Machine learning prediction method for fracture constraint parameters based on Transformer-LSTM framework

Abstract

This invention relates to a machine learning prediction method for fracture constraint parameters based on the Transformer-LSTM framework, comprising the following steps: S1, using Abaqus software to perform three-dimensional finite element simulation calculations on dissimilar material SENT specimens to obtain a dataset as model input; S2, organizing and normalizing the dataset obtained in step one, and then organizing multiple input features in each group of samples into a feature sequence in a fixed order; obtaining a high-dimensional representation containing feature position information through linear embedding and positional encoding; and extracting global dependencies between input features using a Transformer encoder; S3, inputting the enhanced feature sequence output by the Transformer into an LSTM network for further integration, and outputting the predicted value of constraint parameter A through a fully connected regression layer; This invention overcomes the limitations of traditional methods in handling multi-parameter and nonlinear problems, improves the accuracy, universality, and stability of prediction results, and provides a fast and high-precision prediction tool for fracture analysis.

Description

Technical Field

[0001] This invention relates to the field of accurate characterization of crack tip constraint effect in dissimilar metal welded joints, and particularly to a machine learning prediction method for fracture constraint parameters based on the Transformer-LSTM framework. Background Technology

[0002] Accurately describing the stress and strain field at the crack tip is a prerequisite for accurate structural fracture assessment and analysis. In elastoplastic fracture failure evaluation, fracture criterion methods based on single-parameter J-integrals are often too conservative. To address this issue, constraint parameters characterizing the constraints are introduced and used in conjunction with the J-integral (elastoplastic) or stress intensity factor K (linear elastic) characterizing the load to describe the crack tip field.

[0003] For linear elastic fracture, the constraint parameter K is generally used. For elastoplastic fracture, the constraint parameter Q is developed based on the plastic deformation energy theory. In addition, by analyzing the higher-order terms of the asymptotic expansion of the elastoplastic crack tip field, constraint parameters A2 and A are proposed.

[0004] The aforementioned constraint parameters are primarily designed for homogeneous isotropic materials. However, in practical engineering, the application of dissimilar metal components is becoming increasingly common. Due to the mismatch in material properties, the crack confinement effect in these dissimilar material structures is also affected. Therefore, in recent years, numerous applications have been filed regarding the constraint effect caused by material property mismatch. However, these applications are all based on traditional methods, resulting in limited applicability, poor universality, and low efficiency.

[0005] In recent years, with the rapid development of artificial intelligence and data-driven technologies, machine learning, as a major branch and important tool, has shown great application potential in fracture mechanics applications. Especially in the field of material property prediction, machine learning technology has become an important application method. Through machine learning, useful information can be quickly extracted from large amounts of experimental and computational simulation data, revealing hidden patterns and thus improving the efficiency of new material discovery and material property prediction.

[0006] Machine learning and data-driven methods have been applied to data analysis, fatigue analysis, and life prediction of engineering structures, which has also enabled fatigue crack propagation and remaining life prediction.

[0007] Machine learning technology has demonstrated unique advantages and application potential in fatigue and fracture mechanics applications. However, most existing applications only use machine learning for applications and predictions of fatigue life, drag curves, and fracture energy, while applications for predicting constraint parameters remain unexplored. Therefore, applying machine learning to the prediction of constraint parameters has become an urgent technical problem to be solved. Summary of the Invention

[0008] The purpose of this invention is to provide a machine learning prediction method for fracture constraint parameters based on the Transformer-LSTM framework, which can overcome the limitations of traditional methods in handling multi-parameter and nonlinear problems, improve the accuracy and stability of prediction results, and provide a fast and high-precision prediction tool for fracture analysis.

[0009] To achieve the above objectives, the technical solution adopted by this invention is: a machine learning prediction method for fracture constraint parameters based on the Transformer-LSTM framework, comprising the following steps:

[0010] S1. Use Abaqus software to perform three-dimensional finite element simulation calculations on the SENT specimen of dissimilar materials to obtain the dataset as input to the model.

[0011] S2. The dataset obtained in step one is organized and normalized. Then, multiple input features in each group of samples are organized into a feature sequence in a fixed order. A high-dimensional representation containing feature position information is obtained through linear embedding and positional encoding. The global dependency between input features is extracted using the Transformer encoder.

[0012] S3. The enhanced feature sequence output by the Transformer is input into the LSTM network for further integration, and the predicted value of the constraint parameter A is output through the fully connected regression layer.

[0013] Preferably, the dataset in S1 is derived from Abaqus finite element simulation results. Each set of samples corresponds to a constraint parameter A calculated under a combination of material performance parameters, geometric parameters, and applied loads. The input features include variables such as material yield strength, hardening index, material coefficient, crack size, specimen thickness, and applied loads. The output target is the constraint parameter A under the corresponding working condition.

[0014] For the i-th sample, the input-output relationship is expressed as:

[0015]

[0016]

[0017] in, Let represent the input feature vector of the i-th sample group. , ,⋯ , Let m represent different input variables, and m represent the number of input features. This represents the true constraint parameter A corresponding to this set of samples.

[0018] Min-Max normalization is applied to the input feature X and the output target y respectively, linearly mapping each variable to the [0,1] interval. The calculation formula is as follows:

[0019]

[0020] Where x represents the original data, and These represent the minimum and maximum values ​​of the variable in the sample data, respectively. This represents the normalized data.

[0021] Preferably, multiple input features in each set of samples are organized into a feature sequence in a fixed order. For a set of input samples:

[0022]

[0023] Each of them This represents a specific input feature. These features are input into the network in a fixed order so that each feature can be regarded as an element in the feature sequence.

[0024] Preferably, the linear embedding process in S2 is represented as follows:

[0025]

[0026] in, Represents the j-th input feature. and These represent the weights and biases of the linear embedding layer, respectively. This represents the high-dimensional embedding representation corresponding to the input feature.

[0027] Positional encoding is added after feature embedding to introduce the positional information of the features into the model. The positional encoding is constructed using sine and cosine functions, and its form is as follows:

[0028]

[0029]

[0030] in, This indicates the position of the feature in the input sequence, k represents the dimension index, and d represents the embedding dimension;

[0031] Finally, the feature representation input into the Transformer encoder is as follows:

[0032]

[0033] in, This represents the j-th feature representation after adding positional encoding. This indicates the position code for the corresponding location.

[0034] Preferably, after feature embedding and position encoding are completed, the feature sequence is input into the Transformer encoder. The core of the Transformer encoder is the multi-head self-attention mechanism, which calculates the degree of correlation between input features, thereby extracting global feature dependencies.

[0035] For input feature representation The self-attention mechanism first linearly maps it to a query matrix. Key matrix Sum matrix :

[0036]

[0037]

[0038]

[0039] in, , and The first matrix represents the weight matrix learned during model training. Subsequently, the self-attention mechanism calculates the correlation between different features using the query matrix and the key matrix, and then uses this correlation to perform a weighted summation of the value matrix. The calculation form is as follows:

[0040]

[0041] in, The dimension of the key vector. Used to scale the dot product results to improve the stability of model training;

[0042] Multi-head self-attention mechanisms can learn feature relationships in parallel across multiple different feature subspaces. Their basic form is as follows:

[0043]

[0044] Where h represents the number of attention heads, This represents the output of the i-th attention head. This represents the output mapping matrix; after processing by multiple Transformer encoders, the output result is a feature sequence enhanced by global context.

[0045] Preferably, the enhanced feature sequence output by the Transformer encoder is then fed into the LSTM network. The LSTM's forget gate is used to control how much information from the previous state is retained, and its calculation form is as follows:

[0046]

[0047] in, Indicates the output of the forget gate. This indicates the hidden state at the previous moment. This represents the Transformer encoded features of the current input. and These represent the weight and bias of the forget gate, respectively. This represents the Sigmoid activation function;

[0048] The input gate controls how much of the current input information is written to the cell state.

[0049]

[0050] Candidate memory content is represented as follows:

[0051]

[0052] The cell state is updated in the following ways:

[0053]

[0054] in, Indicates the current cell state. This indicates the previous cell state. This indicates element-wise multiplication;

[0055] The output gate is used to determine how much information from the current cell state is output as a hidden state:

[0056]

[0057]

[0058] in, Indicates the current hidden state;

[0059] Through the above gating mechanism, LSTM further filters and integrates the global feature relationships extracted by Transformer; the hidden state of the last step of LSTM is taken as the comprehensive feature representation of the entire input sample; this comprehensive representation contains the complex coupling information between material parameters, geometric parameters and load parameters, which is used for the regression prediction of subsequent constraint parameter A.

[0060] Preferably, after integration by the LSTM network, a comprehensive hidden feature representation of each input sample is obtained. To convert this hidden feature into a predicted value for the specific constraint parameter A, a fully connected regression output layer is set after the LSTM.

[0061] This process can be represented as:

[0062]

[0063] in, The constraint parameter A is obtained from the model prediction. This represents the comprehensive hidden features output by the LSTM. and These represent the weights and biases of the regression output layer, respectively.

[0064] The technical effects of this invention are as follows:

[0065] 1. By using a hybrid model, the model can overcome the limitations of traditional methods in handling multi-parameter and nonlinear problems, improve the accuracy and stability of prediction results, and provide a fast and high-precision prediction tool for fracture analysis.

[0066] 2. Applying the Transformer-LSTM model to the prediction of constraint parameter A, the computational efficiency of constraint parameters can be significantly improved through machine learning methods. Based on the constraint parameter dataset generated by finite element simulation, the prediction model shows excellent performance under various material property mismatch conditions. Attached Figure Description

[0067] Figure 1 The typical finite element mesh for the heterogeneous SENT specimen model is a / W=0.4, t / W=0.25.

[0068] Figure 2 This is a diagram illustrating the training process of the Transformer-LSTM model.

[0069] Figure 3 This is a structural diagram of the multi-head attention mechanism.

[0070] Figure 4 This is a diagram of the LSTM structure.

[0071] Figure 5 This is a comparison chart of the predicted and simulated values ​​of each model under three mismatch conditions in the ablation experiment.

[0072] Figure 6 This is a comparison chart showing the predicted and simulated values ​​of each model under three mismatch conditions in the experiment. Detailed Implementation

[0073] To enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be described in detail below with reference to the accompanying drawings. The description in this part is only exemplary and explanatory, and should not be used to limit the scope of protection of the present invention in any way.

[0074] like Figure 1-6As shown, this application is a machine learning prediction method for fracture constraint parameters based on the Transformer-LSTM framework. The following describes the scheme of this application in a progressive manner with multiple modules.

[0075] 1. Fracture mechanics theory and simulation experiments

[0076] 1.1 JA Two-Parameter Method

[0077] A similar three-term expression for the gradually expanding crack tip field is the expression for the JA two-parameter method. This includes two fracture parameters: the J integral characterizing the load and the constraint parameter A characterizing the constraint effect. The constraint parameter A is essentially a normalized form of A². Furthermore, compared to the constraint parameter Q in the JQ two-parameter method, the A value calculated in the critical region near the crack tip exhibits less fluctuation.

[0078] Under plane strain conditions, the JA two-parameter method describes the stress field at the crack tip using the following three asymptotic expressions:

[0079]

[0080] Where σ ij The stress components (σ) in the polar coordinate system centered at the crack tip rr , σ θθ , σ rθ ); dimensionless radius Defined as J is the integral of J; the power t is an eigenvalue that depends on the hardening exponent n; the power σ0 is the yield stress; and It is a normalized angular stress function; polynomial coefficients , where I n For proportional integrals that depend only on n, For details regarding yield strain, please refer to the relevant papers.

[0081] To perform relevant application analysis based on the JA two-parameter method, the values ​​of two fracture parameters, J and A, must first be calculated. Currently, the integral of J can usually be obtained using mature domain integration methods, but there is no efficient method for determining the constraint parameter A. This application employs a least-squares-based fitting method, which involves fitting the key region near the crack tip (typically 1.5 ≤ A) to the area of ​​the crack tip. ≤5,0 。 ≤θ≤45 。 The value of A is determined by fitting the finite element results data. Compared to traditional point matching methods, this fitting method provides a more accurate and consistent solution for A. The more accurate constraint parameter A value obtained through this method will help improve the accuracy of the prediction model built through subsequent machine learning training.

[0082] 1.2 Finite Element Model

[0083] 1.2.1 Material Properties

[0084] The material model used in this numerical application is based on deformation-plasticity theory. The Ramberg–Osgood power-law strain hardening relation is provided in the finite element analysis software Abaqus used in this application. This relation can be described as follows under uniaxial loading:

[0085]

[0086] Where σ0 is the yield strength of the material, α is the material coefficient, and n is the material hardening exponent; This is the actual strain, the yield strain ε0 = σ0 / E, where E is Young's modulus. It is the actual stress.

[0087] To predict the value of constraint parameter A using machine learning methods, sufficient data is required. In this application, the value of constraint parameter A under material performance mismatch is prepared for subsequent machine learning by systematically changing the main performance parameters of the material. In this application, while systematically changing the main material performance values, the Poisson's ratio v and Young's modulus E are set to 0.3 and 200 GPa, respectively.

[0088] For dissimilar materials, to calculate the value of constraint parameter A under the condition of material property mismatch, the dissimilar material joint structure is simplified to consist of the upper material (M) UP ) and lower end material (M) down This application presents an ideal dissimilar material interface crack model. It assumes that the two materials forming the dissimilar material joint have the same elastic properties, but different yield strengths, hardening exponents, or material coefficients. The values ​​of yield strength, hardening exponent, and material coefficients cover the three main mismatch states: over-matched, matched, and under-matched material properties. Specific material property mismatch settings are shown in Table 1. Furthermore, the relative crack depth a / W of the model is set to 0.2, 0.3, 0.4, 0.5, and 0.7, and the width-to-thickness ratio t / W is set to 0.25, 0.5, and 1.

[0089] Table 1. The impact of material property mismatch on constraint parameter A on material property settings in the application.

[0090]

[0091] 1.2.2 Finite element model of the specimen

[0092] To prepare data for the constraint parameter A under the material property mismatch in subsequent machine learning, this application uses Abaqus software to perform three-dimensional finite element simulation calculations on the dissimilar material SENT specimen.

[0093] For the finite element model of the SENT specimen of dissimilar materials, since it is only symmetric along the thickness direction, it is possible to perform finite element modeling on only 1 / 2 of the model. Figure 1 A finite element model of a typical SENT specimen (a / W=0.4, t / W=0.25) is presented, in which all elements are selected as 20-node quadratic hexahedral elements (C3D20R) with reduced integrals. A ring-shaped cluster of elements surrounds the crack tip, and 14 mesh layers are arranged along the thickness direction of the model. The first layer of elements, closest to the midplane, is thin enough to approximate the midplane location, while the thickness of the remaining thirteen layers varies geometrically, with the thinnest layer placed on the free surface.

[0094] 2. Transformer-LSTM Constrained Parameter Prediction Model

[0095] To achieve rapid prediction of constraint parameter A under material property mismatch conditions, this application uses a regression prediction model based on Transformer-LSTM. This model is based on data obtained from finite element simulation, takes material property parameters, geometric parameters, and external loads as input features, and takes the corresponding constraint parameter A as the output target. By establishing a nonlinear mapping relationship between the input parameters and constraint parameter A through a machine learning model, it can achieve rapid prediction of constraint parameter A without repeating a large number of finite element calculations.

[0096] The overall process of the Transformer-LSTM model adopted in this application is as follows: First, the finite element simulation data is organized and normalized; second, multiple input features in each group of samples are organized into a feature sequence in a fixed order; then, a high-dimensional representation containing feature position information is obtained through linear embedding and positional encoding; next, the global dependencies between input features are extracted using a Transformer encoder; finally, the enhanced feature sequence output by the Transformer is input into the LSTM. ] The network is further integrated; finally, the predicted value of constraint parameter A is output through a fully connected regression layer.

[0097] This hybrid model overcomes the limitations of traditional methods in handling multi-parameter, nonlinear problems, improving the accuracy and stability of prediction results and providing a fast, high-precision prediction tool for fracture analysis. The training process of the Transformer-LSTM model used in this application is as follows: Figure 2 As shown.

[0098] 2.1 Dataset Structure and Preprocessing

[0099] The data used in this application comes from Abaqus finite element simulation results. Each set of samples corresponds to a constraint parameter A calculated under a combination of material property parameters, geometric parameters, and applied loads. The input features mainly include variables such as material yield strength, hardening index, material coefficient, crack size, specimen thickness, and applied load. The output target is the constraint parameter A under the corresponding working condition.

[0100] For the i-th sample, the input-output relationship is expressed as:

[0101]

[0102]

[0103] in, Let represent the input feature vector of the i-th sample group. , ,⋯ , Let m represent different input variables, and m represent the number of input features. This represents the true constraint parameter A corresponding to this set of samples.

[0104] Because different input variables have different physical meanings and dimensions, their numerical ranges vary considerably. If the raw data is directly input into the model, features with larger values ​​may have a greater impact during training, leading to model instability and even affecting the model's convergence speed and prediction accuracy. Therefore, this application performs Min-Max normalization on both the input feature X and the output target y, linearly mapping each variable to the [0,1] interval. The calculation formula is as follows:

[0105]

[0106] Where x represents the original data, and These represent the minimum and maximum values ​​of the variable in the sample data, respectively. This represents the normalized data.

[0107] After normalization, the numerical ranges of the input features and output targets are unified, which helps to reduce the impact of different units on model training and improve the stability of the model parameter update process. After data preprocessing, the dataset is divided into training and test sets in a 7:3 ratio, where the training set is used for model parameter learning and the test set is used to evaluate the model's predictive performance.

[0108] 2.2 Construction of Input Feature Sequence

[0109] The input data in this application comes from finite element simulation results. In order to enable Transformer and LSTM to model multidimensional input features, this application organizes multiple input features in each group of samples into a feature sequence in a fixed order.

[0110] For a set of input samples:

[0111]

[0112] Each of them This represents a specific input feature, such as material parameters, geometric parameters, or load parameters. The model inputs these features into the network in a fixed order, so that each feature can be considered an element in the feature sequence.

[0113] It should be noted that the term "sequence" in this application does not refer to a chronological order, but rather to a fixed arrangement of input features within the model. In other words, this sequence is a feature sequence composed of different variables such as material, geometry, and load. In this way, the model can learn the interrelationships between different input variables within a unified data structure.

[0114] 2.3 Feature Embedding and Location Encoding

[0115] Before entering the Transformer encoder, the original input features first need to be transformed into a high-dimensional feature representation suitable for deep neural network processing. This application employs a linear embedding method to map each input feature from its original scalar form to a high-dimensional feature space. After linear embedding, each input variable is no longer just a single numerical value, but is represented as a high-dimensional vector, thus providing a foundation for the subsequent model to learn complex feature relationships.

[0116] The linear embedding process can be represented as:

[0117]

[0118] in, Represents the j-th input feature. and These represent the weights and biases of the linear embedding layer, respectively. This represents the high-dimensional embedding representation corresponding to the input feature.

[0119] Since the self-attention mechanism in Transformer does not inherently contain positional information of input elements, without positional encoding, the model struggles to distinguish the positions of different input features within the feature sequence. Therefore, this application incorporates positional encoding after feature embedding to introduce the feature's positional information into the model. The positional encoding is constructed using sine and cosine functions, and its form is as follows:

[0120]

[0121]

[0122] in, This indicates the position of the feature in the input sequence, k represents the dimension index, and d represents the embedding dimension.

[0123] Finally, the feature representation input into the Transformer encoder is as follows:

[0124]

[0125] in, This represents the j-th feature representation after adding positional encoding. This represents the positional encoding of the corresponding location. Through this processing, the model can obtain not only the numerical information of each input feature, but also its positional information in the feature sequence.

[0126] 2.4 Global Feature Modeling of Transformer Encoder

[0127] After feature embedding and positional encoding are completed, the feature sequence is input into the Transformer encoder. The core of the Transformer encoder is the multi-head self-attention mechanism, which calculates the degree of correlation between input features to extract global feature dependencies.

[0128] For input feature representation The self-attention mechanism first linearly maps it to a query matrix. Key matrix Sum matrix :

[0129]

[0130]

[0131]

[0132] in, , and This represents the weight matrix learned during model training. Subsequently, the self-attention mechanism calculates the correlation between different features using the query matrix and key matrix, and then uses this correlation to perform a weighted summation of the value matrix, calculated as follows:

[0133]

[0134] in, The dimension of the key vector. This is used to scale the dot product results to improve the stability of model training.

[0135] For the constraint parameter A prediction task of this application, material property parameters, geometric dimensions, and applied loads are not independent of each other, but rather jointly affect the constraint state at the crack tip. For example, there may be complex nonlinear coupling relationships between material yield strength, hardening index, material coefficient, crack depth, specimen thickness, and applied load. The Transformer encoder can calculate the correlation weight between any two features across the entire input feature sequence, thereby extracting the complex dependencies between input variables from a global perspective.

[0136] Compared to single-head attention mechanisms, multi-head self-attention mechanisms can learn feature relationships in parallel across multiple different feature subspaces. Its basic form can be expressed as:

[0137]

[0138] Where h represents the number of attention heads, This represents the output of the i-th attention head. This represents the output mapping matrix. Through multi-head attention, the model can learn the relationships between input features from different perspectives, improving its ability to represent complex nonlinear problems. The structure of the multi-head attention mechanism is as follows: Figure 3 As shown.

[0139] After processing by multiple Transformer encoders, the output is a feature sequence enhanced with global context. At this point, the representation of each feature position in the sequence not only contains information about the feature itself, but also incorporates the influence of other input features.

[0140] 2.5 LSTM Feature Integration

[0141] The enhanced feature sequence output by the Transformer encoder is then fed into an LSTM network. LSTM is a recurrent neural network with a gating structure, which can selectively retain, update, and output sequence information through forget gates, input gates, and output gates.

[0142] In the model of this application, the LSTM receives the feature sequence output by the Transformer encoder, rather than the original input features. That is, the Transformer first learns the relationship between different input variables from a global perspective, and the LSTM then further integrates and compresses these enhanced feature representations based on this.

[0143] The forget gate in LSTM controls how much information from the previous state is retained, and its calculation form is as follows:

[0144]

[0145] in, Indicates the output of the forget gate. This indicates the hidden state at the previous moment. This represents the Transformer encoded features of the current input. and These represent the weight and bias of the forget gate, respectively. This represents the Sigmoid activation function.

[0146] The input gate controls how much of the current input information is written to the cell state.

[0147]

[0148] Candidate memory content is represented as follows:

[0149]

[0150] The cell state is updated in the following ways:

[0151]

[0152] in, Indicates the current cell state. This indicates the previous cell state. This indicates element-wise multiplication.

[0153] The output gate is used to determine how much information from the current cell state is output as a hidden state:

[0154]

[0155]

[0156] in, Indicates the current hidden state.

[0157] Through the aforementioned gating mechanism, LSTM can further filter and integrate the global feature relationships extracted by Transformer. Finally, the hidden state of the last step of LSTM is taken as the comprehensive feature representation of the entire input sample. This comprehensive representation contains complex coupling information between material parameters, geometric parameters, and load parameters, and can be used for subsequent regression prediction of constraint parameter A. The LSTM model structure is as follows: Figure 4 As shown.

[0158] 2.6 Fully Connected Regression Output Layer

[0159] After integration by the LSTM network, the model obtains a comprehensive hidden feature representation for each set of input samples. To convert this hidden feature into a predicted value for the specific constraint parameter A, this application sets a fully connected regression output layer after the LSTM.

[0160] This process can be represented as:

[0161]

[0162] in, The constraint parameter A is obtained from the model prediction. This represents the comprehensive hidden features output by the LSTM. and These represent the weights and biases of the regression output layer, respectively.

[0163] This application addresses a single-objective regression problem; therefore, the model ultimately outputs a scalar value, which is the predicted result of the constraint parameter A under the current combination of input parameters. After prediction, the predicted value at the normalized scale is denormalized to obtain the constraint parameter A at the true physical scale corresponding to the finite element simulation results.

[0164] 3. Machine Learning Experiments and Analysis

[0165] This application applies the Transformer-LSTM model to predict constraint parameter A, and the computational efficiency of constraint parameters can be significantly improved through machine learning methods. Based on the constraint parameter dataset generated by finite element simulation, the prediction model exhibits excellent performance under various material property mismatch conditions.

[0166] 3.1 Experimental Setup and Evaluation Indicators

[0167] The training data comes from Abaqus finite element simulation results, covering different material parameters (yield strength σ0, hardening exponent n, and material coefficient α) and geometric parameters (crack depth a / W and model thickness t / W). The dataset contains 14,904 samples, divided into training and validation sets in a 7:3 ratio. Input features include material property parameters, geometric dimensions, and applied load (σ), while the output target is the constraint parameter A.

[0168] Regarding the model, this application employs a hybrid architecture integrating Transformer and LSTM networks to train and establish the prediction model for constraint parameter A. Furthermore, to reduce the impact of data of different dimensions and orders of magnitude on the model training stability, this application uses Min-Max normalization for both the input feature X and the prediction target y, linearly mapping each dimension of the variable to the [0,1] interval.

[0169] The model training uses mean squared error as the loss function, and the Adam optimizer is used to update the parameters. The learning rate is set to 1×10. −4 The batch size is 32, and the number of training epochs is 400. The model performance evaluation metrics include mean squared error (MSE) and coefficient of determination (R²). 2 The mean absolute percentage error (MAPE) was used for evaluation. Detailed parameters of the Transformer-LSTM model are shown in Table 2.

[0170] Table 2 Transformer-LSTM Model Parameters

[0171]

[0172] In terms of evaluation metrics, this application uses three relevant metrics to measure the predictive performance of the Transformer-LSTM model: mean squared error (MSE), coefficient of determination (R²), and mean squared error (MSE). 2 ) and mean absolute percentage error (MAPE).

[0173] Mean Squared Error (MSE) measures the average of the squared differences between predicted and true values. It is one of the most commonly used and fundamental loss functions and evaluation metrics in regression tasks. Due to its squared nature, MSE penalizes larger errors more severely, making it sensitive to outliers. A smaller MSE value indicates higher prediction accuracy. The calculation formula is:

[0174]

[0175] Coefficient of determination (R) 2 This is used to quantify the model's ability to explain the fluctuations of the target variable; the closer its value is to 1, the better the model's fit. The calculation formula is:

[0176]

[0177] The Mean Absolute Percentage Error (MAPE) reflects the percentage deviation of a predicted value from the true value and is unaffected by dimensions. A smaller MAPE value indicates better prediction accuracy. The calculation formula is:

[0178]

[0179] in, For the true value, For predicted values, The mean of the true values. This represents the number of samples.

[0180] To ensure the comparability of experimental conclusions, subsequent ablation experiments and control experiments were conducted under the same data partitioning, normalization methods, and training strategies, and a consistent evaluation index system was adopted.

[0181] 3.2 Ablation Experiment

[0182] To verify the effectiveness of the Transformer-LSTM hybrid model used in this application, ablation experiments were first conducted on the Transformer-LSTM hybrid model in the experimental section. Two models, Transformer and LSTM, were constructed separately for comparison in the ablation experiments. All ablation experiments were conducted on the same dataset, with the same hyperparameter settings and training environment. The evaluation metrics of each model in the ablation experiments are shown in Table 3.

[0183] Table 3 Evaluation results of each ablation experiment model

[0184] Transformer 0.0004 0.9769 6.01% LSTM 0.0008 0.9509 7.76% Transformer-LSTM 0.0002 0.9892 3.39%

[0185] Table 3 shows the evaluation results of the ablation experiment. It can be seen that, among the three performance evaluation indicators MSE, R... 2 On both the MSE and MAPE scales, the Transformer-LSTM model performed best. Its MSE was 0.0002, lower than the Transformer model's 0.0004 and the LSTM model's 0.0008, indicating that the hybrid model effectively reduced prediction error. Meanwhile, the R-value of the Transformer-LSTM model was also lower. 2 The accuracy reached 0.9892, higher than the Transformer model's 0.9769 and the LSTM model's 0.9509, indicating a better fit to the test data. In terms of the MAPE metric, the Transformer-LSTM model achieved 3.39%, significantly lower than the other two models. Overall, the Transformer-LSTM model, by combining the global feature extraction capabilities of the Transformer with the sequence feature modeling capabilities of the LSTM, improved the model's prediction accuracy and stability, validating the effectiveness of the hybrid structure design.

[0186] Therefore, the above results indicate that the Transformer-LSTM model can significantly improve the accuracy and stability of the prediction model and has better practical usability.

[0187] from Figure 5The curves of constraint parameter A under different mismatch conditions in the ablation experiment show that the curve of constraint parameter A predicted by the Transformer-LSTM prediction model is closer to the curve of the finite element simulation results under the conditions of hardening exponent mismatch, yield strength mismatch, and material coefficient mismatch. In contrast, the curves of constraint parameter A of the Transformer model and the LSTM model show significant deviations in certain intervals. This further verifies that the Transformer-LSTM hybrid model used in this application has stronger generalization ability under the conditions of hardening exponent mismatch, yield strength mismatch, and material coefficient mismatch.

[0188] 3.3 Comparative Experiment

[0189] To more objectively and comprehensively evaluate the performance of the Transformer-LSTM hybrid model used in this application, four models—CNN, RNN, MLP, and LR—were introduced for comparison. The comparative experiments were conducted using the same dataset, hyperparameter settings, and training environment. The evaluation metrics for each model in the comparative experiments are shown in Table 4.

[0190] Table 4 Comparison results of different models

[0191] CNN 0.0004 0.9780 5.27% RNN 0.0005 0.9714 6.30% MLP 0.0005 0.9707 5.74% LR 0.0044 0.7376 22.46% Transformer-LSTM 0.0002 0.9892 3.39%

[0192] The evaluation index results of the comparative experiment in Table 3 show that the Transformer-LSTM model performed best among the different models, with the lowest MSE (0.0002) and R0. 2 The highest accuracy was 0.9892, while the lowest was MAPE at 3.39%. Compared to models such as CNN, RNN, and MLP, Transformer-LSTM exhibits higher prediction accuracy; its advantage is even more pronounced compared to LR models, indicating a strong nonlinear relationship between constraint parameter A and input features, which a single linear model cannot accurately describe. Overall, the Transformer-LSTM model can more effectively capture the complex nonlinear relationship between geometric parameters, material parameters, and constraint parameter A, thus demonstrating higher prediction accuracy and stability.

[0193] from Figure 6The comparative experiments show that the prediction curves of the various prediction models under three different mismatch conditions for constraint parameter A are more consistent with the finite element simulation results. In contrast, the RNN, CNN, MLP, and LR models exhibit varying degrees of deviation in certain intervals, with the LR model showing the most significant deviation. This result demonstrates that the relationship between constraint parameter A and material parameters, geometric parameters, and applied loads is non-linear, and further proves that the Transformer-LSTM model used in this application has superior prediction performance.

[0194] 3.4 Analysis of Experimental Conclusions

[0195] In this application, through ablation experiments and comparative experiments, the superior performance of the prediction model with constraint parameter A established using the Transformer-LSTM model in handling complex nonlinear physical relationship data is demonstrated. The Transformer-LSTM prediction model achieves excellent performance across three evaluation metrics: the lowest MSE (0.0002) and MAPE (3.39%), and the highest R-value. 2 The Transformer-LSTM model (0.9892) not only outperforms the standalone Transformer and LSTM models in ablation experiments, but also surpasses all four comparative models in comparative experiments. The results of both ablation and comparative experiments demonstrate the performance gain resulting from the effective combination of the Transformer's global attention mechanism and the LSTM's local feature extraction capabilities. Furthermore, they show that its unique hybrid architecture most effectively captures and models the complex nonlinear dependencies and structural relationships between features, thereby achieving higher prediction accuracy and stability. Therefore, the Transformer-LSTM model used in this application is a feasible prediction model for efficiently predicting constraint parameter A.

[0196] Based on the Transformer-LSTM hybrid model in machine learning, this application trains and establishes a predictive model for constraint parameter A by analyzing the values ​​of constraint parameter A on the intermediate plane at the interface crack in SENT specimens of dissimilar material joints under numerous finite element material property mismatches (including yield strength, hardening index, and material coefficient mismatches). This predictive model can quickly and effectively determine the value of constraint parameter A, thereby improving the computational efficiency of constraint parameters in the JA two-parameter method and the efficiency of related applications. It also provides preliminary experience and an effective tool for subsequent applications.

[0197] It should be noted that, in this application, the terms “comprising,” “including,” or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0198] This application uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only for the purpose of helping to understand the method and core ideas of the present invention. The above descriptions are only preferred embodiments of the present invention. It should be noted that due to the limitations of written expression, while there are objectively infinite specific structures, those skilled in the art can make several improvements, modifications, or changes without departing from the principles of the present invention, and can also combine the above technical features in an appropriate manner. These improvements, modifications, changes, or combinations, or the direct application of the inventive concept and technical solution to other situations without modification, should all be considered within the scope of protection of the present invention.

Claims

1. A machine learning prediction method for fracture constraint parameters based on the Transformer-LSTM framework, characterized in that, Includes the following steps: S1. Use Abaqus software to perform three-dimensional finite element simulation calculations on the SENT specimen of dissimilar materials to obtain the dataset as input to the model. S2. The dataset obtained in step one is organized and normalized. Then, multiple input features in each group of samples are organized into a feature sequence in a fixed order. A high-dimensional representation containing feature position information is obtained through linear embedding and positional encoding. The global dependency between input features is extracted using the Transformer encoder. S3. The enhanced feature sequence output by the Transformer is input into the LSTM network for further integration, and the predicted value of the constraint parameter A is output through the fully connected regression layer.

2. The machine learning prediction method for fracture constraint parameters based on the Transformer-LSTM framework according to claim 1, characterized in that, The dataset in S1 comes from Abaqus finite element simulation results. Each set of samples corresponds to a constraint parameter A calculated under a combination of material performance parameters, geometric parameters, and applied loads. Input features include variables such as material yield strength, hardening index, material coefficient, crack size, specimen thickness, and applied loads. The output target is the constraint parameter A under the corresponding working condition. For the i-th sample, the input-output relationship is expressed as: in, Let represent the input feature vector of the i-th sample group. , ,⋯ , Let m represent different input variables, and m represent the number of input features. This represents the true constraint parameter A corresponding to this set of samples. Min-Max normalization is applied to the input feature X and the output target y respectively, linearly mapping each variable to the [0,1] interval. The calculation formula is as follows: Where x represents the original data, and These represent the minimum and maximum values ​​of the variable in the sample data, respectively. This represents the normalized data.

3. The machine learning prediction method for fracture constraint parameters based on the Transformer-LSTM framework according to claim 2, characterized in that, Multiple input features in each set of samples are organized into a feature sequence in a fixed order. For a set of input samples: Each of them This represents a specific input feature. These features are input into the network in a fixed order so that each feature can be regarded as an element in the feature sequence.

4. The machine learning prediction method for fracture constraint parameters based on the Transformer-LSTM framework according to claim 3, characterized in that, The linear embedding process in S2 is represented as follows: in, Represents the j-th input feature. and These represent the weights and biases of the linear embedding layer, respectively. This represents the high-dimensional embedding representation corresponding to the input feature. Positional encoding is added after feature embedding to introduce the positional information of the features into the model. The positional encoding is constructed using sine and cosine functions, and its form is as follows: in, This indicates the position of the feature in the input sequence, k represents the dimension index, and d represents the embedding dimension; Finally, the feature representation input into the Transformer encoder is as follows: in, This represents the j-th feature representation after adding positional encoding. This indicates the position code for the corresponding location.

5. The machine learning prediction method for fracture constraint parameters based on the Transformer-LSTM framework according to claim 4, characterized in that, After feature embedding and position encoding are completed, the feature sequence is input into the Transformer encoder. The core of the Transformer encoder is the multi-head self-attention mechanism, which calculates the degree of correlation between input features to extract global feature dependencies. For input feature representation The self-attention mechanism first linearly maps it to a query matrix. Key matrix Sum matrix : in, , and The first matrix represents the weight matrix learned during model training. Subsequently, the self-attention mechanism calculates the correlation between different features using the query matrix and the key matrix, and then uses this correlation to perform a weighted summation of the value matrix. The calculation form is as follows: in, The dimension of the key vector. Used to scale the dot product results to improve the stability of model training; Multi-head self-attention mechanisms can learn feature relationships in parallel across multiple different feature subspaces. Their basic form is as follows: Where h represents the number of attention heads, This represents the output of the i-th attention head. This represents the output mapping matrix; after processing by multiple Transformer encoders, the output result is a feature sequence enhanced by global context.

6. The machine learning prediction method for fracture constraint parameters based on the Transformer-LSTM framework according to claim 5, characterized in that, The enhanced feature sequence output by the Transformer encoder is then fed into an LSTM network. The LSTM's forget gate controls how much information from the previous state is retained, and its calculation is as follows: in, Indicates the output of the forget gate. This indicates the hidden state at the previous moment. This represents the Transformer encoded features of the current input. and These represent the weight and bias of the forget gate, respectively. This represents the Sigmoid activation function; The input gate controls how much of the current input information is written to the cell state. Candidate memory content is represented as follows: The cell state is updated in the following ways: in, Indicates the current cell state. This indicates the previous cell state. This indicates element-wise multiplication; The output gate is used to determine how much information from the current cell state is output as a hidden state: in, Indicates the current hidden state; Through the above gating mechanism, LSTM further filters and integrates the global feature relationships extracted by Transformer; the hidden state of the last step of LSTM is taken as the comprehensive feature representation of the entire input sample; this comprehensive representation contains the complex coupling information between material parameters, geometric parameters and load parameters, which is used for the regression prediction of subsequent constraint parameter A.

7. The machine learning prediction method for fracture constraint parameters based on the Transformer-LSTM framework according to claim 6, characterized in that, After integration by the LSTM network, a comprehensive hidden feature representation for each set of input samples is obtained. To convert this hidden feature into a predicted value for the specific constraint parameter A, a fully connected regression output layer is set after the LSTM. This process can be represented as: in, The constraint parameter A is obtained from the model prediction. This represents the comprehensive hidden features output by the LSTM. and These represent the weights and biases of the regression output layer, respectively.

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