Method and system for optimizing performance of carbon fiber composite material based on multi-physics reduced order model

Abstract

The application discloses a kind of carbon fiber composite material performance optimization method and system based on multi-physical field reduced order model, and it is related to carbon fiber composite material design field.Method includes: generating sample point in design variable space and carrying out high-fidelity simulation, extract full-field response data to construct snapshot matrix;Eigenvalue orthogonal decomposition is carried out to snapshot matrix to extract leading mode and constitute reduced order base, construct deep neural network to establish the nonlinear mapping of design parameter to reduced order coordinate, train network using the total loss function of data fitting loss and physical residual loss weighted summation;Reduced order base and neural network are encapsulated as fast predictor;Predictor is integrated into optimization algorithm, and the process of recommending candidate point, predicting performance, updating historical data is carried out, and the optimal design scheme is output.The application shortens single analysis time from hour level to second level by reduced order technique, and physical information constraint ensures model reliability, to realize the efficient and high-precision optimization design of composite structure.

Description

Technical Field

[0001] This invention relates to the field of carbon fiber composite material design, specifically to a method and system for optimizing the properties of carbon fiber composite materials based on a multiphysics reduced-order model. Background Technology

[0002] Carbon fiber composites are increasingly used in high-end equipment such as aerospace due to their excellent properties. Their performance is highly dependent on design parameters such as layup sequence and angles; therefore, optimization design through numerical simulation is crucial.

[0003] Currently, the industry standard is to use high-fidelity finite element models for simulation-driven optimization. However, accurate multiphysics model calculations are extremely time-consuming, and the optimization process requires calling the model thousands of times, resulting in design cycles that can last for weeks or even months. Computational costs have become a core bottleneck restricting innovative design of composite materials. To accelerate this process, existing technologies mostly employ data-based surrogate models or empirical formulas. However, these methods either lack sufficient accuracy to capture the complex anisotropy of composite materials, or they are black-box models, with prediction results lacking physical transparency and questionable reliability, making them difficult to apply to product designs with high safety requirements.

[0004] Therefore, there is an urgent need in this field for a new analysis and optimization method that can achieve orders-of-magnitude speed improvements while strictly ensuring physical accuracy. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a method and system for optimizing the properties of carbon fiber composite materials based on a multiphysics reduced-order model, thereby improving the computational efficiency of multiphysics performance analysis and optimization design of carbon fiber composite materials.

[0006] This invention is achieved through the following technical solution: In a first aspect, this application provides a method for optimizing the properties of carbon fiber composite materials based on a multiphysics reduced-order model, comprising the following steps: Step 1: Generate N sample points in the design variable space of carbon fiber composite material; perform high-fidelity multiphysics finite element simulation on each sample point, extract the full-field response data, and construct a snapshot matrix S; Step 2: Perform eigenorthogonal decomposition on the snapshot matrix S to extract the dominant POD modes and form a reduced-order basis; A deep neural network model is constructed, with the design variable vector as input and the reduced-order coordinate vector as output. The deep neural network model is trained using a total loss function composed of the weighted sum of data fitting loss and physical residual loss, and a nonlinear mapping relationship from the design parameter space to the reduced-order subspace is established. The physical residual loss is obtained by calculating the residual of the sampling points in the computational domain based on the physical control equation; Step 3: Construct a reduced-order model using the trained reduced-order basis and the mapping function G. The reduced-order model is used to output the corresponding performance index based on the input design parameters. Step 4: Integrate the fast predictor of the reduced-order model into the optimization algorithm. During the iterative optimization process, the optimization algorithm recommends candidate design points based on historical data in the design parameter space, calls the reduced-order model for performance evaluation, and adds the evaluation results to the historical data to update the search direction; repeat the iteration until the termination condition is met to obtain the optimal design scheme.

[0007] Preferably, in step 1, the design variable vector includes at least one of fiber volume fraction, ply angle, ply thickness, and interface performance parameters.

[0008] Preferably, in step 1, N sample points are generated in the design variable space using optimal Latin hypercube sampling or Sobol sequence.

[0009] Preferably, the physical residual loss in step 2 is calculated in the following way: Random sampling within the geometric computational domain of carbon fiber composite structures One point; The displacement field is reconstructed based on the reduced-order coordinates predicted by the deep neural network; The strain field is calculated by automatically differentiating the displacement field. The stress field is calculated from the strain field based on the constitutive relation; the stress field is then substituted into the physical control equations to calculate the residuals at each sampling point. The physical residual loss is constructed based on the residual norm of all sampling points.

[0010] Preferably, in step 3, the prediction method of the reduced-order model includes: Input design parameter vector; Calculate reduced-order coordinates using a deep neural network model; Reconstructing the full-field displacement by reducing the order basis; Extract one or more global performance metrics from the reconstructed global response.

[0011] Preferably, the global performance index includes at least one of the following: total structural mass, maximum equivalent stress, failure index based on the Tsai-Wu criterion or the Hashing criterion, natural frequency, buckling load factor, and equivalent thermal conductivity.

[0012] Preferably, the optimization algorithm in step 4 is a multi-objective Bayesian optimization algorithm or a constrained genetic algorithm.

[0013] Preferably, in step 4, during the iterative optimization process, when the cumulative number of new data points reaches a preset number or the number of iterations meets a preset period, the reduced-order model is fine-tuned and updated using the current historical dataset to obtain the updated reduced-order model for subsequent iterations.

[0014] Preferably, after the iteration terminates in step 4, the optimal design scheme is selected and verified by the high-fidelity multiphysics finite element simulation to confirm that its performance indicators meet the design requirements.

[0015] Secondly, this application provides a method for optimizing the properties of carbon fiber composite materials based on a multiphysics reduced-order model, including: The sample library construction module is used to generate N sample points in the design variable space of carbon fiber composite materials; high-fidelity multiphysics finite element simulation is performed on each sample point to extract the full-field response data and construct a snapshot matrix S; The reduced-order model training module is used to perform eigenorthogonal decomposition on the snapshot matrix S and extract the dominant POD modes to form a reduced-order basis. A deep neural network model is constructed, with the design variable vector as input and the reduced-order coordinate vector as output. The deep neural network model is trained using a total loss function composed of the weighted sum of data fitting loss and physical residual loss, and a nonlinear mapping relationship from the design parameter space to the reduced-order subspace is established. The physical residual loss is obtained by calculating the residual of the sampling points in the computational domain based on the physical control equation; The predictor encapsulation module, the trained reduced basis, and the mapping function G construct a reduced model, which is used to output the corresponding performance index based on the input design parameters. An optimization integration module is used to integrate the fast predictor of the reduced-order model into the optimization algorithm. During the iterative optimization process, the optimization algorithm recommends candidate design points based on historical data in the design parameter space, calls the reduced-order model for performance evaluation, and adds the evaluation results to the historical data to update the search direction. The iteration is repeated until the termination condition is met to obtain the optimal design scheme.

[0016] Compared with the prior art, the present invention has the following beneficial technical effects: This invention provides a method for optimizing the performance of carbon fiber composite materials based on a multiphysics reduced-order model. Its core principle lies in compressing high-dimensional finite element simulation data into a low-dimensional reduced-order basis through intrinsic orthogonal decomposition, and constructing a deep neural network to establish a nonlinear mapping from design parameters to reduced-order coordinates. Simultaneously, physical information constraints are introduced to ensure the physical consistency of the model. Specifically, firstly, sample points are generated in the design space and high-fidelity simulation is performed to construct a snapshot matrix. Then, intrinsic orthogonal decomposition is performed on the snapshot matrix to extract the dominant modes to form the reduced-order basis, and a deep neural network is trained to learn the mapping relationship between design parameters and reduced-order coordinates. During training, the residuals of the physical control equations are introduced as a loss function, enabling the model to simultaneously fit the simulation data and follow physical laws. Finally, the trained reduced-order model is encapsulated as a fast predictor and integrated into the optimization algorithm. The optimal design scheme is obtained through iterative optimization. This method reduces the single analysis time from hours to seconds through the reduced-order technique, achieving a thousand-fold speedup. Simultaneously, physical information constraints ensure the reliability of the model during sample extrapolation, solving the defects of insufficient accuracy and black-box characteristics of traditional surrogate models, and providing a complete solution for efficient and high-precision optimization design of composite material structures.

[0017] This application also proposes an optimization system for the properties of carbon fiber composites based on a multiphysics reduced-order model, an electronic device, and a computer storage medium, which possess all the advantages of the aforementioned optimization method for the properties of carbon fiber composites based on a multiphysics reduced-order model. Attached Figure Description

[0018] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a flowchart of the method for optimizing the properties of carbon fiber composite materials based on a multiphysics field reduced-order model according to the present invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0021] Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of the application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0022] An optimization method for the properties of carbon fiber composites based on a multiphysics reduced-order model includes the following steps: Step 1: Generate N sample points in the design variable space of carbon fiber composite material; perform high-fidelity multiphysics finite element simulation on each sample point, extract the full-field response data, and construct a high-dimensional snapshot matrix S; The design variables of carbon fiber composites (such as layup angle, thickness, and fiber volume fraction) are quantified into a vector μ, and N representative sample points are generated within their feasible region using a space-filling design (such as optimal Latin hypercube sampling). Subsequently, a commercial finite element method solver is invoked via an automated script to perform high-fidelity multiphysics simulations on each sample point. The massive high-dimensional data from the discrete sample points are then combined into a snapshot matrix S.

[0023] Step 2: Perform eigenorthogonal decomposition on the snapshot matrix S and extract the top k dominant POD modes to form a reduced-order basis; A deep neural network model G is constructed as a mapping function, with the design variable vector μ as input and the reduced-order coordinate vector a(μ) as output. The deep neural network model is trained using the high-fidelity simulation data to establish a nonlinear mapping relationship from the design parameter space to the reduced-order subspace. Singular value decomposition (SVD) is performed on the snapshot matrix S based on intrinsic orthogonal decomposition (POD). The essence of this operation is to find a set of optimal orthogonal basis modes Ψ such that the physical field response under any condition can be represented by a linear combination of these basis modes. By extracting the top k dominant modes with extremely high energy proportions to form the reduced-order basis Ψ_k, we successfully compressed the million-degree-of-freedom of the original finite element model to a reduced-order coordinate a(μ) with only k degrees of freedom, achieving dimensionality reduction. To establish the mapping between the design parameters μ and the reduced-order coordinate a(μ), a deep neural network G is introduced. This network learns to approximate the nonlinear functional relationship from the design parameters to the projection coefficients. Ultimately, it realizes the surrogate capability of inputting design parameters to obtain the reduced-order coordinates, transforming the complex physical field solution problem into a purely mathematical mapping problem.

[0024] Step 3: Encapsulate the trained reduced basis and the mapping function G into a ROM fast predictor; the ROM fast predictor is used to predict the corresponding performance index vector based on the input new design point.

[0025] For any new design point, instead of relying on time-consuming finite element solvers, only two simple calculations are required: First, a pre-trained deep neural network G is invoked for forward propagation, calculating the corresponding reduced-order coordinates in milliseconds; then, using pre-stored reduced-order bases, the complete displacement field is linearly reconstructed through simple matrix multiplication, and finally, the stress field, strain field, and various global performance indices are derived through geometric equations and constitutive relations. The final result is extremely significant: the time for a single performance analysis is reduced from hours in traditional simulations to seconds or milliseconds, achieving a computational speedup of over a thousand times.

[0026] Step 4: Integrate the ROM fast predictor encapsulated in Step 3 into the optimization algorithm and execute the iterative optimization process. In each iteration, the optimization algorithm recommends candidate design points based on the historical dataset, calls the ROM fast predictor to perform performance evaluation, and adds the evaluation results to the historical dataset to update the search strategy. Repeat the iteration until the termination condition is met and output the optimal design scheme.

[0027] The optimization algorithm preferably employs a multi-objective Bayesian optimization algorithm or a constrained genetic algorithm. The Bayesian optimization algorithm, by constructing a Gaussian process surrogate model and using a sampling function to balance exploration and utilization, is particularly suitable for combination with a ROM fast predictor, further reducing the number of iterations while ensuring optimization quality.

[0028] The core principle of integrating a pre-packaged ROM fast predictor into the optimization algorithm is to replace the time-consuming high-fidelity simulation in traditional optimization with the second-level response capability of the reduced-order model, transforming the optimization problem into an iterative loop of recommendation-evaluation-update. Specifically, the optimization algorithm constructs a probabilistic surrogate model (such as a Gaussian process) based on the current historical dataset. Through a data acquisition function, it automatically weighs the exploration of unknown regions against utilizing known optimal regions, recommending the next most promising candidate design point. Subsequently, the ROM fast predictor is called to perform an instantaneous performance evaluation of this point, and the evaluation results are fed back to the historical dataset to update the hyperparameters of the surrogate model and the search direction of the optimization algorithm. The technical effects of this mechanism are reflected in three aspects: First, it reduces the time of a single evaluation from hours to seconds, making large-scale iterations (thousands or even tens of thousands of times) possible, which were previously impossible due to computational costs, thus effectively avoiding the optimization process from getting trapped in local optima; Second, the full-field reconstruction capability of the reduced-order model ensures that each evaluation can output a complete performance index vector, supporting the parallel processing of multi-objective and multi-constraint optimization problems; Third, the continuous accumulation of historical data during the iteration process can trigger the periodic fine-tuning of the reduced-order model, enabling the model's prediction accuracy in key exploration areas to adaptively improve with the optimization process, and the final output of the optimal design scheme has both computational efficiency and physical reliability.

[0029] Example 1 See Figure 1An optimization method for the properties of carbon fiber composites based on a multiphysics reduced-order model includes the following steps: Step 1, Parametric Modeling and High-Fidelity Sample Library Construction: Define the design variable vector μ for carbon fiber composite materials, and generate N sample points in the design variable space using experimental design methods; perform high-fidelity multiphysics finite element simulation on each sample point, extract the full-field response data, and construct a high-dimensional snapshot matrix S; S1.1, Parameterization of Design Variables: Define a design variable vector μ, which fully describes the design space of the composite material:

[0030] in, This represents the fiber volume fraction. The angle of the nth ply. Let n be the thickness of the nth ply. Here, n represents the interface performance parameters, and n represents the total number of layers.

[0031] S1.2 Experimental Design and Sampling Points: Optimal Latin Hypercube Sampling (OLHS) or Sobol sequence is used to generate N sample points within the feasible region of the design variables.

[0032] These two methods were chosen because they offer excellent space-filling and uniformity, avoiding the clustering issues that can occur with traditional random sampling. This allows for maximum coverage of the high-dimensional, nonlinear composite material design space with the fewest possible samples. The method ensures uniformity and space-filling in the multidimensional space, maximizing sample representativeness.

[0033] S1.3 Perform high-fidelity multiphysics simulation (FOM) on each sample point to obtain full-field response data.

[0034] Specifically, high-fidelity multiphysics simulations are performed using commercial finite element software (such as Abaqus and ANSYS), and the sample points are converted into output files of the finite element software (e.g., .inp files for Abaqus, and .mac or .ans files for ANSYS).

[0035] Using the application programming interface (API) or command line interface (CLI) provided by the commercial software, its solver can be automatically launched as a background process (e.g., via the command abaqus cae nogui=script.py or ansysXXX -b -i input.mac). The solver then solves the output file to obtain simulation results (such as the .odb file for Abaqus and the .rst file for ANSYS), and the full-field response data can be extracted. At the same time, global performance indicators can be obtained based on the full-field response data.

[0036] A. The full-field response data includes displacement field vector, stress field vector, strain field vector, and mode shape.

[0037] 1) Displacement field vector U: refers to the spatial displacement vector field of the carbon fiber composite structure under load (usually containing components in the X, Y, and Z directions).

[0038] The displacement field vector is the most fundamental field variable, from which the strain field is derived through geometric equations. Stress calculations also depend on it. For modal analysis, the mode shape itself is a displacement field.

[0039] 2) Stress field σ: refers to the distribution of internal forces per unit area within the material, and is a tensor field. It is usually represented as a vector using Voigt notation.

[0040] The stress field is a direct basis for assessing structural strength and predicting failure. Most strength criteria require stress components as input.

[0041] 3) Strain field ε: refers to the measure of local deformation of the material, and is also a tensor field, notated as Voigt notation:

[0042] The strain field is used to assess stiffness and is also the basis for analyzing damage evolution.

[0043] 4) Mode shape: refers to the characteristic displacement field shape of a structure when it vibrates freely at a specific natural frequency. It reflects the dynamic stiffness characteristics of the structure. For example, different modes (such as first-order bending and first-order torsion) have different design sensitivities.

[0044] B. Global performance metrics are single scalar values ​​or simple vectors extracted from the above global response data. They are performance indicators used to evaluate the quality of a design.

[0045] Global performance metrics include stiffness-related metrics, strength and failure-related metrics, and stability metrics. Parameters such as maximum equivalent stress, natural frequencies of each order, buckling load factor, and total mass are used for subsequent optimization and model verification.

[0046] 1) Stiffness-related indicators include: Equivalent elastic constant: Equivalent Young's modulus Tensile / compressive stiffness along the principal direction of the material (or the global coordinate direction).

[0047] Equivalent shear modulus In-plane and out-of-plane shear stiffness.

[0048] Equivalent Poisson's ratio .

[0049] 2) Strength and failure-related indicators include: Maximum equivalent stress (max) ): The maximum value of the scalar stress field calculated according to the von Mises or maximum distortion energy criterion, used for preliminary strength assessment.

[0050] function:

[0051] Failure Index (FI): An index calculated using composite material failure criteria (such as the Tsai-Wu criterion and the Hashingin criterion). FI ≥ 1 indicates failure.

[0052] Functions (using Tsai-Wu as an example): In this context, X, Y, and S represent material strength parameters. F1, F2, F11, F22, F66, and F12 are material strength parameters (or strength tensor components) defined in the Tsai-Wu failure criterion. They are not variables, but constant coefficients calculated from the material's own basic strength properties.

[0053] (1) Linear term coefficient (characterizing the asymmetry of tensile and compressive strength of materials)

[0054] Physical meaning: This reflects the characteristic that the tensile and compressive strengths of a material are not equal in the fiber direction (1-direction). If the tensile and compressive strengths of the material are the same (X_T = X_C), then this term is zero.

[0055]

[0056] Physical meaning: It reflects the characteristic that the tensile and compressive strengths of a material are not equal in the transverse (2-direction).

[0057] (2) Quadratic coefficient (characterizing the basic strength)

[0058] Physical meaning: It mainly characterizes the load-bearing capacity in the fiber direction.

[0059]

[0060] Physical meaning: Primarily represents the lateral load-bearing capacity.

[0061] F66=

[0062] Physical meaning: Characterizes in-plane shear bearing capacity.

[0063] (3) Interaction term coefficient F12 Physical meaning: Characterizes the influence of the coupling effect between normal stress and failure on the failure. This is a key feature of the Tsai-Wu criterion, but F12 cannot be directly determined by simple experiments. F12 is usually calculated using a simplified formula or fitted through complex biaxial test data. The most commonly used simplified calculation formula is:

[0064] Output: Global maximum failure index max(FI) or failure area.

[0065] 3) Stability indicators include: Buckling load factor: The ratio of the first critical load obtained from eigenvalue buckling analysis to the applied load. A buckling load factor > 1 indicates no instability.

[0066] 4) Dynamic performance indicators include: Natural frequencies: The natural frequencies of a structure's free vibration, typically focusing on the first few orders (e.g., f_1, f_2, f_3). High stiffness usually corresponds to high frequencies. Avoiding resonance is a fundamental requirement of dynamic design.

[0067] Modal mode node / nodal line location: The region in the mode where the displacement is zero. Crucial for the placement of sensors / actuators.

[0068] 5) Thermal performance indicators include: Equivalent thermal conductivity: Calculated through steady-state thermal analysis, it determines the equivalent thermal conductivity along different directions. It is crucial for thermal management design.

[0069] Maximum thermal stress: The maximum stress value generated under the action of a temperature field, used for strength assessment under thermo-mechanical coupling conditions.

[0070] 6) Weight specifications include: Total mass: ,in .

[0071] Total mass is the core quantitative objective in lightweight design of carbon fiber composite materials, directly reflecting the lightweight level of the design scheme. It can be transformed into a typical multi-objective optimization problem, expressed as: Objective function (minimization) 1. Total mass (μ) 2. Maximum failure exponent max(FI(μ)) Constraints: First-order natural frequency The lower limit of the first-order natural frequency required by the design Buckling Load Factor (Safety factor) Design variable boundaries

[0072] In this embodiment, the high-fidelity multiphysics simulation process is completed automatically under the control of the main control script without manual intervention, thereby ensuring the efficiency and repeatability of the sample library construction process.

[0073] Step 2: Construct a high-dimensional snapshot matrix S based on the full-field response data, perform intrinsic orthogonal decomposition (POD) on the snapshot matrix S, extract the first k dominant POD modes, form a reduced-order basis from these k modes, and then determine the reduced-order subspace.

[0074] Based on the reduced-order subspace, a deep neural network model G is constructed as the mapping function, with the design variable vector μ as the model input and the reduced-order coordinate vector a(μ) as the model output. The deep neural network model is trained using high-fidelity simulation data, ultimately establishing a nonlinear mapping relationship from the design parameter space to the reduced-order subspace, i.e., a(μ) = G(μ). This process includes the following sub-steps: S2.1. For a combination of full-field response data (e.g., displacement field U) from N sample points, construct a snapshot matrix S, whose mathematical expression is:

[0075] Where M is the number of degrees of freedom of the high-fidelity finite element model, and its value is usually much larger than the total number of samples N (i.e., M >> N). This represents the vector corresponding to the first design parameter. The high-fidelity full-field response vector; N is the total number of samples; The snapshot matrix S is an M-row, N-column real matrix.

[0076] The singular value decomposition of the snapshot matrix S is performed as follows:

[0077] In the formula, The column vectors of form a set of orthonormal bases, i.e., POD modes; is a diagonal matrix containing singular values.

[0078] According to the decay of singular values, select the first k POD modes that can characterize the main energy of the system to form a reduced-order basis , where k is much smaller than M (k << M). At this time, the full-field response U(μ) corresponding to any design parameter μ can be approximately expressed as a linear combination of this reduced-order basis:

[0079] where, is the reduced-order coordinate vector corresponding to the design parameter μ, which represents the projection coefficients of the original high-dimensional field on the low-dimensional subspace spanned by the dominant POD modes.

[0080] S2.2. Construct a non-linear mapping relationship between the design parameters and the reduced-order coordinates; thus, the reduced-order coordinates of any new design point can be obtained without performing time-consuming full-order simulations.

[0081] Construct a deep neural network G as the mapping function. The number of nodes in its input layer corresponds to the dimension of the design variable vector μ, and the number of nodes in the output layer is equal to the dimension k of the reduced-order coordinates. This network G learns the mapping relationship from μ to a(μ) through training, i.e.: a ( μ ) = G ( μ ; ω ) where, represents the weight parameters to be trained of the neural network. The training objective is to minimize the error between the reduced-order coordinates predicted by the network and the true reduced-order coordinates (i.e., ) calculated by projection from high-fidelity simulation data. In this way, the trained neural network G can achieve instantaneous prediction of the reduced-order coordinates of any new design parameter μ.

[0082] In this embodiment, a deep neural network (DNN) is used as the mapping function G to capture complex non-linear relationships.

[0083] The deep neural network is a fully connected neural network with multiple hidden layers.

[0084] Input layer: The number of nodes is equal to the dimension dim(μ) of the design variable μ.

[0085] Hidden layer: 3 - 5 layers, with 128 - 256 neurons in each layer, using the Swish or ReLU activation function.

[0086] Output layer: The number of nodes is equal to the dimension k of the reduced-order coordinates, and a linear activation function is used.

[0087] The loss function for deep neural networks is the mean squared error loss.

[0088] Where ω is the weight parameter of the DNN, These are the true reduced-order coordinates obtained by projecting the high-fidelity solution.

[0089] S2.3. Physical information constraints are introduced during the training process of deep neural networks to solve the problem of physical irrationality in data-driven models when extrapolating samples. Taking linear elastic statics as an example, its governing equations include equilibrium equations and constitutive equations; Equilibrium equations: , where σ is the stress tensor and f is the volume force vector; Constitutive equation: ,in Let ε be a fourth-order elastic tensor that depends on the design parameter μ, and let ε be the strain tensor.

[0090] Based on the above governing equations, a physical residual loss function is constructed. The calculation process is as follows: First, randomly select within the computational domain of the structure. sampling points For each sampling point Perform the following operations: Reduced coordinates predicted by deep neural network G Reconstructing the displacement field ; By analyzing the displacement field Automatic differentiation is performed to calculate the strain field. ; According to the constitutive equation, from the strain field Calculate the stress field ; stress field Substitute into the equilibrium equation and calculate its residual. .

[0091] The physical residual loss is defined as the mean square value of the L2 norm of the balance equation residuals at all sampling points. The physical residual is calculated as follows:

[0092] in, The L2 norm of a vector is used to represent the Euclidean norm.

[0093] Ultimately, the total loss function for training the deep neural network G is a weighted sum of the data fitting loss and the physical residual loss: Total loss function:

[0094] In the formula, The mean squared error loss between the predicted reduced-order coordinates and the true reduced-order coordinates, as defined in sub-step 2-2; To balance the hyperparameters, the weight of physical constraints in the total loss is adjusted.

[0095] By introducing the aforementioned physical information constraints, this method forces the prediction results of the deep neural network G to not only fit the limited high-fidelity simulation data, but also approximately satisfy the governing equations of elasticity throughout the entire computational domain. This mechanism draws on the idea of ​​physical information neural networks, effectively improving the prediction reliability and physical rationality of the reduced-order model in sparse data regions.

[0096] Step 3: Reduce the trained base order (i.e., POD base) is encapsulated with a deep neural network mapping model G to construct a unified fast prediction function, denoted as This fast prediction function predicts the corresponding performance indicators based on the design parameters. The prediction method is as follows: S3.1. Call the trained deep neural network G to perform forward propagation calculations and obtain the corresponding reduced-order coordinate prediction values. .

[0097] S3.2, Using order reduction basis Reconstructing the full-field displacement response .

[0098] S3.3, Displacement Field Based on Reconstruction Through geometric equations ( Calculate the strain field Then, based on the constitutive relation of the material ( Calculate the stress field .

[0099] S3.4 Extract one or more predefined global performance indices from the reconstructed global response (displacement, strain, stress) to form a performance index vector. The global performance indicators include, but are not limited to: total structural mass, maximum equivalent stress, failure index based on the Tsai-Wu or Hashin criteria, natural frequencies of each order, buckling load factor, equivalent thermal conductivity, etc., that is, corresponding to the design parameters. Performance index vector .

[0100] With the above encapsulation, the performance evaluation time for any new design point is shortened from hours in traditional finite element analysis to seconds or milliseconds.

[0101] Step 4: Integrate the current reduced-order model into the optimization algorithm and perform the following iterative optimization process: In each iteration, the optimization algorithm recommends at least one candidate design point within the feasible range of the current design parameters based on the historical dataset; the reduced-order model is used to predict the performance index corresponding to the candidate design point; the candidate design point and its predicted performance index are added to the historical dataset as a new data pair for the optimization algorithm to update the search strategy in subsequent iterations; the above process is repeated until the preset iteration termination condition is met, and the optimal design parameters are output.

[0102] The closed-loop optimization method based on the order reduction model is as follows: The preferred approach is to use a multi-objective Bayesian optimization algorithm or a constrained genetic algorithm as the global optimization engine. Among them, Bayesian optimization is particularly suitable for combining with the reduced-order model in this scheme because it can make full use of historical evaluation information to construct a probabilistic surrogate model and intelligently balance exploration and utilization using a collection function. This can further reduce the number of calls to the high-fidelity model while ensuring optimization quality.

[0103] The closed-loop optimization process is as follows: Initialization phase: Using the constructed high-fidelity sample library (containing N sample points and their corresponding full-field response and global performance metrics), the initial reduced-order model and its encapsulation function are trained according to the method described above. .

[0104] Iterative optimization phase: Execute the following loop until the termination condition is met: The current optimization algorithm is based on existing knowledge (i.e., the historical evaluation data set). Within the feasible design space, recommend one or more promising new design points. .

[0105] Call the current reduced-order model predictor The predicted performance index of the new design point can be obtained within seconds. .

[0106] The newly generated data Add to historical dataset .

[0107] To improve the prediction accuracy of the reduced-order model in key exploration areas during the optimization process, periodic triggering conditions can be set (such as every K iterations) to utilize the currently accumulated historical dataset. The reduced-order model is fine-tuned and updated to obtain the improved model. .

[0108] Termination and Verification Phase: Termination criterion: The optimization algorithm terminates when it meets a preset termination condition (e.g., when the maximum number of iterations is reached). If the objective function value does not show significant improvement in multiple iterations (i.e., convergence), stop the iteration.

[0109] Output: Outputs the optimal solution set for the optimization problem. For multi-objective optimization problems, outputs the Pareto front solution set; for single-objective optimization problems, outputs the optimal design point. .

[0110] Final verification: To ensure the reliability of the optimization results of the reduced-order model, the key design point on the Pareto front or the finally recommended optimal design point is selected. The high-fidelity finite element model described in step S1 is then used for final simulation verification to confirm that its performance indicators meet the design requirements.

[0111] Through the above steps, this invention constructs a complete and automated closed-loop system for the optimization design of carbon fiber composite structures. This system fully utilizes the efficiency of the reduced-order model and the global search capability of the intelligent optimization algorithm, achieving a balance between design efficiency and computational accuracy.

[0112] Compared with existing technologies, the rapid analysis and optimization method for carbon fiber composite materials based on a multiphysics reduced-order model described in this invention has the following advantages: (i) Significantly improve computational efficiency and break through the bottleneck of the optimization design cycle. This invention employs a data-driven, non-intrusive reduction model, transforming the traditional high-fidelity simulation process, which relies on high-degree-of-freedom (tens to hundreds of degrees of freedom) finite element analysis, into a rapid prediction problem for low-dimensional reduced coordinates (tens to hundreds of dimensions). Specifically, by compressing the high-dimensional physical field into a low-dimensional subspace spanned by the dominant modes of intrinsic orthogonal decomposition, and establishing a deep neural network mapping from design parameters to reduced coordinates, the computation time for a single performance analysis is reduced from hours or even days using traditional methods to seconds or milliseconds, achieving a computational speedup of over a thousand times. Based on this, large-scale parameterization research and optimization design, which previously required weeks to complete using large computing clusters, can now be completed on ordinary workstations within hours to days, significantly shortening the product development cycle.

[0113] (ii) Balancing computational efficiency and physical accuracy to ensure the reliability of optimization results This invention is not simply a data fitting model; its core lies in the physical field dimensionality reduction technique based on intrinsic orthogonal decomposition. The POD basis modes are extracted from the snapshot matrix of high-fidelity simulation data through singular value decomposition, which can capture the essential characteristics of the physical field in the optimal way. This ensures that, within the sample space, the physical field reconstructed by the reduced-order model is highly consistent with the calculation results of the full-order finite element model (the relative error can be controlled within 1% to 5%).

[0114] Building upon this foundation, this invention further introduces a physical information constraint mechanism, incorporating the residuals of the elasticity control equations (equilibrium equations, constitutive equations) as part of the loss function into the deep neural network training process. This mechanism forces the model's predictions to approximately satisfy fundamental physical laws across the entire computational domain, effectively overcoming the inherent defects of purely data-driven models, such as decreased prediction accuracy outside the training sample coverage area and the potential for physically unreasonable results. This significantly improves the model's extrapolation ability and engineering reliability. The resulting rapid analysis results possess both clear physical meaning and engineering credibility.

[0115] (iii) Possesses full-site response and reconstruction capabilities, providing in-depth analysis and insights. Unlike traditional surrogate models, which can only approximate predictions for a few preset global indices (such as maximum stress and natural frequencies), this invention uses a reduced-order model to instantly reconstruct the complete full-field response (including displacement, stress, strain, and mode shapes). Based on this reconstruction, engineers can flexibly extract performance indices at any local location or global level (such as stress concentration factor at any point, spatial distribution cloud map of failure index, and mode shapes of a specific order) as needed for analysis, without having to re-call the high-fidelity simulation program. This capability of one-time reconstruction and comprehensive analysis provides a quantitative analysis tool for a deeper understanding of the anisotropic behavior of composite materials and the revelation of complex failure mechanisms, supporting more refined and reliable engineering design decisions.

[0116] (iv) Construct an automated closed-loop optimization process to improve the level of intelligent design. This invention integrates a reduced-order model predictor with sub-second response capabilities with advanced global optimization algorithms (such as Bayesian optimization and multi-objective genetic algorithms) to construct an automated closed-loop optimization system encompassing design generation, rapid evaluation, intelligent search, and model updating. This system autonomously explores high-dimensional complex design spaces, efficiently handles multi-objective and multi-constraint optimization problems, and outputs a Pareto-optimal solution set for designers to choose from. Through this closed-loop process, designers are freed from repetitive tasks, allowing them to focus on higher-level design innovation and decision-making, truly realizing the technological vision of simulation-driven design.

[0117] (v) It adopts a non-intrusive implementation strategy, which has good versatility and easy integration. The method for constructing a reduced-order model described in this invention employs a non-intrusive strategy, requiring no access to or modification of the core solver code of commercial finite element software. Data interaction can be achieved solely through the software's standard input / output interfaces (such as modifying INP files and parsing ODB / RST files). This characteristic allows for easy coupling and integration with mainstream commercial finite element software (including but not limited to Abaqus and ANSYS), facilitating its widespread application in existing engineering design processes.

[0118] Furthermore, the technical framework of this invention has good scalability, and is not only applicable to static analysis, modal analysis, buckling analysis and thermal analysis of carbon fiber composite materials, but can also be extended to other multi-physics coupling problems (such as fluid-structure interaction, damage evolution analysis, etc.) and a variety of advanced material systems, showing broad engineering application prospects and industry promotion value.

[0119] Example 2 This application provides a method for optimizing the properties of carbon fiber composite materials based on a multiphysics reduced-order model, including: The sample library construction module is used to generate N sample points in the design variable space of carbon fiber composite materials; high-fidelity multiphysics finite element simulation is performed on each sample point to extract the full-field response data and construct a snapshot matrix S; The reduced-order model training module is used to perform eigenorthogonal decomposition on the snapshot matrix S and extract the dominant POD modes to form a reduced-order basis. A deep neural network model is constructed, with the design variable vector as input and the reduced-order coordinate vector as output. The deep neural network model is trained using a total loss function composed of the weighted sum of data fitting loss and physical residual loss, and a nonlinear mapping relationship from the design parameter space to the reduced-order subspace is established. The physical residual loss is obtained by calculating the residual of the sampling points in the computational domain based on the physical control equation; The predictor encapsulation module, the trained reduced basis, and the mapping function G construct a reduced model, which is used to output the corresponding performance index based on the input design parameters. An optimization integration module is used to integrate the fast predictor of the reduced-order model into the optimization algorithm. During the iterative optimization process, the optimization algorithm recommends candidate design points based on historical data in the design parameter space, calls the reduced-order model for performance evaluation, and adds the evaluation results to the historical data to update the search direction. The iteration is repeated until the termination condition is met to obtain the optimal design scheme.

[0120] It should be noted that, in the several embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of modules is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules may be combined or integrated into another device, or some features may be ignored or not executed. The modules described as separate components may or may not be physically separated. The components shown as modules may be one or more physical units, that is, they may be located in one place or distributed in multiple different places. Some or all of the modules can be selected to achieve the purpose of the solution in this embodiment according to actual needs.

[0121] Furthermore, in the various embodiments of the present invention, the modules can be integrated into one processing unit, or each module can exist physically separately, or two or more modules can be integrated into one unit. The integrated unit described above can be implemented in hardware or as a software functional unit.

[0122] An electronic device provided in this application includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements the steps of the method for optimizing the properties of carbon fiber composite materials based on a multiphysics reduced-order model as described in any of the above embodiments.

[0123] Another electronic device provided in this application embodiment may further include: an input port connected to a processor for transmitting multimodal data collected by an external acquisition device to the processor; a display unit connected to the processor for displaying the processor's processing results to the outside world; and a communication module connected to the processor for enabling communication between the electronic device and the outside world. The display unit may be a display panel, a laser scanning display, etc.; the communication method adopted by the communication module includes, but is not limited to, Mobile High Definition Link (HML), Universal Serial Bus (USB), High Definition Multimedia Interface (HDMI), and wireless connection (including Wi-Fi, Bluetooth, Bluetooth Low Energy, and IEEE 802.11s-based communication technology).

[0124] This application provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it implements the steps of the method for optimizing the properties of carbon fiber composite materials based on a multiphysics reduced-order model as described in any of the above embodiments.

[0125] For descriptions of relevant parts of the carbon fiber composite performance optimization system, electronic device, and computer-readable storage medium based on a multiphysics reduced-order model provided in this application, please refer to the detailed descriptions of the corresponding parts in the carbon fiber composite performance optimization method based on a multiphysics reduced-order model provided in this application, which will not be repeated here. Furthermore, parts of the technical solutions provided in this application that are consistent with the implementation principles of corresponding technical solutions in the prior art have not been described in detail to avoid excessive elaboration.

[0126] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A method for optimizing the properties of carbon fiber composite materials based on a multiphysics reduced-order model, characterized in that, Includes the following steps: Step 1: Generate N sample points in the design variable space of carbon fiber composite materials; High-fidelity multiphysics finite element simulation was performed on each sample point to extract the full-field response data and construct a snapshot matrix S; Step 2: Perform eigenorthogonal decomposition on the snapshot matrix S to extract the dominant POD modes and form a reduced-order basis; A deep neural network model is constructed, with the design variable vector as input and the reduced-order coordinate vector as output. The deep neural network model is trained using a total loss function composed of the weighted sum of data fitting loss and physical residual loss, and a nonlinear mapping relationship from the design parameter space to the reduced-order subspace is established. The physical residual loss is obtained by calculating the residual of the sampling points in the computational domain based on the physical control equation; Step 3: Construct a reduced-order model using the trained reduced-order basis and the mapping function G. The reduced-order model is used to output the corresponding performance index based on the input design parameters. Step 4: Integrate the fast predictor of the reduced-order model into the optimization algorithm. During the iterative optimization process, the optimization algorithm recommends candidate design points based on historical data in the design parameter space, calls the reduced-order model for performance evaluation, and adds the evaluation results to the historical data to update the search direction. Repeat the iteration until the termination condition is met to obtain the optimal design scheme.

2. The method for optimizing the properties of carbon fiber composite materials based on a multiphysics reduced-order model according to claim 1, characterized in that, In step 1, the design variable vector includes at least one of fiber volume fraction, ply angle, ply thickness, and interface performance parameters.

3. The method for optimizing the properties of carbon fiber composite materials based on a multiphysics reduced-order model according to claim 1, characterized in that, In step 1, N sample points are generated in the design variable space using optimal Latin hypercube sampling or Sobol sequence.

4. The method for optimizing the properties of carbon fiber composite materials based on a multiphysics reduced-order model according to claim 1, characterized in that, The physical residual loss mentioned in step 2 is calculated in the following way: Random sampling within the geometric computational domain of carbon fiber composite structures One point; The displacement field is reconstructed based on the reduced-order coordinates predicted by the deep neural network; The strain field is calculated by automatically differentiating the displacement field. The stress field is calculated from the strain field based on the constitutive relation; the stress field is then substituted into the physical control equations to calculate the residuals at each sampling point. The physical residual loss is constructed based on the residual norm of all sampling points.

5. The method for optimizing the properties of carbon fiber composite materials based on a multiphysics reduced-order model according to claim 1, characterized in that, In step 3, the prediction method of the reduced-order model includes: Input design parameter vector; Calculate reduced-order coordinates using a deep neural network model; Reconstructing the full-field displacement by reducing the order basis; Extract one or more global performance metrics from the reconstructed global response.

6. The method for optimizing the properties of carbon fiber composite materials based on a multiphysics reduced-order model according to claim 5, characterized in that, The global performance indicators include at least one of the following: total structural mass, maximum equivalent stress, failure index based on the Tsai-Wu criterion or the Hashing criterion, natural frequency, buckling load factor, and equivalent thermal conductivity.

7. The method for optimizing the properties of carbon fiber composite materials based on a multiphysics reduced-order model according to claim 1, characterized in that, The optimization algorithm mentioned in step 4 is a multi-objective Bayesian optimization algorithm or a constrained genetic algorithm.

8. The method for optimizing the properties of carbon fiber composite materials based on a multiphysics reduced-order model according to claim 1, characterized in that, In step 4, during the iterative optimization process, when the cumulative number of new data points reaches a preset number or the number of iterations meets a preset period, the reduced-order model is fine-tuned and updated using the current historical dataset to obtain the updated reduced-order model for subsequent iterations.

9. The method for optimizing the properties of carbon fiber composite materials based on a multiphysics reduced-order model according to claim 1, characterized in that, After the iteration terminates in step 4, the optimal design scheme is selected and verified by high-fidelity multiphysics finite element simulation to confirm that its performance indicators meet the design requirements.

10. A method for optimizing the properties of carbon fiber composite materials based on a multiphysics reduced-order model, characterized in that, include: The sample library construction module is used to generate N sample points in the design variable space of carbon fiber composite materials; High-fidelity multiphysics finite element simulation was performed on each sample point to extract the full-field response data and construct a snapshot matrix S; The reduced-order model training module is used to perform eigenorthogonal decomposition on the snapshot matrix S and extract the dominant POD modes to form a reduced-order basis. A deep neural network model is constructed, with the design variable vector as input and the reduced-order coordinate vector as output. The deep neural network model is trained using a total loss function composed of the weighted sum of data fitting loss and physical residual loss, and a nonlinear mapping relationship from the design parameter space to the reduced-order subspace is established. The physical residual loss is obtained by calculating the residual of the sampling points in the computational domain based on the physical control equation; The predictor encapsulation module, the trained reduced basis, and the mapping function G construct a reduced model, which is used to output the corresponding performance index based on the input design parameters. An optimization integration module is used to integrate the fast predictor of the reduced-order model into the optimization algorithm. During the iterative optimization process, the optimization algorithm recommends candidate design points based on historical data in the design parameter space, calls the reduced-order model for performance evaluation, and adds the evaluation results to the historical data to update the search direction. The iteration is repeated until the termination condition is met to obtain the optimal design scheme.

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