A laplacian spectrum-based composite part cure state prediction method

Abstract

A composite part curing state prediction method based on Laplace spectrum can establish a curing state prediction model for any shape of composite part. The method first divides the composite part model into grids; secondly, according to the type of the divided grid, the corresponding Laplace operator is defined, and a group of Laplace spectrum reflecting the frequency domain information of the part geometry is solved; then N groups of curing process data and the corresponding composite part curing state data are obtained; finally, based on the Laplace spectrum, a Laplace kernel integral module is constructed, and then a neural operator model is established, and the model parameters are trained through the obtained data samples, so that the curing state prediction model of the composite part can be obtained. The present application can be widely applied to the curing state prediction task of any shape of composite part, and the obtained curing state prediction model can realize the rapid prediction of the curing state of the composite part, and can be used for curing process optimization, curing process monitoring and other scenes.

Description

Technical Field

[0001] This invention relates to a curing and molding technology for composite material parts, and more particularly to a curing state prediction technology for composite material parts, specifically a method for predicting the curing state of composite material parts based on Laplace spectra. Background Technology

[0002] Composite materials, with their advantages of being lightweight, high-strength, and highly designable, have become the preferred material for weight reduction and efficiency improvement in high-end equipment in aerospace, automotive, and shipbuilding industries. Composite material curing refers to the process of causing physical and chemical changes in resin under specific curing conditions to form composite material parts with both geometric shape and load-bearing capacity. An unreasonable curing process can lead to uneven temperature fields, curing degree fields, and large residual stresses within the composite material parts, resulting in curing defects such as ablation, delamination, and deformation, significantly reducing the manufacturing yield and molding quality of the composite material parts. Therefore, the curing process design for composite material parts often requires extensive iterative optimization based on predictions of curing states such as temperature field, curing degree field, and stress field.

[0003] Traditional physical model prediction methods rely on simulations such as finite element analysis and finite difference to obtain curing state information of composite parts under a given curing process, providing high-precision and comprehensive prediction results. However, this method involves a complex modeling process, requiring the model to be rebuilt and recalculated when the curing process changes, resulting in low prediction efficiency. This is particularly problematic for large and complex parts, where it struggles to meet the practical needs of iterative optimization of the curing process. In recent years, data-driven methods have been widely applied to modeling tasks in fields such as computer vision, system fault diagnosis, and state prediction. These methods learn the mapping relationships between variables from training data, enabling rapid prediction once training is complete, providing a new approach to predicting the curing state of composite material parts.

[0004] Patent CN115470669A invented a method, device, and storage medium for predicting the curing deformation of composite material structures. This method utilizes a convolutional neural network to establish a prediction model from a color image of the composite material's layup angle to a curing deformation cloud image of the part, enabling fast and efficient prediction of curing deformation. However, the use of convolutional neural networks requires arranging the training data into a regular matrix according to their relative positions on the part, making this method only suitable for predicting the curing state field of simple composite material parts with regular boundaries. It cannot be directly applied to complex two-dimensional or three-dimensional parts commonly used in engineering. Patent CN114065578A proposed a composite material curing process modeling method. This method maps the curing process to the curing state information of composite material parts based on a neural operator model. The neural operator model involved is a Fourier neural operator, which parameterizes the data in the frequency domain space through fast Fourier transform, significantly reducing model complexity. However, since fast Fourier transform can only handle regular rectangular data, this method still cannot predict the curing state of composite material parts with complex shapes.

[0005] The core of the Fourier neural operator lies in projecting the input data onto a frequency domain space described by a set of Fourier bases through the Fast Fourier Transform, thus simplifying the model while maintaining powerful modeling capabilities. Therefore, a key challenge in predicting the curing state of composite material parts lies in how to describe the frequency domain information of complex geometries, i.e., finding a set of bases that can reflect the frequency domain information of complex geometries. Besides Fourier bases, the Laplace spectrum can also provide frequency domain bases in Euclidean space and can describe the frequency domain information of the geometric shapes of arbitrary spatial curved surfaces and three-dimensional solid parts. Therefore, this invention proposes a curing state prediction method for composite material parts based on the Laplace spectrum, which can establish a curing state prediction model for composite material parts of arbitrary shapes. Summary of the Invention

[0006] The purpose of this invention is to address the limitation that existing methods for predicting the curing state of composite material parts are only applicable to simple, regular parts. This invention proposes a method for predicting the curing state of composite material parts based on Laplace spectra. By constructing a neural operator model using the Laplace spectrum, which reflects the frequency domain information of the part's geometry, a curing state prediction model can be established for composite material parts of arbitrary shapes.

[0007] The technical solution of this invention is:

[0008] A method for predicting the curing state of composite material parts based on Laplace spectroscopy is characterized by the following steps: First, the composite material part model is meshed; second, a corresponding Laplace operator is defined according to the mesh type, and a set of Laplace spectra Ψ reflecting the frequency domain information of the part's geometry is solved; then, N sets of curing process data x are obtained. i and each xi Curing state data of composite material parts y i Finally, a Laplace kernel integral module is constructed based on the Laplace spectrum Ψ, and a neural operator model is established. Then, through data samples {(x... i ,y i By training the model parameters in the range of |i=1,…,N}, a prediction model for the curing state of composite material parts can be obtained.

[0009] The curing process data x i It refers to n on composite material parts m The curing process information at each grid node, including temperature process information or pressure process information, can be characterized by a finite number of parameters through parameterization or discretization. For example, the temperature process information of a single insulation platform can be represented by the initial temperature, heating time, insulation temperature, insulation time and cooling time.

[0010] The curing state data y of the composite material parts i This refers to the n on composite material parts during the curing process. m The curing state values ​​at each grid node, including temperature, degree of curing, stress, strain, stiffness, flexibility, and deformation, can be solved using the finite element method, finite difference method, or commercial simulation software, or obtained by monitoring during the curing experiment.

[0011] The Laplace kernel integral module constructed based on the Laplace spectrum Ψ is specifically constructed by combining a frequency domain transformation submodule, a linear transformation submodule, or a nonlinear activation submodule, and the construction method is one of the following:

[0012] It contains only the frequency domain transform submodule;

[0013] It includes a frequency domain transformation submodule and a linear transformation submodule;

[0014] It includes a frequency domain transformation submodule and a nonlinear activation submodule;

[0015] It includes a frequency domain transformation submodule, a linear transformation submodule, and a nonlinear activation submodule.

[0016] The frequency domain transformation submodule includes three steps: encoding, parameterization, and decoding. Encoding uses the Laplace spectrum Ψ to map the input data of the Laplace kernel integral module from the original space to the frequency domain space, obtaining the coordinates of the input data in that spectrum. Parameterization is to perform linear or nonlinear transformation on the coordinates obtained after encoding. Decoding is to restore the coordinates obtained after parameterization to the original space based on the Laplace spectrum Ψ.

[0017] The linear transformation submodule is constructed by performing a linear transformation on the input data of the Laplace kernel integral module.

[0018] The nonlinear activation submodule is constructed by performing nonlinear processing on its input data using a nonlinear activation function. The input to the nonlinear activation submodule can be the input data of the Laplace kernel integral module, the output data of the frequency domain transform submodule, the output data of the linear transform submodule, or a combination of all three.

[0019] The aforementioned neural operator model specifically includes one or more Laplacian kernel integration modules. To improve the modeling capability of the neural operator model, in addition to the Laplacian kernel integration module, one or more feature mapping modules can be added to the neural operator model architecture. Each feature mapping module transforms, increases, or reduces the dimensionality of the data, and is constructed using one or more fully connected layers or convolutional layers.

[0020] The beneficial effects of this invention are:

[0021] The Laplace spectrum-based curing state prediction method for composite material parts proposed in this invention constructs a neural operator model based on the Laplace spectrum by solving the Laplace spectrum over the geometric domain of the composite material part. It can be applied to the curing state prediction of composite material parts of arbitrary shapes, providing an effective approach for the curing state prediction of composite material parts with complex geometries commonly used in engineering. The method can also be extended to other prediction tasks with similar scenarios. Attached Figure Description

[0022] Figure 1 This is a flowchart illustrating the implementation of the present invention.

[0023] Figure 2 This is a schematic diagram of the composite material part model, temperature field, and deformation field used in a specific embodiment of the present invention. Figure 2 'a' represents a composite material part model; Figure 2 b represents the temperature field of the composite material part; Figure 2 c represents the deformation field corresponding to the temperature field.

[0024] Figure 3 This is a temperature process curve diagram of a single insulation platform in an embodiment of the present invention.

[0025] Figure 4 This is a convergence graph of the training loss and test loss of the method described in the embodiments of the present invention.

[0026] Figure 5 This is a distribution map of the prediction error of the method on all grid nodes in all samples of the test set in a specific embodiment of the present invention. Detailed Implementation

[0027] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0028] like Figure 1-5 As shown.

[0029] This embodiment aims to address the following problem: Partial heat curing is an effective means of controlling the curing deformation of composite material parts. By applying different temperature fields to different regions of the composite material part, deformation caused by curing stress can be compensated. The predictive model of the temperature field to deformation field of the composite material part is the basis for optimizing the partial heat curing process. The composite material part model used in this embodiment is as follows: Figure 2 As shown in Figure a, considering the limitations of the curing process and actual needs, the inner and outer surfaces of the part are divided into 20 independent temperature-controlled zones. A set of temperature fields for composite material parts is shown below. Figure 2 As shown in b, the corresponding deformation field is as follows Figure 2 As shown in c.

[0030] Traditional physical model prediction methods offer high accuracy but suffer from low efficiency, making them unsuitable for extensive iterative optimization. Existing data-driven prediction methods cannot be applied to complex parts. Therefore, this embodiment will establish a prediction method based on the aforementioned approach. Figure 1 The model shown is a prediction model of the temperature field to deformation field of the part.

[0031] A method for predicting the curing state of composite material parts based on Laplace spectrum is proposed. By establishing a neural operator model based on Laplace spectrum, a curing state prediction model can be established for composite material parts of arbitrary shape.

[0032] Specifically, the following steps are included:

[0033] Step 1: Mesh the composite material part model.

[0034] In this embodiment, the composite material part model is divided into quadrilateral meshes using finite element analysis software. The resulting part model includes 8576 mesh nodes. Figure 2 As shown in a. The method does not limit the type of mesh created; triangular meshes, tetrahedral meshes, pentahedral meshes, hexahedral meshes, etc., are all acceptable.

[0035] Step 2: Define the corresponding Laplacian operator according to the mesh type, and solve for a set of Laplacian spectra Ψ that reflect the frequency domain information of the part's geometry.

[0036] Each mesh type has a strictly defined Laplace operator in differential geometry. After defining the Laplace operator for the geometric mesh, a set of Laplace spectra Ψ on the geometric domain of the part can be solved using the Galerkin method or the power method. The first k of the Laplace spectra can be retained as needed. m From the 1 mode, the Laplace spectral matrix is ​​obtained. in n x This is the number of mesh nodes in the part model. In this embodiment, nx =8576. Considering the complexity of three-dimensional parts, the first 128 modes of the Laplace spectrum are taken, i.e., k. m =128, then

[0037] Step 3: Obtain N sets of curing process data x i and each x i Curing state data of composite material parts y i .

[0038] The curing process data x i It refers to n on composite material parts m The curing process information at each grid node, including temperature process information or pressure process information, can be characterized by a finite number of parameters through parameterization or discretization. For example, the temperature process information of a single insulation platform can be represented by the initial temperature, heating time, insulation temperature, insulation time and cooling time.

[0039] The curing state data y of the composite material parts i This refers to the n on composite material parts during the curing process. m The curing state values ​​at each grid node, including temperature, degree of curing, stress, strain, stiffness, flexibility, and deformation, can be solved using the finite element method, finite difference method, or commercial simulation software, or obtained by monitoring during the curing experiment.

[0040] In this embodiment, the curing process information considers temperature process information, specifically, 20 independent temperature control zones each use different single-insulation temperature process curves (e.g., ...). Figure 3 As shown in the figure, the insulation temperature of all areas was randomly generated between 370K and 400K, while other parameters remained constant. A total of 300 sets of data were obtained, i.e., N=300. Therefore, each set of curing process data x i Specifically, the temperature and process information at 8576 mesh nodes on the composite material part is expressed in terms of insulation temperature. In each set of curing process data x i Below, the curing state data y of composite material parts are obtained through multiphysics simulation software. i Specifically, this refers to the deformation at 8576 mesh nodes on the composite material part.

[0041] Step 4: Construct a Laplace kernel integral module based on the Laplace spectrum Ψ, then establish a neural operator model, and finally use data samples {(x i ,y i By training the model parameters in the group (i = 1, ..., N), a prediction model for the curing state of composite material parts can be obtained.

[0042] The Laplace kernel integral module constructed based on the Laplace spectrum Ψ is specifically constructed by combining a frequency domain transformation submodule, a linear transformation submodule, or a nonlinear activation submodule, and the construction method is one of the following:

[0043] It contains only the frequency domain transform submodule;

[0044] It includes a frequency domain transformation submodule and a linear transformation submodule;

[0045] It includes a frequency domain transformation submodule and a nonlinear activation submodule;

[0046] It includes a frequency domain transformation submodule, a linear transformation submodule, and a nonlinear activation submodule.

[0047] The frequency domain transformation submodule includes three steps: encoding, parameterization, and decoding. Encoding uses the Laplace spectrum Ψ to map the input data of the Laplace kernel integral module from the original space to the frequency domain space, obtaining the coordinates of the input data in that spectrum. Parameterization is to perform linear or nonlinear transformation on the coordinates obtained after encoding. Decoding is to restore the coordinates obtained after parameterization to the original space based on the Laplace spectrum Ψ.

[0048] The linear transformation submodule performs a linear transformation on the input data of the Laplace kernel integral module, which can be achieved through matrix multiplication, fully connected neural networks, convolution operations, etc.

[0049] The aforementioned nonlinear activation submodule performs nonlinear processing on its input data using a nonlinear activation function. The input to the nonlinear activation submodule can be the input data of the Laplace kernel integral module, the output data of the frequency domain transform submodule, the output data of the linear transform submodule, or a combination of all three.

[0050] The aforementioned neural operator model specifically includes one or more Laplacian kernel integration modules. To improve the modeling capability of the neural operator model, in addition to the Laplacian kernel integration module, one or more feature mapping modules can be added to the neural operator model architecture. Each feature mapping module transforms, increases, or reduces the dimensionality of the data, and is constructed using one or more fully connected layers or convolutional layers.

[0051] The Laplace kernel integral module used in this embodiment includes a frequency domain transform submodule, a linear transform submodule, and a nonlinear activation submodule. Let the input data of the Laplace kernel integral module be... Output data is Linear transformation submodule W on A t A linear transformation can be expressed as: Convolution operations are used; the nonlinear activation submodule σ performs nonlinear processing on the results of the frequency domain transform submodule F and the linear transform W using a nonlinear activation function to obtain A. t+1 , can be represented as A t+1 =(W(A) t )+(A t The specific steps of the frequency domain transformation submodule D are as follows:

[0052] Encoding module E: Using the Laplace spectral matrix Φ to encode A t Projecting onto the frequency domain, the resulting coordinates in It is the pseudo-inverse of the Laplace spectral matrix Φ.

[0053] The parameterization module θ: performs a linear transformation on the encoded coordinates, denoted as Where the matrix Training is required; tensor operations are defined as follows:

[0054] Decoding module D: Restores the parameterized frequency domain features to the original function space, obtaining the output data of the frequency domain transform submodule, represented as...

[0055] In this embodiment, the established neural operator model is constructed by serially arranging one feature mapping module I, four Laplace kernel integration modules, and one feature mapping module O. The feature mapping module I processes the solidification process data. To increase the dimensionality, we obtain Here d v =32; then A 0i After passing through four Laplace kernel integral modules, we obtain... Feature mapping module O to A 4i Dimensionality reduction is performed to obtain the final output data, namely the predicted solidification state data. In this embodiment, feature mapping module I is implemented through a single fully connected neural network, and feature mapping module O is implemented through two fully connected neural networks.

[0056] Step 3 yielded 300 sets of curing process and curing state data for composite material parts. 200 sets were used as the training dataset, and the remaining 100 sets as the test dataset. The parameters of the established neural operator model were trained using gradient descent to minimize the loss function. The loss function is defined as follows:

[0057]

[0058] During training, the learning rate was set to 0.001, the batch size to 100, the number of iterations to 1000, and the optimizer to Adam. Figure 4 ab is the convergence plot of the training loss and test loss with the number of iterations. The method achieves a test loss of less than 1% after about 100 iterations. After training, the training loss is 0.060% and the test loss is 0.889%. Moreover, the maximum deformation prediction error of all nodes on all test samples is only 0.037mm. Figure 5 The prediction error distribution of all nodes on all samples in the test set is given. The prediction error distribution of the method shows a Gaussian distribution with an approximate mean of 0 and a prediction standard deviation of only 0.0164 mm. It can be seen that the method has the potential to achieve accurate prediction of the overall curing state of composite material parts in a uniform and comprehensive manner.

[0059] The parts not covered in this invention are the same as those in the prior art and are implemented using existing technologies.

Claims

1. A method for predicting the curing state of composite material parts based on Laplace spectroscopy, characterized in that, Includes the following steps: First, the composite material part model is meshed; Secondly, based on the mesh type, define the corresponding Laplacian operator and solve for a set of Laplacian spectra that reflect the frequency domain information of the part's geometry. ; Then, obtain Group curing process data and each Curing state data of composite material parts ; Ultimately, based on the Laplace spectrum Construct a Laplace kernel integral module, then establish a neural operator model, and finally use data samples. By training the model parameters, a prediction model for the curing state of composite material parts can be obtained. Based on Laplace spectrum The Laplace kernel integral module is constructed by combining frequency domain transformation submodules, linear transformation submodules, or nonlinear activation submodules; the construction of the frequency domain transformation submodule... Includes the following steps: Encoding: Using the Laplace spectrum The input data of the Laplace kernel integral module is mapped from the original space to the frequency domain space to obtain the coordinates of the input data in the spectrum. Parameterization: Performing linear or nonlinear transformations on the coordinates obtained after encoding; Decoding: Based on the Laplace spectrum The parameterized coordinates are then restored to their original space.

2. The method according to claim 1, characterized in that, The curing process data Refers to composite material parts The curing process information at each grid node, including temperature or pressure process information, can be characterized by a finite number of parameters through parameterization or discretization.

3. The method according to claim 1, characterized in that, Curing state data of the composite material parts It refers to the composite material parts during the curing process. The curing state values ​​at each grid node, including temperature, degree of curing, stress, strain, stiffness, flexibility, and deformation, are solved using the finite element method, finite difference method, or one of commercial simulation software, or obtained by monitoring during the curing experiment.

4. The method according to claim 1, characterized in that, The construction method is one of the following: It contains only the frequency domain transform submodule; It includes a frequency domain transformation submodule and a linear transformation submodule; It includes a frequency domain transformation submodule and a nonlinear activation submodule; It includes a frequency domain transformation submodule, a linear transformation submodule, and a nonlinear activation submodule.

5. The method according to claim 1, characterized in that, The establishment of the neural operator model specifically includes one or more Laplace kernel integral modules.

6. The method according to claim 4, characterized in that, The linear transformation submodule is constructed by performing a linear transformation on the input data of the Laplace kernel integral module.

7. The method according to claim 4, characterized in that, The nonlinear activation submodule is constructed by using a nonlinear activation function to perform nonlinear processing on the input data of the nonlinear activation submodule.

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