oxide. i Let δ be the dissociation energy of the i-th oxide. i V is the optimization coefficient for the dissociation energy of the i-th oxide. m,i Let be the molar volume of the i-th oxide. The dissociation energies and molar volumes of the oxides are shown in Table 1 below:

[0148] Table 1. Dissociation energy and molar volume of oxides

[0149]

[0150] (4) The calculated optimization coefficients are shown in Table 2 below:

[0151] Table 2 Optimization Coefficients

[0152]

[0153] (5) The modulus and correlation parameters of the glass material were fitted using the original software, and a mathematical model between the correlation parameters and the glass modulus was established:

[0154]

[0155] (6) The accuracy of the model was verified using glass data from the SiO2-Al2O3-MgO system. Figure 2 This is the model proposed in this invention. It can be seen that the glass data for the SiO2-Al2O3-MgO system all lie around the fitted line drawn by the model proposed in this invention. In contrast, existing models still show a significant discrepancy between the calculated glass modulus of the SiO2-Al2O3-MgO system and its actual modulus, such as... Figure 3 and Figure 4 As shown.

[0156] (7) The generalizability of the model proposed in this invention was verified by glass experimental data. The glass composition and properties are shown in Table 3 below.

[0157] Table 3 Glass composition and properties

[0158]

[0159] As shown in Table 3, the error between the glass modulus calculated using the method proposed in this invention and the experimental modulus is less than 1 GPa across different modulus ranges. This fully demonstrates that the fiber glass modulus calculation method proposed in this invention has good generalization ability and is accurate in calculating the fiber glass modulus, which is helpful for designing high-modulus glass fiber compositions. In contrast, the error in predicting the glass modulus based on the original MM formula is quite significant, making it difficult to use as a tool for accurately calculating high-modulus fiber glass. For models based on melting enthalpy and formation energy, the error in calculating the modulus is relatively small for glass systems without MgO, but the error becomes significant when the MgO content increases. For example, in Examples 4, 5, and 6, the error between the calculated modulus and the experimental modulus for both models exceeds 20 GPa.

[0160] In summary, this invention can accurately predict the elastic modulus of glass fibers in different systems, while simplifying the calculation process and improving calculation efficiency, providing an effective tool for the rapid design of high-performance glass fibers.

[0161] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention without departing from its spirit and scope should be included within the protection scope of the present invention.

Claims

1. A method for predicting the modulus of fiber glass based on an optimized Makishima-Mackenzie formula, characterized in that, The method includes the following steps: Step 1: Collect composition and Young's modulus data of glass fibers of different systems from publicly available glass performance databases to form a dataset, which includes data of the SiO2-Al2O3-MgO ternary system and its extended systems; and establish corresponding glass molecular models for the composition of glass fibers of different systems. Step 2: Calculate the total number of atoms and the total number of different cations in each glass molecule model; Step 3: Based on the total number of atoms, the total number of different cations, the dissociation energy of different oxides, and the molar volume, construct a correlation model between the composition of glass fiber and its Young's modulus. Step 4: Based on the dataset, optimize the association model using a genetic algorithm to minimize the root mean square error between the predicted modulus and the experimental modulus; Step 5: Based on the dataset, select data from different Young's modulus intervals to verify the generalization of the association model, and adjust it according to the verification results to obtain the final association model. Step 6: For the glass fiber to be predicted, input its composition into the final correlation model and output the corresponding Young's modulus result; The correlation model between the composition of glass fiber and its Young's modulus constructed in step 3 is as follows: ； In the formula, F represents the modulus-related parameter, N represents the total number of atoms in the model, and i represents the type of oxide. Let i be the molar ratio of the components of the i-th oxide. Let be the dissociation energy of the i-th oxide. Let be the optimization coefficient for the dissociation energy of the i-th oxide. Let i be the molar volume of the i-th oxide. This indicates the total number of oxide types.

2. The method for predicting the modulus of fiber glass based on the optimized Makishima-Mackenzie formula according to claim 1, characterized in that, In step 4, the NGAS-II algorithm is used to optimize the association model.

3. The method for predicting the modulus of fiber glass based on the optimized Makishima-Mackenzie formula according to claim 2, characterized in that, Step 4 involves optimizing the association model using the NGAS-II algorithm, specifically including: Step 4-1: Divide the dataset from Step 1 into a training set, a test set, and a validation set; Step 4-2, construct the optimization objective function: ； In the formula, n is the number of training samples, and E pred,j Let E be the predicted Young's modulus for the j-th sample. exp,j The corresponding experimental Young's modulus measurement value; the optimization objective is to minimize the root mean square error (RMSE) value; Step 4-3: Set the initial range of values ​​for the dissociation energy coefficient δᵢ of each oxide, and generate an initial solution set with a population size of Q, where each individual represents a complete combination of dissociation energy coefficients. Step 4-4: For each individual in the population, i.e., a set of dissociation energy coefficient combinations, perform the following operations: ① Substitute this set of dissociation energy coefficients into the correlation model established in step 3; ② Calculate the modulus-related parameter F for all glass fibers in the training set; ③ Establish the modulus-related parameter F and the experimental Young's modulus E. exp Linear regression relationship between them: E exp = a·F + b The coefficients a and b are determined using the least squares method; ④ Calculate the RMSE value corresponding to the set of dissociation energy coefficient combinations as a fitness index. The smaller the RMSE, the higher the fitness. Steps 4-5 involve genetic manipulation, including: The selection process is carried out by randomly selecting m individuals each time using the tournament selection method. The individual with the highest fitness is selected to enter the next generation. This process is repeated until a number of individuals equal to the population size are selected. Perform crossover operation with probability P c Selected individuals are paired, and offspring are generated using a simulated binary crossover method; for each parent pair ( , The formula for calculating the offspring coefficient is: ； in, Let be the dissociation energy coefficient of the i-th oxide in the first parent generation. Let be the dissociation energy coefficient of the i-th oxide of the second parent generation. Let be the dissociation energy coefficient of the i-th oxide in the first offspring. β is the dissociation energy coefficient of the i-th oxide of the second offspring, and β is the cross-distribution parameter; Perform a mutation operation with probability P m The individuals are mutated using a polynomial mutation method, specifically the dissociation energy coefficient of the selected individuals. The perturbation is performed according to the following formula: ； In the formula, The dissociation energy coefficient of the i-th oxide after the mutation. The dissociation energy coefficient of the i-th oxide before the mutation. Let be the maximum value of the dissociation energy coefficient of oxide i. This represents the minimum value of the dissociation energy coefficient of the i-th oxide. A random number within the range [-0.1, 0.1]; Steps 4-6 involve iterative optimization, using the new population generated through selection, crossover, and mutation operations as the next generation population. The optimal fitness value and corresponding dissociation energy coefficient combination are recorded for each generation. The iteration terminates when any of the following conditions are met: ； In the formula, the units of the second preset threshold and the third preset threshold are both... ; Steps 4-7 output the final optimized dissociation energy coefficients of each oxide. The optimal value is obtained by outputting the optimal set of dissociation energy coefficients, thereby obtaining the optimized correlation model.

4. The method for predicting the modulus of fiber glass based on the optimized Makishima-Mackenzie formula according to claim 3, characterized in that, In step 4-2, the initial value range is set to [0.5, 2.0].

5. The method for predicting the modulus of fiber glass based on the optimized Makishima-Mackenzie formula according to claim 3, characterized in that, In steps 4-6, the first preset threshold is set to 500, and the second preset threshold is set to 0.

01. , The third preset threshold value is 0.

5. .

6. The method for predicting the modulus of fiber glass based on the optimized Makishima-Mackenzie formula according to claim 3, characterized in that, The verification process in step 5 includes: Using the optimized association model from step 4, perform Young's modulus prediction on the validation set data outside the training set, and calculate the prediction error of the validation set. If the prediction error of the validation set is greater than the error of the training set and the difference exceeds the preset threshold, then the genetic algorithm parameters are adjusted or the training set is expanded, and then the process returns to step 4 to re-optimize the association model.

7. A fiber glass modulus prediction system based on the method of any one of claims 1 to 6, characterized in that, The system includes: The first module is used to: collect composition and Young's modulus data of glass fibers of different systems from publicly available glass performance databases to form a dataset, which includes data of the SiO2-Al2O3-MgO ternary system and its extended systems; and establish corresponding glass molecular models for the composition of glass fibers of different systems. The second module is used to calculate the total number of atoms and the total number of different cations in each glass molecule model. The third module is used to realize: based on the total number of atoms, the total number of different cations, the dissociation energy of different oxides and molar volume, construct a correlation model between the composition of glass fiber and its Young's modulus; The fourth module is used to: optimize the association model based on the dataset using a genetic algorithm to minimize the root mean square error between the predicted modulus and the experimental modulus; The fifth module is used to: verify the generalization of the association model by selecting data from different Young's modulus ranges based on the dataset, and adjust it according to the verification results to obtain the final association model; The sixth module is used to: input the composition of the glass fiber to be predicted into the final correlation model and output the corresponding Young's modulus result.

8. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method according to any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 6.

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