Bayesian probability fatigue strength evaluation method for structural member with defects

Abstract

The invention discloses a Bayesian probability fatigue strength evaluation method for a structural member with defects, and relates to the technical field of fatigue strength prediction of aerospace metal structural members. The method comprises the following steps: firstly, drawing a fatigue limit curve based on test data of a defective material sample, embedding a physical rule of an El Hadad curve through a synthetic data set, and establishing physical priori knowledge of a defect size and a fatigue strength behavior; training model parameters by using test data of the structural member, constructing a Bernoulli likelihood function, and matching an actual failure tag of the structural member; and finally, fusing the prior distribution and the likelihood function through the Bayesian theorem to obtain probability distribution after parameter updating, and outputting a predicted failure probability expected value and uncertainty. According to the method, material sample data containing defects are fused as physical prior based on the Bayesian theory, and the probability fatigue strength is evaluated through experimental data of a small amount of structural parts.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of fatigue strength prediction of aerospace metal structures, and particularly relates to a Bayesian probability fatigue strength evaluation method for a structure containing defects. BACKGROUND

[0002] In the production, manufacturing and service process of aerospace structural components, various defects are difficult to completely avoid. These defects usually change the local geometric characteristics of the structure, causing stress concentration, and then significantly accelerating the initiation and propagation of cracks, ultimately leading to a significant decrease in the fatigue strength and carrying capacity of the material and structure. Traditional methods are often based on ideal defect-free conditions, and it is difficult to accurately evaluate the actual impact of defects on fatigue performance. Therefore, developing fatigue life evaluation technology of materials and structures considering the influence of defects is of great significance to improve the safety and reliability of aircraft. Such evaluation technology is based on the concept of defect tolerance, systematically studies the mechanism of defects on material fatigue behavior, and builds a life prediction model that can reflect the real working conditions, which not only helps to improve the theoretical description method of fatigue failure, but also provides scientific basis and engineering support for the defect tolerance design of aerospace structural components, thereby laying a solid theoretical and methodological foundation.

[0003] Currently, the defect tolerance life evaluation method for engineering structural components is mainly verified by experiments and numerical simulations, but many studies focus on material level defects such as scratches and corrosion defects, and the defects are assumed to be cracks, and the influence of defects on fatigue performance is evaluated by using fracture mechanics. For example, Paris model, Murakami model and El Haddad model can determine a representative characteristic length for such defects, and then evaluate the fatigue life and fatigue limit of metal materials through semi-empirical fatigue crack propagation models. However, there is no systematic fatigue strength evaluation method for structural simulation components and full-size structures containing defects, and the experiment is difficult, costly and time-consuming. SUMMARY

[0004] Therefore, it is necessary to provide a Bayesian probability fatigue strength evaluation method for a structure containing defects in view of the above technical problems.

[0005] The present specification adopts the following technical solutions: The present specification provides a Bayesian probability fatigue strength evaluation method for a structure containing defects, comprising: obtaining a standard structural component material sample containing defects, and performing a fatigue test on the material sample to obtain standard structural component test data; performing enhancement processing on the standard structural component test data through an El Haddad model to obtain a synthetic data set , and establishing physical prior knowledge of defect size and fatigue strength behavior; The K-fold cross-validation method and the marginal likelihood function are used to select the candidate neural network, and an optimal model is obtained; fatigue test is performed on the structure with defects to obtain test data of the structure D n ; Based on the feature vector of the test data of the structure D n , the failure probability of the test data of the structure is obtained through the optimal model; and a Bernoulli likelihood function of the failure probability of the test data of the structure is constructed The parameter posterior distribution is obtained by fusing the physical prior knowledge and the Bernoulli likelihood function through the Bayes theorem, and the fatigue strength of the structure with defects is evaluated according to the parameter posterior distribution.

[0006] Further, the experimental data is enhanced by the El Haddad model to obtain a synthetic data set , comprising: According to the test data of the material sample with defects, an El Haddad curve based on the test data of the material sample with defects is drawn; A two-dimensional plane is formed based on the defect feature size parameters and the stress range parameters of the El Haddad curve, and uniform grid points are generated; For other defect feature parameters that cannot be directly provided by the physical model, auxiliary defect description feature parameters are generated, and random sampling is performed according to the Gaussian distribution of the real defects, combined with the grid points to form a complete input vector; According to the El Haddad curve equation, the fatigue limit corresponding to each input vector is calculated, and the data labels are combined to form a synthetic data set ; The formula for calculating the fatigue limit is: ; Wherein, is the stress range ； is the fatigue limit of the smooth sample without defects; is the El Haddad critical defect size; is the defect feature size; The expression of the complete input vector is: ; Wherein, is the equivalent diameter of the defect; is the sphericity of the defect; is the fatigue stress range; is the defect feature size; a defect feature vector; The synthetic data set is represented as: ; wherein, represents being labeled as failure, represents being labeled as safe; is represented as the total amount of synthetic data.

[0007] Further, the physical prior knowledge of the defect size and fatigue strength behavior is established, including: using the synthetic data set training an initial neural network model and obtaining a prior distribution of network parameters ; embedding the prior distribution into the physical law of the El Haddad curve to obtain the physical prior knowledge of the defect size and fatigue strength behavior.

[0008] Further, the candidate neural network is selected based on the K-fold cross-validation method and the marginal likelihood function to obtain the optimal model, including: selecting the optimal architecture through K-fold cross-validation, calculating the marginal likelihood of each architecture on the training data on different numbers of layers and neurons of the given candidate neural network, and selecting the architecture with the highest evidence value as the optimal model; The evidence value of the optimal model is represented as: ; wherein, is the likelihood when the parameter ; is the prior distribution under the parameter ; represents integrating the parameter space; is the proxy neural network; is the sum of the parameters of the weights and biases in the network.

[0009] Further, the Bernoulli likelihood function of the failure probability of the structure test data is constructed, specifically including: Through the Bernoulli likelihood function, for the structure test data fatigue strength assessment determines whether to fail or not; training network parameters by minimizing cross-entropy loss so that the predicted value matches the actual label; wherein, for a set of network parameters , the likelihood is: ; wherein, is the network prediction for the i-th a probability of a sample predicting failure; is a true failure label.

[0010] Further, the parameter posterior distribution is obtained by fusing the physical prior knowledge and the Bernoulli likelihood function through the Bayes theorem, and specifically includes: Based on the Bayes theorem, the catalytic prior is combined with the likelihood function to obtain the posterior distribution of the parameter; According to the posterior distribution of the parameter, Hamilton Monte Carlo is used for sampling or approximation, so as to obtain the posterior distribution of the parameter; The posterior distribution is expressed as: ; Wherein ， is expressed as a likelihood function of a structural part; is expressed as a prior distribution of a material sample through an El Haddad model; is expressed as an edge likelihood function; is expressed as an updated posterior distribution finally fused by the prior distribution of the material sample and the likelihood function of the structural part.

[0011] Further, the fatigue strength of the structural part is evaluated according to the parameter posterior distribution, and specifically includes: For a new structural part with defects, a group of corresponding predicted values can be obtained by extracting a large number of parameter samples from the posterior distribution; the mean value is the expected failure probability of the structural part under a given load; The expected failure probability has a calculation formula as: ; Wherein, is the predicted value of the parameter sample; is the failure probability of the parameter sample; j is the i-th parameter sample; j is the total number of parameter samples. J

[0012] The present specification provides a computer readable storage medium, which stores a computer program, and the computer program is executed by a processor to implement the above-mentioned Bayesian probability fatigue strength evaluation method.

[0013] The present specification provides a computer device, which includes a memory, a processor, and a computer program stored on the memory and executable on the processor, and the processor executes the program to implement the above-mentioned Bayesian probability fatigue strength evaluation method.

[0014] The above-mentioned at least one technical scheme adopted by the present specification can achieve the following beneficial effects: ​In the Bayesian probability fatigue strength evaluation method provided in the specification, the data of the material sample containing defects is fused as physical prior by using the Bayesian theory, the physical information containing defects is fused by the data-driven Bayesian method, and the probability fatigue strength of the structure can be more efficiently and accurately predicted.

[0015] Further, the method provided by the application can be easily applied to fatigue strength prediction of materials containing different defects, and is particularly suitable for probability fatigue strength prediction of a small number of structure components, and provides a high-reliability data method for fatigue strength design and prediction of defect-tolerant structures. BRIEF DESCRIPTION OF DRAWINGS

[0016] The drawings described herein are used to provide further understanding of the application, and form a part of the application. The illustrative embodiments of the application and their descriptions serve to explain the application, and do not constitute an improper limitation on the application. In the drawings:

[0017] Figure 1 A Bayesian probability fatigue strength evaluation method for a structure containing defects provided in the specification is shown in the flowchart; Figure 2 A physical prior knowledge E-H curve diagram provided in the specification is shown in the flowchart; Figure 3 A synthetic data set provided in the specification is shown in the flowchart In A distribution diagram of failure and safe samples on a plane is shown in the flowchart; Figure 4 A material sample catalytic prior distribution diagram provided in the specification is shown in the flowchart; Figure 5 A structure sample posterior distribution diagram provided in the specification is shown in the flowchart. DETAILED DESCRIPTION

[0018] In order to make the purpose, technical scheme and advantages of the specification clearer, the technical scheme of the application will be described in detail below with reference to the specific embodiments of the specification and the corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of the application, not all the embodiments. Based on the embodiments in the specification, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the application.

[0019] In recent years, data-driven methods have been successfully applied to material performance prediction, and have significant advantages in prediction accuracy and efficiency. Therefore, there is an urgent need for a data-driven method that can integrate multi-dimensional defect features and save structural test cycle and cost, reduce the dependence on structural test data through physical prior knowledge, and reduce test cost and cycle. Bayesian method provides probabilistic prediction by integrating physical laws and experimental data, which is more in line with engineering practice, and can be extended to fatigue strength evaluation of different defect types (such as scratches, impacts, corrosion) and materials (such as titanium alloy, aluminum alloy). This method can effectively support the defect tolerance fatigue strength design of aerospace key components. Based on this, the application provides a Bayesian probabilistic fatigue strength evaluation method for defect-containing structural components.

[0020] The core of the application is to integrate defect-containing material sample data as physical prior based on Bayesian theory, and to realize probabilistic fatigue strength evaluation through a small amount of experimental data of structural components. The method covers the physical prior of small sample data EH curve, synthetic data, catalytic prior distribution, structural component data model training, Bayesian fusion and posterior distribution calculation process. Through the above implementation, the application can be used for Bayesian probabilistic fatigue strength evaluation of defect-containing structural components, and provides a high-reliability data method for defect tolerance structural fatigue strength design and prediction.

[0021] The technical solutions provided by the embodiments of the application will be described in detail below with reference to the drawings.

[0022] Figure 1 For a Bayesian probabilistic fatigue strength evaluation method for defect-containing structural components in the specification, the specific steps include the following steps: S101: Based on the defect-containing material sample test data, the life curve is drawn, and the synthetic data set is obtained The physical law of El Haddad curve is embedded to establish the physical prior knowledge of defect size and fatigue strength behavior.

[0023] In this embodiment, the physical prior knowledge is established based on the above material sample test data, which specifically includes: (1) According to the defect-containing material sample test data, the fatigue limit is calculated using the El Haddad model formula: ; Where the fatigue limit of a smooth sample without defects is obtained by standard test , the material performance database or test calibration El Haddad Critical defect size , is the defect characteristic size, that is, the square root of the projected area of the defect in the direction of the maximum principal stress, and the EH curve drawn is as follows Figure 2As shown; (2) In the defect feature size and stress range On the constructed two-dimensional plane, uniform grid points are generated, covering common defect sizes and stress levels. (3) For each grid point, generate other defect characteristic parameters, such as the equivalent diameter of the defect. sphericity These parameters are simulated by random sampling from a Gaussian distribution to represent the statistical characteristics of real defects, forming a complete input vector: (4) For each input vector The fatigue limit is calculated based on the El Haddad curve. The applied stress level... If it exceeds this limit, it is marked as a failure. Conversely, it is marked as safe. Generate a synthetic dataset:

[0024] ; like Figure 3 As shown, the synthetic dataset exist The plane shows the distribution of failed (fractured) and safe (overrun) samples, with failed samples concentrated above the curve and safe samples concentrated below the curve; (5) Using synthetic datasets Train an initial neural network model to obtain the prior distribution of the network parameters. This prior distribution embeds the physical laws governing the El Haddad curve. For example... Figure 4 As shown, the catalytic prior distribution illustrates the probability density of the parameters, reflecting the uncertainty of physical prior knowledge.

[0025] S102: Utilizing test data from structural components The model parameters are trained to construct a Bernoulli likelihood function, which is then matched with the actual failure labels of the structural components.

[0026] In this embodiment, based on the above-mentioned structural component test data... Model training and likelihood function construction include: (1) A fully connected feedforward neural network is used, and the input layer corresponds to the feature vector. The output layer represents the failure probability. ; (2) Select the optimal architecture through K-fold cross-validation. Given a set of candidate architectures, such as different numbers of layers and neurons, calculate the marginal likelihood of each architecture on the training data, and select the architecture with the highest evidence value as the final model. The model evidence is as follows: (3) For structural test data Fatigue strength assessment determines failure or not by Bernoulli likelihood function. For a set of network parameters , the likelihood is:

[0027] wherein, is the probability of network predicting failure for the th sample, is the true failure label. Then, by minimizing the cross-entropy loss, the network parameters are trained to match the predicted value and the actual label.

[0028] S103: By Bayes' theorem, the prior distribution and the likelihood function are fused to obtain the probability distribution of the updated parameters, and the expected value of the predicted failure probability and the uncertainty are output.

[0029] In this embodiment, based on the above fusion of prior distribution and likelihood function by Bayes' theorem, the parameter posterior distribution is obtained and used for prediction, specifically including: (1) Apply Bayes' theorem to combine the catalytic prior and the likelihood function to obtain the posterior distribution of the parameters : Since the posterior distribution is difficult to calculate directly, Hamilton Monte Carlo (HMC) is used for sampling or approximation to obtain a parameter sample set .

[0030] (2) For a new structure containing defects, the feature vector is . By extracting a large number of parameter samples from the posterior distribution , a set of corresponding predicted values can be obtained.

[0031] (3) Calculate the expected failure probability: Quantify the prediction uncertainty: Finally, the 95% confidence interval is calculated by quantile, as shown in Figure 5 , the structure posterior distribution shows the probability density of the updated parameters, and the prediction uncertainty is significantly lower than the prior.

[0032] Any technical features in the above embodiments can be combined, and for the sake of brevity, not all possible combinations are described, however, any combination of the technical features is considered to be within the scope of the present specification.

Claims

1. A Bayesian probabilistic fatigue strength assessment method for a defective structure, characterized by, The application relates to a method for predicting the fatigue strength of a structure containing defects. The method comprises the following steps: The standard structural part test data is enhanced by an El Haddad model to obtain a synthetic data set and a physical a priori knowledge of the defect size and fatigue strength behavior is established; The optimal model is obtained by selecting the candidate neural network based on a K-fold cross-validation method and a marginal likelihood function D n ; Based on structural test data D n a feature vector of the structural test data, obtaining a failure probability of the structural test data through the optimal model; and constructing a Bernoulli likelihood function of the failure probability of the structural test data; Obtaining a standard structure material sample containing defects, and performing a fatigue test on the material sample to obtain standard structure test data; 2. A Bayesian probabilistic fatigue strength assessment method for a flawed structure according to claim 1, characterized in that, The experimental data is enhanced by El Haddad model to obtain a synthetic data set comprising: Fusing physical prior knowledge and Bernoulli likelihood function through Bayes theorem to obtain parameter posterior distribution, and evaluating the fatigue strength of the structure containing defects according to the parameter posterior distribution. According to the test data of the standard structure material sample containing defects, an El Haddad curve based on the test data of the standard structure material sample containing defects is drawn; A two-dimensional plane is formed based on the defect characteristic size parameter and the stress range parameter of the El Haddad curve, and uniform grid points are generated; Each input vector is calculated according to the El Haddad curve equation The corresponding fatigue limit is split into data labels and a synthetic dataset is generated ; For other defect characteristic parameters that cannot be directly provided by a physical model, auxiliary defect description characteristic parameters are generated, and random sampling is performed according to the Gaussian distribution of the auxiliary defect description characteristic parameters in real defects, and the grid points are combined to form a complete input vector; ； wherein, is the stress range ； is the fatigue limit of a smooth specimen free of defects; is the El Haddad critical defect size; is the defect characteristic size; The fatigue limit is calculated according to the following formula: ； wherein, is an equivalent diameter of the defect; is a sphericity of the defect; is a fatigue stress range; is a defect characteristic dimension; is a defect feature vector; The complete input vector is expressed as: ； wherein, indicates marked as failed, indicates marked as safe; indicates total amount of synthetic data.

3. A Bayesian probabilistic fatigue strength assessment method for a flawed structure according to claim 1, characterized in that, The synthetic data set is expressed as: Using synthetic data sets training an initial neural network model and obtaining a prior distribution of network parameters ; The physical prior knowledge of the defect size and fatigue strength behavior is established, and the establishment comprises:

4. A Bayesian probabilistic fatigue strength assessment method for a flawed structure according to claim 1, wherein, The prior distribution is embedded into the physical law of the El Haddad curve to obtain the physical prior knowledge of the defect size and fatigue strength behavior. The optimal model is obtained by selecting a candidate neural network based on the K-fold cross-validation method and the marginal likelihood function, and the optimal model comprises: An optimal architecture is selected through K-fold cross-validation, the marginal likelihood of each architecture on the training data is calculated on different numbers of layers and neurons of the given candidate neural network, and the architecture with the highest evidence value is selected as the optimal model; ； where is a parameter likelihood of the data given the parameters; is a parameter prior distribution over the parameters; denotes integration over the parameter space; is a neural network that is a proxy; is the sum of the parameters for weights and biases in the network.

5. A Bayesian probabilistic fatigue strength assessment method for a flawed structure as claimed in claim 1, wherein, The evidence value of the optimal model is expressed as: By Bernoulli likelihood function, for structural test data Fatigue strength assessment determines whether failure occurs or not; Training network parameters by minimizing cross-entropy loss Matching predicted values to actual labels where, for a set of network parameters whose likelihood is: ； wherein, is the network's probability of predicting failure for the first sample; is the true failure label.

6. A Bayesian probabilistic fatigue strength assessment method for a flawed structure as claimed in claim 1, wherein, The Bernoulli likelihood function for constructing the failure probability of the structure test data comprises: The parameter posterior distribution is obtained by fusing the physical prior knowledge and the Bernoulli likelihood function through Bayes theorem, and the fusing comprises: Based on Bayes theorem, the prior and the likelihood function are combined to obtain the posterior distribution of the parameters; According to the posterior distribution of the parameters, Hamilton Monte Carlo is used for sampling or approximation, so that the posterior distribution of the parameters is obtained; ； wherein ， is represented as a likelihood function of the structure; is represented as a prior distribution of the material coupon through the El Haddad model; is represented as a marginal likelihood function; is represented as an updated posterior distribution fused from the final prior distribution of the material coupon and the likelihood function of the structure.

7. A Bayesian probabilistic fatigue strength assessment method for a flawed structure as claimed in claim 1, wherein, The posterior distribution is expressed as: The fatigue strength of the structure is evaluated according to the parameter posterior distribution, and the evaluating comprises: For a new structure containing defects, a group of predicted values can be obtained by extracting a large number of parameter samples from the posterior distribution; the mean value is the expected failure probability of the structure under the given load; ； wherein, is a prediction value for a parameter sample; is a failure probability for a parameter sample; j is a parameter sample; j is a parameter sample; J is a total number of parameter samples.

8. A computer-readable storage medium, characterized in that, The expected failure probability is calculated according to the following formula:

9. A computer device, comprising: The storage medium stores a computer program, and the computer program is executed by the processor to realize the method in any one of claims 1-7. The application relates to a method for predicting the fatigue strength of a structure containing defects. The method comprises the following steps: Obtaining a standard structure material sample containing defects, and performing a fatigue test on the material sample to obtain standard structure test data; Fusing physical prior knowledge and Bernoulli likelihood function through Bayes theorem to obtain parameter posterior distribution, and evaluating the fatigue strength of the structure containing defects according to the parameter posterior distribution. According to the test data of the standard structure material sample containing defects, an El Haddad curve based on the test data of the standard structure material sample containing defects is drawn; A two-dimensional plane is formed based on the defect characteristic size parameter and the stress range parameter of the El Haddad curve, and uniform grid points are generated; For other defect characteristic parameters that cannot be directly provided by a physical model, auxiliary defect description characteristic parameters are generated, and random sampling is performed according to the Gaussian distribution of the auxiliary defect description characteristic parameters in real defects, and the grid points are combined to form a complete input vector; The fatigue limit is calculated according to the following formula: The complete input vector is expressed as: The synthetic data set is expressed as: The physical prior knowledge of the defect size and fatigue strength behavior is established, and the establishment comprises: The prior distribution is embedded into the physical law of the El Haddad curve to obtain the physical prior knowledge of the defect size and fatigue strength behavior. The optimal model is obtained by selecting a candidate neural network based on the K-fold cross-validation method and the marginal likelihood function, and the optimal model comprises: An optimal architecture is selected through K-fold cross-validation, the marginal likelihood of each architecture on the training data is calculated on different numbers of layers and neurons of the given candidate neural network, and the architecture with the highest evidence value is selected as the optimal model; The evidence value of the optimal model is expressed as: The Bernoulli likelihood function for constructing the failure probability of the structure test data comprises: The parameter posterior distribution is obtained by fusing the physical prior knowledge and the Bernoulli likelihood function through Bayes theorem, and the fusing comprises: Based on Bayes theorem, the prior and the likelihood function are combined to obtain the posterior distribution of the parameters; According to the posterior distribution of the parameters, Hamilton Monte Carlo is used for sampling or approximation, so that the posterior distribution of the parameters is obtained; The posterior distribution is expressed as: The fatigue strength of the structure is evaluated according to the parameter posterior distribution, and the evaluating comprises: For a new structure containing defects, a group of predicted values can be obtained by extracting a large number of parameter samples from the posterior distribution; the mean value is the expected failure probability of the structure under the given load; The expected failure probability is calculated according to the following formula: The storage medium stores a computer program, and the computer program is executed by the processor to realize the method in any one of claims 1-7. The application relates to a method for predicting the fatigue strength of a structure containing defects. The method comprises the following steps: Obtaining a standard structure material sample containing defects, and performing a fatigue test on the material sample to obtain standard structure test data; Fusing physical prior knowledge and Bernoulli likelihood function through Bayes theorem to obtain parameter posterior distribution, and evaluating the fatigue strength of the structure containing defects according to the parameter posterior distribution.

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