SiCp / Al composite material residual stress dynamic coupling prediction method based on FEM-ML

Abstract

The invention relates to an SiCp / Al composite material residual stress dynamic coupling prediction method based on a finite element method (FEM) and machine learning (ML), and the method comprises the steps: building a numerical model of an SiCp / Al composite material through finite element software, and obtaining related data; then preprocessing the data, and respectively constructing a particle swarm optimization support vector regression (PSO-SVR) model and a back propagation artificial neural network (BP-ANN) model for predicting residual stress; and finally, comparing the two models through multiple evaluation indexes, and selecting a better prediction model. In practical application, the method can dynamically update the model according to newly acquired data so as to adapt to different working conditions and material parameter changes. According to the method, efficient and accurate prediction of the residual stress of the SiCp / Al composite material is achieved, the dynamic adaptive capacity is achieved, the prediction cost can be remarkably reduced, and powerful support is provided for design and optimization of the composite material.

Description

Technical Field

[0001] The present invention relates to the interdisciplinary field of materials science and computer technology, and in particular to a dynamic coupling prediction method for residual stress of SiCp / Al composite materials based on the combination of finite element method (FEM) and machine learning (ML). Background Art

[0002] SiCp / Al composites, due to their excellent overall properties, including high specific strength, high specific modulus, and good thermal conductivity, hold broad application prospects in aerospace, automotive, and other fields. However, in actual service, these materials are susceptible to residual stresses under complex thermomechanical loads, such as thermal cycling. These residual stresses can degrade the material's mechanical properties and dimensional stability, and can even trigger crack initiation and propagation, severely impacting its reliability and service life under complex operating conditions.

[0003] Currently, the prediction of residual stress in SiCp / Al composites relies primarily on traditional methods. While experimental testing can yield relatively accurate data, it is costly, time-consuming, and destructive, making it difficult to fully reflect the residual stress profile under varying operating conditions and material parameter combinations. Furthermore, prediction methods based on theoretical models often make excessive simplifying assumptions and fail to accurately account for factors such as material microstructure, interfacial properties, and complex loading conditions, resulting in significant deviations between predicted and actual results.

[0004] The development of finite element method (FEM) and machine learning (ML) has opened up new opportunities for residual stress prediction. Finite element methods can numerically simulate the mechanical behavior of materials under complex operating conditions, acquiring large amounts of data, but this approach is computationally time-consuming. Machine learning possesses powerful data learning and prediction capabilities, capable of uncovering underlying patterns within the data, but its prediction accuracy is highly dependent on high-quality training data. To date, no method has been reported that effectively combines the two for residual stress prediction in SiCp / Al composites. Due to the lack of an efficient coupling mechanism between FEM and ML, the synergistic advantages of both methods cannot be fully exploited, making it difficult to achieve high-precision, dynamic, and time-efficient residual stress prediction. Summary of the Invention

[0005] In order to overcome the above-mentioned shortcomings of the existing technology, the present invention proposes a new dynamic coupling prediction method for residual stress of SiCp / Al composite materials based on FEM-ML. This method realizes the rapid, accurate and dynamic prediction of residual stress of SiCp / Al composite materials under different environmental working conditions, effectively reducing time and economic costs, and providing strong technical support for material design optimization, performance evaluation and engineering application.

[0006] The implementation process of the method of the present invention is as follows: 1. Data acquisition and preprocessing (1) A three-dimensional random representative volume element (RVE) model of SiCp / Al composites was constructed using the finite element software ABAQUS / CAE. For different combinations of SiC particle morphology (spherical, irregular polygonal, etc.), volume fraction, particle size, and number of thermal cycles, the corresponding initial calculation file 0*.inp was generated. The initial calculation file was parameterized using Python programming to generate the 1*.inp file, which was then submitted for FEM calculation. The calculated overall residual stress results of the model were written to the 1*.txt file.

[0007] (2) Extract key data from the FEM calculation results and construct the data set required for residual stress prediction of SiCp / Al composite materials, including the volume fraction of silicon carbide Volume_f, the number of hot and cold cycles Cycle_N, the residual stress value Pre_S before the hot and cold cycles, and the residual stress value Aft_S after the hot and cold cycles. Perform comprehensive preprocessing on the original data, including feature selection, to determine the factors that have a significant impact on the residual stress as the structural features of the data set; adopt data normalization method, and use the formula (in x is the value of the original data point, μ is the mean of the data set, σ is the standard deviation of the dataset), scaling the data to a distribution with a mean of 0 and a variance of 1, eliminating the impact of order of magnitude differences between features on model accuracy and reducing model training time.

[0008] (3) The dataset was divided into 80% training set and 20% test set, and 10-fold cross-validation was used within the training set to further optimize the hyperparameters. In each fold of the cross-validation, the training data was further divided into an 80% training subset and a 20% validation subset.

[0009] 2. Build a machine learning prediction model (1) PSO-SVR residual stress prediction model: For the support vector machine regression (SVR) model, the particle swarm optimization algorithm (PSO) is used to optimize its penalty parameter C and kernel function parameter gamma. In the initial stage, the search range of parameters C and gamma is set to lb = np.array ([0.1, 0.01]) and ub = np.array ([10, 1]). The preliminary parameter optimization is performed through pso(svr_cv_mape, lb, ub, maxiter=100, debug = True, phip = 0.5, swarmsize = 30, minfunc = 1e-6). To improve optimization accuracy, we narrowed the search range to lb = np.array([1, 0.0001]) and ub = np.array([100, 0.1]), and increased the number of particles and iterations: xopt,fopt = pso(svr_cv_mape, lb, ub, maxiter=200, debug = True, phip = 0.5, swarmsize = 50, minfunc = 1e-6). Ultimately, we obtained the optimal parameters C and gamma, as well as the minimum mean absolute percentage error (MAPE), and constructed a highly accurate PSO-SVR model.

[0010] (2) BP-ANN residual stress prediction model: A residual stress prediction model is constructed based on the BP-ANN algorithm, with the volume fraction of silicon carbide Volume_f, the number of hot and cold cycles Cycle_N, and the residual stress value Pre_S before the hot and cold cycles as input parameters (the number of input layer nodes is 3), and the residual stress value Aft_S after the hot and cold cycles as output parameters (the number of output layer nodes is 1). Use the empirical equation , (where N, n 1 and n 0 represents the number of nodes in the hidden layer, input layer, and output layer, respectively. α is a constant, and α∈[1, 10]. In this scheme, n 1= 3, n 0 = 1, the value of α is between 3 and 12) to preliminarily determine the number of hidden layer nodes. This model uses 3 hidden layers. The mean square error (MSE) is used as the loss function, and the formula is (in y i is the actual value, is the predicted value, n The model training process uses the Adam optimizer and the early stopping callback function. At the same time, the Dropout layer is added to randomly discard a certain proportion of neurons to prevent overfitting.

[0011] 3. Model evaluation and selection The coefficient of determination (R²), mean square error (MSE), and mean absolute error (MAE) were used to evaluate the accuracy and effectiveness of the PSO-SVR and BP-ANN models. The two models were compared in terms of goodness of fit and prediction accuracy, and the model that performed better was selected as the final residual stress prediction model for SiCp / Al composites.

[0012] 4. Dynamic prediction and update In practical applications, when new experimental data is acquired or operating conditions change, the new data is incorporated into the dataset and data preprocessing, model training, and evaluation are re-performed. The model is dynamically updated based on the new data, enabling it to adapt to changes in material properties and operating conditions in real time, maintaining excellent predictive performance.

[0013] Specifically, this application provides the following technical solutions: A first aspect of the present application provides a dynamic coupled prediction method for residual stress in SiCp / Al composite materials based on FEM-ML, the method comprising: Construct a numerical model of SiCp / Al composites, obtain residual stress data through finite element calculations, and construct a data set containing key features; Preprocess the data set and divide it into training set and test set; A particle swarm optimization support vector regression model (PSO-SVR model) and a deep neural network prediction model (BP-ANN model) were constructed respectively, and the optimal prediction model was determined through parameter optimization and performance evaluation; In actual application, the data set and prediction model parameters are dynamically updated according to the new working condition data to achieve adaptive prediction of residual stress.

[0014] Furthermore, in the method of the present application, the construction of a numerical model of the SiCp / Al composite material includes: constructing a three-dimensional random representative volume element (RVE) model of the SiCp / Al composite material based on the finite element software ABAQUS / CAE, using a script to automatically generate an initial calculation file, using Python to modify the parameters of the initial calculation file and then submitting it for FEM calculation, and writing the output results into the residual stress data set.

[0015] Furthermore, in the method of the present application, the data set is preprocessed, including feature selection, data standardization, and division into 80% training set and 20% test set, and 10-fold cross-validation is performed within the training set.

[0016] Furthermore, in the method of this application, the data normalization adopts the Z-score normalization method, and the calculation formula is:

[0017] in, is the standardized data, x is the value of the original data point, μ is the mean of the data set, σ is the standard deviation of the data set.

[0018] Furthermore, in the method of the present application, the step of constructing the particle swarm optimization support vector regression model includes: optimizing the penalty parameter C and kernel function parameter γ of the support vector machine regression (SVR) model using the particle swarm optimization algorithm (PSO) to determine the optimal parameters and construct the model; The parameter optimization process includes the following two stages: (1) In the initial stage, a global search is performed with the penalty parameter C∈[0.1,10] and the kernel function parameter γ∈[0.01,1]; (2) In the refinement stage, the parameter range is narrowed to C∈[1,100] and γ∈[0.0001,0.1], and the number of particles and the number of iterations are increased to optimize the model.

[0019] Furthermore, in the method of the present application, the steps of constructing the deep neural network prediction model include: taking the volume fraction of silicon carbide, the number of hot and cold cycles, and the residual stress value before the hot and cold cycles as input parameters, and the residual stress value after the hot and cold cycles as output parameters, using an empirical equation to determine the number of hidden layer nodes, using the mean square error as the loss function, using the Adam optimizer to train the model and adding a Dropout layer to prevent overfitting.

[0020] Furthermore, in the method of the present application, the empirical equation for determining the number of hidden layer nodes in the deep neural network prediction model is:

[0021] Among them, N, Represents the number of nodes in the hidden layer, input layer, and output layer respectively, α is a constant and α∈[1,10].

[0022] Furthermore, in the method of the present application, the performance evaluation of the particle swarm optimization support vector regression model and the deep neural network prediction model uses the coefficient of determination (R²), mean square error (MSE) and mean absolute error (MAE) as evaluation indicators.

[0023] Furthermore, in the method of the present application, the dynamic updating of the data set and prediction model parameters according to the new operating condition data includes: Real-time collection of material parameters and residual stress data under new working conditions; After integrating the new data with the original dataset, re-perform data preprocessing, model training, and evaluation; Dynamically update the prediction model.

[0024] A second aspect of the present application provides a device for dynamically coupling residual stress prediction of SiCp / Al composite materials based on FEM-ML, the device comprising: Numerical model building module, used to build a numerical model of SiCp / Al composite materials, obtain residual stress data through finite element calculation, and construct a data set containing key features; Data preprocessing module, used to preprocess the data set and divide it into training set and test set; The prediction model construction module is used to construct a particle swarm optimization support vector regression model and a deep neural network prediction model respectively, and determine the optimal prediction model through parameter optimization and performance evaluation; Dynamic update module, used to dynamically update the data set and prediction model parameters according to new working condition data during actual application, to achieve adaptive prediction of residual stress; When the device is running, the steps of the aforementioned FEM-ML-based dynamic coupling prediction method for residual stress of SiCp / Al composite materials are implemented.

[0025] In summary, the method of the present invention has the following technical advantages: (1) Efficient and accurate prediction: This paper innovatively combines the advantages of FEM and ML, using FEM to provide rich and high-quality training data, solving the problem of data dependence in machine learning. At the same time, with the powerful learning and prediction capabilities of machine learning, it overcomes the low computational efficiency of FEM and achieves rapid and accurate prediction of residual stress in SiCp / Al composite materials. Experiments show that the coefficient of determination (R²) of the BP-ANN model reaches 0.9445, the mean square error (MSE) is 0.0034, and the mean absolute error (MAE) is 0.0391. Compared with traditional methods and single model prediction, the accuracy is significantly improved.

[0026] (2) Dynamic adaptability: The dynamic coupling prediction method proposed in this invention can dynamically update the model when new data or working conditions change, so that the model always maintains good prediction performance, which is more in line with the complex and changeable characteristics of material working conditions in actual engineering applications, and provides a strong guarantee for the life cycle performance evaluation of materials.

[0027] (3) Significant cost-effectiveness: Compared with traditional experimental testing methods, the prediction method of the present invention does not require a large number of expensive and time-consuming experiments, greatly reducing time and economic costs. At the same time, it avoids the destructiveness of the experiment to the sample, improving the efficiency of material research and development and performance evaluation.

[0028] (4) Optimizing material design: Accurately predicting residual stress can provide a scientific basis for the composition design and process optimization of SiCp / Al composite materials. For example, the size and volume fraction of silicon carbide particles can be rationally adjusted based on the prediction results to effectively improve the mechanical properties and thermal fatigue characteristics of the material, thereby increasing the reliability and service life of the material under complex working conditions.

[0029] Other features and advantages of this application will be described in detail in the following description, or will be understood through the implementation of the relevant technical solutions of this application. The objectives and other advantages of this application can be achieved through the technical features and technical means clearly indicated in the description, claims, and drawings, and obtained through the implementation of these technical contents. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] To more clearly illustrate the technical solutions of the embodiments of the present application, the following briefly introduces the drawings involved in the description of the embodiments. It should be noted that the drawings only illustrate some embodiments of the present application. Those skilled in the art can deduce other relevant drawings based on these drawings without engaging in creative work.

[0031] Figure 1 This is a heat map of the correlation analysis between features provided by an embodiment of the present invention.

[0032] Figure 2 A schematic diagram of the division of the training set and the test set provided in an embodiment of the present invention.

[0033] Figure 3 This is a prediction flow chart provided by an embodiment of the present invention.

[0034] Figure 4 This is a diagram of the BP-ANN prediction algorithm model provided by an embodiment of the present invention.

[0035] Figure 5 A graph showing how the training and validation losses change with the number of iterations, provided for an embodiment of the present invention.

[0036] Figure 6 This is a diagram of the ANN model prediction results provided by an embodiment of the present invention.

[0037] Figure 7 Comparison chart of the residual stress BP-ANN predicted value and the finite element calculated value of the SiCp / Al composite material in the test set provided by the embodiment of the present invention.

[0038] Figure 8 The figure is a flow chart of the overall implementation of the method of the present invention.

[0039] Figure 9 It is a structural diagram of the composition of the device of the present invention. DETAILED DESCRIPTION

[0040] In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. It should be understood that the described embodiments are only some embodiments of the present application, not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0041] In this document, the term "including" and any variations thereof (such as "including," "comprising," etc.) are open-ended expressions and should be understood as meaning "including but not limited to," meaning that the listed contents are not exhaustive and may include other contents not explicitly mentioned. The term "based on" should be understood as meaning "based at least in part on," meaning that the basis or condition referred to may not be the only factor and may also involve other relevant factors. The term "one embodiment" should be understood as meaning "at least one embodiment," meaning that the described embodiment is not the only possible implementation method and that other similar embodiments may exist.

[0042] In this application, the terms "a" and "a plurality" are used to modify related elements or features in an illustrative, non-restrictive manner. Unless the context clearly indicates otherwise, "a" should be understood as meaning "at least one," and "a plurality" should be understood as meaning "at least two." Those skilled in the art should interpret these terms appropriately based on the semantics and logical relationships of the context to ensure that they encompass the possibility of "one or more."

[0043] In order to clearly illustrate the technical solution of the present invention, the following will further illustrate it through examples of specific scenarios. Figure 1-Figure 7 The step design and test results during the implementation of the method of this embodiment are demonstrated.

[0044] Figure 8 The figure shows the overall implementation process of the dynamic coupled prediction method for residual stress of SiCp / Al composite materials based on FEM-ML of the present invention, which includes the following steps: S1. Construct a numerical model of SiCp / Al composites and obtain residual stress data through finite element calculations to construct a dataset containing key features. S2. Preprocess the dataset and divide it into training and test sets. S3. Build a particle swarm optimization support vector regression model (PSO-SVR model) and a deep neural network prediction model (BP-ANN model), and determine the optimal prediction model through parameter optimization and performance evaluation. S4. In actual application, the data set and prediction model parameters are dynamically updated according to the new working condition data to achieve adaptive prediction of residual stress.

[0045] For ease of understanding, the complete implementation process of this method will be described in detail below. Figure 3 The prediction process of this method is shown as follows, which includes the following steps: (1) Model construction and data acquisition In the finite element software ABAQUS / CAE, based on the actual microstructural characteristics of SiCp / Al composites, three-dimensional random representative volume element (RVE) models with varying particle morphologies (e.g., spherical, irregular polygonal), volume fractions (e.g., 9% to 18%), and particle sizes (e.g., 2.5 µm to 8.9 µm) were constructed. A Python script was used to automatically modify the model parameters and generate initial calculation files (0*.inp) for different operating conditions. The modified calculation files (1*.inp) were submitted to the ABAQUS solver for FEM calculations to simulate the residual stress distribution of SiCp / Al composites under thermal cycling conditions from -20°C to 160°C. After the calculations were completed, the residual stress data were extracted from the result file (1*.txt) and combined with material parameters (volume fraction, particle size, etc.) and thermal cycling parameters (number of cycles, etc.) to construct the initial dataset.

[0046] (2) Data preprocessing Feature selection was performed on the initial dataset, identifying the silicon carbide volume fraction Volume_f, the number of hot / cold cycles Cycle_N, and the residual stress value before the hot / cold cycles Pre_S as key input features, and the residual stress value after the hot / cold cycles Aft_S as the output feature. The feature data was normalized using StandardScaler in sklearn.preprocessing, converting all feature data to a standard normal distribution with a mean of 0 and a variance of 1. This ensures that all features are equally weighted in model training, improving model training efficiency and prediction accuracy. The dataset was partitioned into an 80% training set and a 20% test set. A 10-fold cross-validation was performed within the training set, further partitioning the training data into an 80% training subset and a 20% validation subset for hyperparameter optimization.

[0047] Eigenvalue correlation analysis is a crucial step in the machine learning prediction process, helping us gain a deeper understanding of the inherent connections between features and providing strong support for subsequent model building. The method of the present invention analyzes the correlations between the various features that influence the material's residual stress, identifying key features that significantly influence residual stress prediction while avoiding multicollinearity issues in the model caused by the high correlation between features, thereby improving the model's prediction accuracy and stability.

[0048] To more intuitively display the data in the correlation matrix, this paper uses the heatmap function in the seaborn library to draw a heatmap. The linear correlation between variables is represented by color and value. The correlation coefficient ranges from -1 to 1, where a value of 1 indicates a perfect positive correlation, a value of -1 indicates a perfect negative correlation, and a value of 0 indicates no linear correlation.

[0049] Figure 1 The correlation matrix between the eigenvalues ​​is shown, revealing diverse correlations between the different eigenvalues. The correlation coefficient for the residual stress values ​​before and after thermal cycling is 0.7, which is considered strong based on the absolute value of the correlation coefficient being greater than 0.6. This strong correlation between the eigenvalues ​​indicates a certain degree of consistency in the residual stress changes before and after thermal cycling in SiCp / Al composites.

[0050] Among the other eigenvalues, the correlation coefficient between volume fraction Volume_f and the residual stress value Pre_S before the thermal cycle is -0.42, indicating a moderate negative correlation, indicating that the residual stress value before the thermal cycle tends to decrease with increasing volume fraction. The correlation coefficient between the number of thermal cycles Cycle_N and the residual stress value Aft_S after the thermal cycle is 0.21, indicating a weak positive correlation between the two, indicating that the residual stress value after the thermal cycle increases slightly with the number of thermal cycles. In the process of predicting residual stress in SiCp / Al composites, the characteristics of the weak correlation coefficient may affect the change in residual stress under certain conditions or in conjunction with other factors. This can provide a more comprehensive data analysis perspective for the model and improve the stability and accuracy of the model prediction to a certain extent.

[0051] In addition, for the adequacy of the dataset, the dataset used in machine learning should be relatively balanced, representative, and complete. In the present invention, the dataset is generated by changing the morphology, size, volume fraction, and number of hot and cold cycles of SiC particles. In order to ensure the representativeness of the dataset, the dataset is divided into a training set (80%) and a test set (20%). The hyperparameters are optimized by implementing 10-fold cross-validation. In each fold of the cross-validation, the training data is further divided into an 80% training set and a 20% validation set. Each set of data is processed in the same way, such as Figure 2 shown.

[0052] (3) Model training and optimization PSO-SVR model training: Following the PSO-SVR model's parameter optimization strategy, a particle swarm optimization algorithm is developed in Python using relevant libraries (such as pyswarms). Initially, a preliminary optimization search is performed within a larger parameter search range to obtain a set of optimal parameters. A more refined optimization search is then performed by narrowing the search range, increasing the number of particles and the number of iterations, ultimately determining the optimal penalty parameter C and kernel function parameter gamma to construct a PSO-SVR residual stress prediction model.

[0053] BP-ANN model training: Build a BP-ANN model using a Python deep learning framework (such as Keras or PyTorch). Determine the number of hidden layer nodes based on empirical equations and set the model's input, hidden, and output layer structures. Train the model using the Adam optimizer and the mean squared error loss function. Add a dropout layer during training to prevent overfitting, and use an early stopping callback to prevent overtraining.

[0054] Figure 4 The figure shows the BP-ANN prediction algorithm model provided by the present invention. Figure 4 As shown, the present invention uses the volume fraction of silicon carbide Volume_f, the number of hot and cold cycles Cycle_N, and the residual stress value Pre_S before the hot and cold cycles as input parameters (the number of nodes in the input layer is 3), and the residual stress value Aft_S after the hot and cold cycles as the output parameter (the number of nodes in the output layer is 1).

[0055] Three hidden layers are used in the BP-ANN calculation framework, and the number of nodes in each hidden layer is preliminarily determined using an empirical equation, namely:

[0056] Among them, N, Represents the number of nodes in the hidden layer, input layer, and output layer respectively, is a constant, and ∈[1, 10]. In this embodiment, = 3, = 1, The value of is between 3 and 12.

[0057] In order to measure the prediction effect of the model, the mean squared error (MSE) is used as the loss function of the BP-ANN prediction algorithm model:

[0058] Among them, y i is the actual value, is the predicted value, and n is the number of samples. MSE reflects the mean square error between the predicted value and the true value. The smaller the value, the better the prediction effect.

[0059] The model is trained using the Adam optimizer and an early stopping callback function. To prevent overfitting, a dropout layer is added to the neural network, randomly dropping a certain percentage of neurons to reduce co-adaptability between neurons. During training, if the validation loss no longer decreases, the model automatically stops training and retains the optimal weights.

[0060] Figure 5 This figure shows the training and validation loss trends over the number of epochs during neural network training. The blue curve represents the validation loss, and the black curve represents the training loss. As can be seen from the figure, both training and validation losses decrease with increasing epochs. Initially (approximately the first 10 epochs), the loss decreases rapidly, indicating that the model is able to quickly adapt to the data in the early stages of learning and that the model is gradually converging. Throughout this process, the validation loss remains largely consistent with the training loss, indicating that the model is not overfitting at this stage.

[0061] As training progressed, the training loss continued to decrease, approaching zero at the end of training, indicating that the model's ability to fit the training data gradually improved. However, after decreasing to a certain level (after about 10 epochs), the validation loss slowed down and leveled off, eventually remaining at a relatively stable value, indicating that the model's predictive performance on the validation set was stabilizing.

[0062] (IV) Model evaluation and selection Residual stress prediction was performed on the test data using the trained PSO-SVR and BP-ANN models. The coefficient of determination (R²), mean square error (MSE), and mean absolute error (MAE) of the two models were calculated. Evaluation metrics were compared. If the BP-ANN model performed better in each metric, the BP-ANN model was selected as the final residual stress prediction model for SiCp / Al composites; if the PSO-SVR model performed better, the PSO-SVR model was selected.

[0063] Figure 6 This figure shows the prediction results of the ANN model provided in this example. In this example, a back-propagation artificial neural network (BP-ANN) model was used to predict the residual stress of SiCp / Al composite materials under thermal cycling. Principal component analysis (PCA) was then used to visualize the spatial distribution of the prediction errors. Figure 6The 3D surface plot in Figure 1 shows the relationship between the two principal components after PCA dimensionality reduction and the predicted value, and the distribution of prediction errors is reflected through a color gradient. The figure illustrates the relationship between the predicted value (PredictedValue) and the prediction error (PredictionError) constructed based on the two principal components (PCA Component 1 and PCA Component 2). The 3D surface plot demonstrates the complex nonlinear relationship between the two principal components. The color gradient from blue to red represents the change in prediction error. Blue indicates negative errors, and red indicates positive errors. The distribution of prediction errors can be seen as the colors change. The red dots in the figure correspond to the actual predicted data points.

[0064] from Figure 6 Judging from the shape of the surface, the predicted values ​​show a fluctuating trend, with peaks and valleys within different PCA component ranges. This indicates a clear nonlinear relationship between the features after principal component analysis (PCA) and the model's predictions. Regions with larger principal component values ​​(close to 2.0) appear to correspond to higher predicted values, while negative regions exhibit lower predicted values. Prediction errors are large in certain areas, particularly the red and blue regions at the edges of the surface, indicating that the model's predictions in these areas are somewhat biased. This may be because the data in these areas is sparsely distributed or contains extreme values, making it difficult for the model to accurately fit. In the middle region, however, the model's predicted values ​​are closer to the actual values, as shown by the green region with smaller errors, indicating that the model's predictions in this area are relatively stable.

[0065] Figure 7 The comparison between the actual value obtained by finite element simulation and the predicted value obtained by BP-ANN algorithm is shown. Figure 7 As can be seen from the curve in (a), the finite element simulation results and the predicted values ​​show similar trends at most sample points, indicating that the BP-ANN algorithm can better capture the variation of residual stress. In terms of prediction accuracy, at most sample points, the SiCp / Al composite material predicted by the BP-ANN algorithm is consistent with the finite element calculation results. Figure 7 (b) shows that the R of BP-ANN prediction results and finite element simulation results are 2 It is 0.98321, indicating that the constructed BP-ANN model is fully capable of predicting the residual stress caused by thermal cycling of SiCp / Al composites.

[0066] (V) Dynamic prediction and model updating During the actual application of the material, new experimental data or information on changes in operating conditions is regularly collected. This new data is merged with the original dataset, and data preprocessing, model training, and evaluation are re-performed. The model is adjusted and updated based on the new data to ensure that it accurately reflects the latest trends in the material's residual stress.

[0067] In addition, if Figure 9 As shown, the present invention also provides a device for dynamically coupling residual stress prediction of SiCp / Al composite materials based on FEM-ML, the device comprising: Numerical model building module, used to build a numerical model of SiCp / Al composite materials, obtain residual stress data through finite element calculation, and construct a data set containing key features; Data preprocessing module, used to preprocess the data set and divide it into training set and test set; The prediction model construction module is used to construct a particle swarm optimization support vector regression model and a deep neural network prediction model respectively, and determine the optimal prediction model through parameter optimization and performance evaluation; Dynamic update module, used to dynamically update the data set and prediction model parameters according to new working condition data during actual application, to achieve adaptive prediction of residual stress; When the device is running, the steps of the aforementioned FEM-ML-based dynamic coupling prediction method for residual stress of SiCp / Al composite materials are implemented.

[0068] Although the above discussion contains several specific implementation details, these details should not be interpreted as limiting the scope of this application. The above description is only a preferred embodiment of the present application and an illustration of the technical principles used. Those skilled in the art should understand that the scope of disclosure involved in this application is not limited to the technical solutions formed by the specific combination of the above technical features. At the same time, this application should also cover other technical solutions formed by any combination of the above technical features or their equivalent features without departing from the above disclosed concepts.

[0069] Those skilled in the art should also understand that they may modify the technical solutions described in the aforementioned embodiments, or replace some of the technical features therein with equivalents, without departing from the spirit and scope of the technical solutions of the embodiments of the present application. Such modifications or replacements will not cause the essence of the corresponding technical solutions to deviate from the core spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A dynamic coupling prediction method for residual stress of SiCp / Al composite materials based on FEM-ML, characterized by: The method comprises: Construct a numerical model of SiCp / Al composites, obtain residual stress data through finite element calculations, and construct a data set containing key features; Preprocess the data set and divide it into training set and test set; Construct particle swarm optimization support vector regression model and deep neural network prediction model respectively, and determine the optimal prediction model through parameter optimization and performance evaluation; In actual application, the data set and prediction model parameters are dynamically updated according to the new working condition data to achieve adaptive prediction of residual stress.

2. The method according to claim 1, characterized in that The method comprises constructing a numerical model of the SiCp / Al composite material, comprising: constructing a three-dimensional random representative volume element model of the SiCp / Al composite material based on finite element software ABAQUS / CAE, automatically generating an initial calculation file using a script, modifying parameters of the initial calculation file using Python, and then submitting the initial calculation file for FEM calculation, and writing the output results into a residual stress dataset.

3. The method according to claim 1, characterized in that The data set was preprocessed, including feature selection, data standardization, and partitioning into 80% training set and 20% test set, and 10-fold cross validation was performed within the training set.

4. The method according to claim 3, characterized in that The data standardization adopts the Z-score normalization method, and the calculation formula is: in, is the standardized data, x is the value of the original data point, μ is the mean of the data set, σ is the standard deviation of the data set.

5. The method according to claim 1, wherein The particle swarm optimization support vector regression model construction step includes: using the particle swarm optimization algorithm to optimize the penalty parameter C and the kernel function parameter γ of the support vector machine regression model, and determining the optimal parameters to construct the model; The parameter optimization process includes the following two stages: (1) In the initial stage, a global search is performed with the penalty parameter C∈[0.1,10] and the kernel function parameter γ∈[0.01,1]; (2) In the refinement stage, the parameter range is narrowed to C∈[1,100] and γ∈[0.0001,0.1], and the number of particles and the number of iterations are increased to optimize the model.

6. The method according to claim 1, characterized in that The steps of constructing the deep neural network prediction model include: using the volume fraction of silicon carbide, the number of hot and cold cycles, and the residual stress value before the hot and cold cycles as input parameters, and the residual stress value after the hot and cold cycles as output parameters, using an empirical equation to determine the number of hidden layer nodes, using the mean square error as the loss function, using the Adam optimizer to train the model, and adding a Dropout layer to prevent overfitting.

7. The method according to claim 6, characterized in that The empirical equation for determining the number of hidden layer nodes in the deep neural network prediction model is: Among them, N, and Represents the number of nodes in the hidden layer, input layer, and output layer respectively, α is a constant and α∈[1, 10].

8. The method according to claim 1, characterized in that The performance evaluation of the particle swarm optimization support vector regression model and the deep neural network prediction model uses the determination coefficient, mean square error and mean absolute error as evaluation indicators.

9. The method according to claim 1, characterized in that The dynamic updating of the data set and prediction model parameters according to the new operating condition data includes: Real-time collection of material parameters and residual stress data under new working conditions; After integrating the new data with the original dataset, re-perform data preprocessing, model training, and evaluation; Dynamically update the prediction model.

10. A dynamic coupled prediction device for residual stress of SiCp / Al composite materials based on FEM-ML, characterized in that: The device comprises: Numerical model building module, used to build a numerical model of SiCp / Al composite materials, obtain residual stress data through finite element calculation, and construct a data set containing key features; Data preprocessing module, used to preprocess the data set and divide it into training set and test set; The prediction model construction module is used to construct a particle swarm optimization support vector regression model and a deep neural network prediction model respectively, and determine the optimal prediction model through parameter optimization and performance evaluation; The dynamic update module is used to dynamically update the data set and prediction model parameters according to the new working condition data in the actual application process to achieve adaptive prediction of residual stress.

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