A method for predicting elastic properties of fiber-reinforced composite materials

Abstract

The present invention discloses a method for predicting the elastic properties of fiber-reinforced composite materials, aiming to solve the problems of low precision, low efficiency and difficulty in handling multi-scale correlations in traditional methods. First, a random algorithm is used to generate representative volume units, and a high-quality training data set is constructed by combining Sobol sequence sampling and SMOGN data enhancement technology. Secondly, a deep neural network embedded with residual blocks and physical constraints is designed and trained, and the model generalization ability is improved through Bayesian optimization and adaptive parameter adjustment. Finally, a variety of macro-structure models are established to achieve end-to-end prediction of multi-scale elastic properties. This method achieves breakthroughs in prediction accuracy and computational efficiency: the time taken for a single analysis is shortened from several hours to minutes and seconds, and the average prediction error is less than 5%. This technology can be widely used in aerospace, new energy vehicles, wind power and other fields, providing intelligent support for the design and manufacture of high-performance composite materials.

Description

Technical Field

[0001] The present invention relates to the technical field of composite material computational design and performance prediction, and in particular to a method for predicting the elastic properties of fiber-reinforced composite materials. Background Art

[0002] Fiber-reinforced composites, with their exceptional specific strength and stiffness, as well as their high degree of designability, have become key structural materials in cutting-edge manufacturing sectors such as aerospace, new energy vehicles, wind power generation, and rail transit. By precisely controlling the distribution, orientation, and stacking of high-performance fibers (such as carbon and glass fibers) within a matrix, these materials enable customized design of mechanical properties at a macroscale to meet the demanding requirements of lightweighting, high load-bearing capacity, and functional integration under complex operating conditions.

[0003] In the design and analysis of composite structures, engineering elastic constants (i.e., elastic modulus, Poisson's ratio, and shear modulus) are fundamental core parameters for describing the mechanical response of materials. However, the inherent multiscale nature of composite materials—their macroscopic performance is determined by complex physical mechanisms at both the microscale (fiber-matrix properties, interface bonding) and the mesoscale (geometry of single-layer plates and woven units)—poses significant challenges to the accurate and efficient prediction of these key parameters. Currently, mainstream prediction methods in the industry suffer from the following technical limitations:

[0004] First, traditional analytical and semi-empirical models, such as the classic Rule of Mixtures (ROM) and the Halpin-Tsai equation, while computationally simple and fast, are based on idealized assumptions and ignore the influence of real structural characteristics such as the randomness of fiber distribution and microscopic defects. As a result, these models often produce large errors in predicting transverse and shear properties, and their accuracy cannot meet the requirements of high-fidelity design.

[0005] Secondly, numerical simulation technology based on the finite element method (FEM) can precisely simulate the micromechanical behavior of materials by constructing representative volume elements (RVEs), thereby achieving high prediction accuracy. However, this method also has significant drawbacks: from geometric modeling and meshing to the application of boundary conditions and nonlinear solutions, the entire process is computationally expensive and time-consuming. A single simulation can take hours to days, which severely restricts the rapid screening of materials, parameter optimization, and iterative design of large-scale structures, making it difficult to adapt to the pace of modern agile product development.

[0006] More importantly, existing methods generally suffer from "scale barriers," meaning they lack effective cross-scale correlation mechanisms. Most models are limited to single-scale analysis, making it difficult to capture how perturbations in microscopic parameters (such as fluctuations in fiber volume fraction) ultimately affect the overall performance of macroscopic components through mesoscopic structures (such as changes in ply sequence and weave pattern). This disconnect between scales limits the models' generalization and engineering applicability, hindering their ability to fully describe the integrated "component-structure-performance" relationship of materials.

[0007] Therefore, the industry urgently needs a new prediction paradigm that can break through existing technological bottlenecks. This paradigm should effectively integrate high-fidelity physical simulation with efficient computational intelligence, shortening computation time from hours to seconds while ensuring prediction accuracy. It should also establish end-to-end mapping capabilities from the micro to the macro level, providing efficient and reliable technical support for the entire intelligent design and verification process of high-performance composite materials. Summary of the Invention

[0008] In view of this, the purpose of the present invention is to provide a method for predicting the elastic properties of fiber-reinforced composites. By combining deep neural networks with multi-scale modeling, it can replace finite element analysis at the micro and meso scales, effectively balance computational efficiency and accuracy, and provide efficient support for the intelligent design of composite materials.

[0009] In order to solve the above technical problems, the technical solution of the present invention is: a method for predicting the elastic properties of fiber-reinforced composite materials, comprising the following steps:

[0010] S1. Constructing a training dataset: This is performed by numerically analyzing a plurality of representative volume elements (RVEs) covering a predetermined parameter range, wherein the parameter range includes at least a fiber volume fraction, a fiber elastic parameter, and a matrix elastic parameter; the numerical analysis is performed to solve for a transversely isotropic elastic parameter corresponding to each RVE, and the parameter range and the solved elastic parameter are used as data pairs to form a training dataset;

[0011] S2. Training the model: using the training data set constructed in step S1, training a deep neural network to establish a nonlinear mapping relationship between the preset parameters and the transversely isotropic elastic parameters;

[0012] S3. Predicting performance: Taking parameters including material and microstructure information and macrostructure parameters as input, using the deep neural network model trained in step S2, predict the macroscopic equivalent elastic properties of the fiber-reinforced composite material.

[0013] To implement the above technical solution, by using numerical analysis to homogenize the representative volume element (RVE) in step S1, the insufficient accuracy of traditional empirical formulas is overcome, providing high-fidelity basic data for subsequent deep learning models. In steps S2 and S3, the introduction of deep neural networks for training and prediction greatly improves computational efficiency, transforming the time-consuming (several hours) of traditional finite element simulation into fast predictions in seconds or even milliseconds, meeting the pace of modern agile product development. More importantly, by incorporating material and microstructure information as well as macrostructural parameters as inputs to the deep neural network in step S3, this method successfully establishes an end-to-end mapping relationship from fiber-matrix composition, microstructure, to macroscopic equivalent elastic properties. This completely breaks through the "scale barrier" of existing methods that lacks an effective cross-scale correlation mechanism, significantly enhancing the model's generalization ability and engineering applicability, thereby achieving high-precision, high-efficiency, and cross-scale prediction of composite material elastic properties, meeting the industry's urgent need for a new prediction paradigm.

[0014] As a preferred solution of the present invention, in step S1, the process of generating the representative volume element (RVE) includes: recursively subdividing the RVE area using a quadtree algorithm to establish an index for quickly querying adjacent fibers; and performing conflict detection based on the Monte Carlo method to randomly generate fiber coordinates that meet preset spacing conditions within the RVE area, thereby obtaining an RVE model with random fiber distribution.

[0015] To implement the above technical solution, a quadtree algorithm is used to recursively subdivide the RVE region, effectively establishing a spatial index for quickly querying neighboring fibers. This significantly improves the computational efficiency of fiber arrangement within the RVE and avoids repeated and inefficient global searches. Furthermore, a Monte Carlo method is used for conflict detection and random generation of fiber coordinates that meet preset spacing conditions. This ensures that the fibers in the generated RVE model have truly random distribution characteristics and avoids overlap and excessive aggregation between fibers. This enables the RVE model to more accurately reflect the microstructure of the actual composite material, providing a high-fidelity, physically accurate geometric foundation for subsequent numerical homogenization analysis, thereby ensuring the representativeness and accuracy of the training dataset.

[0016] As a preferred solution of the present invention, in step S1, the fiber volume fraction, fiber elastic parameters and matrix elastic parameters are uniformly sampled in high-dimensional space using the Sobol sequence sampling method to generate input parameter combinations for constructing the multiple representative volume elements (RVEs).

[0017] To implement the above technical solution, the Sobol sequence, as a low-discrepancy sequence, can generate more evenly distributed sample points in a high-dimensional parameter space compared to traditional pseudo-random sampling. This ensures that when constructing the multiple representative volume elements (RVEs), the selected input parameter combinations can fully and systematically cover the entire preset parameter space, avoiding the clustering or sparse areas of sample points, thereby making the training data set obtained through subsequent numerical homogenization analysis more representative. This uniform sampling characteristic is crucial for capturing the variations in the elastic properties of composite materials under different component parameters and microstructures, effectively improving the quality of training data and the generalization ability of the model, thereby laying a solid foundation for the accurate training and reliable prediction of deep neural networks.

[0018] As a preferred solution of the present invention, step S1 also includes: after obtaining the transversely isotropic elastic parameters through numerical analysis, using the SMOGN algorithm to enhance the data, the SMOGN algorithm identifies sparse areas of target values ​​based on the K-nearest neighbor algorithm and uses Gaussian noise synthesis technology to generate oversampled samples.

[0019] To implement the above technical solution, the SMOGN algorithm identifies sparse regions of target values ​​based on the K-nearest neighbor algorithm and uses Gaussian noise synthesis technology to generate oversampled samples, effectively solving the data imbalance or sample sparsity problems that may occur in the prediction of composite material properties. In particular, under certain extreme parameter combinations, numerical homogenization analysis may find it difficult to generate enough representative data points, resulting in a decrease in the model's prediction accuracy in these areas. The SMOGN algorithm can specifically expand the amount of data in these sparse areas, increasing the diversity and coverage of the training data set, thereby enabling deep neural networks to learn more fully under these complex or boundary conditions, significantly improving the model's generalization ability, robustness, and prediction accuracy over the full parameter range.

[0020] As a preferred solution of the present invention, the deep neural network model is a deep residual network including residual blocks.

[0021] To implement the above technical solution, the deep residual network introduces residual blocks, allowing the network to learn residual mappings between input and output rather than direct mappings. This design effectively solves the gradient vanishing / explosion problems and network degradation problems faced by deep neural networks during training, allowing the model to build deeper network layers without causing performance degradation. Therefore, the use of deep residual networks can enhance the learning and expression capabilities of the model, enabling it to more effectively capture the deep nonlinear characteristics and implicit laws in the multi-scale complex data of fiber-reinforced composites, thereby further improving the model's prediction accuracy and stability, and ensuring the accuracy and reliability of elastic property predictions in complex material systems.

[0022] As a preferred embodiment of the present invention, in step S2, a loss function including physical constraints is used to optimize the model, and the physical constraints include at least a transverse isotropy condition constraint, which forces the predicted shear modulus G to be 23 Satisfy formula G 23 =E 22 / (2×(1+V 23 )).

[0023] Implementing the above technical solution allows the neural network to embed the basic physical principles of materials science during the learning process, rather than relying solely on data-driven methods. By introducing this physical constraint term into the loss function, the model will be guided and corrected by physical laws during the optimization process, effectively avoiding prediction results that do not conform to actual physical meaning, significantly enhancing the model's physical interpretability, prediction accuracy, and robustness. This not only improves the model's prediction reliability in areas where data is sparse or unevenly distributed, but also reduces dependence on large-scale training data to a certain extent, ensuring that the prediction results are highly consistent with the inherent mechanical behavior of the material, thereby enhancing the scientific nature and engineering practical value of the entire prediction method.

[0024] As a preferred solution of the present invention, the physical constraint also includes a Poisson's ratio boundary constraint, which is achieved by 23 A penalty term is imposed on the predicted value.

[0025] Implementing the aforementioned technical solution and introducing this boundary constraint forces the neural network to avoid outputting anomalous Poisson's ratio predictions that are inconsistent with actual physical meaning during the learning process, such as values ​​that are excessively large or excessively negative. This not only further improves the physical plausibility and reliability of the model's predictions, effectively avoiding the non-physical predictions that may occur when the model is generalized to unseen data, but also indirectly improves the model's convergence and stability by guiding the model to focus on the physically valid space for learning, ensuring the overall accuracy and engineering applicability of elastic performance predictions.

[0026] As a preferred solution of the present invention, step S2 further includes automatically searching for hyperparameters of the deep neural network model using a Bayesian optimization method.

[0027] To implement the above technical solution, Bayesian optimization, a highly efficient global optimization strategy, intelligently leverages historical evaluation results to guide the exploration of the next hyperparameter combination, rapidly approaching the optimal performance region with fewer attempts. This significantly improves the efficiency and automation of model tuning, effectively avoiding the impact of suboptimal hyperparameter configurations on predictive performance. This ensures that the deep neural network model achieves optimal accuracy and generalization when predicting the elastic properties of fiber-reinforced composites, further enhancing the intelligence and reliability of the entire prediction method.

[0028] As a preferred solution of the present invention, the macro-structural parameters in step S3 include the ply sequence of the laminate and / or the yarn spacing ratio and yarn curl of the woven composite material.

[0029] By implementing the aforementioned technical solution, this prediction method is not limited to microscale material composition optimization but can also be extended to mesoscale and macroscale structural design. Specifically, it can rapidly evaluate the impact of different layup designs or braiding structure parameters on the mechanical properties of the final component, thereby enabling full-chain performance prediction and optimization, from material composition to structural configuration. This greatly enhances the method's engineering practicality and design flexibility, enabling rapid iterative design and performance customization of complex composite structures, and providing a powerful tool for multi-scale integrated design.

[0030] In summary, the present invention has the following beneficial effects:

[0031] 1. Improved accuracy: By integrating multi-scale data with deep neural networks, we can break through the accuracy limitations of traditional empirical formulas and achieve accurate prediction of elastic parameters.

[0032] 2. Efficiency Innovation: The time required for a single analysis is reduced from several hours to minutes and seconds, significantly improving computing efficiency. Through neural network structure design and hyperparameter tuning, training stability and efficiency are ensured.

[0033] 3. Engineering universality: The random RVE model based on periodic boundary conditions can accurately characterize the macroscopic homogeneous properties of materials and adapt to the complex structural design needs of multiple fields such as aerospace, new energy vehicles, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 This is the specific implementation process of the method of the present invention;

[0035] Figure 2 Examples of random distribution cross-sectional images of RVE fibers at the same volume fraction generated by the algorithm, where (a) Vf = 30%, (b) Vf = 50%;

[0036] Figure 3 The scatter plots of the fiber and matrix elastic modulus and fiber volume fraction distributions obtained by Sobol sampling (a) and the Poisson's ratio of the fiber and matrix and fiber volume fraction distributions (b) are shown.

[0037] Figure 4 It is the basic architecture of the neural network model;

[0038] Figure 5 This is a flowchart of Bayesian optimization hyperparameters;

[0039] Figure 6is the model training and validation loss graph;

[0040] Figure 7 This is a comparison chart of the model's true value and predicted value (400 samples);

[0041] Figure 8 It is the principal stress contour of the 1-direction of the quasi-isotropic ply laminate (PLY-1);

[0042] Figure 9 It is the principal stress cloud diagram in the 1 direction of the braided composite material. DETAILED DESCRIPTION

[0043] The specific embodiments of the present invention are further described below in conjunction with the accompanying drawings to make the technical solutions of the present invention easier to understand and grasp.

[0044] A method for predicting the elastic properties of fiber-reinforced composites is described. This method considers composite materials at multiple scales: at the microscale, both the fiber and matrix are modeled as isotropic materials; at the mesoscale, the composite is considered as a transversely isotropic reinforcement; and at the macroscale, the overall material properties are determined by the specific layup sequence or weaving method. Based on this, a neural network is applied to predict the multi-scale elastic response. The relevant composite parameters are detailed in Table 1.

[0045] Table 1 Fiber and matrix parameters

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[0047] This method comprises the following steps:

[0048] Step 1: A random and uniform distribution of fibers is achieved through a combination of spatial partitioning, dynamic parameter adjustment, and the Monte Carlo method. The specific steps are as follows: 1. Region Division: A quadtree algorithm is used to recursively subdivide the RVE region, ensuring that each node can store a maximum of four fibers. When a node is full, it is automatically divided into four child nodes, continuously accelerating collision detection. When inserting a new fiber, it quickly queries neighboring fibers within a certain radius to avoid global traversal. 2. Dynamic Spacing Adjustment: As the volume fraction increases, the minimum spacing is reduced to enhance fiber accommodation capacity under high Vf. 3. Monte Carlo Trial: Coordinates are randomly generated in a loop and quickly determined using the quadtree to determine whether they conflict with existing fibers. If they do, they are inserted into the quadtree and the fiber data is recorded. 4. Final Conflict Check: After generation, all fibers are traversed again to remove potentially conflicting fibers. The actual volume fraction is calculated and output to verify the effectiveness of the algorithm.

[0049] Step 2: Use Sobol sequence sampling to generate highly evenly distributed sample points, reducing the "clustering" phenomenon, more efficiently covering the sampling space, and significantly improving the convergence speed of numerical integration, optimization, or simulation.

[0050] Step 3: Apply periodic boundary conditions to the created RVE, solve for the elastic modulus according to Equation (1), the shear modulus according to Equation (2), and the Poisson's ratio according to Equation (3). A total of 1024 sets of samples are output. The SMOGN algorithm is used to oversample a few areas: new samples are generated in areas with few target values, and to undersample most areas: the number of samples in areas with dense target values ​​is reduced. The dataset is then enhanced to 5120 sets, and the insufficient number of samples is supplemented by resampling and random perturbation.

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[0054] Step 4: Split the dataset into training, validation, and test sets in a ratio of 8:1:1, then build a deep neural network regression model. Train, optimize, and evaluate the model based on the Pytorch deep learning framework. Steps 5 to 11 are the specific process.

[0055] Step 5: Data preprocessing: Use StandardScaler to standardize the input feature X and output target y to eliminate the dimension effect, convert the data into PyTorch's TensorDataset, encapsulate it as DataLoader, and set the batch size to 32.

[0056] Step 6: Model construction: The residual network structure mainly includes input and output layers and residual blocks. The weights are initialized using Xavier and the bias is initialized to 0.01. The loss function adds physical constraints, mainly including: 1. Transverse isotropy condition constraint: Force the predicted shear modulus G 23 =E 22 / (2*(1+V 23 )) to enforce that the predicted values ​​satisfy physical constraints. 2. The Poisson's ratio of isotropic materials is constrained to V23 < 0.5, and values ​​exceeding this are penalized using the ReLU function. The total loss is the weighted sum of the MSE and the physical constraint loss (weight alpha = 0.5).

[0057] Step 7: Training Configuration: Select Adam as the optimizer, set the initial learning rate to 0.002, and use ReduceLROnPlateau for learning rate scheduling. If the validation loss does not improve for five consecutive epochs, the learning rate is reduced to half. Regularization uses gradient clipping, limiting the gradient norm to no more than 1.0 to prevent gradient explosion. An early stopping mechanism is added to terminate training early if the validation loss does not improve for 20 consecutive epochs.

[0058] Step 8: Configure the BayesianOptimization library and set the optimizer. Perform Bayesian optimization on the model's hyperparameters (learning rate, batch size, physical loss weight, dropout ratio, hidden layer size), output the best parameter combination, retrain the model with the optimized hyperparameters, evaluate the performance on the test set, and save the best neural network model.

[0059] Step 9: Training execution, which mainly involves: 1. Forward propagation: Input data passes through the residual network to obtain predicted values. 2. Loss calculation: Calculate the mean square error (MSE) loss between the predicted and true values. 3. Backward propagation and optimization: Clear gradients, backpropagate, clip gradients, and update parameters. 4. Validation phase: Disable gradient calculation and iterate over the test set to calculate validation loss. 5. Learning rate adjustment: Dynamically adjust the learning rate based on validation loss. Always save the model with the lowest validation loss and plot the training and validation loss curves.

[0060] Step 10: Perform principal component analysis (PCA) on the data distribution to ensure data rationality: PCA dimensionality reduction (three principal components) is performed on both the original and augmented data. The visualizations include: 1. 2D faceted plot: Comparing the distribution of the original and augmented data on the PC1-PC2 plane. 2. 3D distribution plot: Displaying the distribution of the data in the PC1-PC2-PC3 space. 3. Explained variance: The number of principal components required to explain 95% of the cumulative variance. 4. Loading heatmap: Analyzing the contribution of each original feature to the principal components.

[0061] Step 11: Model Evaluation and Prediction: 1. Model Evaluation: Calculate MAE, RMSE, and R² scores on the test set. 2. Model Prediction: Normalize the input data, perform model prediction, and then denormalize to obtain the actual values. Output the predicted results for each performance parameter and compare them with the actual values.

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[0065] Table 2 compares the accuracy of a classic machine learning regression model and our neural network model using 1024 original samples. As can be seen, the neural network model achieves significantly higher accuracy than other machine learning methods. Table 3 provides an accuracy evaluation before and after the dataset expansion.

[0066] Table 2 Comparison of the accuracy of neural network models and classic machine learning regression models

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[0068] Table 3 Accuracy evaluation of neural network model before and after dataset expansion

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[0070] Step 12: Establish the solid unit structure of the laminate and design the layup structure. The number of layers is set to 8. The layup sequence uses 6 types of typical quasi-isotropic layup, orthogonal symmetrical layup, high shear layup, angle gradient layup, mixed layup, and unidirectional layup, which are suitable for various working conditions.

[0071] Step 13: Apply PBC to the entire structure, design a homogenization analysis (apply uniaxial load to extract stress-strain curve, etc.), divide the C3D8R mesh, solve it, and output the elastic parameters.

[0072] Step 14: Fine-tune the neural network model, train, optimize, and verify the model based on 6144 sets of data samples to obtain the optimal model and achieve cross-scale prediction of the elastic properties of fiber-reinforced composites.

[0073] Step 15: Create a typical structure of a woven composite material in Digimat. Assign the isotropic material properties of the matrix and the transversely isotropic material properties of the fibers. The fiber volume fraction is consistent with the microscopic level setting, and the number of warp and weft yarns is set to be consistent. By changing the yarn spacing ratio Ysr and the yarn curvature Yc by 3 groups each, the data set is expanded from 1024 groups to 9216 groups.

[0074] Step 16: Fine-tune the neural network model again (this time the input is 7 parameters), and train it after optimizing the model to achieve cross-scale prediction of woven composite structures.

[0075] Step 17: Integrate the data from the three dimensions and construct two new neural network models from micro to macro scales, match the input parameters with the output parameters, and finally successfully achieve cross-scale prediction of the elastic properties of fiber-reinforced composites.

[0076] Of course, the above are only typical examples of the present invention. In addition, the present invention may also have many other specific implementation methods. Any technical solutions formed by equivalent replacement or equivalent transformation fall within the scope of protection required by the present invention.

Claims

1. A method for predicting the elastic properties of fiber-reinforced composite materials, characterized in that: The steps include: S1. Constructing a training dataset: This is performed by numerically analyzing a plurality of representative volume elements (RVEs) covering a preset parameter range, wherein the parameter range includes at least a fiber volume fraction, a fiber elastic parameter, and a matrix elastic parameter; the numerical analysis is intended to solve for the transversely isotropic elastic parameter corresponding to each RVE, and the parameter range and the solved elastic parameter are used as data pairs to form a training dataset; S2. Training the model: using the training data set constructed in step S1, training a deep neural network to establish a nonlinear mapping relationship between the preset parameters and the transversely isotropic elastic parameters; S3. Predicting performance: Using the parameters including material and microstructure information and macrostructure parameters as input, and using the deep neural network model trained in step S2, predict the macroscopic equivalent elastic properties of the fiber-reinforced composite material; In step S1, the process of generating the representative volume element RVE includes: recursively subdividing the RVE area using a quadtree algorithm to establish an index for quickly querying adjacent fibers; And based on the Monte Carlo method, conflict detection is performed, and fiber coordinates that meet the preset spacing conditions are randomly generated in the RVE area, so as to obtain an RVE model with random fiber distribution; in the step S1, the fiber volume fraction, fiber elastic parameters and matrix elastic parameters are uniformly sampled in high-dimensional space using the Sobol sequence sampling method to generate an input parameter combination for constructing the multiple representative volume unit RVEs; in the step S2, a loss function containing physical constraints is used to optimize the model, and the physical constraints include at least transverse isotropy condition constraints, and the transverse isotropy condition constraints: the forced predicted shear modulus G 23 Satisfy formula G 23 =E 22 / (2×(1+V 23 )); The macroscopic structural parameters in step S3 include the ply sequence of the laminate and / or the yarn spacing ratio and yarn curl of the woven composite material.

2. The method for predicting elastic properties of fiber-reinforced composite materials according to claim 1, characterized in that: The step S1 further includes: after obtaining the transversely isotropic elastic parameters through numerical analysis, enhancing the data using the SMOGN algorithm, wherein the SMOGN algorithm identifies sparse regions of target values ​​based on the K-nearest neighbor algorithm and generates oversampled samples using Gaussian noise synthesis technology.

3. The method for predicting elastic properties of fiber-reinforced composite materials according to claim 1, characterized in that: The deep neural network model is a deep residual network including residual blocks.

4. The method for predicting elastic properties of fiber-reinforced composite materials according to claim 1, characterized in that: The physical constraints also include Poisson's ratio boundary constraints, which are defined by the Poisson's ratio V 23 A penalty term is imposed on the predicted value.

5. The method for predicting elastic properties of fiber-reinforced composite materials according to claim 1, characterized in that: The step S2 also includes automatically searching for hyperparameters of the deep neural network model using a Bayesian optimization method.

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