Yarn stress analysis method and system based on physical information neural network

Abstract

The invention relates to the field of material analysis, and provides a yarn stress analysis method and system based on a physical information neural network. The method comprises the following steps: carrying out geometric modeling on fiber yarns to obtain a three-dimensional geometric model of the fiber yarns; performing coding identification on different section types of the three-dimensional geometric model to obtain multi-section information; integrating physical constraints and the multi-section information based on a multi-branch residual architecture to obtain a physical information neural network model; performing optimization training on the physical information neural network model to obtain a yarn stress analysis model; and analyzing a to-be-analyzed yarn stress field through the yarn stress analysis model to obtain a yarn stress analysis result. According to the method, the engineering design and safety evaluation efficiency and accuracy of the fiber reinforced composite material are improved.

Description

Technical Field

[0001] This invention relates to the field of materials analysis technology, and in particular to a yarn stress analysis method and system based on physical information neural networks. Background Technology

[0002] Fiber-reinforced composite materials, especially nylon fiber materials, are widely used in aerospace, automotive, textile, and many other fields due to their excellent mechanical properties. Accurately predicting the stress distribution and mechanical response of these composite materials under complex loading conditions is crucial for material design optimization and structural safety assessment.

[0003] Existing mechanical analysis methods for fiber composites are based on Physical Information Neural Networks (PINNs), which achieve an organic integration of data-driven approaches and physical constraints by embedding physical laws into the neural network loss function. However, existing PINN technology still has shortcomings in the field of fiber yarn mechanical analysis.

[0004] First, existing PINN lacks a network architecture design specifically for the characteristics of fiber materials with different cross-sections; second, existing PINN has insufficient ability to identify cross-section types: it cannot effectively process and identify fibers with different cross-section types; in addition, it lacks an effective adaptive training strategy when facing complex boundary conditions. Summary of the Invention

[0005] This invention provides a yarn stress analysis method and system based on physical information neural networks to overcome the shortcomings of existing technologies.

[0006] This invention provides a yarn stress analysis method based on a physical information neural network, comprising:

[0007] S1: Perform geometric modeling on the fiber yarn to obtain a three-dimensional geometric model of the fiber yarn;

[0008] S2: Encode and identify different cross-section types of the three-dimensional geometric model to obtain multi-section information;

[0009] S3: Based on the multi-branch residual architecture, the physical constraints and the multi-section information are integrated to obtain the physical information neural network model;

[0010] S4: Optimize and train the physical information neural network model to obtain a yarn stress analysis model;

[0011] S5: The yarn stress field to be analyzed is analyzed using the yarn stress analysis model to obtain the yarn stress analysis results.

[0012] According to the yarn stress analysis method based on physical information neural network provided by the present invention, in step S1, the model parameters of the three-dimensional geometric model include: fiber quantity, fiber helix radius, fiber volume fraction, and fiber three-dimensional coordinate position.

[0013] According to the yarn stress analysis method based on physical information neural network provided by the present invention, step S2 further includes:

[0014] S21: The different cross-sectional types of the three-dimensional geometric model are encoded and identified using hot coding technology to obtain hot coding vectors;

[0015] S22: Based on the heat-encoded vector, calculate the cross-sectional geometric properties of different cross-sectional types to obtain multi-section information; wherein, the cross-sectional geometric properties include: moment of inertia, polar moment of inertia, and cross-sectional area.

[0016] According to the yarn stress analysis method based on physical information neural network provided by the present invention, step S3 further includes:

[0017] S31: The multi-section information is normalized using a standardization algorithm to obtain a standardized feature vector;

[0018] S32: Extract features from the standardized feature vector using multiple residual blocks to obtain a deep feature representation;

[0019] S33: The deep feature representation is separated by a dual-branch structure to obtain a multi-branch output;

[0020] S34: Based on the material constitutive model of orthogonal anisotropic materials and the multi-branch output, establish a physical constraint loss function that includes material properties;

[0021] S35: Train the multi-branch residual architecture using the physical constraint loss function to obtain a physical information neural network model.

[0022] According to the yarn stress analysis method based on physical information neural network provided by the present invention, step S33 specifically includes:

[0023] The deep feature representation is decoded by the displacement branch in the dual-branch structure to obtain the displacement vector;

[0024] The strain vector is obtained by decoding the deep feature representation through the strain branch in the dual-branch structure.

[0025] According to the yarn stress analysis method based on physical information neural network provided by the present invention, the expression of the material constitutive model in step S34 is as follows:

[0026]

[0027] Q(θ)=T T (θ)Q0T(θ);

[0028] Where Q0 is the principal direction stiffness matrix, Q ij The elements in the principal direction stiffness matrix, Q(θ) is the global coordinate system stiffness matrix, θ is the fiber angle, and T(θ) is the coordinate transformation matrix. T (θ) is the transpose of the coordinate transformation matrix;

[0029] The expression for the physical constraint loss function in step S34 is:

[0030] L total =λ1L physics +λ2L equilibrium +λ3L boundary +λ4L compatibility ;

[0031] Among them, L total Let L be the physical constraint loss function. physics To account for the physical constitutive loss of strain energy density, λ1 is the weight value of the physical constitutive loss, L equilibrium Let L be the balance equation loss, λ2 be the weight value of the balance equation loss, and L be the weight value of the balance equation loss. boundary Let L be the boundary loss, λ3 be the weight value of the boundary loss, and L be the weight value of the boundary loss. compatibility λ4 represents the geometric reconciliation loss, and λ4 is the weight value of the geometric reconciliation loss.

[0032] According to the yarn stress analysis method based on physical information neural network provided by the present invention, step S4 further includes:

[0033] S41: Initialize the computational domain by uniform distribution sampling to obtain the initial training point set;

[0034] S42: Calculate the loss of the initial training point set using a loss evaluation algorithm to obtain loss distribution data;

[0035] S43: Based on the loss distribution data, perform loss threshold filtering to identify high-loss regions;

[0036] S44: Enhance the sampling points in the high-loss region by using encrypted sampling to obtain an optimized training point set;

[0037] S45: Based on the optimized training point set, the physical information neural network model is optimized and trained to obtain the yarn stress analysis model.

[0038] According to the yarn stress analysis method based on physical information neural network provided by the present invention, the expression for the loss threshold used for loss threshold screening in step S43 is as follows:

[0039]

[0040] Among them, L threshold The loss threshold, Let σ be the mean loss, k = 2. L The standard deviation of the loss.

[0041] According to the yarn stress analysis method based on physical information neural network provided by the present invention, the yarn stress analysis results in step S5 include: stress distribution data and equivalent stress data.

[0042] This invention also provides a yarn stress analysis system based on a physical information neural network, used to perform a yarn stress analysis method based on a physical information neural network as described in any of the above claims, comprising:

[0043] Modeling module: Used to perform geometric modeling of fiber yarns to obtain a three-dimensional geometric model of the fiber yarns;

[0044] Encoding module: used to encode and identify different cross-section types of the three-dimensional geometric model to obtain multi-section information;

[0045] Integration module: used to integrate physical constraints and multi-section information based on a multi-branch residual architecture to obtain a physical information neural network model;

[0046] Training module: used to optimize and train the physical information neural network model to obtain a yarn stress analysis model;

[0047] An analysis module is configured to use the yarn stress analysis model trained by the training module to analyze the yarn stress field to be analyzed and obtain yarn stress analysis results.

[0048] This invention provides a yarn stress analysis method and system based on a physical information neural network. By constructing a three-dimensional fiber yarn geometric model, it can accurately describe complex multi-layered helical fiber structures. Compared with the traditional finite element method, it avoids the difficulties of complex geometric modeling and mesh generation, significantly reducing modeling complexity and eliminating computational instability caused by mesh distortion. Secondly, this invention uses hot coding technology to encode and identify different cross-section types, achieving unified modeling and analysis of various cross-section types such as circles, ellipses, triangles, and Y-shapes. This solves the technical problem of traditional methods being unable to handle fibers with multiple cross-section types, making a single model applicable to fiber yarn analysis with various cross-section shapes. In addition, the multi-branch residual architecture physical information neural network model integrates physical constraints and multi-section information, and the residual connection structure effectively alleviates the gradient vanishing problem in deep network training. This allows the network to learn more complex fiber-matrix interactions, while the displacement and strain output design of the bi-branch structure ensures the inherent consistency between mechanical quantities. Furthermore, the stiffness matrix embedding of the constitutive relation of orthogonal anisotropic materials achieves accurate transformation from the principal direction to the global coordinate system through a coordinate transformation matrix, enabling the network model to accurately capture the influence of fiber angle changes on material mechanical properties. This deep integration of physical constraints significantly improves prediction accuracy and ensures the physical rationality of the results. The adaptive region optimization training strategy, through loss distribution analysis and high-loss region identification, achieves intelligent allocation of training resources. Compared with traditional uniform sampling methods, it significantly improves training efficiency under limited computational resources. In particular, the combination of loss threshold screening and dense sampling strategies enables the model to have higher prediction accuracy in key areas such as stress concentration and geometric abrupt changes.

[0049] In the field of stress analysis of fiber composite materials, this invention, based on a physical information neural network, directly embeds physical laws such as the governing equations of elasticity, equilibrium equations, boundary conditions, and geometric compatibility conditions into the loss function. This enables high-precision mechanical prediction without requiring a large amount of experimental data. This physically constrained learning approach gives the model stronger generalization ability and physical consistency. The multi-branch residual architecture is also uniquely designed for the anisotropic characteristics of fiber composite materials, capable of simultaneously handling the complex mapping relationship between displacement and strain. The adaptive training strategy, through loss-driven sampling optimization, achieves efficient utilization of computational resources. Compared with traditional numerical methods, it significantly reduces computation time while maintaining accuracy, making real-time analysis and optimization design of complex fiber structures possible.

[0050] Compared with the traditional finite element method, the overall solution of this invention has achieved significant improvements in computational efficiency, modeling flexibility, prediction accuracy, and engineering applicability, providing a brand-new technical approach for the rapid design optimization and performance prediction of complex fiber composite materials. Attached Figure Description

[0051] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0052] Figure 1 A schematic flowchart of a yarn stress analysis method based on a physical information neural network provided in an embodiment of the present invention;

[0053] Figure 2 A schematic diagram of a yarn stress analysis system based on a physical information neural network is provided for an embodiment of the present invention;

[0054] Figure 3 A comparative diagram of stress-time history provided for embodiments of the present invention;

[0055] Figure 4 A schematic diagram comparing strain-stress relationships provided for embodiments of the present invention;

[0056] Figure 5 This is a schematic diagram of the relative error of PINN prediction provided in an embodiment of the present invention;

[0057] Figure 6 This is a schematic diagram illustrating the statistical analysis of prediction accuracy provided in an embodiment of the present invention.

[0058] Figure 7 A schematic diagram illustrating the theoretical prediction correlation provided in this embodiment of the invention;

[0059] Figure 8 The fiber cross-section mechanical cloud diagram provided for the embodiments of the present invention;

[0060] Figure 9 A schematic diagram comparing the maximum stress of a cross section provided for an embodiment of the present invention. Detailed Implementation

[0061] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, embodiments of this invention, and should not be construed as limiting the invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention. In the description of this invention, it should be understood that the terminology used is for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0062] To better understand this invention, the research background of this invention will be explained in detail below.

[0063] Fiber-reinforced composite materials, especially nylon fiber materials, are widely used in aerospace, automotive, textile, and many other fields due to their excellent mechanical properties. Accurately predicting the stress distribution and mechanical response of these composite materials under complex loading conditions is crucial for material design optimization and structural safety assessment.

[0064] Traditional mechanical analysis of fiber composites primarily relies on the finite element method (FEM), which discretizes the continuous solution domain into a finite number of elements to solve a system of partial differential equations. However, FEM faces numerous challenges when dealing with multi-layered helical fiber yarn structures:

[0065] Geometric modeling complexity: The complex geometry of multi-layered helical fiber structures places extremely high demands on mesh generation, making them prone to mesh distortion and resulting in computational instability; Difficulty in handling multiple cross-section types: Actual fiber yarns encompass various cross-section types such as circles, ellipses, triangles, and Y-shapes, making it difficult to model and analyze them uniformly using traditional methods; Low computational efficiency: Fine mesh generation results in massive computational scale and lengthy computation time, making it difficult to meet the needs of real-time engineering analysis.

[0066] In recent years, Physical Information Neural Networks (PINN) have shown great potential in solving partial differential equations. By embedding physical laws into the neural network loss function, they have achieved an organic integration of data-driven approaches and physical constraints.

[0067] However, existing PINN technology still has shortcomings in the field of fiber yarn mechanical analysis:

[0068] Lack of targeted architecture design: The existing PINN lacks a network architecture design specifically for the characteristics of fiber materials with different cross-sections; Insufficient cross-section type recognition capability: It cannot effectively process and identify fibers with different cross-section types; Training strategy needs optimization: When faced with complex boundary conditions, there is a lack of effective adaptive training strategies.

[0069] Therefore, there is an urgent need to develop a neural network analysis method specifically for physical information of multi-section fiber yarns in order to overcome the above-mentioned technical challenges.

[0070] The embodiments of the present invention are described below with reference to the figures.

[0071] like Figure 1 As shown, this invention provides a yarn stress analysis method based on a physical information neural network, comprising:

[0072] S1: Perform geometric modeling on the fiber yarn to obtain a three-dimensional geometric model of the fiber yarn.

[0073] In step S1, the model parameters of the three-dimensional geometric model include: fiber quantity, fiber helix radius, fiber volume fraction, and fiber three-dimensional coordinate position.

[0074] Specifically, this invention uses a layered spiral arrangement algorithm to generate multi-section fiber yarn structures, where the meanings of each parameter are as follows:

[0075] The number of fibers in the nth layer is expressed as:

[0076] N n =max(1,6(n-1));

[0077] Where n represents the number of layers, counting from layer 1, N n This represents the number of fibers in the nth layer, used to determine the number of fibers in each layer, ensuring that the number of fibers increases reasonably as the number of layers increases;

[0078] The fiber helix radius is expressed as:

[0079] R n =(r fiber +gap)+(n-1)×2(r fiber +gap);

[0080] Where, r fiber R represents the fiber radius, gap represents the fiber spacing, and R represents the fiber radius. n The fiber helix radius is used to calculate the helix radius of each fiber layer based on the number of layers, fiber radius, and gap, thus reflecting the helical characteristics of the yarn structure.

[0081] The parametric equation for the helical spiral is expressed as follows:

[0082]

[0083] Where (x,y,z) are the three-dimensional coordinates of the fiber in three-dimensional space, θ0 is the initial angle used to determine the starting position of the fiber, and pitch is the pitch, which represents the distance in the z direction of the fiber spiraling up for one complete cycle. The above equation determines the coordinate position of the fiber in three-dimensional space by giving parameters.

[0084] Fiber volume fraction, expressed as:

[0085]

[0086] Among them, V f N represents the fiber volume fraction. total R represents the total number of fibers. yarnThe yarn radius is used to calculate the proportion of fiber in the total volume of the yarn, reflecting the fiber content characteristics of the yarn.

[0087] S2: Encode and identify different cross-section types of the three-dimensional geometric model to obtain multi-section information.

[0088] Step S2 further includes:

[0089] S21: The different cross-sectional types of the three-dimensional geometric model are encoded and identified using hot coding technology to obtain hot coding vectors.

[0090] Furthermore, this invention is based on one-hot encoding technology, which assigns a unique position index to each category, marking it as 1 at that position and marking it as 0 at other positions. Specifically, for fiber cross-section type identification, it supports 6 different cross-section types: circle, ellipse, triangle, Y-shaped, cross-shaped, and custom.

[0091] The data processing first establishes a cross-section type mapping table, assigning a unique numerical identifier to each cross-section type: circle corresponds to index 0, ellipse to index 1, triangle to index 2, Y-shape to index 3, cross shape to index 4, and a custom index 5. Each cross-section type is uniquely identified by a hot-coded vector, resulting in a unique binary representation for each cross-section type, which facilitates neural network processing and recognition.

[0092] S22: Based on the heat-encoded vector, calculate the cross-sectional geometric properties of different cross-sectional types to obtain multi-section information; wherein, the cross-sectional geometric properties include: moment of inertia, polar moment of inertia, and cross-sectional area.

[0093] Furthermore, in step S22, the cross-sectional geometric properties are calculated, and the specific parameters include:

[0094] Area: A = f area (type, params), where f area This is a function used to calculate the area. `type` indicates the cross-section type, and `params` are parameters related to that type (such as the radius of a circle, the length and width of a rectangle, etc.). The function calculates the area based on the cross-section type and parameters.

[0095] Moment of inertia: I y =f inertia_y (type,params), I z =f inertia_z (type, params), f inertia_y and f inertia_zTwo functions are used to calculate the moment of inertia of the cross section in the y-axis and z-axis directions;

[0096] Polar moment of inertia: J = f polar (type, params), f polar This is a function for calculating the polar moment of inertia based on the section type and parameters.

[0097] S3: Based on the multi-branch residual architecture, the physical constraints and the multi-section information are integrated to obtain the physical information neural network model.

[0098] Step S3 further includes:

[0099] S31: The multi-section information is normalized using a standardization algorithm to obtain a standardized feature vector.

[0100] In step S31, multi-section information from the previous step is first received, including spatial coordinates, fiber angle information and hot encoding vector. Then, standardized data preprocessing is performed to unify data with different dimensions and numerical ranges into the same numerical range, so as to prevent certain features from dominating the network training process due to excessively large values.

[0101] After standardizing the coordinates, angles, and encoding the vectors, all standardized features are arranged in a fixed order to form a 10-dimensional standardized feature vector. The first three elements of the vector are standardized coordinates, the fourth element is the standardized angle, and the fifth to tenth elements are the encoded vectors. The data type is uniformly converted to 32-bit floating-point numbers for easy processing by neural networks.

[0102] S32: Extract features from the standardized feature vector using multiple residual blocks to obtain a deep feature representation.

[0103] This invention employs six residual blocks for feature extraction, with each residual block containing 256 neurons. When processing data, each residual block receives the output of the previous layer as input. First, feature mapping is performed through a linear transformation layer. Then, the intermediate results undergo a nonlinear transformation using the hyperbolic tangent activation function tanh, which introduces nonlinear features, enabling the network to learn complex nonlinear relationships. Subsequently, the output of the activation function is added to the original input element-wise to achieve residual connections. The purpose is to allow information to be directly transferred across layers, alleviating the gradient vanishing problem.

[0104] For cascaded data processing between multiple residual blocks, the first residual block receives a 10-dimensional normalized feature vector, which is expanded to 256 dimensions through a linear transformation of 256 neurons. The subsequent five residual blocks process the 256-dimensional feature vector in sequence, and the output of each residual block serves as the input of the next residual block. The six residual blocks are cascaded to form a deep feature extraction pipeline, extracting and abstracting feature information layer by layer. The final output is a 256-dimensional deep feature representation, which contains high-level abstract features of the input data.

[0105] S33: The deep feature representation is separated by a dual-branch structure to obtain a multi-branch output.

[0106] Specifically, step S33 includes:

[0107] The deep feature representation is decoded by the displacement branch in the dual-branch structure to obtain the displacement vector; the deep feature representation is decoded by the strain branch in the dual-branch structure to obtain the strain vector.

[0108] Specifically, the displacement vector output by the displacement branch is u = [u x ,u y ,u z ] T u x ,u y ,u z These represent the displacements in the x, y, and z directions, respectively. The strain vector output by the strain branch is ε = [ε xx ,ε yy ,ε zz ,γ xy ,γ xz ,γ yz ] T It is used to output strain in various directions.

[0109] The displacement branch of this invention receives a 256-dimensional deep feature representation as input and performs feature decoding through a unique linear transformation layer. The linear transformation layer of the displacement branch contains a weight matrix W. displacement and bias vector b displacement The weight matrix has a dimension of 3×256, and the bias vector has a dimension of 3×1. The linear transformation calculation process involves multiplying the weight matrix by the 256-dimensional eigenvector, and then adding the bias vector to obtain a 3-dimensional output vector. The three elements of the output vector correspond to the displacement components in the x, y, and z directions, respectively. The displacement branch does not use an activation function and directly outputs the linear transformation result because the displacement values ​​need to maintain their original numerical range and sign characteristics.

[0110] The strain branch of this invention also receives a 256-dimensional deep feature representation as input and performs feature decoding through an independent linear transformation layer. The linear transformation layer of the strain branch contains a weight matrix W. strain and bias vector b strain The weight matrix has a dimension of 6×256, and the bias vector has a dimension of 6×1. The linear transformation calculation process is to multiply the weight matrix by the 256-dimensional eigenvector, and then add the bias vector to obtain a 6-dimensional output vector. The six elements of the output vector correspond to the normal strain component and the shear strain component, respectively. The strain branch also does not use an activation function and directly outputs the linear transformation result.

[0111] Finally, the 3D output vector of the displacement branch and the 6D output vector of the strain branch are combined into a multi-branch output data structure. The two vectors remain independent in the data structure and correspond to different physical quantity types. The multi-branch output data structure contains complete mechanical response information, providing the necessary input data for subsequent physical constraint loss function calculation.

[0112] S34: Based on the constitutive relation of orthogonal anisotropic materials, a physical constraint loss function containing material properties is established using the multi-branch output of the material constitutive model.

[0113] The expression for the material constitutive model in step S34 is as follows:

[0114]

[0115] Where Q0 is the principal direction stiffness matrix, Q ij Elements in the principal direction stiffness matrix Q 44 =G 23 Q 55 =G 13 Q 66 =G 12 Δ=1-v 12 v 21 -v 13 v 31 -v 23 ν 32 -2ν 12 ν 23 ν 31 E1, E2, and E3 represent the elastic modulus of the fiber in different directions, respectively. ij G is Poisson's ratio. ij The above parameters together determine the principal direction stiffness matrix, which is the shear modulus.

[0116] Q(θ)=T T (θ)Q0T(θ);

[0117] Where Q0 is the principal direction stiffness matrix, Q ij The elements in the principal direction stiffness matrix, Q(θ) is the global coordinate system stiffness matrix, θ is the fiber angle, and T(θ) is the coordinate transformation matrix. T (θ) is the transpose of the coordinate transformation matrix. In the above expression, the principal direction stiffness matrix is ​​transformed to the global coordinate system through the coordinate transformation matrix T(θ). T(θ) takes into account the influence of the fiber angle θ.

[0118] The expression for the physical constraint loss function in step S34 is as follows:

[0119] L total =λ1L physics +λ2L equilibrium +λ3L boundary +λ4L compatibility ;

[0120] Among them, L total Let L be the physical constraint loss function. physics To account for the physical constitutive loss of strain energy density, λ1 is the weight value of the physical constitutive loss, L equilibrium Let L be the balance equation loss, λ2 be the weight value of the balance equation loss, and L be the weight value of the balance equation loss. boundary Let L be the boundary loss, λ3 be the weight value of the boundary loss, and L be the weight value of the boundary loss. compatibility λ4 represents the geometric reconciliation loss, and λ4 is the weight value of the geometric reconciliation loss.

[0121] Furthermore, the expression for the balance equation loss is:

[0122]

[0123] The equilibrium equation loss is used to calculate the equilibrium equation loss, ensuring that the network prediction results satisfy the mechanical equilibrium condition. N is the number of training points.

[0124] Boundary condition loss:

[0125] L boundary =L fixed +L loaded ;

[0126]

[0127] L fixed Used to calculate the loss under fixed boundary conditions, N fixed The number of training points is fixed at the boundary; L loaded Used to calculate the loss under loading boundary conditions, N loaded To load the number of training points at the boundary, u target For the target displacement;

[0128] Geometric compatibility loss:

[0129]

[0130] Used to calculate geometric compatibility loss and ensure that strain relationships meet geometric compatibility conditions;

[0131] Physical constitutive loss:

[0132]

[0133] in, The loss function, representing the strain energy density, ensures that the strain energy remains within a reasonable range, where ε is the strain vector, and U... max This represents the maximum strain energy.

[0134] S35: Train the multi-branch residual architecture using the physical constraint loss function to obtain a physical information neural network model.

[0135] In step S35, the network parameters are adjusted according to the aforementioned optimization function. During training, the system updates the network parameters using gradient descent. The training process includes forward propagation, loss calculation, backpropagation, and parameter update. Forward propagation calculates the network output, loss calculation evaluates the prediction error, backpropagation calculates the gradient, and parameter update adjusts the network weights. The training process continues until the convergence condition is met, ultimately obtaining the trained physical information neural network model.

[0136] S4: Optimize and train the physical information neural network model to obtain the yarn stress analysis model.

[0137] Step S4 further includes:

[0138] S41: Initialize the computational domain by uniformly distributed sampling to obtain the initial training point set.

[0139] Furthermore, the computational domain is defined as the internal space of the yarn's geometric boundary, the boundary of which is determined by the multi-section fiber structure generated by the layered spiral arrangement algorithm.

[0140] The data processing first requires determining the three-dimensional boundary of the computational domain. Then, in each coordinate axis direction, the data is divided at equal intervals according to a preset resolution to obtain multiple grid points in each direction. Finally, a set of candidate points is generated by traversing all coordinate combinations through a triple loop.

[0141] For each candidate point, it is necessary to determine whether it is located inside the yarn. The determination method is to calculate the distance from the point to the central axis of the yarn. If the distance is less than or equal to the yarn radius, the point belongs to the yarn and is added to the initial training point set.

[0142] The final generated initial training point set contains multiple data points, each with four basic attributes: three-dimensional coordinates and fiber angles. The data points are evenly distributed throughout the computational domain, providing comprehensive basic data for subsequent neural network training.

[0143] S42: Calculate the loss of the initial training point set using a loss assessment algorithm to obtain loss distribution data.

[0144] Furthermore, in step S42, the present invention calculates the loss value for each data point in the initial training point set using a loss evaluation algorithm. The loss value reflects the prediction accuracy of the current neural network model at that point, and the higher the loss value, the greater the prediction error.

[0145] The data processing begins with the initial set of training points. For each training point, data preprocessing is performed first. Coordinate normalization includes: x_norm = x / R_yarn, y_norm = y / R_yarn, z_norm = z / L. Section type encoding generates a corresponding hot-coded vector based on the section type of the fiber containing that point. The hot-coded vector is a 6-dimensional binary vector, where only one position is 1 and the rest are 0.

[0146] S43: Based on the loss distribution data, perform loss threshold filtering to identify high-loss regions.

[0147] The expression for the loss threshold used for loss threshold filtering in step S43 is as follows:

[0148]

[0149] Among them, L threshold The loss threshold, Let σ be the mean loss, k = 2. L The standard deviation of the loss.

[0150] Furthermore, the above formula is used to determine the loss threshold, thereby dividing the high-loss region. The expression for determining the high-loss region is: when the loss value of the current data point is greater than L... threshold When this point is included in the high-loss area, the specific range of the high-loss area can be determined.

[0151] S44: Enhance the sampling points in the high-loss region by using encrypted sampling to obtain an optimized training point set.

[0152] Furthermore, in step S44, the present invention enhances the sampling density by increasing the number of sampling points by α times in the high-loss region selected in step S43, where α ∈ [2,5]. By increasing the number of sampling points in the high-loss region, the predictive ability of the model in that region is improved.

[0153] S45: Based on the optimized training point set, the physical information neural network model is optimized and trained to obtain the yarn stress analysis model.

[0154] Specifically, the training of the physical information neural network model is divided into the following training phases: Initial training: using the Adam optimizer, with a learning rate lr = 1 × 10⁻⁶. -3 Weight decay wd = 1 × 10 -4 The Adam optimizer is suitable for initial fast training; for fine-tuning: use the L-BFGS second-order optimizer with a tolerance of tol = 1 × 10⁻⁶. -6 L-BFGS is used for fine-tuning in the later stages to improve training accuracy; learning rate scheduling: the ReduceLROnPlateau strategy is adopted with a decay factor of 0.8 and patience = 500. The learning rate is automatically adjusted according to the training situation to improve training efficiency.

[0155] S5: The yarn stress field to be analyzed is analyzed using the yarn stress analysis model to obtain the yarn stress analysis results.

[0156] The yarn stress analysis results in step S5 include: stress distribution data and equivalent stress data.

[0157] Furthermore, in step S5, the present invention outputs the global stress field and displacement field through the trained PINN model, and the specific calculation and evaluation methods are as follows:

[0158] The expression for stress calculation is: σ=Q(θ)ε, that is, the stress is calculated based on the material constitutive relation and strain, where σ is the stress vector.

[0159] The expression for Von Mises equivalent stress is:

[0160]

[0161] The Von Mises equivalent stress is used to comprehensively evaluate the stress state.

[0162] Furthermore, the present invention also performs error assessment on the calculation results: stress error: 100%, by comparing the results with those of the finite element method (FEM), the error in stress prediction was calculated; displacement error: Calculate the error in displacement prediction.

[0163] like Figure 2 As shown, the present invention also provides a yarn stress analysis system based on a physical information neural network, comprising:

[0164] Modeling module 100: Used to perform geometric modeling of fiber yarns to obtain a three-dimensional geometric model of the fiber yarns;

[0165] Encoding module 200: used to encode and identify different cross-section types of the three-dimensional geometric model to obtain multi-section information;

[0166] Integration module 300: used to integrate physical constraints and multi-section information based on a multi-branch residual architecture to obtain a physical information neural network model;

[0167] Training module 400: used to optimize and train the physical information neural network model to obtain a yarn stress analysis model;

[0168] Analysis module 500 is configured to use the yarn stress analysis model trained by training module 400 to analyze the yarn stress field to be analyzed and obtain yarn stress analysis results.

[0169] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0170] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0171] like Figures 3 to 5 The figure shown is a theoretical verification and comparative analysis diagram of PA66 fiber according to the present invention, used to verify the effectiveness and accuracy of the Physical Information Neural Network (PINN) method of the present invention in stress analysis of PA66 fiber yarn.

[0172] Figure 3The figure shows a comparison of stress-time response. The horizontal axis represents time (ms) and the vertical axis represents stress (MPa). The red solid line represents theoretical data and the blue dashed line represents PINN prediction results. The figure shows that the two curves exhibit a nonlinear growth trend. The initial growth is slow, and the growth accelerates in the later stage, which is consistent with the nonlinear mechanical properties of materials. Moreover, the two curves almost completely overlap, which shows that the model of the present invention has high accuracy.

[0173] Figure 4 This diagram illustrates the strain-stress relationship, where the horizontal axis represents strain (%) and the vertical axis represents stress (MPa). The solid red line represents theoretical data, the dashed blue line represents the PINN prediction result, and the dashed yellow line represents the yield strength (282.8 MPa). As shown in the diagram, the stress-strain curve of the material exhibits typical characteristics, including the initial linear segment, the yield point, and the plastic deformation segment. Furthermore, the PINN prediction closely matches the theoretical value, especially near the yield strength, demonstrating the high accuracy of the model in this invention.

[0174] Figure 5 This is a schematic diagram of the PINN prediction error variation of the present invention. The horizontal axis represents time (ms) and the vertical axis represents relative error (%, percentage). The purple curve and the corresponding cross-sectional area show the trend of prediction error variation. As shown in the figure, the error range of the present invention is controlled within ±5% at most time points. The error shows periodic fluctuations and is generally kept within an acceptable range.

[0175] Figure 6 This is a schematic diagram of the statistical analysis of prediction accuracy. In the horizontal axis, the blue histogram represents the mean absolute error, the red histogram represents the maximum error, and the green histogram represents the root mean square error. The vertical axis represents the error values, which are 5.14% for the mean absolute error, 9.59% for the maximum error, and 5.91% for the root mean square error. All errors are relatively small.

[0176] Figure 7 This diagram illustrates the correlation analysis between theory and prediction. The present invention uses a scatter plot and regression analysis for correlation analysis. The horizontal axis represents the theoretical stress (MPa), and the vertical axis represents the PINN predicted stress (MPa). The color gradient on the right represents the time dimension (0-100ms). As shown in the diagram, the data points are closely distributed near the ideal correlation line (red dashed line), with a correlation coefficient of R = 0.994, indicating a high positive correlation between the theoretical and predicted values. This demonstrates that the PINN model of the present invention can accurately capture the stress change trend, proving the model's excellent predictive ability. Furthermore, the scatter points are basically distributed along the y = x straight line without significant deviation, maintaining high accuracy in both low-stress (0-100MPa) and high-stress (300-400MPa) regions. The prediction accuracy remains consistent across different time points, with no time bias.

[0177] Figure 8 This is a schematic diagram of stress analysis at a critical section of PA66 fiber. Figure 8 The mechanical contour diagrams are shown in the order of bottom section, lower section, middle section, upper section, and top section. Figure 9 This is a comparison diagram of the maximum stress at each interface corresponding to the mechanical cloud diagram. The horizontal axis represents the cross-sectional position, namely the bottom cross-section, the lower cross-section, the middle cross-section, the upper cross-section, and the top cross-section. The vertical axis represents the maximum stress, which is 70.7 MPa for the bottom cross-section, 176.7 MPa for the lower cross-section, 353.4 MPa for the middle cross-section, 282.7 MPa for the upper cross-section, and 106.0 MPa for the top cross-section. The theoretical maximum value is 353.4 MPa.

[0178] The yarn stress analysis method based on physical information neural networks (PINN) of this invention has achieved significant results in practical applications. Through a multi-branch residual PINN architecture and an adaptive training strategy, the model training exhibits good convergence. In terms of predicting material mechanical properties, the model's predictions show a high correlation coefficient with actual data, accurately capturing the nonlinear elastic modulus variation of fiber materials within the 0-30% strain range, particularly the complex mechanical behavior in the high-strain region (25-30%) where the elastic modulus rapidly increases from 100 MPa to over 300 MPa.

[0179] Compared with the traditional finite element method, this invention avoids the complex mesh generation problem when dealing with fibers with various cross-sectional types such as circular, elliptical, triangular, and Y-shaped fibers, significantly improving computational efficiency. The stress prediction error and displacement prediction error are both controlled within a reasonable range, providing an efficient and accurate analysis tool for the engineering design and safety assessment of fiber-reinforced composite materials. It is particularly suitable for fields with strict requirements on material performance.

[0180] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A yarn stress analysis method based on a physical information neural network, characterized in that, include: S1: Perform geometric modeling on the fiber yarn to obtain a three-dimensional geometric model of the fiber yarn; S2: Encode and identify different cross-section types of the three-dimensional geometric model to obtain multi-section information; S3: Based on the multi-branch residual architecture, the physical constraints and the multi-section information are integrated to obtain the physical information neural network model; S4: Optimize and train the physical information neural network model to obtain a yarn stress analysis model; S5: The yarn stress field to be analyzed is analyzed using the yarn stress analysis model to obtain the yarn stress analysis results.

2. The yarn stress analysis method based on a physical information neural network according to claim 1, characterized in that, In step S1, the model parameters of the three-dimensional geometric model include: fiber quantity, fiber helix radius, fiber volume fraction, and fiber three-dimensional coordinate position.

3. The yarn stress analysis method based on a physical information neural network according to claim 1, characterized in that, Step S2 further includes: S21: The different cross-sectional types of the three-dimensional geometric model are encoded and identified using hot coding technology to obtain hot coding vectors; S22: Based on the heat-encoded vector, calculate the cross-sectional geometric properties of different cross-sectional types to obtain multi-section information; wherein, the cross-sectional geometric properties include: moment of inertia, polar moment of inertia, and cross-sectional area.

4. The yarn stress analysis method based on a physical information neural network according to claim 1, characterized in that, Step S3 further includes: S31: The multi-section information is normalized using a standardization algorithm to obtain a standardized feature vector; S32: Extract features from the standardized feature vector using multiple residual blocks to obtain a deep feature representation; S33: The deep feature representation is separated by a dual-branch structure to obtain a multi-branch output; S34: Based on the material constitutive model of orthogonal anisotropic materials and the multi-branch output, establish a physical constraint loss function that includes material properties; S35: Train the multi-branch residual architecture using the physical constraint loss function to obtain a physical information neural network model.

5. The yarn stress analysis method based on a physical information neural network according to claim 4, characterized in that, Step S33 specifically includes: The deep feature representation is decoded by the displacement branch in the dual-branch structure to obtain the displacement vector; The strain vector is obtained by decoding the deep feature representation through the strain branch in the dual-branch structure.

6. The yarn stress analysis method based on a physical information neural network according to claim 4, characterized in that, The expression for the material constitutive model in step S34 is: Q(θ)=T T (θ)Q0T(θ); Where Q0 is the principal direction stiffness matrix, Q ij The elements in the principal direction stiffness matrix, Q(θ) is the global coordinate system stiffness matrix, θ is the fiber angle, and T(θ) is the coordinate transformation matrix. T (θ) is the transpose of the coordinate transformation matrix; The expression for the physical constraint loss function in step S34 is: L total =λ1L physics +λ2L equilibroum +λ3L boundary +λ4L compatibility ; Among them, L total Let L be the physical constraint loss function. physics To account for the physical constitutive loss of strain energy density, λ1 is the weight value of the physical constitutive loss, L equilibrium Let L be the balance equation loss, λ2 be the weight value of the balance equation loss, and L be the weight value of the balance equation loss. boundary Let L be the boundary loss, λ3 be the weight value of the boundary loss, and L be the weight value of the boundary loss. compatibility λ4 represents the geometric reconciliation loss, and λ4 is the weight value of the geometric reconciliation loss.

7. The yarn stress analysis method based on a physical information neural network according to claim 1, characterized in that, Step S4 further includes: S41: Initialize the computational domain by uniform distribution sampling to obtain the initial training point set; S42: Calculate the loss of the initial training point set using a loss evaluation algorithm to obtain loss distribution data; S43: Based on the loss distribution data, perform loss threshold filtering to identify high-loss regions; S44: Enhance the sampling points in the high-loss region by using encrypted sampling to obtain an optimized training point set; S45: Based on the optimized training point set, the physical information neural network model is optimized and trained to obtain the yarn stress analysis model.

8. The yarn stress analysis method based on a physical information neural network according to claim 7, characterized in that, The expression for the loss threshold used for loss threshold filtering in step S43 is: Among them, L threshold The loss threshold, Let σ be the mean loss, k = 2. L The standard deviation of the loss.

9. The yarn stress analysis method based on a physical information neural network according to claim 1, characterized in that, The yarn stress analysis results in step S5 include: stress distribution data and equivalent stress data.

10. A yarn stress analysis system based on a physical information neural network, used to execute a yarn stress analysis method based on a physical information neural network as described in any one of claims 1-9, characterized in that, include: Modeling module: Used to perform geometric modeling of fiber yarns to obtain a three-dimensional geometric model of the fiber yarns; Encoding module: used to encode and identify different cross-section types of the three-dimensional geometric model to obtain multi-section information; Integration module: used to integrate physical constraints and multi-section information based on a multi-branch residual architecture to obtain a physical information neural network model; Training module: used to optimize and train the physical information neural network model to obtain a yarn stress analysis model; An analysis module is configured to use the yarn stress analysis model trained by the training module to analyze the yarn stress field to be analyzed and obtain yarn stress analysis results.

Images