A data-driven resin-based composite curing reaction rate prediction method

Abstract

The application discloses a data-driven resin-based composite material curing reaction rate prediction method, relates to the fields of data processing and composite material curing, and is based on existing resin-based composite material C1 non-isothermal curing test data to construct a DNN model as a pre-training curing reaction model; a new resin-based composite material C2 non-isothermal curing test is carried out to obtain new sample data; the new sample data is divided into a training set and a test set based on downsampling and stratified sampling; the pre-training curing reaction model is fine-tuned and trained by using the training set, the fine-tuned curing reaction model is tested, evaluated and optimized by using the test set, and the optimized curing reaction model is used for predicting the curing reaction rate of the new resin-based composite material C2. The application has good generalization ability and can adapt to different resin systems and test conditions.

Description

Technical Field

[0001] This invention relates to the fields of data processing and composite material curing technology, and in particular to a data-driven method for predicting the curing reaction rate of resin-based composite materials. Background Technology

[0002] Resin-based composite materials are widely used in aerospace, automotive manufacturing, and rail transportation due to their high specific strength and stiffness, corrosion resistance, and fatigue resistance. The manufacturing of resin-based composite materials involves a series of heating and pressurizing processes, known as curing, which involves complex physical changes and thermochemical reactions, such as the cross-linking polymerization of polymer resins, thermal effects, and curing shrinkage. These processes can cause temperature gradients within the material, uneven distribution of curing degree, and localized residual stress, affecting the shape, dimensional accuracy, and mechanical properties of the cured composite components. When conducting research on fiber and resin material selection, modification, compatibility, and process optimization, extensive experiments are often required to determine the curing behavior of the composite material for further investigation.

[0003] Currently, the curing process of resin-based composites is mainly described parametrically using curing reaction kinetic equations. However, different fiber and resin combinations require separate experiments to select appropriate curing kinetic models, fit experimental data to determine model parameters, and predict the curing reaction rate. These models are typically only applicable to specific resin systems and experimental conditions, making them difficult to generalize and lacking in nonlinearity capture capabilities. The parameter fitting analysis process is complex, and the amount of experimental data obtained for different material systems is fixed and independent. Therefore, a large amount of experimental data and computational resources are often required, significantly hindering research progress in material selection, modification, and compatibility during the early stages of development. Summary of the Invention

[0004] To overcome the shortcomings of the prior art, this invention provides a data-driven method for predicting the curing reaction rate of resin-based composite materials. Based on deep neural networks, it efficiently and accurately captures the complex nonlinear relationships in the experimental data of resin-based composite materials, realizes non-parametric prediction of the curing reaction rate of resin-based composite materials, and updates the existing pre-trained curing reaction model based on limited new experimental data of resin-based composite materials. It has good generalization ability and can adapt to different resin systems and experimental conditions.

[0005] To achieve the above objectives, the present invention adopts the following technical solution, including: A data-driven method for predicting the curing reaction rate of resin-based composite materials includes the following steps: S1. The resin-based composite material C1 was subjected to a non-isothermal curing test using differential scanning calorimetry to obtain the curing heat flow curve of C1. Based on the curing heat flow curve of C1, the degree of curing and curing reaction rate of C1 during the non-isothermal curing process were obtained. The temperature, degree of curing and curing reaction rate of C1 during the non-isothermal curing process were used as sample data. S2, use sample data to train a deep neural network model. The model is used to predict the curing reaction rate based on the degree of curing and temperature in the non-isothermal curing process. The trained deep neural network model is the pre-trained curing reaction model. S3. The new resin-based composite material C2 was subjected to a non-isothermal curing test using differential scanning calorimetry to obtain the curing heat flow curve of C2. Based on the curing heat flow curve of C2, the degree of curing and curing reaction rate of C2 during the non-isothermal curing process were obtained. The temperature, degree of curing and curing reaction rate of C2 during the non-isothermal curing process were used as new sample data. S4, based on downsampling and stratified sampling, divides the new sample data into training and test sets; S5. The pre-trained curing reaction model is fine-tuned using the training set to obtain the fine-tuned curing reaction model. The fine-tuned curing reaction model is then tested, evaluated, and optimized using the test set to obtain the optimized curing reaction model, which is used to predict the curing reaction rate of the new resin-based composite material C2.

[0006] Preferably, the specific method of the non-isothermal curing test is as follows: the resin-based composite material is subjected to a non-isothermal curing test using differential scanning calorimetry, the test temperature range is T1~T2, the test is carried out according to M different heating rates, the test at each heating rate is repeated N times, and a total of M×N curing heat flow curves are obtained. When conducting non-isothermal curing tests on the new resin-based composite material C2, the number of test repetitions, N, at each heating rate is either 1 or 2.

[0007] Preferably, the degree of cure and the cure reaction rate are calculated based on the curing heat flow curve, i.e., the relationship curve between temperature T and heat flow ΔH, as shown below: Calculate the degree of cure: α(T) = ΔH T / ΔH S ; Where α(T) is the degree of curing at temperature T; ΔH T ΔH is the heat release during curing at temperature T. S This represents the total heat released during the curing reaction; ΔH T ΔH S The following was obtained by integrating the curing heat flow curve: ; ; in, Indicates the temperature at which curing is complete; Indicates the temperature at which curing begins; This represents the heat flow rate at temperature T. Calculate the curing reaction rate: ; in, β represents the curing reaction rate, i.e., the rate of change of degree of cure over time; β represents the heating rate in the non-isothermal curing test. The rate of change of curing degree with temperature, by... We obtain the result by differentiation.

[0008] Preferably, step S4 is performed in the following manner: Each curing heat flow curve contains P data points. Spline interpolation is used to downsample the data points, reducing the number of data points for each curing heat flow curve from P to P0. The data characteristics of each data point are temperature and degree of curing, and the data label is the curing reaction rate. The P0 data points of each curing heat flow curve constitute a dataset, and M×N curing heat flow curves constitute an M×N dataset. Each dataset is segmented using periodic sampling, resulting in n sub-datasets; a total of n×M×N sub-datasets are obtained from M×N datasets. A subset of the dataset is extracted from each dataset, resulting in a total of M×N subsets. All data points contained in the extracted M×N subsets are aggregated to form the test set. All data points contained in the remaining (n-1)×M×N subsets that were not extracted are aggregated to form the training set.

[0009] Preferably, the architecture of the deep neural network model includes an input layer, a number of hidden layers, and an output layer; the input layer has 2 neurons, corresponding to temperature and curing degree, respectively; the output layer has 1 neuron, corresponding to the predicted curing reaction rate.

[0010] Preferably, the number of hidden layers is 3, i.e., it contains 3 hidden layers. The hidden layers use mixed activation functions, where the first and second hidden layers use the ReLU activation function: ReLU(x) = max(0,x); where x represents the input of the corresponding layer; the third hidden layer uses the Leaky ReLU activation function: Leaky ReLU(x) = max(αx,x), where α is a positive number; the output layer uses the Softplus activation function: Softplus(x) = ln(1 + e^x). x This is used to ensure that the predicted curing reaction rate is non-negative; A Dropout layer is inserted between the second and third hidden layers to randomly drop some neurons during training; the He normal initialization method is used to initialize the model parameters.

[0011] Preferably, the loss function of the deep neural network model is the mean squared error function: ; in, The total number of samples, and These are the actual curing reaction rate and the predicted curing reaction rate for the i-th sample, respectively. Mean squared error; The Adam optimization algorithm is used to update parameters during model training and minimize MSE.

[0012] Preferably, in step S5, when fine-tuning the pre-trained solidified reaction model using the training set, the original model structure remains unchanged, and only the network parameters of some layers in the original model are updated.

[0013] Preferably, under specific heating rate conditions, the curing reaction rate is predicted using a curing reaction model. The curing reaction prediction curve was obtained, with Δt as the time step. The curing reaction prediction curve is as follows: ; in, ; ; In the formula, t represents time, and Δt is the time step. The degree of curing at time t. For time The degree of curing below, This represents the curing reaction model. Let be the temperature at time t. Indicates the temperature at which curing begins. The heating rate is denoted as .

[0014] The present invention also provides a computer program product comprising a computer program / instruction that, when executed by a processor, implements the aforementioned data-driven method for predicting the curing reaction rate of resin-based composite materials.

[0015] The advantages of this invention are: (1) This invention provides a data-driven method for predicting the curing reaction rate of resin-based composite materials. Based on deep neural networks, it efficiently and accurately captures the complex nonlinear relationships in the test data of resin-based composite materials, realizes the non-parametric prediction of the curing reaction rate of resin-based composite materials, and updates the existing pre-trained curing reaction model based on limited new test data of resin-based composite materials. It has good generalization ability and can adapt to different resin systems and test conditions.

[0016] (2) The data-driven method for predicting the curing reaction rate of resin-based composite materials of the present invention avoids the difficulties in model selection, complex model parameter fitting, limited applicability, and weak nonlinear relationship processing of current parametric models. The model of the present invention directly establishes the nonlinear correlation law between temperature, degree of curing and curing reaction rate. The method is applicable to different resin systems and curing conditions, and has good generalization ability, adaptability and flexibility. It reduces the user's requirements for relevant professional knowledge and can quickly and efficiently make accurate predictions of curing reaction rate based on experimental data.

[0017] (3) The present invention updates the existing pre-trained curing reaction model based on limited and small amount of new resin-based composite material test data, and realizes the method of predicting the curing reaction rate of new resin-based composite materials. It replaces the current independent curing test and parameterized curing reaction kinetic model of different material systems. It solves the problems of large amount of test data, difficulty in model selection, complex model parameter fitting, limited scope of application, and weak nonlinear relationship processing ability in the existing technology. It can make rapid, non-parametric, accurate and generalizable predictions of the curing reaction rate of new resin-based composite materials based on a small amount of test data.

[0018] (4) When some material components of the resin-based composite material change, the present invention updates the existing pre-trained curing reaction model based on a small amount of experimental data of the new resin-based composite material, retains its model structure, and only updates the network parameters of some layers to achieve the effect of model update. Based on this method, the limited new data can be used efficiently to improve the model performance, so that the new model is suitable for accurately predicting the curing reaction rate of the new resin-based composite material, which greatly reduces the demand for experimental data.

[0019] (5) This invention fully explores the curing reaction characteristics of existing material systems and resin-based composite materials. Based on the similarity between the new material and the old material, the model is updated with only a small amount of experimental data. The amount of experimental data is reduced to half or even less than that of conventional methods, which greatly accelerates the research process of fiber and resin material selection, material modification, material compatibility, process optimization, etc.

[0020] (6) This invention significantly reduces the amount of data by downsampling, improves computational efficiency, smooths the original data, removes noise and unnecessary details, and retains the main local and macroscopic features and trends of the data, facilitating fine-tuning training of the model based on a small amount of data. This application uses stratified sampling to ensure the consistency, representativeness, and balance of the data distribution in the training and test sets, which helps the model learn the entire process information of the solidified response more comprehensively and stably. The model makes full use of the experimental data, ensuring that limited data points play a role in the model training or testing process, thus helping to improve the model's generalization ability.

[0021] (7) This invention uses hybrid activation function, He normal initialization, neuron dropout and other technologies to build DNN network architecture and complete model training, which endows the neural network with the ability to learn and predict the highly nonlinear behavior of the curing reaction of resin-based composite materials, automatically and efficiently extracts the key features behind the curing reaction dynamics, reduces the workload and complexity of manual feature extraction, and achieves high robustness, stability and generalization ability of DNN model.

[0022] (8) The method of the present invention has good scalability and maintainability. The accumulation of new data can be easily added to the dataset. The data analysis and prediction process based on the DNN model is relatively standardized and easy to maintain and update. Attached Figure Description

[0023] Figure 1 This is a flowchart of a data-driven method for predicting the curing reaction rate of resin-based composite materials.

[0024] Figure 2 This is a comparison chart of model predictions and experimental values. Detailed Implementation

[0025] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0026] Example 1 Depend on Figure 1 As shown, a data-driven method for predicting the curing reaction rate of resin-based composite materials includes the following steps: S1. Non-isothermal curing test of resin-based composite material C1 was carried out using differential scanning calorimetry to obtain the curing heat flow curve of C1. Based on the curing heat flow curve of C1, the degree of curing and curing reaction rate of C1 during the non-isothermal curing process were obtained. The temperature, degree of curing and curing reaction rate of C1 during the non-isothermal curing process were used as sample data.

[0027] S2, using sample data to train a deep neural network model, the model is used to predict the curing reaction rate based on the degree of curing and temperature in the non-isothermal curing process, and the trained deep neural network model is the pre-trained curing reaction model.

[0028] S3. The new resin-based composite material C2 was subjected to a non-isothermal curing test using differential scanning calorimetry to obtain the curing heat flow curve of C2. Based on the curing heat flow curve of C2, the degree of curing and curing reaction rate of C2 during the non-isothermal curing process were obtained. The temperature, degree of curing and curing reaction rate of C2 during the non-isothermal curing process were used as new sample data.

[0029] S4, based on downsampling and stratified sampling, divides the new sample data into training and test sets.

[0030] S5. The pre-trained curing reaction model is fine-tuned using the training set to obtain the fine-tuned curing reaction model. The fine-tuned curing reaction model is then tested, evaluated, and optimized using the test set to obtain the optimized curing reaction model, which is used to predict the curing reaction rate of the new resin-based composite material C2.

[0031] In steps S1 and S3, differential scanning calorimetry (DSC) is used to conduct non-isothermal curing tests on the resin-based composite material C1 or the new resin-based composite material C2. The test temperature range is T1~T2, and the tests are carried out at M different heating rates β. The test at each heating rate is repeated N times, resulting in a total of M×N test data. The test data are specifically curing heat flow curves, with temperature T on the horizontal axis and heat flow ΔH on the vertical axis. Each curve consists of P data points. When conducting non-isothermal curing tests on the new resin-based composite material C2, the number of repetitions N at each heating rate is either 1 or 2, meaning that only a small amount of test data is needed for the new resin-based composite material C2.

[0032] In step S1 of this embodiment, the resin-based composite material C1 is a T700 / epoxy resin prepreg, and the temperature range for the non-isothermal curing test is 20~250°C. o C, the heating rate β is set to 5 sequentially. o C / min, 10 o C / min, 15 o C / min and 20 oC / min, the experiment was repeated 5 times for each heating rate, and a total of 20 curing heat flow curves were obtained.

[0033] In step S3 of this embodiment, the new resin-based composite material C2 is a T800 / epoxy resin prepreg. Non-isothermal curing test data of the new resin-based composite material C2 at four heating rates of 5℃ / min, 10℃ / min, 15℃ / min and 20℃ / min are obtained. Each heating rate is tested once, and a total of 4 curing heat flow curves are obtained.

[0034] Compared to resin-based composite material C1, the new resin-based composite material C2 has some changes in material composition, such as changes in the type of fiber, resin composition and ratio.

[0035] In steps S1 and S3, based on each curing heat flow curve (the relationship curve between temperature T and heat flow ΔH), data such as the curing reaction rate and degree of cure in the non-isothermal curing process are obtained, as shown below: Calculate the degree of cure: α(T) = ΔH T / ΔH S ; Where α(T) is the degree of curing at temperature T; ΔH T ΔH is the heat release during curing at temperature T. S This represents the total heat released during the curing reaction; ΔH T ΔH S The following was obtained by integrating the curing heat flow curve: ; ; in, Indicates the temperature at which curing is complete; Indicates the temperature at which curing begins; This represents the heat flow rate at temperature T. Calculate the curing reaction rate: ; in, β represents the curing reaction rate, i.e., the rate of change of degree of curing over time; β represents the heating rate in the experiment. The rate of change of curing degree with temperature can be determined by... We obtain the result by differentiation.

[0036] Therefore, the curing heat flow curves obtained from the non-isothermal curing test are converted into M×N datasets. Each dataset contains P data points, constituting curve or The curves are characterized by temperature T and degree of cure α, and the data labels are the curing reaction rate. .

[0037] Specifically, check the curing degree α value, delete outliers, ensure that all α values ​​are between 0 and 1, and delete points with the same curing degree.

[0038] In step S2, a deep neural network model is trained based on the sample data of the resin-based composite material C1, as detailed below: Based on the characteristics and complexity of the curing process of resin-based composite materials, a deep neural network (DNN) architecture was designed. This architecture includes an input layer, a number of hidden layers, and an output layer. The number of neurons in the input layer is consistent with the dimension of the data features, i.e., 2 (corresponding to temperature and degree of curing), the number of hidden layers is set to 3, and the number of neurons in the output layer is consistent with the dimension of the data labels, i.e., 1 (corresponding to the predicted curing reaction rate).

[0039] In particular, the curing process of resin-based composite materials involves complex physicochemical changes and is a significantly nonlinear process, which can generally be described parametrically as follows: ; Here, k(T) is a temperature-dependent reaction rate constant, and f(α) is a function related to the degree of cure. Both are affected by factors such as the resin system, type of curing agent, curing process conditions, and heating rate. Furthermore, the presence of reinforcing phases such as fibers affects the resin's rheological behavior and thermal conductivity. Therefore, to fully grasp the complex information in the curing test data, comprehensively capture the nonlinear relationship between input and output, and ensure the model's prediction accuracy while avoiding overfitting (overlearning noise signals in the test data), it is recommended that the number of hidden layers in the DNN model be set to 3-5 layers. When the number of hidden layers is set to 3, the number of neurons in each layer is 5, 15, and 5 respectively.

[0040] To control model complexity and avoid the vanishing gradient problem during training, the hidden layers of the DNN model use a hybrid activation function: the first and second layers use the ReLU function: ReLU(x) = max(0,x); the third layer uses the Leaky ReLU function: Leaky ReLU(x) = max(αx,x), where α is a small positive number. Here, a combination of random search and manual adjustment is used to find a suitable value of α to achieve optimal model performance, and finally α is set to 0.03; the output layer uses the Softplus activation function: Softplus(x) = ln(1 + e^x). x This ensures that the fixed reaction rate of the DNN regression prediction output is non-negative, guaranteeing physical rationality, smoothness, and gradual behavior. x represents the input of the corresponding layer.

[0041] The loss function of the DNN model is the mean squared error: ; in, The total number of samples, and These represent the actual curing reaction rate and the predicted curing reaction rate, respectively. The Adam optimization algorithm is used for parameter updates during model training to minimize the MSE. It combines the advantages of momentum and adaptive learning rate, achieving fast convergence and high stability.

[0042] After the model architecture is built, the DNN model is trained using a deep learning framework such as PyTorch. The He normal initialization method is used to initialize the DNN network parameters. Specifically, the weights ω in the neural network start from a value with a mean of 0 and a variance of 1. Initialize in a normal distribution, where n in The number of input units in a layer helps maintain the stability of the network training process and effectively avoids gradient vanishing or gradient exploding. The initial value of the learning rate η is set to 0.005. To further reduce overfitting in the neural network and improve the model's expressive and generalization abilities, a Dropout layer is inserted between the second and third hidden layers. During training, some neurons are randomly dropped, with a dropout rate set to 20%. This increases the model's uncertainty, reduces model complexity, and decreases the interdependence between neurons. Based on forward propagation, loss calculation, and backpropagation in the deep learning framework, network parameters such as weights ω and biases b are updated until the loss function MSE converges or reaches the preset number of training rounds. Training then stops, and a pre-trained, fixed response model is obtained.

[0043] In step S4, the new sample data is divided into a training set and a test set based on downsampling and stratified sampling, as shown below: For each dataset For P data points, a smooth interpolation curve is fitted between φ key points using cubic spline interpolation. The key points are determined by K-means clustering of the P data points. The dataset is then further processed. The starting and ending points of the P data points are keypoints. After obtaining the interpolation function, P0 data points are uniformly generated on the interpolation curve to reconstruct the dataset. By downsampling the dataset, the amount of data is greatly reduced, computational efficiency is improved, the original data is smoothed, noise and unnecessary details are removed, and the main local and macroscopic features and trends of the data are preserved, which facilitates fine-tuning training of models based on a small amount of data.

[0044] Each dataset Uniformly divide into n subsets The method employs periodic sampling, extracting data points from each dataset according to a sampling period of n, forming n subsets. Specifically, the k-th subset... It contains the k-th, k+n, k+2n... points from the original dataset. Since the number of data points P0 in the original dataset is not necessarily divisible by n, some subsets may have one more point than others. When n is 4, the dataset... The 1st, 5th, 9th, 13th... points constitute the first subset of the dataset. The 2nd, 6th, 10th, 14th... points constitute the second subset of the dataset. And so on.

[0045] Through this periodic sampling, from the same dataset The resulting n subsets It has the same characteristics as the original dataset. With a similar data structure and distribution, the size is reduced to 1 / n of the original dataset. The choice of the sampling period n needs to consider balancing the size and representativeness of the subset. For M×N datasets... The dataset L is formed by uniformly dividing the data into n×M×N subsets, which are used to fine-tune the pre-trained curing reaction model. The dataset L contains the key parameters of the new resin-based composite material C2 in the non-isothermal curing process, namely temperature, degree of curing and curing reaction rate, and is used to fine-tune the training and evaluate the curing reaction model.

[0046] Dataset L is divided into training and testing sets using stratified sampling. Dataset L contains n×M×N subsets, each subset... Containing P0 / n points, it forms a curing reaction rate curve. Due to the subset data... From the same dataset The data were obtained by uniform partitioning, and they have similar data structures and distributions. Therefore, these n subsets are... As a layer, a subset of the dataset is randomly selected from each layer. A total of M×N subsets can be extracted, each derived from one of the corresponding M×N original datasets. All data points from these M×N subsets are aggregated to form the test set. The remaining (n-1)×M×N subsets of dataset L are aggregated to form the training set.

[0047] Specifically, the normalized temperature T' is obtained by normalizing the temperature T in the dataset L: ; Among them, T min The minimum temperature, Tmax This represents the maximum temperature.

[0048] In step S5, the deep neural network model obtained in step S2 is loaded as a pre-trained curing reaction model, retaining its model structure and parameters. The first few layers of the model are frozen, i.e., the parameters of the first few layers of the model remain unchanged. The pre-trained curing reaction model is fine-tuned (updated) using the training set. The network parameters of the last few layers (e.g., layers 1-2) of the model are adjusted (updated) to achieve the effect of model update. Based on this method, the limited new data can be used efficiently to improve the model performance, making the new model suitable for accurately predicting the curing reaction rate of the new resin-based composite material C2, greatly reducing the demand for experimental data.

[0049] After completing the fine-tuning training of the model, a comprehensive evaluation of the fine-tuned solidified response model was performed using a test set. Performance metrics included MSE, MAE, and R. 2 Error analysis was performed on the prediction results on the test set to identify shortcomings in the model's predictions, providing a basis for further optimization. Through hyperparameter adjustments (such as the number of hidden layers, number of neurons, initial learning rate, and Dropout ratio) and model structure adjustments (activation function selection, adding or removing Dropout layers, etc.), the model's prediction accuracy and generalization ability for the curing reaction of specific resin systems were further improved. Finally, the optimized curing reaction model achieved MSE, MAE, and R-values ​​on the test set. 2 1.4×10 -8 3.30×10 -4 The value of 0.89 indicates that the model has excellent performance, and based on this model, the curing reaction rate of the new resin-based composite material C2 under specific conditions can be predicted quickly and accurately.

[0050] In this invention, compared to the resin-based composite material C1, the new resin-based composite material C2 has some changes in material composition, such as changes in fiber type, resin composition and ratio. Based on a small amount of experimental data of the new resin-based composite material C2, the deep neural network model obtained in step S2, i.e., the pre-trained curing reaction model, is updated. This method can efficiently utilize limited new data to improve model performance, making the optimized curing reaction model suitable for accurately predicting the curing reaction rate of the new resin-based composite material C2, and greatly reducing the need for experimental data.

[0051] like Figure 2 As shown, the optimized curing reaction model at a heating rate β=5 o The predicted curing reaction rate of the new resin-based composite material at C / min showed a high degree of agreement with the value of the non-isothermal curing test, indicating that this data-driven method for predicting the curing reaction rate of resin-based composite materials has good accuracy and reliability.

[0052] In addition, the present invention can also utilize the curing reaction rate predicted by the curing reaction model. The curing reaction prediction curve under specific heating rate conditions was obtained. With Δt as the time step, the curing reaction prediction curve is as follows: ; ; ; ; ; Where t represents time, the initial value of time t is 0, and after each step of the calculation is completed, the time t is updated to t + Δt. This represents the curing reaction model. Indicates the temperature at which curing begins. The degree of curing at time t. For time The degree of curing below, The curing reaction process of resin-based composite materials can be obtained through multiple iterations to determine the heating rate.

[0053] Example 2 In addition to the methods described above, embodiments of this application may also be computer program products, which include computer program instructions that, when executed by a processor, cause the processor to perform the steps in the decision-making behavior decision-making method according to various embodiments of this application as described in Embodiment 1 above.

[0054] The computer program product can be written in any combination of one or more programming languages ​​to perform the operations of the embodiments of this application. The programming languages ​​include object-oriented programming languages ​​such as Java and C++, as well as conventional procedural programming languages ​​such as C or similar languages. The program code can be executed entirely on the user's computing device, partially on the user's computing device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server.

[0055] The above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A data-driven method for predicting the curing reaction rate of resin-based composite materials, characterized in that, Includes the following steps: S1. The resin-based composite material C1 was subjected to a non-isothermal curing test using differential scanning calorimetry to obtain the curing heat flow curve of C1. Based on the curing heat flow curve of C1, the degree of curing and curing reaction rate of C1 during the non-isothermal curing process were obtained. The temperature, degree of curing and curing reaction rate of C1 during the non-isothermal curing process were used as sample data. S2, use sample data to train a deep neural network model. The model is used to predict the curing reaction rate based on the degree of curing and temperature in the non-isothermal curing process. The trained deep neural network model is the pre-trained curing reaction model. S3. The new resin-based composite material C2 was subjected to a non-isothermal curing test using differential scanning calorimetry to obtain the curing heat flow curve of C2. Based on the curing heat flow curve of C2, the degree of curing and curing reaction rate of C2 during the non-isothermal curing process were obtained. The temperature, degree of curing and curing reaction rate of C2 during the non-isothermal curing process were used as new sample data. S4, based on downsampling and stratified sampling, divides the new sample data into training and test sets; S5. The pre-trained curing reaction model is fine-tuned using the training set to obtain the fine-tuned curing reaction model. The fine-tuned curing reaction model is then tested, evaluated, and optimized using the test set to obtain the optimized curing reaction model, which is used to predict the curing reaction rate of the new resin-based composite material C2. The specific method of the non-isothermal curing test is as follows: the resin-based composite material is subjected to a non-isothermal curing test using differential scanning calorimetry. The test temperature range is T1~T2. The test is carried out according to M different heating rates. The test at each heating rate is repeated N times to obtain a total of M×N curing heat flow curves. Among them, when conducting non-isothermal curing tests on the new resin-based composite material C2, the number of test repetitions, N, at each heating rate is 1 or 2. The specific method for step S4 is as follows: Each curing heat flow curve contains P data points. Spline interpolation is used to downsample the data points, reducing the number of data points for each curing heat flow curve from P to P0. The data characteristics of each data point are temperature and degree of curing, and the data label is the curing reaction rate. The P0 data points of each curing heat flow curve constitute a dataset, and M×N curing heat flow curves constitute an M×N dataset. Each dataset is segmented using periodic sampling, resulting in n sub-datasets; a total of n×M×N sub-datasets are obtained from M×N datasets. A subset of the dataset is extracted from each dataset, resulting in a total of M×N subsets. All data points contained in the M×N subsets are aggregated to form the test set. All data points contained in the remaining (n-1)×M×N subsets that were not extracted are aggregated to form the training set. The architecture of a deep neural network model includes an input layer, a number of hidden layers, and an output layer; the input layer has 2 neurons, corresponding to temperature and curing degree respectively; the output layer has 1 neuron, corresponding to the predicted curing reaction rate. The system has three hidden layers. These layers use mixed activation functions: the first and second hidden layers use ReLU activation: ReLU(x) = max(0,x), where x represents the input of the corresponding layer; the third hidden layer uses LeakyReLU activation: Leaky ReLU(x) = max(αx,x), where α is a positive number; and the output layer uses Softplus activation: Softplus(x) = ln(1 + e^x). x This is used to ensure that the predicted curing reaction rate is non-negative; A Dropout layer is inserted between the second and third hidden layers to randomly drop some neurons during training; the He normal initialization method is used to initialize the model parameters.

2. The data-driven method for predicting the curing reaction rate of resin-based composite materials according to claim 1, characterized in that, Based on the curing heat flux curve, i.e., the relationship curve between temperature T and heat flux ΔH, the degree of cure and the curing reaction rate are calculated, as shown below: Calculate the degree of cure: α(T)=ΔH T / ΔH S ; Where α(T) is the degree of curing at temperature T; ΔH T ΔH is the heat release during curing at temperature T. S This represents the total heat released during the curing reaction; ΔH T ΔH S The following was obtained by integrating the curing heat flow curve: in, Indicates the temperature at which curing is complete; Indicates the temperature at which curing begins; This represents the heat flow rate at temperature T. Calculate the curing reaction rate: in, β represents the curing reaction rate, i.e., the rate of change of degree of cure over time; β represents the heating rate in the non-isothermal curing test. The rate of change of curing degree with temperature, by... We obtain the result by differentiation.

3. The data-driven method for predicting the curing reaction rate of resin-based composite materials according to claim 1, characterized in that, The loss function of a deep neural network model is the mean squared error function: in, The total number of samples, and These are the actual curing reaction rate and the predicted curing reaction rate for the i-th sample, respectively. Mean squared error; The Adam optimization algorithm is used to update parameters during model training and minimize MSE.

4. The data-driven method for predicting the curing reaction rate of resin-based composite materials according to claim 1, characterized in that, In step S5, when fine-tuning the pre-trained solidified reaction model using the training set, the original model structure remains unchanged, and only the network parameters of some layers in the original model are updated.

5. The data-driven method for predicting the curing reaction rate of resin-based composite materials according to claim 1, characterized in that, The curing reaction rate predicted using a curing reaction model under specific heating rate conditions. The curing reaction prediction curve was obtained, with Δt as the time step. The curing reaction prediction curve is as follows: in, In the formula, t represents time, and Δt is the time step. The degree of curing at time t. For time t The degree of curing below, This represents the curing reaction model. Let be the temperature at time t. Indicates the temperature at which curing begins. The heating rate is denoted as .

6. A computer program product, characterized in that, It includes a computer program / instruction that, when executed by a processor, implements a data-driven method for predicting the curing reaction rate of resin-based composite materials as described in any one of claims 1 to 5.

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