Multi-axial fatigue life prediction method based on physical information

Abstract

The invention discloses a multi-axial fatigue life prediction method based on physical information, aiming at the problem of multi-axial fatigue damage of a material, an MLP-Attention model provided by the invention adopts a multi-layer sensor MLP to process a complex nonlinear relationship, and meanwhile, aiming at the characteristics of complex data and strong nonlinearity of a multi-axial fatigue experiment, the multi-axial fatigue life prediction method based on the physical information can be used for predicting the multi-axial fatigue life of the material. A self-attention mechanism Attention is introduced, and the accuracy of a model prediction result is improved through adaptive feature weighting; for the difficulty that the multi-axial fatigue life has large discreteness, Gaussian process regression is selected and fused to perform uncertainty analysis on the prediction result so as to predict the fatigue life interval, the practicability and prediction precision of the prediction model are greatly improved, and the problem that uncertainty cannot be quantified in the traditional technology is solved.

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-axial fatigue life prediction method based on physical information. Background Art

[0002] In practical engineering applications, various aerospace devices, such as mechanical structures of nuclear power plants, power plants, and automobiles, are mostly in a multi-axial fatigue load state in most cases. The multi-axial fatigue mechanism is complex. At present, for the evaluation of multi-axial fatigue failure, generally based on the uniaxial fatigue evaluation, the complex multi-axial stress state is equivalent to the uniaxial stress and strain, and then the uniaxial fatigue life evaluation criterion is used for fatigue life prediction. However, the above uniaxial fatigue life evaluation method cannot cope with the actual complex multi-axial fatigue state, has poor prediction accuracy, is only applicable to specific materials or loading conditions, and has insufficient applicability, with theoretical and empirical limitations. Summary of the Invention

[0003] In order to solve the above problems existing in the prior art, the present invention provides a multi-axial fatigue life prediction method based on physical information. The technical problems to be solved by the present invention are realized through the following technical solutions: The present invention provides a multi-axial fatigue life prediction method based on physical information, and the method includes: Obtain multi-axial fatigue test data of a target material; Based on the multi-axial fatigue test data, obtain FS model damage parameters, SWT model damage parameters, and equivalent strain model damage parameters; use the multi-axial fatigue test data, the FS model damage parameters, the SWT model damage parameters, and the equivalent strain model damage parameters as sample data based on physical information; Perform logarithmic normalization processing and decimal scaling normalization processing on the sample data based on 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; Optimize the hyperparameters of the MLP-Attention model using the Bayesian optimization algorithm; 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 a prediction result; Construct a Gaussian process regression GPR model; use the Gaussian process regression GPR model to perform uncertainty analysis on the prediction result and predict the fatigue life interval.

[0004] Advantages of the present invention: In the solution provided by the present invention, the MLP-Attention model adopts a multi-layer perceptron (MLP) to achieve the processing of complex non-linear relationships. At the same time, in view of the characteristics of complex and highly non-linear 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 the 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 interval, greatly improving the practicability and prediction accuracy of the prediction model, and solving the problem that the uncertainty cannot be quantified in the traditional technology. Description of the drawings

[0005] Figure 1 It is a schematic diagram of the steps of a method for predicting multi-axial fatigue life based on physical information provided by an embodiment of the present invention; Figure 2 It is a detailed flowchart of a method for predicting multi-axial fatigue life based on physical information provided by an embodiment of the present invention; Figure 3 It is a schematic diagram of all loading paths in a method for predicting multi-axial fatigue life based on physical information provided by an embodiment of the present invention; Figure 4 It is a scatter plot of sensitivity analysis feature density in a method for predicting multi-axial fatigue life based on physical information provided by an embodiment of the present invention; Figure 5 It is a global feature importance diagram of sensitivity analysis in a method for predicting multi-axial fatigue life based on physical information provided by an embodiment of the present invention; Figure 6 It is a schematic diagram of the principle of the MLP-Attention model in a method for predicting multi-axial fatigue life based on physical information provided by an embodiment of the present invention; Figure 7 It is a flowchart of Bayesian hyperparameter optimization in a method for predicting multi-axial fatigue life based on physical information provided by an embodiment of the present invention; Figure 8 It is a historical diagram of Bayesian hyperparameter optimization of pure titanium material in a method for predicting multi-axial fatigue life based on physical information provided by an embodiment of the present invention; Figure 9 It is a schematic diagram of the principle of K-fold cross-validation in a method for predicting multi-axial fatigue life based on physical information provided by an embodiment of the present invention; Figure 10 It is a prediction result diagram of TC4 aluminum alloy material in a method for predicting multi-axial fatigue life based on physical information provided by an embodiment of the present invention; Figure 11 It is a prediction result diagram of a pure titanium material in a multi-axial fatigue life prediction method based on physical information provided by an embodiment of the present invention; Figure 12 It is a prediction result diagram of an SS316 material in a multi-axial fatigue life prediction method based on physical information provided by an embodiment of the present invention; Figure 13 It is an uncertainty analysis result diagram in a multi-axial fatigue life prediction method based on physical information provided by an embodiment of the present invention. Specific Embodiments

[0006] The following further describes the present invention in detail with reference to specific embodiments, but the embodiments of the present invention are not limited thereto.

[0007] Figure 1 and Figure 2 are respectively a step schematic diagram and a detailed process schematic diagram of a multi-axial fatigue life prediction method based on physical information provided by an embodiment of the present invention. The following will combine Figure 1 and Figure 2 to specifically illustrate the embodiments of the present invention.

[0008] An embodiment of the present invention provides a multi-axial fatigue life prediction method based on physical information. As Figure 1 and Figure 2 shown, it may include: S1. Obtain multi-axial fatigue test data of the target material.

[0009] For S1, it may include: Select a corresponding loading path based on the type of the target material to obtain multi-axial fatigue test data; wherein, the target material may include: pure titanium, 1Cr-Mo-V, LY12CZ, 7075-T651, SS316L, and Titanium Alloy TC4; the loading path may include: uniaxial tension-compression, pure torsion, 45° multi-axial proportional, and multi-axial non-proportional loading; the multi-axial fatigue test data may include: the amplitude of the normal strain , the amplitude of the shear strain , the amplitude of the normal stress , the amplitude of the shear stress and the experimental life , where represents the amplitude.

[0010] Specifically, the loading paths involved in obtaining the multi-axial fatigue test data are as Figure 3As shown, there are a total of 7 different loading paths, namely uniaxial tension-compression, pure torsion, 45° multiaxial proportional, and multiaxial non-proportional loading. Among them, the phase differences of multiaxial non-proportional loading can include 30°, 45°, 90°, 135°, and 180° out-of-phase loads. It can be understood that the images corresponding to phase differences of 30° and 45° are the same. The loading modes can include two methods of stress and strain control. The fatigue life covers low-cycle fatigue and high-cycle fatigue. There are a total of 152 experimental data points. Taking the SS316L material as an example for illustration, the 20 sets of multiaxial fatigue experimental data corresponding to 20 data points under four loading paths, patha, path b, path c, and path d, are shown in Table 1.

[0011] Table 1 Multiaxial Fatigue Experimental Data of SS316L Material

[0012] As can be seen from Table 1, the data of the six materials collected cover different loading conditions and are typical and representative. Therefore, the prediction results of each material can illustrate the wide applicability of the multiaxial fatigue life prediction method proposed in the embodiments of the present invention.

[0013] S2. Based on the multiaxial fatigue experimental data, obtain the damage parameters of the FS model, the damage parameters of the SWT model, and the damage parameters of the equivalent strain model; use the multiaxial fatigue experimental data, the damage parameters of the FS model, the damage parameters of the SWT model, and the damage parameters of the equivalent strain model as the sample data based on physical information.

[0014] Regarding S2, based on the multiaxial fatigue experimental data, obtaining the damage parameters of the FS model, the damage parameters of the SWT model, and the damage parameters of the equivalent strain model may include: Obtain strain parameters based on the multiaxial fatigue experimental data; the strain parameters may include: the maximum shear strain amplitude , the normal normal strain amplitude and the maximum normal stress on the critical plane ; Obtain the damage parameters of the FS model, the damage parameters of the SWT model, and the damage parameters of the equivalent strain model according to the strain parameters.

[0015] It is understandable that the physics-informed neural network adds the widely used life prediction experience to the input variables of the neural network based on the fatigue damage parameters that drive the physical equations to provide variables for establishing the constraints of the physical equations. Among various multiaxial fatigue life prediction models, the static strength model and the critical plane model are the most widely used. Among them, the prediction result of the critical plane model is more accurate. Therefore, two critical plane models and one static strength model are introduced into the pre-constructed MLP-Attention model. The three multiaxial fatigue life prediction models are: the FS (Fatemi-Socie) model with high prediction accuracy on torsional and non-proportional load paths and applicable to materials with shear failure modes, the SWT (Smith-Watson-Topper) model with insufficient prediction performance on non-proportional and torsional load paths and applicable to materials with tensile failure modes, and the equivalent strain model: the VM (Von Mises) model that is only valid under proportional cyclic loading. Before calculating the damage parameters, the corresponding strain parameters need to be obtained based on multiaxial fatigue experimental data.

[0016] The strain parameters can include: the maximum shear strain amplitude , the normal strain amplitude and the maximum normal stress on the critical plane .

[0017] Specifically, under multiaxial load conditions, the expression of the azimuth angle of the plane where the maximum shear strain is located is as follows: ; where 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 represents the phase relationship between stress and strain.

[0018] Under multiaxial non-proportional loading conditions, the expression of the maximum shear strain amplitude in any direction perpendicular to the free surface is as follows: ; where represents the normal strain amplitude, represents the loading strain ratio, represents the azimuth angle of the plane where the maximum shear strain is located, represents the equivalent Poisson's ratio, represents the phase difference.

[0019] The expression of the normal strain amplitude is as follows: ; The maximum normal stress on the critical plane has the following expression: ; wherein, represents the normal stress amplitude, represents the shear stress amplitude.

[0020] Based on the above three strain parameters, the damage parameters corresponding to the three models can be further calculated.

[0021] Specifically, obtaining the damage parameters of the FS model, the damage parameters of the SWT model, and the damage parameters of the equivalent strain model according to the strain parameters may include: According to the critical plane criterion, based on the maximum shear strain amplitude and the maximum normal stress on the critical plane , the damage parameter of the FS model is obtained by using the first formula; The first formula is as follows: ; wherein, represents an empirical parameter related to the material, represents the yield strength; Based on the normal strain amplitude and the maximum normal stress on the critical plane , the damage parameter of the SWT model is obtained by using the second formula; 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 damage parameters of the equivalent strain model are obtained by using the third formula and the fourth formula; the damage parameters of the equivalent strain model include: the damage parameter of the equivalent stress model and the damage parameter of the equivalent strain model; The third formula is as follows: ; The fourth formula is as follows: ; wherein, represents the equivalent Poisson's ratio.

[0022] S3. Perform logarithmic normalization processing and decimal scaling normalization processing on the sample data based on physical information to obtain the normalized sample data.

[0023] For S3, it may include: Perform logarithmic normalization on the experimental life in the sample data based on physical information to obtain the experimental life after normalization processing; Perform decimal scaling normalization on the remaining data in the sample data based on physical information except for the experimental life to obtain the partially normalized sample data after normalization processing; Use the experimental life after normalization processing and the partially normalized sample data after normalization processing as the normalized sample data.

[0024] It can be understood that for the sample data of machine learning models, different evaluation indicators often have different dimensions, dimension units, and magnitudes. To eliminate the dimensional influence between indicators, the present invention performs data normalization processing on the sample data. After the original data is processed by data normalization, each indicator is at the same order of magnitude, which is suitable for comprehensive comparative evaluation.

[0025] Regarding the multi-axial fatigue problem, the output data is the multi-axial fatigue life. Therefore, it is appropriate to use logarithmic normalization to process the experimental life in the sample data for processing.

[0026] Specifically, the formula for logarithmic normalization is as follows: ; where represents the data after logarithmic normalization, represents the experimental life the original data point in the corresponding data set, and are respectively the minimum and maximum values in the data set corresponding to the experimental life ;

[0027] In this way, the original data can be mapped to the range of 0 - 1 while maintaining the relative proportion of the data unchanged.

[0028] The input data includes multi-axial experimental loading conditions and damage parameters of three multi-axial fatigue models. Perform decimal scaling normalization on the remaining data in the sample data based on physical information except for the experimental life to obtain the partially normalized sample data after normalization processing.

[0029] Specifically, the formula for decimal scaling normalization is as follows: ; where represents the data after decimal scaling normalization, represents the input data, is an optional integer. By selecting an appropriate the data points after decimal scaling normalization fall within the interval .

[0030] This method is simple and effective, and can quickly scale the data to a smaller range, which helps to improve the stability and performance of the algorithm.

[0031] It can be understood that through step S3, the distribution characteristics of the data can be effectively improved, laying a foundation for subsequent data analysis and modeling. This method of comprehensively using 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.

[0032] S4. Use the SHAP tool to perform sensitivity analysis on each feature in the normalized sample data to obtain the sample data corresponding to the important features.

[0033] For S4, it can include: Use the SHAP tool to process the normalized sample data to obtain the SHAP value of each feature in the normalized sample data; For each feature in the normalized sample data, if the SHAP value corresponding to this feature meets the preset threshold, regard this feature as an important feature; Take the normalized sample data corresponding to all important features as the sample data corresponding to the important features.

[0034] Specifically, use the SHAP calculation formula to process the normalized sample data to obtain the SHAP value of each feature in the normalized sample data.

[0035] The SHAP calculation formula is as follows: ; where represents the SHAP value corresponding to the th feature in the sample data, represents the subset composed of all features in the normalized sample data except the th feature, represents the subset size, represents the set obtained by removing the element from the set i , represents the total number of features in the normalized sample data, represents the model prediction function on the feature subset , represents the a feature represents the predicted value of the -th feature on the feature subset represents the predicted output of the i -th feature on the feature subset formed by adding the -th feature to the feature subset S represents the factorial operation.

[0036] After obtaining the SHAP values corresponding to all features, sort all the SHAP values to obtain the corresponding sensitivity analysis feature density scatter plot as Figure 4 shown. It can be intuitively reflected from Figure 4 the degree of influence of each feature on the model predicted value. Figure 4 In Figure 5 , one point 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 samples, the greater the influence of the feature. The sensitivity analysis global feature importance diagram is as Figure 5 shown. It can be seen from

[0037] that the SHAP values of the damage parameters of the SWT model, the equivalent strain model VM damage parameter, and the FS model damage parameter are relatively large.

[0038] Finally, set a preset threshold, and screen the SHAP values corresponding to each feature in the normalized sample data according to the screening formula. Remove the features whose SHAP values are lower than or equal to the preset threshold as features with insignificant contributions to the model, and regard the features whose SHAP values are greater than the preset threshold as important features. ; where represents the SHAP value corresponding to the -th feature, represents the preset threshold.

[0039] Through step S4, it can be obtained that the damage parameters based on the equivalent strain model, the FS model, and the SWT model have relatively large contributions to the machine learning model, and the contributions of the stress mean and the strain mean in the multiaxial fatigue test data are relatively small. Among them, the stress can include normal stress and shear stress, and the strain can include normal strain and shear strain.

[0040] Compared with the traditional machine learning method, the embodiment of the present invention uses the SHAP tool to perform sensitivity analysis on the features in the sample data, improves the interpretability of the model, and also reduces the complexity of the model by removing unimportant features, thereby improving the training efficiency and prediction accuracy of the model.

[0041] S5. Build the MLP-Attention model based on the multi-layer perceptron (MLP) and the self-attention mechanism (Attention).

[0042] The MLP-Attention model, as Figure 6 shown, may include: An input layer (Input Layer), multiple hidden layers (Hidden Layers), an attention layer (AttentionLayer), and an output layer (Output Layer) connected in sequence; The MLP-Attention model uses the Sigmoid function as the activation function and the mean squared error as the loss function; it is trained through the backpropagation algorithm and the Adam optimization algorithm to minimize the loss function.

[0043] Specifically, the specific descriptions of the activation function, optimization algorithm, and loss function used in the MLP-Attention model are as follows: The expression of the Sigmoid function used is as follows: ; where represents the input value.

[0044] It can be understood that the purpose of using the Sigmoid function as the activation function is to introduce non-linearity and enhance the expressive power of the model. The Sigmoid function can map the input value to the range between 0 and 1, making it particularly suitable for models where the output needs to be interpreted as a probability.

[0045] The MLP-Attention model selects 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 an adaptive learning rate), and accelerates convergence by calculating the adaptive learning rate for each parameter. Its update rules are as follows: ; ; ; ; ; where represents the number of iterations, represents the first moment estimate corresponding to the th iteration, represents the The second - moment estimate corresponding to the is the exponential decay rate of the first moment, is the exponential decay rate of the second moment, usually and can be set to 0.9 and 0.999, represents the first - moment estimate corresponding to the -th iteration, represents the - 1 - th iteration's second - moment estimate, represents the -th iteration's first - moment estimate bias correction, represents the -th iteration's exponential decay rate of the first moment, represents the -th iteration's second - moment estimate bias correction, represents the -th iteration's exponential decay rate of the second moment. represents the -th iteration's corresponding gradient, represents the learning rate, represents a small constant used to prevent the denominator from being 0. represents the -th iteration's model parameters, represents the -th iteration's model parameters.

[0046] It can be understood that the number of iterations corresponds to the loop of t - times training and validation after data partitioning using K - fold cross - validation subsequently.

[0047] The mean squared error MSE is used as the loss function, and the expression of this loss function is as follows: ; where, represents the true value corresponding to the sample , represents the predicted value corresponding to the sample , represents the number of samples to be input into the loss function.

[0048] It can be understood that the MLP-Attention model proposed in the embodiments of the present invention uses a multi-layer perceptron (MLP) to implement a non-linear transformation between sample data based on physical information and multi-axial fatigue life. By introducing a self-attention mechanism (Attention) before the output layer, adaptive feature weighting is performed according to the importance of input features to improve the accuracy of prediction results. The entire model is trained through a backpropagation algorithm and an Adam optimizer to minimize the above loss function.

[0049] S6. Optimize the hyperparameters of the MLP-Attention model using the Bayesian optimization algorithm.

[0050] For the flowchart of Bayesian hyperparameter optimization, please refer to Figure 7 as shown below. Next, the specific explanation of step S6 will be combined with Figure 7 For S6, optimizing the hyperparameters of the MLP-Attention model using the Bayesian optimization algorithm may include: S61. Define the hyperparameters and the preset maximum number of iterations; the hyperparameters include: the 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 the number of training epochs.

[0051] Specifically, the hyperparameters that need to be adjusted for the MLP-Attention model include: the learning rate (Learning Rate), the number of hidden layers (Hidden Layers), the number of neurons per layer (Units per Layer), and the number of training epochs (Epochs); among them, The learning rate can control the step size of each weight update of the model. An overly high learning rate may lead to instability, while an overly low learning rate will result in a slow convergence rate or non-convergence.

[0052] The number of hidden layers can determine the complexity of the network and its representation ability, but too many layers may lead to overfitting.

[0053] The number of neurons per layer can determine the feature extraction ability of each layer. Too many may increase the computational burden, while too few may not be able to learn complex features.

[0054] The number of training epochs can ensure that the model is fully trained, but too many epochs may lead to overfitting, while too few epochs mean that the model is not fully trained.

[0055] It can be understood that hyperparameters refer to the parameters that need to be set before training a machine learning model, and they determine the training process and final performance of the model.

[0056] S62. Construct an objective function based on the MLP-Attention model, use the K-fold cross-validation method to partition the sample data corresponding to the important features, combine the objective function to output the model performance, and use the model performance as the value of the objective function.

[0057] After obtaining the objective function, the mean squared error MSE can be selected as the value of the objective function.

[0058] S63. Use the Bayesian optimization algorithm to optimize the hyperparameters of the MLP-Attention model in combination with the objective function.

[0059] Specifically, S63 can include: S631. Randomly select several parameters from the hyperparameters to form multiple hyperparameter combinations as prior data, and calculate the values of the objective function corresponding to the prior data.

[0060] S632. Use the Bayesian optimization algorithm to construct a probability model, and use the probability model to estimate the performance probability distribution of each hyperparameter combination in the prior data.

[0061] Specifically, Optuna uses Bayesian optimization to construct a probability model. Optuna is an automated hyperparameter optimization software framework that can efficiently find the best hyperparameter combination for a model in machine learning. It intelligently searches the hyperparameter space through methods such as Bayesian optimization and evolutionary strategies, thereby improving the performance of the model. Optuna is easy to use and supports multiple machine learning frameworks.

[0062] S633. Select the optimal hyperparameter combination as the new sampling point according to the performance probability distribution of each hyperparameter combination.

[0063] It can be understood that the optimal hyperparameter combination is the hyperparameter combination most likely to improve the objective function.

[0064] S634. Update the probability model using the value of the objective function corresponding to the new sampling point.

[0065] 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 region.

[0066] S635. Continuously select the corresponding parameters from the hyperparameters as the hyperparameter set using the strategy of Bayesian optimization, and use the value of the objective function corresponding to the hyperparameter set to iteratively update the probability model until the number of iterative updates reaches the preset maximum number of iterations to complete the optimization of the hyperparameters of the MLP-Attention model.

[0067] For the Bayesian hyperparameter optimization history graph of pure titanium materials, please refer to Figure 8 , Figure 8The abscissa is the number of iterations of the Bayesian hyperparameter optimization algorithm, and the ordinate is the objective function value at each iteration. As can be seen from Figure 8 , through the above steps, the hyperparameter space of the MLP-Attention model can be systematically explored to find the best configuration, thereby improving the performance and generalization ability of the model. The optimal hyperparameters of the pure titanium material are shown in Table 2: Table 2 Optimal Hyperparameters of Pure Titanium Material

[0068] For 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.

[0069] For S7, it can include: Use the K-fold cross-validation method to divide the sample data corresponding to the important features into subsets of equal size; Perform cycles of training and validation on the optimized MLP-Attention model to obtain performance metrics, and use the average value of the performance metrics as the prediction result; in each cycle, select a different subset as the validation set, and combine the remaining subsets into 1 training set; The process of one training and validation includes: Select 1 subset from the subsets as the validation set, combine the remaining subsets into 1 training set, use the training set to train the optimized MLP-Attention model, use the validation set to evaluate the model performance, and record the performance metrics corresponding to the validation set.

[0070] Specifically, aiming at the problems of high cost and few test data in multi-axis fatigue tests, and the poor generalization ability and overfitting of machine learning models using small sample data, use the K-fold cross-validation method to divide the sample data corresponding to the important features to complete the training and result evaluation of the MLP-Attention network.

[0071] Specifically, the schematic diagram of K-fold cross-validation is as shown in Figure 9 . 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 subsets, called folds. Then, the model is trained on different training sets for The training and validation are carried out. In each training, one fold is used as the validation set, and the remaining folds are used as the training set. This generates models and the corresponding validation scores. Among them, Figure 9 illustrates the situation of , and Figure 9 in represents the average value of all validation set performance metrics.

[0072] The specific training steps of the model are as follows: S01, Divide the original dataset into subsets.

[0073] S02, For each subset, use it as the validation set, and the remaining subsets as the training set.

[0074] S03, Train the model and evaluate the model performance on the validation set, and record the obtained performance metrics.

[0075] S04, Repeat steps S02 and S03 for a total of times until each subset has served as the validation set once, thus generating evaluation metrics.

[0076] S05, Take the average of the evaluation metrics as the final model performance evaluation metric.

[0077] After each iteration, calculate the performance metrics on the validation set. Finally, the average value of these metrics can be calculated to obtain a comprehensive performance evaluation as the prediction result. This method helps to reduce the performance fluctuations caused by the randomness of data partitioning and provides a more stable and reliable performance estimate. K-fold cross-validation can better utilize the limited data, reduce the variance of the estimate through multiple iterations, and provide a more robust performance evaluation. Through this method, the performance of the MLP-Attention model in the case of small samples can be evaluated more accurately, providing a solid foundation for subsequent model adjustment and optimization.

[0078] Finally, output the prediction results, conduct model evaluation and accuracy verification. The prediction results of three materials, TC4, pure titanium, and SS316, are respectively as shown in Figure 10 , 11 , and 12. The abscissa in the figure is the test life value, and the ordinate is the predicted life value. It can be seen from the figure that 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. For Figure 10For the TC4 aluminum alloy material shown, only a very small number of predicted values are outside the 2-fold dispersion band. For the other two materials, such as Figure 11 the pure titanium material shown Figure 12 and the SS316 material shown

[0079]

[0079]

[0080] the predicted fatigue life is in good agreement with the experimental fatigue life. These results indicate that the method proposed in the present invention has good prediction ability for uniaxial load (UN), multiaxial proportional load (P), and multiaxial non-proportional load (NP).

[0081] 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 of the Gaussian process regression (GPR) model to generate a probability density function of a normal distribution, and this probability density function and the multiaxial fatigue life experimental data conform to a 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.

[0082] Gaussian process regression is a non-parametric Bayesian non-linear regression method, in which any combination of a finite number of random variables follows a multivariate Gaussian distribution. Specifically, for a given input set its corresponding output set follows a joint Gaussian distribution: ; where represents the total number of samples in the input set, represents the covariance matrix, the element in and represents the covariance between the input and the predicted result corresponding to the -th input set, represents the true result corresponding to the

[0083] The covariance matrix Determined by a kernel function, which is a similarity measure between two inputs. In the embodiments of the present invention, the radial basis function is selected as the kernel function.

[0084] Covariance matrix The expression is as follows: ; Wherein, Represents the observation noise variance, Represents the exponential function, Represents the L1 norm, Represents the length scale parameter.

[0085] It can be understood that for the new input , its predicted output also follows a Gaussian distribution, and its mean and variance are respectively: ; ; Wherein, Represents the covariance vector between the test data and the training data, Represents the transpose of the covariance vector between the test data and the training data, Represents the covariance matrix, Represents the observation noise variance, Represents the identity matrix, Represents the output set.

[0086] Generally, the maximum likelihood function or the log marginal likelihood function is used to optimize the hyperparameters of the kernel function. The log marginal likelihood function used in the embodiments of the present invention is as follows: ; Wherein, Represents the natural logarithm of the likelihood function, Represents the number of samples in the input set, Represents the absolute value of, Represents the identity matrix.

[0087] Regarding S8, the Gaussian process regression GPR model is used to perform uncertainty analysis on the prediction results, and the fatigue life interval can be predicted, including: Taking the prediction results and the true results as the input set; Determining the mean function and the covariance function; Using maximum likelihood estimation combined with Bayes' theorem, based on the mean function and the covariance function, obtaining the posterior distribution corresponding to the input set; Predict the mean and variance corresponding to the new input set through the posterior distribution as the fatigue life interval.

[0088] It can be understood that by adding Gaussian process regression and performing uncertainty analysis on the output results, the uncertainty of multiaxial fatigue life prediction can be well addressed. 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 for the pure titanium material are as Figure 13 shown. Figure 13 In [figure reference], the abscissa represents the test life value and the ordinate represents the predicted life value. From Figure 13 it can be seen that the prediction results for the pure titanium material have the mean of the 95% prediction interval.

[0089] In the embodiment of the present invention, aiming at the problem of multiaxial fatigue failure of materials, a physical-information-based MLP-Attention-GPR multiaxial fatigue life prediction method is proposed. The MLP-Attention model in this method adopts a multi-layer perceptron (MLP) to achieve the processing of complex non-linear relationships. At the same time, considering the characteristics of complex and strongly non-linear multiaxial fatigue experimental data, a self-attention mechanism (Attention) is introduced to improve the accuracy of the model prediction results through adaptive feature weighting. Aiming at the difficulty of large discreteness of multiaxial fatigue life, Gaussian process regression is selected to perform uncertainty analysis on the prediction results to predict the fatigue life interval, greatly improving the practicability and prediction accuracy of the prediction model and solving the problem of inability to quantify uncertainty in traditional technologies.

[0090] It should be noted that in the description of the present invention, it should be understood that the terms "first" and "second" are only used for descriptive purposes and cannot be construed as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include one or more of such features. In the description of the present invention, "a plurality" means two or more unless otherwise specifically defined.

[0091] The above are only the preferred embodiments of the present invention and are not intended to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention are included in the protection scope of the present invention.

Claims

1. A multi-axial fatigue life prediction method based on physical information, characterized in that: include: Obtain multiaxial fatigue test data of target materials; 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; Performing logarithmic normalization and decimal calibration normalization on the sample data based on the physical information to obtain normalized sample data; Using the SHAP tool to perform sensitivity analysis on each feature in the normalized sample data 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; 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 result; A Gaussian process regression (GPR) model is constructed; and the prediction result is subjected to uncertainty analysis 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 step of obtaining multiaxial fatigue test data of the target material comprises: The corresponding loading path is selected 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.

3. The multi-axial fatigue life prediction method based on physical information according to claim 2 is characterized in that: Based on the multiaxial fatigue test data, the FS model damage parameters, SWT model damage parameters and equivalent strain model damage parameters are obtained, including: Based on the multiaxial fatigue test data, strain parameters are obtained; the strain parameters include: maximum shear strain amplitude , normal strain amplitude and the maximum normal stress on the critical surface ; The FS model damage parameters, the SWT model damage parameters and the equivalent strain model damage parameters are obtained according to the strain parameters.

4. The multi-axial fatigue life prediction method based on physical information according to claim 3 is characterized in that: 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 , using the first formula to obtain the FS model damage parameter ; The first formula is as follows: ； in, represents empirical parameters related to materials, It represents the yield strength; Based on the normal strain amplitude and the maximum normal stress on the critical surface , the damage parameters of the SWT model are obtained using the second formula ; 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 by 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.

5. The multi-axial fatigue life prediction method based on physical information according to claim 3 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 the 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 for the above are normalized by decimal calibration to obtain normalized partial sample data; The normalized experimental life and the normalized part of the sample data are used as the normalized sample data.

6. 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: Using the SHAP tool to process the normalized sample data 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.

7. 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 by the back propagation algorithm and the Adam optimization algorithm to minimize the loss function.

8. The multi-axial fatigue life prediction method based on physical information according to claim 1 is characterized in that: The method of optimizing the hyperparameters of the MLP-Attention model using the Bayesian optimization algorithm includes: 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 of 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 the 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.

9. 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 result, 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 is After a training and validation cycle, we get performance indicators, The average of the performance indicators is taken 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 with the training set, the model performance is evaluated with the validation set, and the performance indicators corresponding to the validation set are recorded.

10. The multi-axial fatigue life prediction method based on physical information according to claim 1, 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 results and the actual results 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, 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.

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