Material multi-axial fatigue life prediction method based on physical information residual neural network
By introducing physical information residual connections into the neural network and combining it with the Mises equivalent stress model, the accuracy and stability problems of material fatigue life prediction in the existing technology are solved, and more efficient multi-axis fatigue life prediction is achieved.
Patent Information
- Application Number
- CN202510776571.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-06-11
- Publication Date
- 2025-10-17
AI Technical Summary
Existing technologies have problems with insufficient accuracy and stability in material fatigue life prediction, especially under complex multi-axial loading conditions, and data-driven methods lack the ability to explain fatigue mechanisms.
A method based on physical information residual neural network is adopted. The prior physical information of the Mises equivalent stress model is introduced into the neural network model through residual connection. Combined with the data-driven method, a physical information residual neural network model is constructed to improve the prediction accuracy and stability.
The accuracy and stability of multiaxial fatigue life prediction are significantly improved, especially under small sample sizes and complex loading conditions, and the generalization ability and physical consistency of the model are enhanced.
Smart Images
Figure CN120805653A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of fatigue life prediction, and in particular to a material multi-axial fatigue life prediction method based on physical information residual neural network. Background Art
[0002] Predicting material fatigue life is an important research topic in engineering, particularly in industries such as aerospace, automotive manufacturing, and nuclear energy. The fatigue performance of structural materials under complex multiaxial loading directly impacts the safety and reliability of structures. Traditional fatigue life prediction methods often rely on experimental data or empirical formulas. While these methods can provide a certain degree of prediction accuracy, they often have limitations due to their reliance on large amounts of test data and their inability to fully consider material behavior under complex loading conditions. With the advancement of computing power and artificial intelligence technology, data-driven fatigue life prediction methods have gradually gained widespread application. In particular, machine learning methods such as neural networks can capture the nonlinear relationship between material fatigue life and loading characteristics by learning from large amounts of experimental data, thereby improving prediction accuracy to a certain extent. However, purely data-driven methods are prone to overfitting when modeling small samples, high-dimensional data, and complex physical processes, and lack the ability to explain fatigue mechanisms. Summary of the Invention
[0003] The purpose of the present invention is to overcome the shortcomings of the existing technology and provide a material multi-axial fatigue life prediction method based on physical information residual neural network. The prior physical information based on the theoretical prediction model is introduced into the neural network model through residual connection, which improves the prediction accuracy and stability, and can effectively solve the accuracy and stability problems existing in the material fatigue life prediction under complex multi-axial load conditions.
[0004] The present invention solves the technical problem by the following technical solutions:
[0005] A multi-axial fatigue life prediction method based on physical information residual neural network, characterized in that the prediction method comprises the following steps:
[0006] 1) Collect multiaxial fatigue test sample data sets of materials under different stress levels and different multiaxial loading paths. Each sample collection includes the corresponding axial stress amplitude σ a , torsional stress amplitude τ a and fatigue life value N f ;
[0007] 2) Based on the axial stress amplitude and torsional stress amplitude of each multiaxial fatigue test sample, the Mises equivalent stress amplitude σ of each sample is calculated using formula (1): Mises , and further calculate the corresponding theoretical fatigue life value N based on formula (2)f,Mises ;
[0008]
[0009] σ Mises = σ f (N f,Mises ) b (2)
[0010] Wherein, σ f is the material fatigue strength coefficient, b is the material fatigue strength index.
[0011] 3) Taking the axial stress amplitude σ a , the torsional stress amplitude τ a and the Mises equivalent stress amplitude σ Mises of the experimental sample as input features, and taking the logarithmic fatigue life value lg(N f ) as output feature, an artificial neural network model including several hidden layers is designed;
[0012] 4) On the basis of the designed artificial neural network model including several hidden layers, the theoretical fatigue life value N f,Mises is logarithmically processed and connected with the artificial neural network model prediction value, and finally a physical information residual neural network model fusing Mises equivalent stress model information is established;
[0013] 5) Based on the aforementioned constructed physical information residual neural network model, the fatigue experimental sample data set collected is used for training, and in the training process, the error between the logarithm of the fatigue life value measured by experiment lg(N f ) and the logarithm of the model prediction value lg(N f,pre ) is taken as the objective function, and the loss function value is calculated. Through the iterative updating of each layer weight parameter in the neural network by the back propagation algorithm, the model structure is constantly optimized, so that the prediction value can be as close as possible to the experimental value, and the prediction error is reduced to the maximum extent; after the training is completed, the current model parameters are saved as the final version of the fatigue life prediction model;
[0014] 6) The experimental sample data not participating in the training process is input into the aforementioned trained physical information residual neural network model, and the fatigue life prediction value corresponding to the sample is obtained through forward calculation, so as to realize the rapid estimation and prediction of the multi-axial fatigue life of the new sample, and verify the generalization ability and actual application effect of the constructed model.
[0015] Moreover, in the step 2), the material fatigue strength coefficient σf and the material fatigue strength index b can be obtained by carrying out a series of fatigue experiments on the material under uniaxial stress loading conditions and performing regression analysis and fitting on the experimental data, thereby realizing the close connection between the model parameters and the actual fatigue performance of the material and improving the physical consistency of the model.
[0016] Moreover, in the step 3), the input layer neuron number of the constructed artificial neural network model is 3, the number of hidden layers is not less than 1 layer, the output layer neuron number is 1, and the activation function type is selected as LeakyReLU function as shown in formula (3), so as to enhance the robustness and convergence performance of the network when processing nonlinear fatigue characteristics.
[0017]
[0018] wherein x is the output value of each neuron; and α is a constant, which is 0.01 in the present patent.
[0019] Moreover, in the step 3), in order to improve the stability of model training and the accuracy of prediction, the input and output features of the artificial neural network model include the axial stress amplitude, the torsional stress amplitude, the Mises equivalent stress amplitude and the logarithmic value of fatigue life, all of which are subjected to z-score normalization processing, i.e., the data is standardized by subtracting the mean value and dividing by the standard deviation, as shown in formula (4):
[0020]
[0021] wherein x represents the input and output features of the artificial neural network model; E(x) is the average value of the features in the data set; and D(x) represents the standard deviation of the features in the data set.
[0022] Moreover, in the step 4), the residual connection mode in the physical information residual neural network is a feature addition mode, i.e., the fatigue life value predicted by the artificial neural network model is weighted and superimposed with the theoretical fatigue life value calculated based on the Mises equivalent stress, so as to enhance the physical consistency and generalization ability of the model, as shown in formula (5)
[0023] lg(N f,pre )=lg(N f,NN )+lg(N f,Mises ) (5)
[0024] wherein lg(N f,pre ) is the fatigue life prediction value, N f,NN is the artificial neural network model prediction value, and N f,Mises is the theoretical fatigue life value.
[0025] Moreover, in step 5), the loss function is selected as the root mean square error function, and the neural network model is trained using the stochastic gradient descent optimization algorithm, and the model parameters are continuously adjusted through back propagation to minimize the error between the predicted value and the actual experimental value.
[0026] The beneficial effects of the present invention are:
[0027] 1. The material multi-axial fatigue life prediction method based on physical information residual neural network of the present invention solves the accuracy and stability problems of existing data-driven methods under complex multi-axial loads by constructing a physical information residual neural network and combining prior physical information such as the Mises equivalent stress model, thereby significantly improving the accuracy of multi-axial fatigue life prediction.
[0028] 2. The multi-axial fatigue life prediction method based on the physical information residual neural network of the present invention integrates physical prior information and deep learning models, effectively enhancing the generalization ability of the model, especially under small sample and complex load conditions, achieving better prediction performance and stronger physical consistency.
[0029] 3. The multi-axial fatigue life prediction method based on the physical information residual neural network of the present invention introduces the prior physical information based on the theoretical prediction model into the neural network model through the residual connection method, thereby improving the prediction accuracy and stability, especially under complex multi-axial loads and small sample conditions, showing excellent performance. The proposal of the present invention can not only improve the physical consistency of the existing model, but also better handle the nonlinear fatigue life prediction problem, providing more reliable technical support for the fatigue life assessment of structural materials. BRIEF DESCRIPTION OF THE DRAWINGS
[0030] Figure 1 This is a flow chart of the material multi-axial fatigue life prediction method based on physical information residual neural network of the present invention;
[0031] Figure 2a Illustration of the loading path for multiaxial fatigue test (uniaxial)
[0032] Figure 2b Illustration of the loading path for multiaxial fatigue test (torsion)
[0033] Figure 2c Illustration of the loading path for multiaxial fatigue test (scale)
[0034] Figure 2d Illustration of the loading path for multiaxial fatigue testing (90° not to scale);
[0035] Figure 3 Distribution diagram of multiaxial fatigue test samples of additively manufactured Ti6Al4V material;
[0036] Figure 4 A physical information residual neural network model designed for the present application is shown in the schematic diagram;
[0037] Figure 5 is a schematic diagram of a machine learning model for predicting performance comparison, wherein:
[0038] Figure 5a A schematic diagram of a machine learning model for predicting performance comparison (artificial neural network model);
[0039] Figure 5b A schematic diagram of a machine learning model for predicting performance comparison (random forest model);
[0040] Figure 5c A schematic diagram of a machine learning model for predicting performance comparison (support vector machine model);
[0041] Figure 6 is a comparison chart of the prediction results among different models, wherein:
[0042] Figure 6a A comparison chart of the prediction results of the artificial neural network model;
[0043] Figure 6b A comparison chart of the prediction results of the random forest model;
[0044] Figure 6c A comparison chart of the prediction results of the support vector machine model;
[0045] Figure 6d A comparison chart of the prediction results of the physical information residual neural network model of the present application. DETAILED DESCRIPTION
[0046] The present application will be further described in detail below through specific embodiments, which are only descriptive and not limiting, and cannot limit the protection scope of the present application.
[0047] A multi-axial fatigue life prediction method based on a physical information residual neural network, for the common problems of insufficient precision and stability in multi-axial fatigue life prediction, the present application uses a physical information residual neural network model, by introducing the combination of physical information and data-driven model, significantly improves the prediction precision; in order to enhance the understanding of the model to fatigue damage, such as Figure 1 As shown in the flowchart of the present application, the Mises equivalent stress prediction result and the neural network prediction result are combined by residual connection, realizing the effective embedding of physical information. The prediction method comprises the following steps:
[0048] 1) Collecting multi-axial fatigue experimental sample data sets of materials under different stress levels and different multi-axial loading paths, each sample collection including corresponding axial stress amplitude σ a , torsional stress amplitude τ aand fatigue life value N f .
[0049] This example uses the multiaxial fatigue test samples of additively manufactured Ti6Al4V materials from the published literature as an example data set, including 20 samples, as shown in Figure 2, involving four different multiaxial load paths: uniaxial, torsion, proportional, and 90° non-proportional. The overall fatigue life distribution is shown in Figure 2. Figure 3 As shown. The axial stress amplitude σ of each sample was collected a , torsional stress amplitude τ a and fatigue life value N f Table 1 details the multiaxial fatigue test samples of additively manufactured Ti6Al4V materials collected in this embodiment.
[0050] Table 1 Multiaxial fatigue test samples of additively manufactured Ti6Al4V materials
[0051]
[0052]
[0053] This method can be applied to any suitable material fatigue life.
[0054] 2) Based on the axial stress amplitude and torsional stress amplitude of each multiaxial fatigue test sample, the Mises equivalent stress amplitude σ of each sample is calculated using formula (1): Mises , and further calculate the corresponding theoretical fatigue life value N based on formula (2) f,Mises ;
[0055]
[0056] σ Mises =σ f (N f,Mises ) b (2)
[0057] Among them, σ f is the material fatigue strength coefficient, b is the material fatigue strength index. In this embodiment, σ f is the fatigue strength coefficient of additively manufactured Ti6Al4V material; b is the fatigue strength index of additively manufactured Ti6Al4V material. σ is obtained by fitting the uniaxial experimental data. f =2176.84MPa, b=-0.121.
[0058] The material fatigue strength coefficient σf and the material fatigue strength index b can be obtained by carrying out a series of fatigue experiments on the material under uniaxial stress loading conditions and performing regression analysis and fitting on the experimental data, so as to realize the close connection between the model parameters and the actual fatigue performance of the material and improve the physical consistency of the model.
[0059] 3) the axial stress amplitude σ of the experimental sample a , the torsional stress amplitude τ a , and the Mises equivalent stress amplitude σ Mises as input features, and the logarithmic fatigue life value lg(N f ) as an output feature, to design an artificial neural network model including several hidden layers;
[0060] In step 3), the number of input layer neurons of the constructed artificial neural network model is 3, the number of hidden layers is not less than 1 layer, the number of output layer neurons is 1, and the type of activation function is selected as LeakyReLU function, as shown in formula (3), to enhance the robustness and convergence performance of the network when processing nonlinear fatigue characteristics,
[0061]
[0062] wherein x is the output value of each neuron; and α is a constant, which is 0.01 in the present patent.
[0063] In the present embodiment, a physical information residual neural network model as shown in Figure 4 is designed. The artificial neural network model part thereof takes the axial stress amplitude σ a , the torsional stress amplitude τ a , and the Mises equivalent stress amplitude σ Mises as input features, and the logarithmic fatigue life value as an output feature lg(N f ). The specific model structure is shown in Figure 4 , including 5 neural network layers (1 input layer, 3 hidden layers, and 1 output layer), and the number of neurons in each layer is 6, 64, 32, 16, and 1, respectively, and all neurons use LeakyReLU activation function.
[0064] To improve the stability of model training and the accuracy of prediction, the input and output features of the artificial neural network model include the axial stress amplitude, the torsional stress amplitude, the Mises equivalent stress amplitude, and the logarithmic value of fatigue life, which are all processed by z-score normalization, i.e., the data is standardized by subtracting the mean value and dividing by the standard deviation, as shown in formula (4):
[0065]
[0066] Wherein, x represents the input and output characteristics of the artificial neural network model; E(x) is the average value of the characteristics in the data set; D(x) represents the standard deviation of the characteristics in the data set
[0067] The mean and standard deviation of the axial stress amplitude are 184.3 MPa and 152.13 MPa; the mean and standard deviation of the torsional stress amplitude are 215.8 MPa and 174.01 MPa; the mean and standard deviation of the Mises equivalent stress amplitude are 480.2 MPa and 238.76 MPa; and the mean and standard deviation of the logarithmic fatigue life are 4.743558 and 0.988331.
[0068] 4) Based on the designed artificial neural network model including several hidden layers, the theoretical fatigue life value N f,Mises is taken logarithm and connected with the artificial neural network model prediction value, and finally a physical information residual neural network model fusing Mises equivalent stress model information is established;
[0069] As shown in FIG. 5, the residual connection mode in the physical information residual neural network is a characteristic summation mode, that is, the theoretical fatigue life value lg(N f,Mises ) and the neural network model prediction value lg(N f,NN ) are connected in residual through the characteristic summation mode as shown in equation (5), and the final prediction fatigue life value lg(N f,pre ) is output to obtain the physical information residual neural network model to enhance the physical consistency and generalization ability of the model;
[0070] lg(N f,pre )=lg(N f,NN )+lg(N f,Mises ) (5)
[0071] Wherein, lg(N f,pre ) is the fatigue life prediction value, N f,NN is the artificial neural network model prediction value, and N f,Mises is the theoretical fatigue life value.
[0072] 5) Based on the physical information residual neural network model constructed as described above, the fatigue experimental sample data set collected is used to train it, and in the training process, the error between the logarithm lg(N f ) of the fatigue life value measured by experiment and the logarithm lg(N f,pre ) of the model prediction value is taken as the objective function to calculate the loss function value. The weight parameters of each layer in the neural network are updated iteratively through the back propagation algorithm, the model structure is optimized continuously, the prediction value is made as close as possible to the experimental value, and the prediction error is reduced to the maximum extent; after the training is completed, the current model parameters are saved as the final version of the fatigue life prediction model;
[0073] The loss function thereof is selected as a root mean square error function, and a neural network model is trained by using a stochastic gradient descent optimization algorithm, and model parameters are continuously adjusted by back propagation to minimize the error between the predicted value and the actual experimental value.
[0074] The collected fatigue test samples are divided into a training set and a test set at a ratio of 1:1, the physical information residual neural network model is trained by using the training set data, a mean square error function is used as a loss function, an Adam optimization algorithm is used as a back propagation algorithm to train and update the model parameters, and the model with the best training performance is selected as the trained model.
[0075] 6) The experimental sample data not participating in the training process is input into the trained physical information residual neural network model, a forward calculation is performed to obtain the fatigue life prediction value corresponding to the sample, the multi-axial fatigue life of the new sample is quickly estimated and predicted, and the generalization ability and actual application effect of the constructed model are verified.
[0076] The test set data is input into the trained model to obtain the corresponding predicted life result, and the multi-axial fatigue life prediction of the Ti6Al4V material is realized. The prediction results of the physical information residual neural network model are compared with those of artificial neural network, random forest and support vector machine and other machine learning models, as shown in FIG. 5. As shown in FIG. 6, it can be seen that the prediction effect of the physical information residual neural network model is better than that of other machine learning models, and the prediction results are all distributed within a double error band.
[0077] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement to part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.
Claims
1. A method for predicting multiaxial fatigue life of materials based on physical information residual neural network, characterized by: The prediction method comprises the following steps: 1) Collect multiaxial fatigue test sample data sets of materials under different stress levels and different multiaxial loading paths. Each sample collection includes the corresponding axial stress amplitude σ a , torsional stress amplitude τ a and fatigue life value N f ; 2) Based on the axial stress amplitude and torsional stress amplitude of each multiaxial fatigue test sample, the Mises equivalent stress amplitude σ of each sample is calculated using formula (1): Mises , and further calculate the corresponding theoretical fatigue life value N based on formula (2) f,Mises ; s Mises =s f (N f,Mises ) b (2) Among them, σ f is the material fatigue strength coefficient, and b is the material fatigue strength index. 3) Take the axial stress amplitude σ of the experimental sample a , torsional stress amplitude τ a and Mises equivalent stress amplitude σ Mises As input features, the logarithmic fatigue life value lg(N f ) as the output feature, and design an artificial neural network model including several hidden layers; 4) Based on the designed artificial neural network model including several hidden layers, the theoretical fatigue life value N f,Mises The logarithm is processed and connected with the predicted value of the artificial neural network model, and finally a physical information residual neural network model integrating the Mises equivalent stress model information is established; 5) Based on the physical information residual neural network model constructed above, the fatigue test sample data set collected is used to train it. During the training process, the logarithm of the fatigue life value measured by the experiment, lg(N f ) and the logarithm of the model prediction value lg(N f,pre ) as the objective function and calculate the loss function value. The weight parameters of each layer in the neural network are iteratively updated through the back-propagation algorithm, and the model structure is continuously optimized to make the predicted value as close to the experimental value as possible and minimize the prediction error. After the training is completed, the current model parameters are saved as the final version of the fatigue life prediction model. 6) The experimental sample data that did not participate in the training process is input into the physical information residual neural network model that has been trained above, and the fatigue life prediction value corresponding to the sample is obtained through forward calculation, so as to realize the rapid estimation and prediction of the multi-axial fatigue life of the new sample and verify the generalization ability and practical application effect of the constructed model.
2. The method for predicting multiaxial fatigue life of materials based on physical information residual neural network according to claim 1, characterized in that: In step 2), the material fatigue strength coefficient σf and the material fatigue strength index b can be obtained by conducting a series of fatigue experiments on the material under uniaxial stress loading conditions and performing regression analysis and fitting on the experimental data, thereby achieving a close correlation between the model parameters and the actual fatigue performance of the material and improving the physical consistency of the model.
3. The method for predicting multiaxial fatigue life of materials based on physical information residual neural network according to claim 1, characterized in that: In the step 3), the number of input layer neurons of the constructed artificial neural network model is 3, the number of hidden layers is not less than 1, the number of output layer neurons is 1, and the activation function type is selected as the LeakyReLU function, as shown in formula (3), to enhance the robustness and convergence performance of the network when processing nonlinear fatigue characteristics. Wherein, x is the output value of each neuron; α is a constant, which is 0.01 in this patent.
4. The method for predicting multiaxial fatigue life of materials based on physical information residual neural network according to claim 1, characterized in that: In step 3), in order to improve the stability of model training and the accuracy of prediction, the input and output features of the artificial neural network model include the axial stress amplitude, torsional stress amplitude, Mises equivalent stress amplitude and the logarithm of fatigue life, all of which are normalized by z-score processing, that is, the data are normalized by subtracting the mean and dividing by the standard deviation, as shown in formula (4): Among them, x represents the input and output features of the artificial neural network model; E(x) is the average value of the features in the dataset; D(x) represents the standard deviation of the features in the dataset.
5. The method for predicting multiaxial fatigue life of materials based on physical information residual neural network according to claim 1, characterized in that: In step 4), the residual connection mode in the physical information residual neural network is the feature addition mode, that is, the fatigue life value predicted by the artificial neural network model and the theoretical fatigue life value calculated based on the Mises equivalent stress are weightedly superimposed to enhance the physical consistency and generalization ability of the model, as shown in formula (5): lg(N f,pre )=lg(N f,NN )+lg(N f,Mises ) (5) Among them, lg(N f,pre ) is the fatigue life prediction value, N f,NN is the predicted value of the artificial neural network model, N f,Mises is the theoretical fatigue life value.
6. The method for predicting multiaxial fatigue life of materials based on physical information residual neural network according to claim 1, characterized in that: In step 5), the loss function is selected as the root mean square error function, and the neural network model is trained using the stochastic gradient descent optimization algorithm, and the model parameters are continuously adjusted through back propagation to minimize the error between the predicted value and the actual experimental value.