A method for thermo-chemical simulation of composite curing based on physical information neural network

Abstract

The application discloses a kind of based on physical information neural network's composite material curing thermal-chemical simulation method, constructs and constructs the attention mechanism and the multiscale network structure of composite material curing thermal-chemical coupling neural network, for extracting and fusing different scales temperature field and curing degree characteristics;Temperature field Fourier heat conduction control equation, curing degree phenomenological dynamics model and stress-strain relationship equation are embedded in the loss function of the coupling neural network, form comprehensive loss function, and the weight coefficient of physical equation is adjusted dynamically by curing progress, enhance the description ability of the coupling neural network to the coupling behavior of multiple physical fields in curing process;Improved AdamW optimization algorithm is used to train the coupling neural network combined with cosine annealing learning rate strategy;The coupling neural network is verified and optimized in actual production, and relative error and root mean square error index are introduced to evaluate the precision of neural network.

Description

Technical Field

[0001] This invention relates to a thermo-chemical simulation method for the curing of composite materials based on a physical information neural network. Background Technology

[0002] Early methods used neural networks to approximate predictions of composite material curing processes relied on large amounts of data for learning and prediction. Furthermore, obtaining suitable data samples was often difficult if the structure was changed, and prediction accuracy depended heavily on data accuracy, although computational efficiency was high. More recently, unsupervised learning combining physical information as a loss function with convolutional neural networks has been employed to simulate the thermo-chemical processes of composite material curing. This approach can accurately simulate the temperature and degree of curing at any given time and location. However, the point-to-point mapping method used in these networks results in lower computational efficiency compared to traditional finite element methods. Summary of the Invention

[0003] The present invention provides a thermo-chemical simulation method for the curing of composite materials based on physical information neural networks in order to solve the problems existing in the prior art.

[0004] The technical solutions adopted in this invention are as follows:

[0005] A thermo-chemical simulation method for composite material curing based on Physical Information Neural Network (PINN) includes the following steps:

[0006] S1: Construct a composite material curing thermo-chemical coupled neural network that includes an attention mechanism and a multi-scale network structure to extract and fuse temperature field and curing degree features at different scales;

[0007] S2: The Fourier heat conduction control equation of the temperature field, the phenomenological dynamic model of curing degree, and the stress-strain relationship equation are embedded into the loss function of the coupled neural network to form a comprehensive loss function. The weight coefficients of the physical equation are dynamically adjusted according to the curing progress to enhance the ability of the coupled neural network to describe the multi-physics coupling behavior of the curing process.

[0008] S3: The coupled neural network is trained using an improved AdamW optimization algorithm combined with a cosine annealing learning rate strategy;

[0009] S4: In actual production, the coupled neural network is verified and optimized, and relative error and root mean square error indices are introduced to evaluate the accuracy of the neural network.

[0010] 2. The thermo-chemical simulation method for composite material curing based on a physical information neural network as described in claim 1, characterized in that: in S1, the formula for calculating the attention weight in the attention mechanism is:

[0011]

[0012] Where: α i W represents the attention weight at position i. a and b a These are the weight matrix and bias term of the attention mechanism, respectively, used to learn the importance of features at different locations; f i Let be the feature vector at the i-th position, and n be the total number of feature vectors.

[0013] This formula calculates the weights of features at each location, enabling the network to automatically focus on key areas in the composite material curing process, thereby improving the model's ability to capture important physical phenomena.

[0014] Furthermore, in S1, within the multi-scale network structure, the formula for extracting the temperature field features at the k-th scale is:

[0015] T(k)=Conv scale-k (T input )

[0016] Among them, T (k) Represents the temperature field features extracted at the k-th scale, Conv scale-k The convolution operation at the k-th scale is used to extract temperature information at different scales; T input The input temperature field data;

[0017] The feature fusion formula is:

[0018]

[0019] Among them, T fuse and C fuse These represent the temperature field and curing degree characteristics after fusion, W k and b fuse represents the weight matrix and bias term of the fusion layer, used for weighted fusion of features at different scales; m represents the number of scales. Through multi-scale feature extraction and fusion, the complex physical phenomena in the curing process of composite materials can be more comprehensively characterized.

[0020] Furthermore, in S2, the comprehensive loss function is:

[0021]

[0022] in, This is the overall loss function; Loss due to the physical equations of the temperature field; For the phenomenological dynamics model loss of solidification degree; λ represents the loss in the stress-strain equation; λ is the weighting coefficient.

[0023] Furthermore, in S2, the formula for calculating the curing progress index is:

[0024]

[0025] Where C(x,t) is the degree of curing at position x and time t, C max V represents the maximum degree of curing, and V is the volume of the composite material.

[0026] The formula for dynamically adjusting the weighting coefficients is:

[0027]

[0028] Where λ(t) is the weighting coefficient at time t, λ0 is the initial weighting coefficient, and p max This represents the maximum curing progress.

[0029] By dynamically adjusting the weight coefficients of the physical equations, the composite material curing thermo-chemical coupled neural network can better adapt to the actual physical process at different curing stages, thereby improving the accuracy and efficiency of the simulation.

[0030] Furthermore, in S3, the improved AdamW optimization algorithm modifies the weight decay in the original AdamW optimization algorithm. The improved formula is:

[0031]

[0032] Among them, w t+1 w represents the model weights at time step t+1. t η represents the model weights at time step t; η is the learning rate, which controls the step size for parameter updates.

[0033] The gradient of the loss function indicates the direction of parameter updates; v t ∈ is the exponentially weighted average of the squared gradients, used for adaptively adjusting the learning rate; ∈ is the numerical stability term to prevent the denominator from being zero;

[0034] The learning rate adjustment formula is:

[0035]

[0036] Where, η t Let η be the learning rate at time step t. max is the maximum learning rate, and T is the learning rate adjustment period.

[0037] By improving the optimization algorithm, the training speed of the composite material curing thermo-chemical coupled neural network can be accelerated, and its convergence performance and generalization ability can be improved.

[0038] Furthermore, in S4, the formula for calculating the relative error index is as follows:

[0039]

[0040] Wherein, Relative Error is the relative error, which measures the relative deviation between the model's predicted value and the value calculated by the finite element method; y PINN yFEM represents the prediction result of the coupled neural network, while yFEM represents the calculation result of the finite element method.

[0041] The formula for calculating the root mean square error index is:

[0042]

[0043] Where RMSE is the root mean square error, used to evaluate the average difference between the model's predicted values ​​and the values ​​calculated by the finite element method; N is the number of data points, and y PINN,i and y FEM,i These are the predicted values ​​of the coupled neural network and the finite element method at the i-th data point, respectively.

[0044] By introducing multiple validation metrics, the accuracy and reliability of the composite material curing thermo-chemical coupled neural network can be evaluated more comprehensively, providing a strong basis for model optimization.

[0045] Furthermore, the expression for the kernel integral operator of the coupled neural network is:

[0046]

[0047] Wherein, the input function v of the i-th Fourier layer i (x, t) undergoes Fourier kernel integral transform It is then connected to the spatial convolution operator W, and after passing through the activation function σ, the output function v of the i-th Fourier layer is obtained. i+1 (x, t).

[0048] The present invention has the following beneficial effects:

[0049] This patented technology innovatively improves simulation accuracy and efficiency by integrating physical information neural networks with composite material curing simulation. Through dynamic adjustment of weight coefficients and the introduction of multiple verification indicators, it accurately simulates the curing process, ensuring reliable results. Improved optimization algorithms and efficient network structures enhance computational efficiency, meeting practical production needs. Multi-scale network structures and dynamic weight adjustments comprehensively consider multi-physics coupling behavior, adapting to different process conditions. Attached Figure Description

[0050] Figure 1 This paper compares the finite element method of the center point of the 10mm laminate of the present invention with the temperature and curing degree of PINN.

[0051] Figure 2This is a comparison of the finite element method and PINN calculation results for the 10mm laminate of this invention.

[0052] Figure 3 This paper compares the finite element method of the center point of the 20mm laminate of this invention with the temperature and curing degree of PINN.

[0053] Figure 4 This is a comparison of the finite element method and PINN calculation results for the 20mm laminate of this invention.

[0054] Figure 5 This paper compares the finite element method of the center point of the 30mm laminate of the present invention with the temperature and curing degree of PINN.

[0055] Figure 6 This is a comparison of the finite element method and PINN calculation results for the 30mm laminate of this invention. Detailed Implementation

[0056] The invention will now be further described with reference to the accompanying drawings.

[0057] This invention discloses a thermo-chemical simulation method for the curing of composite materials based on a Physical Information Neural Network (PINN), comprising the following steps:

[0058] S1: Construct a composite material curing thermo-chemical coupled neural network that includes an attention mechanism and a multi-scale network structure to extract and fuse temperature field and curing degree features at different scales;

[0059] S2: The Fourier heat conduction control equation of the temperature field, the phenomenological dynamic model of curing degree, and the stress-strain relationship equation are embedded into the loss function of the coupled neural network to form a comprehensive loss function. The weight coefficients of the physical equation are dynamically adjusted according to the curing progress to enhance the ability of the coupled neural network to describe the multi-physics coupling behavior of the curing process.

[0060] S3: The coupled neural network is trained using an improved AdamW optimization algorithm combined with a cosine annealing learning rate strategy;

[0061] S4: In actual production, the coupled neural network is verified and optimized, and relative error and root mean square error indices are introduced to evaluate the accuracy of the neural network.

[0062] In S1, the formula for calculating attention weights in the attention mechanism is:

[0063]

[0064] Where: α i W represents the attention weight at position i. a and b a These are the weight matrix and bias term of the attention mechanism, respectively, used to learn the importance of features at different locations; fi Let be the feature vector at the i-th position, and n be the total number of feature vectors.

[0065] This formula calculates the weights of features at each location, enabling the network to automatically focus on key areas in the composite material curing process, thereby improving the model's ability to capture important physical phenomena.

[0066] In a multi-scale network structure, the formula for extracting temperature field features at the k-th scale is:

[0067] T (k) =Conv scale-k (T input )

[0068] Among them, T (k) Represents the temperature field features extracted at the k-th scale, Conv scale-k The convolution operation at the k-th scale is used to extract temperature information at different scales; T input The input temperature field data;

[0069] The feature fusion formula is:

[0070]

[0071] Among them, T fuse and C fuse These represent the temperature field and curing degree characteristics after fusion, W k and b fuse represents the weight matrix and bias term of the fusion layer, used for weighted fusion of features at different scales; m represents the number of scales. Through multi-scale feature extraction and fusion, the complex physical phenomena in the curing process of composite materials can be more comprehensively characterized.

[0072] In S2, the comprehensive loss function is:

[0073]

[0074] in, This is the overall loss function; Loss due to the physical equations of the temperature field; For the phenomenological dynamics model loss of solidification degree; λ represents the loss in the stress-strain equation; λ is the weighting coefficient.

[0075] The formula for calculating the curing progress index is:

[0076]

[0077] Where C(x,t) is the degree of curing at position x and time t, C max V represents the maximum degree of curing, and V is the volume of the composite material.

[0078] The formula for dynamically adjusting the weighting coefficients is:

[0079]

[0080] Where λ(t) is the weighting coefficient at time t, λ0 is the initial weighting coefficient, and p max To maximize the curing progress, the weighting coefficients of the physical equations are dynamically adjusted so that the composite material curing thermo-chemical coupled neural network can better adapt to the actual physical process at different curing stages, thereby improving the accuracy and efficiency of the simulation.

[0081] The expression for the kernel integral operator of the coupled neural network is:

[0082]

[0083] Wherein, the input function v of the i-th Fourier layer i (x, t) undergoes Fourier kernel integral transform It is then connected to the spatial convolution operator W, and after passing through the activation function σ, the output function v of the i-th Fourier layer is obtained. i+1 (x, t).

[0084] By employing a kernel integral operator to perform Fast Fourier Transform, low-frequency filtering, linear transformation, Inverse Fast Fourier Transform, and nonlinear activation on the curing process temperature, the output of the temperature and degree of curing at any given moment within the composite material is obtained, thus achieving function-to-function mapping. Compared to point-to-point mapping, using the kernel integral operator to calculate the curing of composite materials improves efficiency by more than 10 times.

[0085] In S3, the improved AdamW optimization algorithm modifies the weight decay in the original AdamW optimization algorithm. The improved formula is:

[0086]

[0087] Among them, w t+1 w represents the model weights at time step t+1. t η represents the model weights at time step t; η is the learning rate, which controls the step size for parameter updates.

[0088] The gradient of the loss function indicates the direction of parameter updates; v t ∈ is the exponentially weighted average of the squared gradients, used for adaptively adjusting the learning rate; ∈ is the numerical stability term to prevent the denominator from being zero;

[0089] The learning rate adjustment formula is:

[0090]

[0091] Where, η t Let η be the learning rate at time step t. max is the maximum learning rate, and T is the learning rate adjustment period.

[0092] By improving the optimization algorithm, the training speed of the composite material curing thermo-chemical coupled neural network can be accelerated, and its convergence performance and generalization ability can be improved.

[0093] In S4, the formula for calculating the relative error index is as follows:

[0094]

[0095] Wherein, Relative Error is the relative error, which measures the relative deviation between the model's predicted value and the value calculated by the finite element method; y PINN yFEM represents the prediction result of the coupled neural network, while yFEM represents the calculation result of the finite element method.

[0096] The formula for calculating the root mean square error index is:

[0097]

[0098] Where RMSE is the root mean square error, used to evaluate the average difference between the model's predicted values ​​and the values ​​calculated by the finite element method; N is the number of data points, and y PINN,i and y FEM,i These represent the predicted values ​​of the coupled neural network and the finite element method at the i-th data point, respectively. By introducing multiple validation metrics, the accuracy and reliability of the coupled neural network for composite material curing thermo-chemical processes can be more comprehensively evaluated, providing a strong basis for model optimization.

[0099] Figures 1 to 6 Models with three different thicknesses of 10mm, 20mm, and 30mm were built. The comparison shows that the accuracy is excellent and the computational efficiency is higher than that of the finite element method.

[0100] The above description is only a preferred embodiment of the present invention. It should be noted that those skilled in the art can make several improvements without departing from the principle of the present invention, and these improvements should also be considered within the scope of protection of the present invention.

Claims

1. A thermo-chemical simulation method for composite material curing based on physical information neural networks, characterized in that: Includes the following steps: S1: Construct a composite material curing thermo-chemical coupled neural network that includes an attention mechanism and a multi-scale network structure to extract and fuse temperature field and curing degree features at different scales; S2: The Fourier heat conduction control equation of the temperature field, the phenomenological dynamic model of curing degree, and the stress-strain relationship equation are embedded into the loss function of the coupled neural network to form a comprehensive loss function. The weight coefficients of the physical equation are dynamically adjusted according to the curing progress to enhance the ability of the coupled neural network to describe the multi-physics coupling behavior of the curing process. S3: The coupled neural network is trained using an improved AdamW optimization algorithm combined with a cosine annealing learning rate strategy; S4: In actual production, the coupled neural network is verified and optimized, and relative error and root mean square error indices are introduced to evaluate the accuracy of the neural network.

2. The thermo-chemical simulation method for composite material curing based on physical information neural networks as described in claim 1, characterized in that: In S1, the formula for calculating attention weights in the attention mechanism is: ， Where: α i W represents the attention weight at position i. a and b a These are the weight matrix and bias term of the attention mechanism, respectively, used to learn the importance of features at different locations; f i Let be the feature vector at the i-th position, and n be the total number of feature vectors.

3. The thermo-chemical simulation method for composite material curing based on physical information neural networks as described in claim 1, characterized in that: In S1, within the multi-scale network structure, the formula for extracting the temperature field features at the k-th scale is: ， Among them, T (k) Represents the temperature field features extracted at the k-th scale, Conv scale−k The convolution operation at the k-th scale is used to extract temperature information at different scales; T input The input temperature field data; The feature fusion formula is: ， Among them, T fuse and C fuse These represent the temperature field and curing degree characteristics after fusion, W k and b fuse represents the weight matrix and bias term of the fusion layer, used for weighted fusion of features at different scales; m is the number of scales.

4. The thermo-chemical simulation method for composite material curing based on physical information neural networks as described in claim 1, characterized in that: In S2, the comprehensive loss function is: ， in, This is the overall loss function; Loss due to the physical equations of the temperature field; For the phenomenological dynamics model loss of solidification degree; λ represents the loss in the stress-strain equation; λ is the weighting coefficient.

5. The thermo-chemical simulation method for composite material curing based on physical information neural networks as described in claim 4, characterized in that: In S2, the formula for calculating the curing progress index is: ， Where C(x,t) is the degree of curing at position x and time t, C max V represents the maximum degree of curing, and V is the volume of the composite material. The formula for dynamically adjusting the weighting coefficients is: ， Where λ(t) is the weighting coefficient at time t, λ0 is the initial weighting coefficient, and p max This represents the maximum curing progress.

6. The thermo-chemical simulation method for composite material curing based on physical information neural networks as described in claim 5, characterized in that: In S3, the improved AdamW optimization algorithm modifies the weight decay in the original AdamW optimization algorithm. The improved formula is: ， Among them, w t+1 w represents the model weights at time step t+1. t η represents the model weights at time step t; η is the learning rate, which controls the step size for parameter updates. v is the gradient of the loss function; t ϵ is the exponentially weighted average of the squared gradients; ϵ is the numerical stability term. The learning rate adjustment formula is: ， Where, η t Let η be the learning rate at time step t. max is the maximum learning rate, and T is the learning rate adjustment period.

7. The thermo-chemical simulation method for composite material curing based on physical information neural networks as described in claim 5, characterized in that: In S4, the formula for calculating the relative error index is as follows: ， Where, Relative Error is the relative error; y PINN yFEM represents the prediction result of the coupled neural network, while yFEM represents the calculation result of the finite element method. The formula for calculating the root mean square error index is: ， Where RMSE is the root mean square error; N is the number of data points, and y PINN,i and y FEM,i These are the predicted values ​​of the coupled neural network and the finite element method at the i-th data point, respectively.

8. The thermo-chemical simulation method for composite material curing based on physical information neural networks as described in claim 1, characterized in that: The expression for the kernel integral operator of the coupled neural network is: ， Wherein, the input function of the i-th Fourier layer After Fourier kernel integral transform It is connected to the spatial convolution operator W, and after passing through the activation function σ, the output function of the i-th Fourier layer is obtained. .

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