Microcosmic physical field prediction method based on improved convolutional neural network

Abstract

The invention discloses a microscopic physical field prediction method based on an improved convolutional neural network, and the method comprises the following steps: S1, collecting the microscopic geometric structure and physical field data of a composite component, dividing the data into a training data set, a verification data set and a test data set, and carrying out the preprocessing; s2, constructing an improved convolutional neural network model; s3, taking the training data set in the microscopic geometric structure and the physical field of the composite material component in the step S1 as input and output data of the model in the step S2, and training the improved convolutional neural network model to obtain a trained improved convolutional neural network model; and S4, performing performance evaluation on the trained improved convolutional neural network model by adopting the verification data set, and putting the microscopic geometric structure in the test data set into the model trained in the step S3 to realize rapid and accurate prediction of the microscopic physical field. According to the invention, the efficiency and accuracy of microcosmic physical field prediction are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of microphysical field prediction, and particularly to a microphysical field prediction method based on an improved convolutional neural network. Background Art

[0002] Composite components are widely used in various fields due to their excellent mechanical properties and versatility. With the increasingly complex operating conditions and performance requirements faced by composite structures, it is crucial to improve material properties and optimize mechanical structures. To predict the local mechanical response in the microscopic state, nonlinear analysis is required to determine the key physical fields in the microstructure under external loads. Therefore, the analysis and prediction of physical fields are of great significance for evaluating the effectiveness of computational analysis and improving the mechanical properties of composite structures. However, the nonlinear analysis of stress fields mainly relies on analytical or numerical methods. And the finite element analysis method requires constructing material properties, geometric structures, boundary conditions, and load conditions, and for refined models, it consumes a large amount of computational resources and is not suitable for real-time monitoring situations. Therefore, an alternative method that combines high efficiency and high precision can quickly predict the physical field distribution in the composite microstructure under complex loading conditions and reduce the dependence on traditional analysis methods. Summary of the Invention

[0003] To solve the above technical problems, the purpose of the present invention is to provide a microphysical field prediction method based on an improved convolutional neural network, including the following steps: S1. Collect the microscopic geometric structure and physical field data of composite components, divide them into training data sets, validation data sets, and test data sets, and perform preprocessing; S2. Construct an improved convolutional neural network model; S3. Use the training data sets of the microscopic geometric structure and physical field in step S1 as the input and output data of the model in step S2, and train the improved convolutional neural network model to obtain a trained improved convolutional neural network model; S4. Use the validation data set to evaluate the performance of the trained improved convolutional neural network model, and put the microscopic geometric structure in the test data set into the model trained in step S3 to achieve fast and accurate prediction of the microphysical field.

[0004] Further, the specific operation process of step S1 is as follows: S11. In finite element analysis, automatically generate the microscopic geometric structure according to the actual microscopic morphology for numerical simulation; S12. Add boundary conditions to the microscopic geometric structure and use the finite element method to obtain the corresponding physical field; S13. Divide the collected corresponding input and output data into a training data set, a validation data set, and a test data set according to the ratio of 7:2:1; S14. Perform min-max normalization on the corresponding inputs and outputs in the training data set and the validation data set, and perform min-max normalization on the inputs in the test data set to obtain the processed corresponding data; S15. Use the normalized data as the new training data set, validation data set, and test data set for training, validating, and testing the model.

[0005] Furthermore, the formula for the normalization process in step S14 is as follows: , where, m and n represent the length and width of the input and output matrices respectively, c represents the number of physical fields to be predicted, represents the normalized value, represents the original value, represents the maximum value under each physical field component, represents the minimum value under each physical field component.

[0006] Furthermore, step S2 includes the following steps: S21. Introduce a residual structure in each convolutional block of the conventional convolutional model encoder. The formula for the residual structure is as follows: , where, x represents the input image information, which is a feature map, represents the weight parameters of the convolutional layer, represents the output after processing through several convolutional layers and non-linear activation functions, y represents the output after residual connection; S22. Incorporate a multi-head self-attention mechanism in the transition region of the model. The formula for the multi-head self-attention mechanism is as follows: , where, Q represents the query vector, K represents the key matrix, represents the transpose of the key matrix, V represents the value vector, represents the scaling factor used to avoid gradient vanishing caused by excessive dot products, represents the learnable parameter, represents the learnable parameter, represents the learnable parameter, Denote the output weights, head1 represents the first attention subspace, head2 represents the second attention subspace, and head3 represents the third attention subspace; S23. Construct a decoder in the model. In the convolutional block of the decoder, introduce a residual structure to reconstruct the extracted main information into the corresponding microphysical field; S24. Perform Xavier uniform initialization on the trainable weights in the model to obtain an improved convolutional neural network model. The Xavier uniform initialization formula is as follows: , where, represents the weight connecting the i th input and the j th output, represents a value uniformly randomly drawn from the interval [a, b], represents the number of input nodes in the current layer, represents the number of output nodes in the current layer.

[0007] Furthermore, the step S3 includes the following steps: S31. Construct a mean absolute error (MAE) loss function, and the formula is as follows: , where, M represents the size of the input and output matrices, represents the predicted value at the corresponding matrix position, represents the true value at the corresponding matrix position, m and n respectively represent the length and width of the input and output matrices; S32. Determine the Adaptive Moment Estimation (Adam) as the optimizer for training the model, and adopt a dynamic learning rate to make the loss value converge to the lowest point; The Adam optimizer formula is as follows: First-order moment estimation: , Bias correction: , Update parameters: , where, represents the gradient at time step t , represents the momentum decay coefficient (default is about 0.9), represents the second-order decay coefficient (default is about 0.999), represents the momentum of the gradient, represents the weighted average of the square of the gradient, and respectively represent at the t-th iteration and value, is the learning rate, is a constant used to prevent the denominator from being zero, represents the parameters of the model at the t th iteration, represents the parameters of the model at the t ([th] + 1)th iteration; S33. Use the micro - geometric structure and the corresponding physical field of the pre - processed training data set as input and output data respectively and put them into the improved model for training, and adopt dynamic loss change. The initial learning rate is set to 0.001, the scaling factor is 0.1, and the patience value is 4. That is, if the validation loss does not continuously decrease in 4 consecutive epochs, the learning rate will be dynamically reduced by a scaling factor of 0.1.

[0008] Furthermore, step S4 includes the following steps: S41. Evaluate the performance of the trained model using the validation data set, and evaluate the accuracy of the model using the fitting degree, SSIM and PSNR metrics; S42. Input the micro - geometric structure in the test data set into the model to predict the physical field, and compare the physical field predicted by the model with the finite - element method using the relative error.

[0009] The beneficial effects of the present invention are as follows: By combining the residual structure and the multi - head self - attention mechanism in the traditional convolutional neural network model, the accuracy of micro - physical field prediction is significantly improved, and problems such as low computational efficiency of analyzing micro - physical fields by the traditional finite - element method are avoided; at the same time, the multi - head self - attention mechanism enhances the model's ability to capture key features of the micro - structure, improves the prediction accuracy of complex physical fields, and the introduction of the residual structure effectively alleviates the gradient disappearance problem of deep networks, improves the training stability and generalization ability of the model, enabling it to adapt to the prediction requirements of randomly changing micro - structure physical fields; in addition, the model's convergence performance is further optimized through data normalization and dynamic learning rate adjustment strategies, making it more stable during training and avoiding over - fitting or under - fitting; at the same time, this method adopts an end - to - end deep - learning framework, realizing the full - process intelligent processing from micro - geometric structure input to physical field prediction output, making the whole prediction process more efficient. This integrated modeling method simplifies the complex intermediate processing in traditional methods, significantly improves the overall performance and usability of the prediction system; using multiple evaluation metrics and relative error analysis ensures the consistency between the model prediction results and the finite - element method, verifies the reliability and practicability of the method, and provides an efficient computational tool for material design, performance optimization and engineering applications. Description of the Drawings

[0010] Figure 1 is the flowchart of the method of the present invention; Figure 2 is the structural diagram of the improved convolutional neural network model; Figure 3 is the comparison diagram of the prediction of the microscopic physical field of the fiber composite material. Specific implementation manners

[0011] Next, the technical solutions in the embodiments of the present invention will be described with reference to the accompanying drawings in the embodiments of the present invention.

[0012] As Figure 1 shown, the method includes the following steps: S1. Collect the microscopic geometric structure and physical field data of the composite material component, divide it into a training data set, a validation data set, and a test data set, and perform preprocessing; The specific operation process of step S1 is: S11. In finite element analysis, automatically generate the microscopic geometric structure according to the actual microscopic morphology for numerical simulation; S12. Add boundary conditions to the microscopic geometric structure, and use the finite element method to obtain the corresponding physical field; S13. Divide the collected corresponding input and output data into a training data set, a validation data set, and a test data set according to the ratio of 7:2:1; S14. Perform maximum-minimum normalization on the corresponding inputs and outputs in the training data set and the validation data set, and perform maximum-minimum normalization on the inputs in the test data set to obtain the processed corresponding data; The formula for the normalization process in step S14 is as follows: , where m and n respectively represent the lengths and widths of the input and output matrices, c represents the number of physical fields to be predicted, represents the normalized value, represents the original value, represents the maximum value under each physical field component, represents the minimum value under each physical field component.

[0013] S15. Use the normalized image data as the new training data set, validation data set, and test data set for training, validating, and testing the model.

[0014] S2. Construct an improved convolutional neural network model; The specific operation process of step S2 is: According to Figure 2Describe in detail the improved convolutional neural network model in steps S21, S22, and S23: The constructed improved convolutional neural network model has the following specific structure Figure 2 as shown. The model structure is mainly divided into three parts: an encoding region, a transition region, and a decoding region. The specific implementation of each region is as follows: In the encoding region, after the preprocessing is completed, the data is put into the model according to the structure of the model input, and the number of input channels can be adjusted according to the task requirements. In each layer of the encoding region, there are 2 convolutional modules with 3×3 convolutional kernels and 2 ReLU activation functions. Subsequently, a 2×2 max pooling layer is used for feature downsampling, and a residual connection is incorporated into each layer, connecting the features in the first convolutional block of each layer to the max pooling part.

[0015] The formula of the ReLU activation function is as follows:

[0016] where, when x > 0, the output is x ; when x ≤ 0, the output is 0.

[0017] The formula of the residual structure is as follows: , where, x represents the input image information, which is a feature map, represents the weight parameters of the convolutional layer, represents the output after being processed by several convolutional layers and non-linear activation functions, y represents the output after the residual connection; Taking the last layer in the encoding region as an example, the running method is specifically explained. Without changing the number of channels, through 2×2 max pooling, the length and width are changed to half of the original, and the number of channels remains 128. Subsequently, through 2 convolutional kernels of 3×3 and 2 ReLU activation functions, the number of channels becomes 256. Finally, during the max pooling process, part of the features from the first convolutional block are received through the residual connection.

[0018] In the transition region, the processed features are subjected to max pooling operations and convolutional operations, and the number of channels becomes 256. Subsequently, through 8 consecutive attention layers, each attention layer includes a normalization layer and a multi-head attention mechanism. To prevent the features from being diluted during transmission, the features are extracted from the input part and combined with the output part. Before each attention layer, the position information of the features needs to be encoded. After 8 attention layers, the number of channels of the features becomes 512, and convolutional operations are performed to further extract the main features.

[0019] The position information encoding formula is as follows:

[0020] where pos represents the current position index, i represents the index of half of the current dimension, represents the total number of dimensions of the feature vector, and the constant 10000 represents an empirically set base number.

[0021] The formula for the normalization layer is as follows:

[0022] where, represents the mean on the feature dimension, represents the variance on the feature dimension, represents the learnable scaling factor for the i th dimension, represents the learnable offset factor for the i th dimension, represents the i th feature dimension of the input, represents a small constant to prevent division by zero.

[0023] The formula for multi-head self-attention is as follows: , where, Q represents the query vector, K represents the key matrix, represents the transpose of the key matrix, V represents the value vector, represents the scaling factor used to avoid vanishing gradients caused by overly large dot products, represents the learnable parameter, represents the learnable parameter, represents the learnable parameter, represents the output weight, head1 represents the first attention subspace, head2 represents the second attention subspace, and head3 represents the third attention subspace; In the decoding region, the features processed in the transition region are reconstructed. In each layer of the decoding region, there are two convolutional modules with 3×3 convolutional kernels and two ReLU activation functions. Subsequently, 2×2 transposed convolution is used for upsampling the features, and a residual connection is incorporated in each layer, connecting the features in the first convolutional block of each layer to the transposed convolution part (except for the last layer). After performing the corresponding operations, reconstruction needs to be carried out according to the specific requirements of the output. For the last convolutional operation, a linear activation function is used to convert the number of channels according to the specific requirements of the task.

[0024] The formula for the linear activation function is as follows:

[0025] Among them, W represents the weight of the convolutional kernel, x represents the input feature map, b represents the bias term, and * represents the convolution operation.

[0026] Taking the last layer in the decoding region as an example, the operation mode is specifically described. Without changing the number of channels, through a 2×2 transposed convolution operation, the length and width are halved, and the number of channels remains 64. Subsequently, through two 3×3 convolutional kernels and two ReLU activation functions, the number of channels becomes 64. A linear activation function is used to change the number of channels to the number of channels required for the specific task. In the last convolution process, part of the features from the first convolutional block are received through the residual connection. In the encoding region and the decoding region, the corresponding convolutional blocks are connected through skip connections to retain certain features during the convolution process.

[0027] S24. Perform Xavier uniform initialization on the trainable weights in the model to obtain the improved convolutional neural network model. The Xavier uniform initialization formula is as follows: , Among them, represents the weight connecting the i th input and the j th output, represents a value uniformly randomly drawn from the interval [a, b], represents the number of input nodes in the current layer, represents the number of output nodes in the current layer.

[0028] S3. Use the training data set of the microscopic geometric structure and physical field of the composite material component in step S1 as the input and output data of the model in step S2, and train the improved convolutional neural network model to obtain the trained improved convolutional neural network model; The specific operation process of step S3 is as follows: S31. Construct the Mean Absolute Error (MAE) loss function, the formula is as follows: , where, M represents the size of the input and output matrices, represents the predicted value at the corresponding matrix position, represents the true value at the corresponding matrix position, m and n represent the length and width of the input and output matrices respectively; S32. Determine the Adaptive Moment Estimation (Adam) as the optimizer for the training model, and adopt a dynamic learning rate to make the loss value converge to the lowest point; the formula of the Adam optimizer is as follows: First-order moment estimation: , Bias correction: , Update parameters: , where, represents the gradient at time step t , represents the momentum decay coefficient (default is about 0.9), represents the second-order decay coefficient (default is about 0.999), represents the momentum of the gradient, represents the weighted average of the square of the gradient, and represent the values of and at the t-th iteration respectively, is the learning rate, is a constant used to prevent the denominator from being zero, represents the parameters of the model at the t -th iteration, represents the parameters of the model at the t +1-th iteration; S33. Put the micro-geometric structure and the corresponding physical field of the preprocessed training dataset into the improved model as input and output data respectively for training, and adopt dynamic loss variation. The initial learning rate is set to 0.001, the scaling factor is 0.1, and the patience value is 4. That is, if the validation loss does not continuously decrease in 4 consecutive epochs, the learning rate will be dynamically reduced by a factor of 0.1.

[0029] S4. Use the validation dataset to evaluate the performance of the trained improved convolutional neural network model. Put the micro-geometric structure in the test dataset into the model trained in step S3 to achieve fast and accurate prediction of the micro-physical field.

[0030] The specific operation process of step S4 is as follows: S41. Evaluate the performance of the trained model using the validation dataset, and evaluate the accuracy of the model using the fitting degree, SSIM, and PSNR metrics; S42. Input the microscopic geometric structure in the test dataset into the model to predict the physical field, and compare the physical field predicted by the finite element method with that of the model using the relative error.

[0031] According to the above steps, taking the representative unit volume of fiber composite materials as an example, an improved convolutional neural network model is used to realize the prediction of the physical field. According to the fiber random distribution and random volume fraction algorithm, a random fiber microscopic geometric structure is created in the CAE software, boundary conditions are applied to it, and the corresponding equivalent stress distribution is obtained by the finite element analysis method. The equivalent stress field of the microscopic geometric structure is directly predicted using the pre-trained structure. To compare the accuracy of this method in predicting the physical field, the results of the traditional encoding-decoding model and the improved convolutional model are compared. As Figure 3 shown, compared with the finite element method, the average relative error of the improved convolutional model is 0.6%. Compared with the finite element method, the average relative error of the traditional encoding-decoding model is 1.3%. And it can be shown by Figure 3 that the relative error of this method is below that of the traditional encoding-decoding model.

[0032] In terms of computational efficiency, it takes 1 - 2 minutes for the finite element method to analyze a microscopic geometric structure, excluding the time for microscopic geometric structure modeling and boundary condition application, while the convolutional model prediction only takes 0.2 seconds to complete. This is particularly crucial when analyzing a large number of samples. For example, when 1000 randomly analyzed microscopic geometric structure samples need to be analyzed, the finite element method requires 1000 - 2000 minutes, while the improved convolutional model only requires 200 seconds, greatly improving the analysis efficiency.

Claims

1. A method for predicting microphysical fields based on an improved convolutional neural network, characterized in that It includes the following steps: S1. Collect the micro-geometric structure and physical field data of composite material components, divide them into training data set, validation data set and test data set, and perform preprocessing; S2. Build an improved convolutional neural network model; S3. Use the training data set of the micro-geometric structure and physical field in step S1 as the input and output data of the model in step S2, train the improved convolutional neural network model, and obtain the trained improved convolutional neural network model; S4. Use the validation data set to evaluate the performance of the trained improved convolutional neural network model, put the micro-geometric structure in the test data set into the model trained in step S3, and realize the fast and accurate prediction of the micro-physical field.

2. The microphysical field prediction method based on an improved convolutional neural network according to claim 1, characterized in that The specific operation process of step S1 is as follows: S11. In finite element analysis, automatically generate the micro-geometric structure according to the actual micro-topography for numerical simulation; S12. Add boundary conditions to the micro-geometric structure, and use the finite element method to obtain the corresponding physical field; S13. Divide the collected corresponding input and output data into training data set, validation data set and test data set according to the ratio of 7:2:1; S14. Perform max-min normalization on the corresponding input and output in the training data set and validation data set, and perform max-min normalization on the input in the test data set to obtain the processed corresponding data; S15. Use the normalized data as the new training data set, validation data set and test data set for training, validating and testing the model.

3. The microphysical field prediction method based on an improved convolutional neural network according to claim 1, wherein Step S2 includes the following steps: S21. Introduce a residual structure into each convolutional block in the encoder of the conventional convolutional model; S22. Combine the multi-head self-attention mechanism in the transition area of the model; S23. Build a decoder in the model, introduce a residual structure in the convolutional block of the decoder, and reconstruct the extracted main information into the corresponding micro-physical field; S24. Perform Xavier uniform initialization on the trainable weights in the model to obtain the improved convolutional neural network model.

4. The microphysical field prediction method based on an improved convolutional neural network according to claim 1, characterized in that The said step S3 includes the following steps: S31. Build a mean absolute error MAE loss function; S32. Determine the adaptive moment estimation Adam as the optimizer for training the model, and use a dynamic learning rate to make the loss value converge to the lowest point; S33. Put the micro-geometric structure and the corresponding physical field of the preprocessed training data set into the improved model as input and output data respectively for training, and use dynamic loss change, set the initial learning rate to 0.001, the scaling factor to 0.1, and the patience value to 4, that is, if the validation loss does not continuously decrease in 4 consecutive rounds, the learning rate will be dynamically reduced by a scaling factor of 0.

1.

5. The microphysical field prediction method based on an improved convolutional neural network according to claim 1, characterized in that Step S4 includes the following steps: S41. Use the validation data set to evaluate the performance of the trained model, and use the fitting degree, SSIM and PSNR indicators to evaluate the accuracy of the model; S42. Input the micro-geometric structure in the test data set into the model to predict the physical field, and use the relative error to compare the physical field predicted by the finite element method and the model.

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