A multiaxial fatigue life prediction method based on physical information

Abstract

The present invention discloses a multi-axial fatigue life prediction method based on physical information. To address the multi-axial fatigue failure problem of materials, the MLP-Attention model proposed in the present invention adopts a multi-layer perceptron (MLP) to process complex nonlinear relationships. At the same time, in view of the complex and highly nonlinear characteristics of multi-axial fatigue test data, a self-attention mechanism (Attention) is introduced to improve the accuracy of the model prediction results through adaptive feature weighting. In view of the difficulty that multi-axial fatigue life has a large discreteness, the prediction results are subjected to uncertainty analysis by fusion Gaussian process regression to predict the fatigue life interval, which greatly improves the practicality and prediction accuracy of the prediction model and solves the problem of the inability to quantify uncertainty in traditional technologies.

Description

Technical Field

[0001] The present invention belongs to the technical field of fatigue reliability evaluation and fatigue life prediction of materials, and particularly relates to a multi-axis fatigue life prediction method based on physical information. Background Art

[0002] In actual engineering applications, various aerospace devices, such as nuclear power plants, power plants, and mechanical structures such as automobiles, are often subjected to multiaxial fatigue loading. The multiaxial fatigue mechanism is complex. Currently, multiaxial fatigue failure assessment is generally based on uniaxial fatigue assessment, which equates the complex multiaxial stress state to uniaxial stress and strain, and then uses uniaxial fatigue life assessment criteria to predict fatigue life. However, the above-mentioned uniaxial fatigue life assessment method cannot cope with the actual complex multiaxial fatigue state, has poor prediction accuracy, is only applicable to specific materials or loading conditions, has insufficient applicability, and has theoretical and empirical limitations. Summary of the Invention

[0003] To address the above-mentioned problems in the prior art, the present invention provides a multi-axial fatigue life prediction method based on physical information. The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0004] The present invention provides a multi-axial fatigue life prediction method based on physical information, the method comprising:

[0005] Obtain multiaxial fatigue test data of target materials;

[0006] Based on the multiaxial fatigue test data, FS model damage parameters, SWT model damage parameters and equivalent strain model damage parameters are obtained; the multiaxial fatigue test data, the FS model damage parameters, the SWT model damage parameters and the equivalent strain model damage parameters are used as sample data based on physical information;

[0007] Performing logarithmic normalization and decimal scaling normalization on the sample data based on the physical information to obtain normalized sample data;

[0008] Perform sensitivity analysis on each feature in the normalized sample data using the SHAP tool to obtain sample data corresponding to important features;

[0009] Construct an MLP-Attention model based on the multi-layer perceptron MLP and the self-attention mechanism Attention;

[0010] Using Bayesian optimization algorithm to optimize the hyperparameters of the MLP-Attention model;

[0011] Use the K-fold cross-validation method to divide the sample data corresponding to the important features, and input the divided sample data into the optimized MLP-Attention model to obtain the prediction results;

[0012] A Gaussian process regression (GPR) model is constructed; and uncertainty analysis is performed on the prediction results using the Gaussian process regression (GPR) model to predict the fatigue life interval.

[0013] Beneficial effects of the present invention:

[0014] In the solution provided by the present invention, the MLP-Attention model adopts a multi-layer perceptron (MLP) to realize the processing of complex nonlinear relationships. At the same time, in view of the complex and highly nonlinear characteristics of multi-axis fatigue test data, a self-attention mechanism (Attention) is introduced to improve the accuracy of the model prediction results through adaptive feature weighting. In view of the difficulty that multi-axis fatigue life has a large discreteness, the Gaussian process regression is selected to perform uncertainty analysis on the prediction results to predict the fatigue life range, which greatly improves the practicality and prediction accuracy of the prediction model and solves the problem of the inability to quantify uncertainty in traditional technologies. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 A schematic diagram of the steps of a multi-axial fatigue life prediction method based on physical information provided by an embodiment of the present invention;

[0016] Figure 2 A detailed flow chart of a multi-axial fatigue life prediction method based on physical information provided by an embodiment of the present invention;

[0017] Figure 3 A schematic diagram of all loading paths in a multi-axial fatigue life prediction method based on physical information provided by an embodiment of the present invention;

[0018] Figure 4 A characteristic density scatter plot of sensitivity analysis in a multi-axial fatigue life prediction method based on physical information provided by an embodiment of the present invention;

[0019] Figure 5 A global feature importance diagram for sensitivity analysis in a multi-axial fatigue life prediction method based on physical information provided by an embodiment of the present invention;

[0020] Figure 6 A schematic diagram of the MLP-Attention model in a multi-axial fatigue life prediction method based on physical information provided by an embodiment of the present invention;

[0021] Figure 7A flowchart of Bayesian hyperparameter optimization in a multi-axial fatigue life prediction method based on physical information provided by an embodiment of the present invention;

[0022] Figure 8 A Bayesian hyperparameter optimization history graph of pure titanium material in a multi-axial fatigue life prediction method based on physical information provided by an embodiment of the present invention;

[0023] Figure 9 A schematic diagram of the K-fold cross validation principle in a multi-axial fatigue life prediction method based on physical information provided by an embodiment of the present invention;

[0024] Figure 10 A diagram showing the prediction results of TC4 aluminum alloy material in a multi-axial fatigue life prediction method based on physical information provided in an embodiment of the present invention;

[0025] Figure 11 A diagram showing prediction results of pure titanium material in a multi-axial fatigue life prediction method based on physical information provided by an embodiment of the present invention;

[0026] Figure 12 This is a diagram showing the prediction results of SS316 material in a multi-axial fatigue life prediction method based on physical information provided by an embodiment of the present invention;

[0027] Figure 13 This is a diagram of uncertainty analysis results in a multi-axial fatigue life prediction method based on physical information provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0028] The present invention will be further described in detail below with reference to specific examples, but the embodiments of the present invention are not limited thereto.

[0029] Figure 1 and Figure 2 The following are respectively a schematic diagram of the steps and a detailed flow chart of a multi-axial fatigue life prediction method based on physical information provided by an embodiment of the present invention. Figure 1 and Figure 2 The embodiments of the present invention are described in detail.

[0030] The embodiment of the present invention provides a multi-axial fatigue life prediction method based on physical information, such as Figure 1 and Figure 2 As shown, this may include:

[0031] S1, obtain multiaxial fatigue test data of target material.

[0032] For S1, this may include:

[0033] Select the corresponding loading path based on the type of target material to obtain multiaxial fatigue test data; among them, target materials can include: pure titanium, 1Cr-Mo-V, LY12CZ, 7075-T651, SS316L and Titanium Alloy TC4; loading paths can include: uniaxial tension and compression, pure torsion, 45° multiaxial proportional and multiaxial non-proportional loading; multiaxial fatigue test data can include: normal strain amplitude , shear strain amplitude , normal stress amplitude , shear stress amplitude and experimental life ,in, Indicates amplitude.

[0034] Specifically, the loading paths involved in obtaining multiaxial fatigue test data are as follows: Figure 3 As shown in the figure, there are seven different loading paths: uniaxial tension and compression, pure torsion, 45° multiaxial proportional loading, and multiaxial non-proportional loading. The phase differences for multiaxial non-proportional loading can include 30°, 45°, 90°, 135°, and 180° out-of-phase loading. As can be understood, the images corresponding to phase differences of 30° and 45° are the same. Loading modes can include stress and strain control. Fatigue life covers both low-cycle fatigue and high-cycle fatigue, with a total of 152 experimental data points. Taking SS316L material as an example, the 20 sets of multiaxial fatigue test data corresponding to 20 data points under the four loading paths, patha, pathb, pathc, and pathd, are shown in Table 1.

[0035] Table 1 Multiaxial fatigue test data of SS316L material

[0036]

[0037] As can be seen from Table 1, the collected data of the six materials cover different loading conditions and are typical and representative. Therefore, the prediction results of each material can illustrate the wide applicability of the multi-axial fatigue life prediction method proposed in the embodiment of the present invention.

[0038] S2, based on the multiaxial fatigue test data, obtain the FS model damage parameters, SWT model damage parameters and equivalent strain model damage parameters; the multiaxial fatigue test data, FS model damage parameters, SWT model damage parameters and equivalent strain model damage parameters are used as sample data based on physical information.

[0039] For S2, based on the multiaxial fatigue test data, the FS model damage parameters, SWT model damage parameters and equivalent strain model damage parameters are obtained, which can include:

[0040] Obtain strain parameters based on multiaxial fatigue test data; strain parameters may include: maximum shear strain amplitude , normal strain amplitude and the maximum normal stress on the critical surface ;

[0041] The damage parameters of the FS model, SWT model and equivalent strain model are obtained according to the strain parameters.

[0042] As can be understood, the physics-based neural network incorporates widely used life prediction experience into the neural network's input variables based on the fatigue damage parameters driving the physical equations, providing variables for establishing physical equation constraints. Among various multiaxial fatigue life prediction models, the static strength model and critical surface model are the most widely used. The critical surface model offers more accurate predictions. Therefore, two critical surface models and one static strength model are incorporated into the pre-built MLP-Attention model. The three multiaxial fatigue life prediction models are: the FS (Fatemi-Socie) model, which has high prediction accuracy under torsional and non-proportional load paths and is suitable for materials with shear failure modes; the SWT (Smith-Watson-Topper) model, which has insufficient prediction performance under non-proportional and torsional load paths and is suitable for materials with tensile failure modes; and the VM (Von Mises) model, an equivalent strain model that is only effective under proportional cyclic loading. Before calculating damage parameters, the corresponding strain parameters must be obtained from multiaxial fatigue experimental data.

[0043] Strain parameters may include: Maximum shear strain amplitude , normal strain amplitude and the maximum normal stress on the critical surface .

[0044] Specifically, under multiaxial loading conditions, the expression for the azimuth angle of the plane where the maximum shear strain is located is as follows:

[0045] ;

[0046] in, represents the loading strain ratio, , represents the shear strain amplitude, represents the normal strain amplitude, represents the equivalent Poisson's ratio, which is related to the material properties. represents the phase difference, which specifically indicates the phase relationship between stress and strain.

[0047] The maximum shear strain amplitude in any direction perpendicular to the free surface under multiaxial non-proportional loading conditions The expression is as follows:

[0048] ;

[0049] in, represents the normal strain amplitude, represents the loading strain ratio, represents the azimuth of the plane of maximum shear strain, represents the equivalent Poisson's ratio, Indicates the phase difference.

[0050] Normal strain amplitude The expression is as follows:

[0051] ;

[0052] Maximum normal stress on the critical surface The expression is as follows:

[0053] ;

[0054] in, represents the normal stress amplitude, represents the shear stress amplitude.

[0055] Based on the above three strain parameters, the damage parameters corresponding to the three models can be further calculated.

[0056] Specifically, the FS model damage parameters, SWT model damage parameters, and equivalent strain model damage parameters are obtained according to the strain parameters, which may include:

[0057] According to the critical surface criterion, based on the maximum shear strain amplitude and the maximum normal stress on the critical surface , use the first formula to get the FS model damage parameter ;

[0058] The first formula is as follows:

[0059] ;

[0060] in, Expressed as empirical parameters related to the material, represents yield strength;

[0061] Based on the normal strain amplitude and the maximum normal stress on the critical surface , use the second formula to get the SWT model damage parameter ;

[0062] The second formula is as follows:

[0063] ;

[0064] Based on the normal strain amplitude , shear strain amplitude , normal stress amplitude and shear stress amplitude , the equivalent strain model damage parameters are obtained using the third and fourth formulas; the equivalent strain model damage parameters include: equivalent stress model damage parameters and equivalent strain model damage parameters ;

[0065] The third formula is as follows:

[0066] ;

[0067] The fourth formula is as follows:

[0068] ;

[0069] in, represents the equivalent Poisson's ratio.

[0070] S3, performing logarithmic normalization and decimal scaling normalization on the sample data based on the physical information to obtain normalized sample data.

[0071] For S3, this can include:

[0072] Experimental lifetime in sample data based on physical information Perform logarithmic normalization to obtain the normalized experimental lifespan;

[0073] In addition to the experimental life of the sample data based on physical information The rest of the data except the 1 is normalized by decimal calibration to obtain normalized partial sample data;

[0074] The normalized experimental life and the normalized partial sample data are taken as the normalized sample data.

[0075] It is understandable that for the sample data of the machine learning model, different evaluation indicators often have different dimensions, dimensional units and magnitudes. In order to eliminate the dimensional influence between indicators, the present invention performs data normalization on the sample data. After the original data is normalized, the various indicators are at the same order of magnitude, which is suitable for comprehensive comparative evaluation.

[0076] For multiaxial fatigue problems, the output data is multiaxial fatigue life, so it is appropriate to use logarithmic normalization to normalize the experimental life in the sample data. to be processed.

[0077] Specifically, the logarithmic normalization formula is as follows:

[0078] ;

[0079] in, represents the log-normalized data, Indicates experimental life The original data points in the corresponding dataset, and Experimental lifespan The minimum and maximum values ​​in the corresponding dataset.

[0080] In this way, the original data can be mapped to the range of 0-1 while keeping the relative scale of the data unchanged.

[0081] The input data include multiaxial experimental loading conditions and damage parameters of three multiaxial fatigue models. The remaining data except the , are normalized by decimal calibration to obtain the normalized partial sample data.

[0082] Specifically, the formula for decimal scaling normalization is as follows:

[0083] ;

[0084] in, represents the data after decimal calibration and normalization, Represents input data, is an integer that can be selected by choosing the appropriate Make the data points normalized after decimal scaling Falling into the range Inside.

[0085] This method is simple and effective, and can quickly scale data to a smaller range, helping to improve the stability and performance of the algorithm.

[0086] As can be understood, step S3 can effectively improve the distribution characteristics of the data, laying the foundation for subsequent data analysis and modeling. This method of combining multiple normalization techniques not only improves the flexibility of data processing, but also enhances the adaptability and robustness of the model to different types of data.

[0087] S4, use the SHAP tool to perform sensitivity analysis on each feature in the normalized sample data to obtain sample data corresponding to important features.

[0088] For S4, this may include:

[0089] Use the SHAP tool to process the normalized sample data to obtain the SHAP value of each feature in the normalized sample data;

[0090] For each feature in the normalized sample data, if the SHAP value corresponding to the feature meets the preset threshold, the feature is regarded as an important feature;

[0091] The normalized sample data corresponding to all important features are used as the sample data corresponding to the important features.

[0092] Specifically, the normalized sample data is processed using the SHAP calculation formula to obtain the SHAP value of each feature in the normalized sample data.

[0093] The SHAP calculation formula is as follows:

[0094] ;

[0095] in, Indicates the first The SHAP value corresponding to each feature, Indicates that after normalization, the sample data is The subset of all features except features, Representation subset The size of Represents from the set Remove elements from i The resulting set, Represents the total number of features of the normalized sample data, Indicated in feature subset The model prediction function on Indicates the Features, Indicates the first The predicted value of a feature, Indicates that in the feature subset S plus the i On the feature subset composed of features The predicted output of features, Represents the factorial operation.

[0096] After obtaining the SHAP values ​​corresponding to all features, all SHAP values ​​are sorted to obtain the corresponding sensitivity analysis feature density scatter plot as shown in the figure. Figure 4 As shown, from Figure 4 The influence of each feature on the model prediction value can be intuitively reflected in Figure 4Each point in the figure represents a sample data. Therefore, the redder the color in the figure, the larger the SHAP value of the feature itself, and the bluer the color, the smaller the SHAP value of the feature itself. The more dispersed the distribution of the sample, the greater the influence of the feature. The sensitivity analysis global feature importance diagram is as follows Figure 5 As shown, from Figure 5 It can be seen that the SHAP values ​​of the damage parameters of the SWT model, the equivalent strain model VM damage parameters and the FS model damage parameters are larger.

[0097] Finally, a preset threshold is set, and the SHAP value corresponding to each feature in the normalized sample data is screened according to the screening formula. Features with SHAP values ​​lower than or equal to the preset threshold are removed as features that do not contribute significantly to the model, and features with SHAP values ​​greater than the preset threshold are regarded as important features.

[0098] The screening formula is as follows:

[0099] ;

[0100] in, Indicates the The SHAP value corresponding to each feature, Indicates the preset threshold.

[0101] Through step S4, it can be concluded that the damage parameters based on the equivalent strain model, FS model, and SWT model have a greater contribution to the machine learning model, while the contribution of the stress mean and strain mean in the multiaxial fatigue test data is relatively small. Stress can include normal stress and shear stress, and strain can include normal strain and shear strain.

[0102] Compared with traditional machine learning methods, the embodiments of the present invention use the SHAP tool to perform sensitivity analysis on features in sample data, thereby improving the interpretability of the model and reducing the complexity of the model by removing unimportant features, thereby improving the training efficiency and prediction accuracy of the model.

[0103] S5, builds an MLP-Attention model based on the multi-layer perceptron MLP and self-attention mechanism Attention.

[0104] MLP-Attention model, such as Figure 6 As shown, this may include:

[0105] The input layer, multiple hidden layers, attention layer and output layer are connected in sequence;

[0106] The MLP-Attention model uses the Sigmoid function as the activation function and the mean square error as the loss function; it is trained through the backpropagation algorithm and the Adam optimization algorithm to minimize the loss function.

[0107] Specifically, the activation function, optimization algorithm, and loss function used in the MLP-Attention model are described as follows:

[0108] The expression of the Sigmoid function used is as follows:

[0109] ;

[0110] in, Represents the input value.

[0111] As you can understand, the purpose of using the Sigmoid function as an activation function is to introduce nonlinearity and enhance the expressiveness of the model. The Sigmoid function can map input values ​​to a range between 0 and 1, making it particularly suitable for models where the output needs to be interpreted as probabilities.

[0112] The MLP-Attention model uses the Adam (Adaptive Moment Estimation) optimization algorithm to effectively train the model and minimize the loss function. The Adam optimization algorithm combines the advantages of the momentum method and RMSProp (Root Mean Square Propagation, an optimization algorithm with adaptive learning rates) to accelerate convergence by calculating an adaptive learning rate for each parameter. Its update rule is as follows:

[0113] ;

[0114] ;

[0115] ;

[0116] ;

[0117] ;

[0118] in, represents the number of iterations, Indicates the The first-order moment estimate corresponding to the iteration is, Indicates the The second-order moment estimate corresponding to the iteration is, is the exponential decay rate of the first-order moment, is the exponential decay rate of the second-order moment, usually and Can be set to 0.9 and 0.999, Indicates the The first-order moment estimate corresponding to the iteration is, Indicates the -1 iteration corresponding to the second-order moment estimate, Indicates the The first-order moment estimation bias correction corresponding to the iteration is Indicates the The exponential decay rate of the first-order moment corresponding to the iteration, Indicates the The second-order moment estimation bias correction corresponding to the iteration is Indicates the The exponential decay rate of the second-order moment corresponding to the iterations. Indicates the The corresponding gradient at the iteration is, represents the learning rate, Represents a small constant used to prevent the denominator from being zero. Indicates the The model parameters at the iteration, Indicates the The model parameters at the iteration.

[0119] Understandably, the number of iterations This corresponds to the subsequent cycle of t training and validation after data partitioning using K-fold cross validation.

[0120] The mean square error (MSE) is used as the loss function, and the expression of the loss function is as follows:

[0121] ;

[0122] in, Representation sample The corresponding true value, Representation sample The corresponding predicted value, Indicates the number of samples that need to be input into the loss function.

[0123] It can be understood that the MLP-Attention model proposed in the embodiment of the present invention uses a multi-layer perceptron MLP to realize the nonlinear transformation between sample data based on physical information and multi-axis fatigue life. By introducing the self-attention mechanism Attention before the output layer Output Layer, adaptive feature weighting is performed according to the importance of the input features to improve the accuracy of the prediction results; the entire model is trained through the backpropagation algorithm and the Adam optimizer to minimize the above loss function.

[0124] S6, uses the Bayesian optimization algorithm to optimize the hyperparameters of the MLP-Attention model.

[0125] For a flowchart of Bayesian hyperparameter optimization, see Figure 7 As shown below, we will combine Figure 7 A detailed explanation of step S6 is provided. For S6, the hyperparameters of the MLP-Attention model are optimized using the Bayesian optimization algorithm, which may include:

[0126] S61, define hyperparameters and preset maximum number of iterations; the hyperparameters include: learning rate, the number of hidden layers in the MLP-Attention model, the number of neurons in each layer of the MLP-Attention model, and the optimization space of training rounds.

[0127] Specifically, the hyperparameters that need to be adjusted for the MLP-Attention model include: learning rate, number of hidden layers, number of neurons per layer (Units per Layer), and training rounds (Epochs);

[0128] The learning rate can control the step size of each weight update of the model. Too high a learning rate may cause instability, while too low a learning rate may lead to slow convergence or even failure to converge.

[0129] The number of hidden layers can determine the complexity of the network and its representation ability, but too many layers may lead to overfitting.

[0130] The number of neurons in each layer determines the feature extraction capability of each layer. Too many neurons may increase the computational burden, while too few neurons may not be able to learn complex features.

[0131] The number of training epochs ensures that the model is fully trained, but too many epochs may lead to overfitting, while too few epochs may result in undertraining.

[0132] As you can understand, hyperparameters refer to parameters that need to be set before training a machine learning model. They determine the training process and final performance of the model.

[0133] S62, build an objective function based on the MLP-Attention model, use the K-fold cross-validation method to divide the sample data corresponding to important features, combine the objective function to output the model performance, and use the model performance as the value of the objective function.

[0134] After obtaining the objective function, you can choose to use the mean square error MSE as the value of the objective function.

[0135] S63, use the Bayesian optimization algorithm combined with the objective function to optimize the hyperparameters of the MLP-Attention model.

[0136] Specifically, S63 may include:

[0137] S631, randomly selecting several parameters from the hyperparameters to form multiple hyperparameter combinations as prior data, and calculating the value of the objective function corresponding to the prior data.

[0138] S632, using a Bayesian optimization algorithm to construct a probability model, and using the probability model to estimate the performance probability distribution of each hyperparameter combination in the prior data.

[0139] Specifically, Optuna uses Bayesian optimization to build probabilistic models. Optuna is an automated hyperparameter optimization software framework that efficiently finds the optimal hyperparameter combination for machine learning models. It intelligently searches the hyperparameter space using methods like Bayesian optimization and evolutionary strategies to improve model performance. Optuna is easy to use and supports multiple machine learning frameworks.

[0140] S633: Select the optimal hyperparameter combination as a new sampling point based on the performance probability distribution of each hyperparameter combination.

[0141] It can be understood that the optimal hyperparameter combination is the hyperparameter combination that is most likely to improve the objective function.

[0142] S634: Update the probability model using the value of the objective function corresponding to the new sampling point.

[0143] It can be understood that by updating the probability model, the distribution of the next sampling is adjusted to be closer to the optimal value area.

[0144] S635, using the Bayesian optimization strategy to continuously select corresponding parameters from the hyperparameters as the hyperparameter set, and iteratively update the probability model using the value of the objective function corresponding to the hyperparameter set until the number of iterative updates reaches the preset maximum number of iterations, so as to complete the optimization of the hyperparameters of the MLP-Attention model.

[0145] For a Bayesian hyperparameter optimization history graph of pure titanium, see Figure 8 , Figure 8 The horizontal axis is the number of iterations of the Bayesian hyperparameter optimization algorithm, and the vertical axis is the objective function value at each iteration. Figure 8 As can be seen from the above steps, the hyperparameter space of the MLP-Attention model can be systematically explored to find the optimal configuration, thereby improving the performance and generalization ability of the model. The optimal hyperparameters for pure titanium material are shown in Table 2:

[0146] Table 2 Optimal hyperparameters of pure titanium material

[0147]

[0148] S7, use the K-fold cross-validation method to divide the sample data corresponding to the important features, and input the divided sample data into the optimized MLP-Attention model to obtain the prediction results.

[0149] For S7, this can include:

[0150] The K-fold cross validation method is used to divide the sample data corresponding to the important features into subsets of equal size;

[0151] The optimized MLP-Attention model After a training and validation cycle, we get performance indicators, The average value of the performance indicators is used as the prediction result; in each cycle, a different subset is selected as the validation set, and the rest The subsets are merged into one training set;

[0152] The training and validation process includes:

[0153] choose One of the subsets is used as the validation set, and the rest The subsets are merged into one training set, the optimized MLP-Attention model is trained using the training set, the model performance is evaluated using the validation set, and the performance indicators corresponding to the validation set are recorded.

[0154] Specifically, given the high cost of multi-axial fatigue testing and the limited amount of test data, using small sample data for machine learning can easily lead to poor model generalization and overfitting. K-fold cross-validation is used to divide the sample data corresponding to important features to complete MLP-Attention network training and result evaluation.

[0155] Specifically, the principle diagram of K-fold cross validation is as follows Figure 9 As shown, K-fold cross-validation is a model evaluation technique used to evaluate the performance of machine learning models on training data. It divides the original dataset into Then, the model on different training sets In each training, one of the folds is used as a validation set, and the remaining folds are used as validation sets. folds are used as training sets. This yields Models and corresponding Verification scores. Figure 9 Indicated situation, Figure 9 middle Represents the average of all validation set performance indicators.

[0156] The specific training steps of the model are as follows:

[0157] S01, divide the original data set into subsets.

[0158] S02, for each subset, use it as a validation set, and the rest A subset is used as the training set.

[0159] S03: Train the model and evaluate the model performance on the validation set, recording the performance indicators obtained.

[0160] S04, repeat steps S02 and S03 for a total of times, until each subset serves as a validation set, thus generating evaluation indicators.

[0161] S05, yes The average of the evaluation indicators is taken as the final model performance evaluation indicator.

[0162] After each iteration, performance metrics are calculated on the validation set. Ultimately, these metrics are averaged to provide a comprehensive performance evaluation as the prediction result. This approach helps reduce performance fluctuations caused by random data partitioning, providing more stable and reliable performance estimates. K-fold cross-validation can better utilize limited data, reducing the variance of estimates through multiple iterations, and providing a more robust performance evaluation. This approach can more accurately evaluate the performance of the MLP-Attention model in small sample sizes, providing a solid foundation for subsequent model tuning and optimization.

[0163] Finally, the prediction results are output to conduct model evaluation and accuracy verification. The prediction results of TC4, pure titanium and SS316 are as follows: Figure 10 、 11 As shown in Figure 12, the horizontal axis is the test life value, and the vertical axis is the predicted life value. As can be seen from the figure, most of the test set predictions of the three materials are within the Twice scatter band, and the predictions within the 1.5 scatter band also account for a high proportion. Figure 10 For the TC4 aluminum alloy shown in the figure, only a few of the predicted values ​​are outside the 2-fold dispersion band. Figure 11 Pure titanium material shown, Figure 12 The predicted life of SS316 material is shown to be in good agreement with the experimental fatigue life. These results indicate that the proposed method has good prediction capabilities for uniaxial loading (UN), multiaxial proportional loading (P) and multiaxial non-proportional loading (NP).

[0164] S8, constructing a Gaussian process regression (GPR) model; using the Gaussian process regression (GPR) model to perform uncertainty analysis on the prediction results and predict the fatigue life range.

[0165] Understandably, multiaxial fatigue life has a large discreteness due to uncertainties arising from uncertainties in the material microstructure and variability in the geometry and manufacturing of the experimental specimens. Therefore, the present invention constructs a Gaussian process regression (GPR) model capable of performing interval fatigue life prediction to quantify these uncertainties.

[0166] Specifically, the relationship between the input variables based on physical information and the target experimental fatigue life can be determined from the prediction results. The prediction results output by the MLP-Attention model are used as the input to the Gaussian Process Regression (GPR) model to generate a normally distributed probability density function. This probability density function and the multiaxial fatigue life experimental data conform to the lognormal distribution. The normal distribution is represented by the mean and covariance. The mean is the prediction result, and the covariance reflects the corresponding uncertainty.

[0167] Gaussian process regression is a nonparametric Bayesian nonlinear regression method in which any finite number of random variables follow a multivariate Gaussian distribution. Specifically, for a given input set , and its corresponding output set Follows a joint Gaussian distribution:

[0168] ;

[0169] in, represents the total number of samples in the input set, represents the covariance matrix, Elements in Represents input and The covariance between Indicates the The prediction results corresponding to the input set, Indicates the The actual result corresponding to the input set.

[0170] Covariance matrix It is determined by a kernel function, which is a similarity measure between two inputs. In this embodiment of the present invention, a radial basis function is selected as the kernel function.

[0171] Covariance matrix The expression is as follows:

[0172] ;

[0173] in, represents the observation noise variance, represents the exponential function, represents the L1 norm, represents the length scale parameter.

[0174] Understandably, for new input , its predicted output Also follows a Gaussian distribution, with a mean and variance They are:

[0175] ;

[0176] ;

[0177] in, represents the covariance vector of the test data and the training data, represents the transpose of the covariance vector of the test data and the training data, represents the covariance matrix, represents the observation noise variance, represents the identity matrix, Represents the output collection.

[0178] Typically, a maximum likelihood function or a log-marginal likelihood function is used to optimize the hyperparameters of the kernel function. The log-marginal likelihood function used in this embodiment of the present invention is as follows:

[0179] ;

[0180] in, represents the natural logarithm of the likelihood function, represents the number of samples in the input set, express The absolute value of Represents the identity matrix.

[0181] For S8, the Gaussian process regression (GPR) model is used to perform uncertainty analysis on the prediction results and predict the fatigue life range, which can include:

[0182] Take the predicted results and the actual results as input sets;

[0183] Determine the mean function and covariance function;

[0184] Using maximum likelihood estimation combined with Bayesian theorem, based on the mean function and covariance function, the posterior distribution corresponding to the input set is obtained;

[0185] The mean and variance corresponding to the new input set are predicted through the posterior distribution as the fatigue life interval.

[0186] It is understandable that by adding Gaussian process regression and performing uncertainty analysis on the output results, the uncertainty of multi-axial fatigue life prediction can be well dealt with. The mean function can be set to 0 to define the Gaussian process. The output of the Gaussian process is the mean and variance, where the mean represents the predicted life value and the variance represents the uncertainty of the prediction. The prediction results of pure titanium material are as follows: Figure 13 As shown, Figure 13 The horizontal axis represents the test life value, and the vertical axis represents the predicted life value. Figure 13 It can be seen that the prediction results for pure titanium material have a mean of 95% prediction interval.

[0187] In response to the multi-axial fatigue failure problem of materials, an embodiment of the present invention proposes a physical information-based MLP-Attention-GPR multi-axial fatigue life prediction method. The MLP-Attention model in this method adopts a multi-layer perceptron (MLP) to process complex nonlinear relationships. At the same time, in view of the complex and highly nonlinear characteristics of multi-axial fatigue test data, a self-attention mechanism (Attention) is introduced to improve the accuracy of the model prediction results through adaptive feature weighting. In view of the difficulty that multi-axial fatigue life has a large discreteness, Gaussian process regression is selected to perform uncertainty analysis on the prediction results to predict the fatigue life range, which greatly improves the practicality and prediction accuracy of the prediction model and solves the problem of the inability to quantify uncertainty in traditional technologies.

[0188] It should be noted that, in the description of the present invention, it should be understood that the terms "first" and "second" are used for descriptive purposes only and should not be understood to indicate or imply relative importance or implicitly specify the number of the technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, "plurality" means two or more, unless otherwise specifically defined.

[0189] The above description is only a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention are included in the scope of protection of the present invention.

Claims

1. A multiaxial fatigue life prediction method based on physical information, characterized in that: include: Obtaining multiaxial fatigue test data of a target material, including: selecting a corresponding loading path based on the type of the target material to obtain multiaxial fatigue test data; wherein the target materials include: pure titanium, 1Cr-Mo-V, LY12CZ, 7075-T651, SS316L and Titanium Alloy TC4; the loading paths include: uniaxial tension and compression, pure torsion, 45° multiaxial proportional and multiaxial non-proportional loading; the multiaxial fatigue test data include: normal strain amplitude , shear strain amplitude , normal stress amplitude , shear stress amplitude and experimental life ,in, Indicates amplitude; Based on the multiaxial fatigue test data, FS model damage parameters, SWT model damage parameters, and equivalent strain model damage parameters are obtained; the multiaxial fatigue test data, the FS model damage parameters, the SWT model damage parameters, and the equivalent strain model damage parameters are used as sample data based on physical information; based on the multiaxial fatigue test data, the FS model damage parameters, the SWT model damage parameters, and the equivalent strain model damage parameters are obtained, including: Strain parameters are obtained based on the multiaxial fatigue test data; the strain parameters include: maximum shear strain amplitude , normal strain amplitude and the maximum normal stress on the critical surface ; According to the strain parameters, the FS model damage parameters, the SWT model damage parameters and the equivalent strain model damage parameters are obtained, including: based on the maximum shear strain amplitude and the maximum normal stress on the critical surface , use the first formula to get the FS model damage parameter ; The first formula is as follows: ； in, represents empirical parameters related to the material, represents yield strength; Based on the normal strain amplitude and the maximum normal stress on the critical surface , use the second formula to get the SWT model damage parameter ; The second formula is as follows: ； Based on the normal strain amplitude , the shear strain amplitude , the normal stress amplitude and the shear stress amplitude , the equivalent strain model damage parameters are obtained using the third formula and the fourth formula; the equivalent strain model damage parameters include: equivalent stress model damage parameters and equivalent strain model damage parameters ; The third formula is as follows: ； The fourth formula is as follows: ； in, represents the equivalent Poisson's ratio; Performing logarithmic normalization and decimal scaling normalization on the sample data based on the physical information to obtain normalized sample data; Perform sensitivity analysis on each feature in the normalized sample data using the SHAP tool to obtain sample data corresponding to important features; Construct an MLP-Attention model based on the multi-layer perceptron MLP and the self-attention mechanism Attention; Using Bayesian optimization algorithm to optimize the hyperparameters of the MLP-Attention model; Use the K-fold cross-validation method to divide the sample data corresponding to the important features, and input the divided sample data into the optimized MLP-Attention model to obtain the prediction results; A Gaussian process regression (GPR) model is constructed; and uncertainty analysis is performed on the prediction results using the Gaussian process regression (GPR) model to predict the fatigue life interval.

2. The multi-axial fatigue life prediction method based on physical information according to claim 1 is characterized in that: The sample data based on the physical information is subjected to logarithmic normalization and decimal scaling normalization to obtain normalized sample data, including: The experimental life of the sample data based on physical information Perform logarithmic normalization to obtain the normalized experimental lifespan; The sample data based on physical information is divided into experimental life The rest of the data except the 1 is normalized by decimal calibration to obtain normalized partial sample data; The normalized experimental life and the normalized partial sample data are used as the normalized sample data.

3. The multi-axial fatigue life prediction method based on physical information according to claim 1 is characterized in that: A sensitivity analysis is performed on each feature in the normalized sample data using the SHAP tool to obtain sample data corresponding to important features, including: The normalized sample data is processed using the SHAP tool to obtain a SHAP value for each feature in the normalized sample data; For each feature in the normalized sample data, if the SHAP value corresponding to the feature meets a preset threshold, the feature is regarded as an important feature; The normalized sample data corresponding to all important features are used as the sample data corresponding to the important features.

4. The multi-axial fatigue life prediction method based on physical information according to claim 1 is characterized in that: The MLP-Attention model includes: The input layer, multiple hidden layers, attention layer and output layer are connected in sequence; The MLP-Attention model uses the Sigmoid function as the activation function and the mean square error as the loss function; it is trained through the back propagation algorithm and the Adam optimization algorithm to minimize the loss function.

5. The multi-axial fatigue life prediction method based on physical information according to claim 1 is characterized in that: The Bayesian optimization algorithm is used to optimize the hyperparameters of the MLP-Attention model, including: Defining hyperparameters and presetting the maximum number of iterations; the hyperparameters include: learning rate, the number of hidden layers in the MLP-Attention model, the number of neurons in each layer of the MLP-Attention model, and the optimization space for training rounds; Constructing an objective function based on the MLP-Attention model, using the K-fold cross-validation method to divide the sample data corresponding to important features, outputting the model performance in combination with the objective function, and using the model performance as the value of the objective function; The hyperparameters of the MLP-Attention model are optimized using a Bayesian optimization algorithm combined with the objective function.

6. The multi-axial fatigue life prediction method based on physical information according to claim 1 is characterized in that: The K-fold cross-validation method is used to divide the sample data corresponding to the important features, and the divided sample data is input into the optimized MLP-Attention model to obtain the prediction results, including: The K-fold cross validation method is used to divide the sample data corresponding to the important features into subsets of equal size; The optimized MLP-Attention model After a training and validation cycle, we get performance indicators, The average value of the performance indicators is used as the prediction result; in each cycle, a different subset is selected as the validation set, and the rest The subsets are merged into one training set; The training and validation process includes: choose One of the subsets is used as the validation set, and the rest The subsets are merged into one training set, the optimized MLP-Attention model is trained using the training set, the model performance is evaluated using the validation set, and the performance indicators corresponding to the validation set are recorded.

7. The multi-axial fatigue life prediction method based on physical information according to claim 1 is characterized in that: The Gaussian process regression (GPR) model is used to perform uncertainty analysis on the prediction results to predict the fatigue life range, including: Taking the predicted result and the actual result as an input set; Determine the mean function and covariance function; Using maximum likelihood estimation combined with Bayesian theorem, based on the mean function and the covariance function, to obtain the posterior distribution corresponding to the input set; The mean and variance corresponding to the new input set are predicted through the posterior distribution as the fatigue life interval.

Images