Machine learning based ceramic based plain weave composite material yarn selection method

Abstract

The application discloses a yarn selection method for ceramic matrix plain weave composite materials based on machine learning, and comprises the following steps: establishing a meso-cell model and a progressive damage model; obtaining a sample database, and dividing the sample database into a training set, a verification set and a test set; constructing a performance prediction neural network model, optimizing the performance prediction neural network model by using the verification set, and evaluating the performance of the optimized performance prediction neural network model by using the test set; taking the optimized performance prediction neural network model which has passed the performance evaluation as a performance prediction proxy model; and establishing a yarn selection optimization model to obtain a Pareto optimal solution set. The application can quickly predict the comprehensive performance of ceramic matrix composites under different loads, reduce the experimental and simulation cost, and improve the material design and performance evaluation efficiency.

Description

Technical Field

[0001] This invention relates to a yarn selection method, specifically a machine learning-based method for selecting yarns for ceramic-based plain weave composite materials, belonging to the field of performance prediction and structural optimization technology for ceramic-based composite materials. Background Technology

[0002] Ceramic matrix composites possess advantages such as high temperature resistance, low density, high specific strength, and oxidation resistance, making them valuable for applications in aerospace, thermal protection structures, and engine hot-end components. Among these, ceramic matrix plain weave composites, due to the stable periodic microstructure formed by the interlacing of warp and weft yarns, exhibit macroscopic mechanical properties closely related to factors such as yarn bundle width-to-thickness ratio, yarn spacing, fiber volume fraction, and load conditions. Accurately predicting the strength, elastic modulus, and damage initiation stress of materials under different geometric parameters is a crucial foundation for material structure design and engineering selection optimization.

[0003] Currently, the performance of ceramic-based plain-weave composite materials is mainly obtained through two methods: experimental testing and finite element simulation. The first method, experimental testing, offers high precision, but sample preparation is costly and time-consuming, and it struggles to cover a large number of geometric parameter combinations. The second method, finite element simulation, can reveal the microscopic damage evolution process of materials, but modeling is complex and computationally time-consuming. Its computational efficiency is low when it requires comprehensive analysis of numerous unit cell structural parameters and load conditions. Furthermore, traditional parametric analysis methods typically only yield performance results at a limited number of design points, making it difficult to achieve rapid reverse engineering under different target performance requirements. Summary of the Invention

[0004] The purpose of this invention is to address the problems in existing technologies, such as high cost of obtaining performance data for ceramic-based plain weave composite materials, long finite element simulation cycles, low performance prediction efficiency under different geometric parameters and load conditions, and difficulty in reverse optimization of unit cell structural parameters based on target performance requirements. This invention provides a machine learning-based yarn selection method for ceramic-based plain weave composite materials. This method combines finite element simulation data with machine learning models to achieve rapid performance prediction of ceramic-based plain weave composite materials and enables reverse optimization of unit cell geometric parameters based on target strength, modulus, and damage initiation stress requirements. This is of great significance for reducing experimental and simulation costs, improving material design efficiency, and achieving intelligent yarn selection.

[0005] This invention achieves the above objective through the following technical solution: a method for selecting yarns for ceramic-based plain weave composite materials based on machine learning, the method comprising the following steps:

[0006] Step 1: Establish a microscopic unit cell model and a progressive damage model for ceramic-based plain weave composite materials;

[0007] Step 2: Establish micro-unit cell models with different sets of geometric parameters in batches, and perform finite element simulations on the micro-unit cell models under different load conditions to obtain a sample database. At the same time, divide the sample database into training set, validation set and test set.

[0008] Step 3: Construct a performance prediction neural network model for ceramic-based plain weave composite materials based on the training set, optimize the performance prediction neural network model using the validation set, and evaluate the performance of the optimized performance prediction neural network model using the test set.

[0009] Step 4: Using the optimized performance prediction neural network model after performance evaluation as a performance prediction surrogate model, the NSGA-II multi-objective genetic algorithm is used for reverse optimization to establish a yarn selection optimization model for ceramic-based plain weave composite materials, and the Pareto optimal solution set is obtained based on the yarn selection optimization model.

[0010] As a further aspect of the present invention: in step one, the microscopic unit cell model is a unit cell model composed of warp yarns, weft yarns, and the encapsulated matrix.

[0011] As a further aspect of the present invention: the parameters of the unit cell model are calculated using the following formula:

[0012] 1) The gap f between yarns along the height direction in the unit cell model is:

[0013]

[0014] 2) The radius R of the arc of the yarn cross-section in the unit cell model is:

[0015]

[0016] 3) The cross-sectional area S of the yarn in the unit cell model is:

[0017] )

[0018] 4) The length L of the straight yarn segment in the unit cell model is:

[0019]

[0020] 5) Inclination angle of the straight yarn segment in the unit cell model for:

[0021]

[0022] 6) Fiber volume content V in the unit cell model f for:

[0023]

[0024] in, , , respectively, represent the length and height of the unit cell, and a and b, respectively, represent the major and minor axes of the yarn cross-section. This represents the fiber convergence rate in the yarn.

[0025] As a further aspect of the present invention: the yarn portion of the progressive damage model uses an improved three-dimensional Hashin strength criterion to determine the damage initiation of the yarn; the matrix portion of the progressive damage model uses the maximum principal stress criterion to determine the damage initiation of the matrix material.

[0026] As a further aspect of the present invention: In step two, the microscopic unit cell model uses the ratio of the width to the thickness of the yarn bundle cross-section as geometric parameter K, and the spacing between the yarn bundles as geometric parameter S; and adopts three load modes as load conditions: uniaxial tension, uniaxial compression, and in-plane shear.

[0027] As a further aspect of the present invention: In step two, the parametric modeling software TexGen is used to generate micro-unit cell models with different combinations of geometric parameters in batches. The generated micro-unit cell models are then subjected to geometric stability screening, and the micro-unit cell models that meet the screening conditions are discretized into voxels to generate voxelized unit cell finite element models for finite element simulation.

[0028] As a further aspect of the present invention: in step three, the performance prediction neural network model adopts an MLP regression model; the input parameters of the MLP regression model include: yarn bundle width-to-thickness ratio K, yarn bundle spacing S, and fiber volume fraction V. f Load conditions; the output parameters of the MLP regression model include: strength, elastic modulus, and damage initiation stress.

[0029] As a further aspect of the present invention: the MLP regression model includes an input layer, a hidden layer, and an output layer; wherein the activation function of the hidden layer is the ReLU function, and the output layer uses a linear activation function; the performance evaluation metrics of the optimized performance prediction neural network model include the coefficient of determination R², the root mean square error RMSE, and the mean absolute error MAE.

[0030] As a further aspect of the present invention, the MLP regression model employs a Bayesian optimization algorithm to optimize the hyperparameters of the MLP regression model, including the number of hidden layers, the number of nodes in each hidden layer, the learning rate, the batch size, the regularization coefficient, and the number of iterations.

[0031] As a further aspect of the present invention: the yarn selection optimization model uses the NSGA-II multi-objective genetic algorithm to optimize the geometric parameters K, S, and fiber volume fraction V. fBy performing reverse optimization, the optimal Pareto unit cell parameter combination that satisfies the requirements of target strength, target modulus and damage initiation stress is obtained.

[0032] The beneficial effects of this invention are:

[0033] 1) This invention constructs a performance database of ceramic-based plain weave composite materials through finite element simulation, and establishes a nonlinear mapping relationship between geometric parameters, load conditions and material properties using machine learning models. This enables rapid prediction of strength, elastic modulus and damage initiation stress under different unit cell structural parameters, reducing the number of repeated finite element simulations and improving the efficiency of performance prediction.

[0034] 2) This invention uses the Bayesian optimization algorithm to optimize the hyperparameters of the MLP regression model, which can avoid the blindness of manual parameter tuning and improve the prediction accuracy and generalization ability of the machine learning model.

[0035] 3) This invention establishes a reverse optimization model based on a trained machine learning proxy model, which can quickly obtain the unit cell geometric parameter combination such as K value, S value and fiber volume fraction that meet the design requirements according to the target strength, target modulus and target damage initiation stress requirements, so as to realize the intelligent selection and optimization design of yarn structure parameters of ceramic matrix plain weave composite material.

[0036] 4) This invention can quickly predict the comprehensive performance of ceramic-based plain weave composite materials under different loads, reduce experimental and simulation costs, and improve the efficiency of material design and performance evaluation. Attached Figure Description

[0037] Figure 1 This is an overall flowchart of the present invention;

[0038] Figure 2 A schematic diagram of the geometric parameters of the microscopic unit cell model provided by this invention.

[0039] Figure 3 This is a schematic diagram of the yarn bundle coordinate system provided by the present invention;

[0040] Figure 4 The calculation flowchart for progressive damage simulation provided by this invention;

[0041] Figure 5 The voxelized finite element model provided for this invention includes K, S, and fiber volume fraction V. f A diagram illustrating the relationships between them;

[0042] Figure 6 For embodiments of the present invention, K=5.500; S=0.694; V f A schematic diagram of the voxelized model with a value of 0.5274;

[0043] Figure 7 For embodiments of the present invention, K=5.500; S=0.694; V f The uniaxial tensile simulation results of the voxelized finite element model with a coefficient of 0.5274 are shown in the stress distribution cloud maps in the 1st, 2nd, and 12th shear directions, respectively.

[0044] Figure 8 For embodiments of the present invention, K=5.500; S=0.694; V f The uniaxial tensile simulation results of the voxelized finite element model with a coefficient of 0.5274 are shown in the damage contour maps in the 1st direction, 2nd direction, and thickness direction, respectively.

[0045] Figure 9 This invention provides a complete process from finite element modeling to dataset generation to neural network construction in its embodiments. Detailed Implementation

[0046] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0047] Example 1, as Figure 1 As shown, this embodiment provides a method for selecting yarns for ceramic-based plain weave composite materials based on machine learning. This method includes the following steps:

[0048] First, a mesoscopic unit cell model of ceramic-based plain weave composite material is established, and a progressive damage model is built upon this model. The mesoscopic unit cell model characterizes the geometry and material distribution of the warp, weft, and matrix (ceramic matrix), providing a geometric basis for finite element discretization, material property assignment, and boundary condition application. The progressive damage model describes the damage initiation and evolution process of the yarn and matrix under load, thereby obtaining the mechanical properties under different structural parameters and load conditions. Furthermore, the progressive damage model is embedded as a material damage and failure model into the finite element analysis process of the mesoscopic unit cell model.

[0049] The established mesoscopic unit cell model of ceramic-based plain weave composite materials is a unit cell model (RVE) consisting of four yarns (two warp yarns and two weft yarns) and the enclosing matrix. The geometric parameters of the unit cell model are as follows: Figure 2 As shown, the relevant parameters of the unit cell model are calculated using the following formula:

[0050] 1) The gap f between yarns along the height direction in the unit cell model is:

[0051]

[0052] 2) The radius R of the arc of the yarn cross-section in the unit cell model is:

[0053]

[0054] 3) The cross-sectional area S of the yarn in the unit cell model is:

[0055] )

[0056] 4) The length L of the straight yarn segment in the unit cell model is:

[0057]

[0058] 5) Inclination angle of the straight yarn segment in the unit cell model for:

[0059]

[0060] 6) Fiber volume content V in the unit cell model f for:

[0061]

[0062] in, , , respectively, represent the length and height of the unit cell, and a and b, respectively, represent the major and minor axes of the yarn cross-section. This represents the fiber convergence rate in the yarn.

[0063] The yarn portion of the established progressive damage model for ceramic-based plain weave composites uses the three-dimensional Hashin strength criterion, specifically including:

[0064] 1) Fiber tensile fracture in one direction and fiber-matrix shear ( ):

[0065]

[0066] 2) Fiber compression damage in one direction and fiber-matrix shear ( ):

[0067]

[0068] 3) 2-direction matrix tensile cracking ( ):

[0069]

[0070] 4) Two-way matrix compression damage ( ):

[0071]

[0072] 5) 3-directional matrix tensile cracking ( ):

[0073]

[0074] 6) Three-directional matrix compression damage ( ):

[0075]

[0076] in, (i,j=1,2,3) represent the stress components in the yarn material coordinate system (e.g., ... Figure 3 (as shown); X 1T X 2T X 3T X 1C X 2C X 3C S 12 S 13 S 23 These represent the tensile, compressive, and shear strengths of the yarn in three directions, respectively. , , , , , Shear contribution factor for various failure modes; This is the shear nonlinearity factor, which can be used to describe the longitudinal shear nonlinear behavior of unidirectional composite materials, i.e.:

[0077]

[0078] When the shear contribution factor and the shear nonlinear factor take different values, the above-mentioned three-dimensional Hashin strength criterion can degenerate into any type of improved three-dimensional Hashin strength criterion or maximum stress criterion, thus facilitating programming calculations and engineering applications. The correspondence between the above-mentioned standardized improved three-dimensional Hashin strength criterion and various other criteria is shown in Table 1.

[0079] Table 1 shows the correspondence between the formally unified improved three-dimensional hashin strength criterion and various other criteria.

[0080]

[0081] In the microscopic unit cell model of ceramic matrix plain weave composite material, the improved three-dimensional Hashin strength criterion is used to determine the damage initiation of the yarn; considering that the matrix is ​​an isotropic material, the maximum principal stress criterion is used to determine the damage initiation of the matrix material.

[0082] like Figure 4 As shown, in the above progressive damage model, after the material meets the corresponding damage initiation criterion, the performance degradation of the material from damage initiation to complete failure is further described through the damage evolution process. For yarn, the damage variables are updated through the damage evolution equation, and the damage variables are introduced into the material stiffness matrix; for the matrix, after meeting the maximum principal stress failure criterion, its performance degradation is described using the direct stiffness reduction method, as follows:

[0083] To reduce the dependence of the calculation results on the mesh generation, the element characteristic length l is introduced into the definition of the equivalent displacement, that is:

[0084]

[0085] in, and For the corresponding strain components.

[0086] Similarly, the equivalent stress can be defined as follows:

[0087]

[0088] Among them, the operator .

[0089] The damage evolution equations under various failure modes are defined by equivalent displacements, namely:

[0090] (I=1T,1C,2T,2C,3T,3C)

[0091] in, This is the equivalent displacement in damage mode I. This is the equivalent displacement corresponding to the initial damage, and ; This is the equivalent displacement corresponding to complete failure, and G I The fracture energy density is selected based on experimental measurements or experience. The equivalent stress at the initial damage, and .

[0092] To further improve the convergence of numerical calculations, the Duvaut-Lions viscosity model is introduced:

[0093] (I=1T,1C,2T,2C,3T,3C)

[0094] in, D is the viscosity coefficient. I and Let be the damage variables before and after considering viscosity, respectively, for damage mode I; discretizing the above equation yields:

[0095]

[0096] Therefore, we can obtain:

[0097]

[0098] Finally, the damage variables in each direction are defined as follows:

[0099]

[0100] The Murakami model is used to characterize yarn damage. This damage model uses the principal values ​​of three damage variables to characterize the damage state of the material, namely:

[0101]

[0102] Among them, D i and n i These are the principal value and principal unit vector of the damage tensor, respectively. Considering the symmetry of the stress tensor, the effective stress tensor can be expressed as:

[0103]

[0104] in, and These are the stress tensor when undamaged and the effective stress tensor, respectively.

[0105] To incorporate the damage variable into the stiffness or flexibility tensor, the energy assumption proposed by Cordebois et al. is adopted, namely:

[0106]

[0107] Where C0 and C(D) are the stiffness tensors when the object is undamaged and damaged, respectively.

[0108] The stiffness tensor under damage can be expressed in matrix form using the principal values ​​of the undamaged stiffness tensor and the damage tensor, i.e.:

[0109]

[0110] Among them, Q ij (i,j=1,2,3) are the stiffness matrix components when there is no damage, and have , , ,

[0111] , , .

[0112] To include the case of shear nonlinearity in the stiffness matrix, the shear nonlinear constitutive relation formula is linearized as follows:

[0113]

[0114]

[0115] Here, the superscript (i) represents the calculation result of step i, and the superscript (i+1) represents the calculation result of step i+1. The final stiffness matrix components Q44 and Q55 can be written as:

[0116]

[0117] When considering shear nonlinearity, d 12 d 13 The above formula is used to calculate the result; when shear nonlinearity is not considered, take d. 12 =d 13 =0.

[0118] Finally, the tangential stiffness of the yarn is written as:

[0119]

[0120] Since the matrix is ​​not the primary load-bearing phase in the composite material, to improve computational efficiency, the performance degradation after matrix material failure is achieved using a direct stiffness reduction method. This means that when the matrix material fails, its corresponding elastic modulus and shear modulus are reduced to a relatively small value. The above progressive damage model was developed using the UMAT user material subroutine module in the commercial finite element software ABAQUS through secondary programming.

[0121] Second, we establish micro-unit cell models with different geometric parameters in batches and perform finite element simulations on them under different load conditions to obtain a sample database (including geometric parameters, load conditions, and mechanical performance parameters). The sample database is divided into training set, validation set, and test set.

[0122] The geometric parameters include the ratio of the width to the thickness of the yarn bundle cross-section used in the unit cell model as geometric parameter one (K), and the spacing between the yarn bundles as geometric parameter two (S); the load conditions include three load modes: uniaxial tension, uniaxial compression, and in-plane shear.

[0123] The parametric modeling software TexGen was used to generate micro-unit cell models of ceramic-based plain weave composite materials with different combinations of geometric parameters in batches. The generated micro-unit cell models were then subjected to geometric stability screening, and the micro-unit cell models that met the screening conditions were discretized into voxels to generate voxelized unit cell finite element models for finite element simulation.

[0124] Among them, the voxelized unit cell finite element model refers to the finite element calculation model formed by discretizing the selected unit cell model according to the preset three-dimensional regular voxel mesh and assigning yarn or matrix material properties to the region where each voxel is located.

[0125] Specifically, it includes:

[0126] First, set the parameter range, step size, and number of samples for the K value, and set the parameter range for the S value. For each set of K and S values, calculate the yarn bundle width W and yarn bundle thickness T based on the K value. The calculation method is: W=K^0.5; T=(1 / K)^0.5, thereby ensuring that the yarn bundle width and thickness satisfy W / T=K.

[0127] Secondly, a micro-unit cell model of a ceramic-based plain weave composite material containing two warp yarns and two weft yarns is established, and the geometric dimensions of the micro-unit cell model are determined according to the yarn bundle width W, yarn bundle thickness T, and yarn spacing S. The yarn center spacing is set to S+W, and the unit cell thickness dimension is set to 2T.

[0128] Then, in the micro-unit cell model of the ceramic-based plain weave composite material, the interlacing positions of the warp and weft yarns were adjusted to form a plain weave structure, and a default computational domain was assigned to the micro-unit cell model. In order to select a geometrically stable micro-unit cell model suitable for finite element simulation, the fiber volume fraction of the micro-unit cell model was calculated under both reference domain closed and reference domain open conditions, and the first fiber volume fraction V was obtained. f1 Second fiber volume fraction V f2 .

[0129] Finally, the relative rate of change of fiber volume fraction under the two states is calculated, and its expression is as follows: When η is less than or equal to the preset threshold, the micro-unit cell model corresponding to the K and S values ​​is determined to meet the geometric stability requirements and is retained; when η is greater than the preset threshold, the micro-unit cell model is determined to have large fluctuations in fiber volume fraction before and after the reference domain change, and is not suitable as a sample for subsequent finite element simulation, and is removed.

[0130] In this embodiment, the preset threshold is 5%. For mesoscopic unit cell models that meet the screening criteria, the rectangular voxel mesh method is used to export them as finite element analysis input files, with the voxel mesh size set to 40×40×30. The exported file name includes the corresponding K value, S value, and fiber volume fraction V. f This is to facilitate the subsequent establishment of a mapping relationship between geometric parameters, load conditions, and mechanical properties.

[0131] like Figure 5 As shown, the selected voxelized finite element model generated by the above method is illustrated, with its K, S, and fiber volume fraction V. f The relationship between them.

[0132] like Figure 6 As shown, this illustrates the generated values: K=5.500; S=0.694; V. f The voxelized finite element model has a value of 0.5274.

[0133] Using the above method, micro-unit cell models of voxelized ceramic-based plain weave composite materials with different combinations of K and S values ​​can be generated in batches and automatically screened, avoiding the problems of low efficiency and poor consistency caused by manual modeling, while ensuring that the models entering the finite element simulation stage have good geometric rationality and volume fraction stability.

[0134] After creating the voxelized unit cell finite element model, the generated voxelized unit cell finite element model is imported into the finite element analysis software. Uniaxial tension, uniaxial compression, and in-plane shear boundary conditions are applied respectively. The strength, elastic modulus, and damage initiation stress under the corresponding working conditions are extracted to form data samples for machine learning training. The data format of each set of samples is as follows: input parameters are: K, S, V. f L; the output parameters are: σ, E, σd.

[0135] Where K is the yarn bundle width-to-thickness ratio, S is the yarn bundle spacing, and V is the yarn bundle pitch. f σ represents the fiber volume fraction, L represents the load condition specification, σ represents the strength, E represents the elastic modulus, and σd represents the damage initiation stress.

[0136] like Figure 7 and Figure 8 As shown, this illustrates K=5.500; S=0.694; V f The uniaxial tensile simulation results of the voxelized finite element model with a coefficient of 0.5274 are shown, displaying stress distribution cloud maps in the 1st, 2nd, and 12th shear directions, as well as damage cloud maps in the 1st, 2nd, and thickness directions.

[0137] Third, a performance prediction neural network model for ceramic-based plain weave composite materials is constructed based on the training set, the model is optimized using the validation set, and the performance of the optimized performance prediction neural network model is evaluated using the test set.

[0138] Before establishing the performance prediction neural network model for ceramic-based plain-woven composite materials, the sample database was preprocessed. First, samples that failed to converge in the finite element calculation, as well as samples with significantly abnormal strength, elastic modulus, or damage initiation stress, were removed. Then, K, S, and V were preprocessed. f The strength, elastic modulus, and damage initiation stress are standardized to have a mean of 0 and a variance of 1, or normalized to map to the [0,1] interval. The processed data are then divided into training, validation, and test sets, with the preferred ratio being 80%:10%:10%.

[0139] The performance prediction neural network model uses a multilayer perceptron (MLP) regression model, with input parameters including: yarn bundle width-to-thickness ratio K, yarn bundle spacing S, and fiber volume fraction V. f Load conditions; output parameters include: strength, elastic modulus, and damage initiation stress.

[0140] The MLP regression model consists of an input layer, three hidden layers, and an output layer. The hidden layers use the ReLU activation function, and the output layer uses a linear activation function. During training, the mean square error (MSE) between the predicted values ​​of strength, elastic modulus, and damage initiation stress obtained from the output layer and their corresponding target values ​​is used as the loss function. The network parameters are updated through backpropagation based on this loss function. The trained MLP regression model is used to predict the mechanical properties of ceramic-based plain-weave composite materials. The predictive performance of the MLP regression model is evaluated using the coefficient of determination (R²), root mean square error (RMSE), and mean absolute error (MAE), specifically to assess the model's accuracy in predicting strength, elastic modulus, and damage initiation stress.

[0141] The MLP regression model employs a Bayesian optimization algorithm to optimize hyperparameters such as the number of hidden layers, the number of nodes in each hidden layer, the learning rate, the batch size, the regularization coefficient, and the number of iterations.

[0142] The MLP regression model has 4 nodes in the input layer, corresponding to the yarn bundle width-to-thickness ratio K, yarn bundle spacing S, and fiber volume fraction V, respectively. f Load conditions; the number of output layer nodes is 3, corresponding to strength, elastic modulus and damage initiation stress respectively.

[0143] The MLP regression model preferably has three hidden layers, with each layer containing 64 to 256 neurons. As a specific implementation, the MLP regression model uses the following network structure: input layer; first hidden layer with 64 neurons; second hidden layer with 128 neurons; third hidden layer with 64 neurons; output layer with 3 neurons.

[0144] The hidden layers use the ReLU activation function, while the output layer uses a linear activation function. To reduce the risk of overfitting, a Dropout layer is added after the hidden layers, with a preferred Dropout ratio of 0.05 to 0.30. An L2 regularization term is added during model training, with a preferred regularization coefficient of 1×10^-6 to 1×10^-3.

[0145] During the training of this MLP regression model, the loss function is the mean squared error (MSE) function, and the optimizer is the Adam optimizer. The learning rate is preferably between 1×10⁻⁴ and 1×10⁻², the batch size is preferably 8, 16, 32, or 64, and the maximum number of iterations is preferably between 200 and 2000 epochs. As a specific implementation, the initial learning rate is set to 0.001, the batch size is set to 32, the maximum number of iterations is set to 1000 epochs, and an early stopping mechanism is implemented, stopping training when the validation set loss does not decrease for 50 consecutive epochs.

[0146] To further improve the prediction accuracy and generalization ability of the MLP regression model, a Bayesian optimization algorithm is used to automatically optimize the hyperparameters of the MLP regression model. The Bayesian optimization algorithm uses the root mean square error of the validation set (RMSE) as the objective function, and the number of hidden layers, the number of neurons in each hidden layer, the learning rate, the batch size, the dropout ratio, the L2 regularization coefficient, and the number of iterations are used as variables to be optimized.

[0147] In this embodiment, the hyperparameter search space for Bayesian optimization is set as follows: the number of hidden layers is 3; the learning rate is 1×10^-3; the batch size is 32; the Dropout ratio is 0.20; the L2 regularization coefficient is 1×10^-4; and the maximum number of iterations is 1000 rounds.

[0148] Bayesian optimization first randomly generates several initial hyperparameter combinations, with an initial sampling number preferably 10 times in this embodiment. Then, a probabilistic surrogate model is established based on the evaluated hyperparameter combinations and their validation set errors, and the next set of hyperparameter combinations to be evaluated is determined through a sampling function. The maximum number of iterations for Bayesian optimization is preferably 50. Finally, the hyperparameter combination with the smallest validation set RMSE is taken as the optimal hyperparameter combination for the MLP regression model.

[0149] The MLP regression model was retrained using the optimal hyperparameters described above, and its performance was evaluated using a test set. Evaluation metrics included the coefficient of determination (R²), root mean square error (RMSE), and mean absolute error (MAE). R² characterizes the goodness of fit between the predicted and finite element simulation values, RMSE characterizes the overall magnitude of the prediction error, and MAE characterizes the average level of the prediction error. The R², RMSE, and MAE of the three output parameters—strength, elastic modulus, and damage initiation stress—were calculated separately to determine whether the model met the prediction accuracy requirements.

[0150] Fourth, the trained and tested MLP regression model is used as a surrogate model for predicting the performance of ceramic-based plain weave composite materials; under a given load condition, the yarn bundle width-to-thickness ratio K, yarn bundle spacing S, and fiber volume fraction V are used as the predictors. f As design variables, strength, elastic modulus, and damage initiation stress are used as optimization objectives or constraints. The NSGA-II multi-objective genetic algorithm is used for reverse optimization to establish a yarn selection optimization model for ceramic-based plain weave composite materials.

[0151] After obtaining the trained MLP regression model, it was used as a performance prediction surrogate model for ceramic-based plain weave composite materials to establish a yarn selection optimization model. The performance prediction surrogate model (reverse optimization model) uses K-values, S-values, and fiber volume fraction V... f Strength, elastic modulus, and damage initiation stress are used as design variables, serving as optimization objectives or constraints. The range of values ​​for these design variables is determined based on the sample ranges in the finite element database; for example, K ranges from 1.0 to 6.0, S ranges from 0.1 to 1.0, and V... f The value ranges from 0.30 to 0.65.

[0152] In this embodiment, the reverse optimization model is solved using the NSGA-II multi-objective genetic algorithm. First, an initial population is randomly generated within the design variable range, with each individual representing a set of K, S, and V. f The parameters are combined; then each individual is input into the trained MLP regression model to obtain the corresponding predicted intensity, predicted elastic modulus and predicted damage initiation stress; then the population is quickly sorted and crowded distance is calculated according to the optimization objective, and the population is updated through selection, crossover, mutation and elite retention strategies.

[0153] The preferred parameter settings for the NSGA-II algorithm are as follows: population size is set to 100, maximum number of generations is set to 200, crossover probability is set to 0.9, mutation probability is set to 0.05, and elite retention ratio is set to 0.2.

[0154] The optimization objectives of the inverse optimization model can be set as follows: maximizing strength σ; maximizing elastic modulus E; maximizing damage initiation stress σd; and minimizing fiber volume fraction V. f .

[0155] When a user specifies target performance requirements, such as a strength not less than σ0, an elastic modulus not less than E0, and a damage initiation stress not less than σd0, the inverse optimization model transforms the target performance requirements into constraints: σ≥σ0; E≥E0; σd≥σd0.

[0156] Based on the above constraints, the NSGA-II algorithm outputs a Pareto optimal solution set. Users can select one or more combinations of unit cell parameters from the Pareto optimal solution set according to design requirements. The output results include K values, S values, and fiber volume fraction V. f Load conditions, predicted strength, predicted elastic modulus, and predicted damage initiation stress.

[0157] like Figure 9 As shown, this embodiment demonstrates the complete process from finite element modeling to dataset generation to neural network construction. Through the above method, the present invention can use finite element simulation data to train an efficient performance prediction proxy model, and based on the proxy model, complete the reverse selection of unit cell structural parameters of ceramic-based plain weave composite materials under different target performance requirements, thereby significantly reducing the computational cost of repeated finite element simulations and improving the efficiency of material structure optimization design.

[0158] The yarn selection optimization model uses the NSGA-II multi-objective genetic algorithm to optimize geometric parameters K, S, and fiber volume fraction V. f By performing reverse optimization, the optimal Pareto unit cell parameter combination that satisfies the requirements of target strength, target modulus and damage initiation stress is obtained.

[0159] Working Principle: By constructing a micro-unit cell model and a progressive damage model of ceramic-based plain weave composite materials, the yarn bundle width-to-thickness ratio, yarn bundle spacing, and fiber volume fraction are used as geometric design variables. Three load conditions—uniaxial tension, uniaxial compression, and in-plane shear—are set. Voxelized micro-unit cell models with different parameter combinations are generated in batches using parametric modeling software. After geometric stability screening, these models are imported into finite element analysis software for progressive damage simulation. Strength, elastic modulus, and damage initiation stress are extracted under each load condition, forming a sample database containing input parameters (geometric parameters and load condition annotations) and output parameters (mechanical performance indicators). The data is preprocessed and divided into training, validation, and test sets. Based on this, an MLP regression model is constructed. Its input layer receives four features, and its output layer outputs three predicted mechanical performance values. The hidden layer uses the ReLU activation function and introduces Dropout and L2 regularization to prevent overfitting. The mean squared error is used as the loss function. The Adam optimizer was used for training, and a Bayesian optimization algorithm was employed to automatically optimize hyperparameters such as hidden layer structure, learning rate, batch size, regularization coefficient, and number of iterations. The root mean square error of the validation set was used as the objective function to obtain the optimal combination of hyperparameters, and the coefficient of determination, root mean square error, and mean absolute error were used to evaluate the model's prediction accuracy. The trained MLP model was then embedded as a surrogate model into the inverse optimization framework. The yarn bundle width-to-thickness ratio, yarn bundle spacing, and fiber volume fraction were used as design variables, and the target strength, target elastic modulus, and target damage initiation stress were used as constraints or optimization objectives. The NSGA-II multi-objective genetic algorithm was used for population initialization, non-dominated sorting, crowding distance calculation, and selection, crossover, mutation, and iterative evolution. Finally, the Pareto optimal unit cell parameter combination that meets the performance requirements was output, thereby realizing rapid selection and structural inverse optimization of ceramic-based plain weave composite yarns based on a combination of finite element simulation data-driven and machine learning surrogate models.

[0160] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0161] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A method for selecting yarns for ceramic-based plain weave composite materials based on machine learning, characterized in that, The method for selecting ceramic-based plain weave composite yarn includes the following steps: Step 1: Establish a microscopic unit cell model and a progressive damage model for ceramic-based plain weave composite materials; Step 2: Establish micro-unit cell models with different geometric parameters in batches, and perform finite element simulations on the micro-unit cell models under different load conditions to obtain a sample database. At the same time, divide the sample database into training set, validation set and test set. Step 3: Construct a performance prediction neural network model for ceramic-based plain weave composite materials based on the training set, optimize the performance prediction neural network model using the validation set, and evaluate the performance of the optimized performance prediction neural network model using the test set. Step 4: Using the optimized performance prediction neural network model after performance evaluation as a performance prediction surrogate model, the NSGA-II multi-objective genetic algorithm is used for reverse optimization to establish a yarn selection optimization model for ceramic-based plain weave composite materials, and the Pareto optimal solution set is obtained based on the yarn selection optimization model.

2. The method for selecting ceramic-based plain weave composite yarns according to claim 1, characterized in that: In step one, the microscopic unit cell model is a unit cell model composed of warp yarns, weft yarns, and the encapsulated matrix.

3. The method for selecting ceramic-based plain weave composite yarns according to claim 2, characterized in that, The parameters of the unit cell model are calculated using the following formula: 1) The gap f between yarns along the height direction in the unit cell model is: ； 2) The radius R of the arc of the yarn cross-section in the unit cell model is: ； 3) The cross-sectional area S of the yarn in the unit cell model is: ) 4) The length L of the straight yarn segment in the unit cell model is: ； 5) Inclination angle of the straight yarn segment in the unit cell model for: ； 6) Fiber volume content V in the unit cell model f for: ； in, , , respectively, represent the length and height of the unit cell, and a and b, respectively, represent the major and minor axes of the yarn cross-section. This represents the fiber convergence rate in the yarn.

4. The method for selecting ceramic-based plain weave composite yarns according to claim 1, characterized in that: In step one, the yarn portion of the progressive damage model uses an improved three-dimensional Hashin strength criterion to determine the initiation of yarn damage. The progressive damage model uses the maximum principal stress criterion to determine the damage initiation of the matrix material.

5. The method for selecting ceramic-based plain weave composite yarns according to claim 1, characterized in that: In step two, the microscopic unit cell model uses the ratio of the width to the thickness of the yarn bundle cross-section as geometric parameter K, and the spacing between the yarn bundles as geometric parameter S; it uses three load modes—uniaxial tension, uniaxial compression, and in-plane shear—as load conditions.

6. The method for selecting ceramic-based plain weave composite yarns according to claim 1, characterized in that, In step two, the parametric modeling software TexGen is used to generate mesoscopic unit cell models with different combinations of geometric parameters in batches. The generated mesoscopic unit cell models are then subjected to geometric stability screening, and the mesoscopic unit cell models that meet the screening conditions are discretized into voxels to generate voxelized unit cell finite element models for finite element simulation.

7. The method for selecting ceramic-based plain weave composite yarns according to claim 1, characterized in that: In step three, the performance prediction neural network model adopts an MLP regression model; the input parameters of the MLP regression model include: yarn bundle width-to-thickness ratio K, yarn bundle spacing S, and fiber volume fraction V. f The load conditions; the output parameters of the MLP regression model include: strength, elastic modulus, and damage initiation stress.

8. The method for selecting ceramic-based plain weave composite yarns according to claim 7, characterized in that: The MLP regression model includes an input layer, a hidden layer, and an output layer; wherein the activation function of the hidden layer is the ReLU function, and the activation function of the output layer is a linear activation function; the performance evaluation metrics of the optimized performance prediction neural network model include the coefficient of determination R², the root mean square error RMSE, and the mean absolute error MAE.

9. The method for selecting ceramic-based plain weave composite yarns according to claim 7, characterized in that: The MLP regression model employs a Bayesian optimization algorithm to optimize hyperparameters such as the number of hidden layers, the number of nodes in each hidden layer, the learning rate, the batch size, the regularization coefficient, and the number of iterations.

10. The method for selecting ceramic-based plain weave composite yarns according to claim 1, characterized in that: In step four, the yarn selection optimization model uses the NSGA-II multi-objective genetic algorithm to optimize the geometric parameters K, S, and fiber volume fraction V. f By performing reverse optimization, the optimal Pareto unit cell parameter combination that satisfies the requirements of target strength, target modulus and damage initiation stress is obtained.

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