Method for predicting fatigue life of machine learning ultra-small sample structure

Abstract

The invention discloses a method for predicting the fatigue life of a machine learning ultra-small sample structure, and belongs to the technical field of material science and engineering application. According to the technology, a high-precision intelligent fatigue life prediction technology is developed on the basis of a very small amount of sample fatigue life test data. The method comprises the following steps: firstly, amplifying measured fatigue life test data into a large amount of mixed fatigue life data by adopting an equivalent fatigue life model; then, through four common machine learning regression methods of random forest regression, gradient enhanced regression, distributed gradient enhanced regression and artificial neural network regression, training is carried out on the mixed data, and a regression method is preferentially selected according to a test result; and obtaining an optimal machine learning model for fatigue life prediction. According to the technology, the problem that a multivariable fatigue life prediction model cannot be obtained by a very small amount of fatigue test data is solved. The new technology has the advantages of high precision and simple application, and can be widely applied to prediction of fatigue properties of different metal materials.

Description

Technical Field

[0001] The present invention relates to the field of material science and engineering application technology, and in particular to a machine learning structure fatigue life prediction method based on a very small amount of test data. Background Art

[0002] Fatigue is the main failure mode of engineering components, and the consequences are also the most serious. Early prediction can effectively avoid fatigue damage of engineering components. Due to the many factors affecting material fatigue performance and the great dispersion of life data, accurate prediction of fatigue life requires a large amount of fatigue life test data. In fact, fatigue testing cycles are long and costly, and usually only a small amount of fatigue life test data can be obtained. However, when the amount of test data is small, traditional mathematical methods cannot directly regress to obtain the fatigue life law of multiple variables, and thus, cannot accurately predict fatigue life. In recent years, with the development of artificial intelligence, a number of machine learning methods have emerged, providing new ideas for multivariate fatigue life prediction. However, the accuracy of machine learning methods is also based on a large amount of data. For this reason, it is urgent to develop technologies that can accurately predict the fatigue life of structures based on very small amounts of test data, thereby promoting anti-fatigue life design and ensuring the safe service of engineering components. Summary of the invention

[0003] The purpose of the present invention is to provide a machine learning structural fatigue life prediction method based on a very small amount of test data. The method takes into account multiple factors that affect fatigue performance, can accurately predict the fatigue life of the structure, help save fatigue performance testing costs, and guide engineering safety service.

[0004] To achieve the above purpose, the technical solution adopted by the present invention is as follows:

[0005] A machine learning ultra-small sample structure fatigue life prediction method includes the following steps:

[0006] (1) Fatigue life test: Fatigue life test is conducted on several fatigue test samples; three or more stress levels are selected during the test, and at least one sample is tested at each stress level; where: S i Refers to the i-th test stress level, i=1,2,…,n, n is the total test stress level, n≥3; after testing the fatigue life of the sample, more than 3 groups of test fatigue lives with the same fatigue failure mechanism are obtained, recorded as N i,j , N i,j is the fatigue life of the jth sample at the i-th stress level, j is the sample order, j=1,2,…,q, q is the total amount of fatigue life test data (total number of samples); in order to fully reflect the differences in the factors affecting fatigue life, the fatigue life range should be as wide as possible;

[0007] (2) Fatigue life test data preparation: Check the fracture of the fatigue failure sample after the test in step (1), and count the size of the defect at the crack source of the fatigue fracture. j (μm) and the location of the defect l j Thus, for each test sample, a set of fatigue life test data (S i ,a j ,l j ,N i,j );

[0008] (3) Hybrid data generation: According to the equivalent fatigue life model, each set of fatigue life test data obtained in step (2) is converted to other stress levels, so that the test fatigue life value N of each sample is i,j Able to calculate multiple equivalent fatigue lives Nˋ k,j , so that in the original test data (S i ,a j ,l j ,N i,j ) based on the new equivalent life data (S k ,a j ,l j ,N k,j ), thus forming mixed data (S i ,a j ,l j ,N i,j ,S k ,N k,j ); If all mixed data are listed, the data (S y ,a y ,l y ,N y ), y=1,2,…,z,S y =S i or S k , a y =a j , l y = l k , N y =N i,j or N k,j , z is the total number of mixed fatigue life data;

[0009] (4) Data normalization: Normalize the data (S y ,a y ,l y ,lgN y ) are normalized to random numbers of standard normal distribution according to formula (5):

[0010]

[0011] In formula (5): x y =S y or a y or y or lgN y ;μ x is x(x y )’s average value; x is x(x y ), X y is a random number from standard normal distribution;

[0012] (5) Random data segmentation: The normalized mixed data is randomly divided into two parts, where 70% of the mixed data is set as the training set and the remaining 30% is set as the test set;

[0013] (6) Machine learning regression: Select a variety of machine learning regression methods to process the data in the training set and test set of step (5); the machine learning regression methods include random forest regression, gradient boosting regression, tree ensemble method of distributed gradient boosting regression and artificial neural network regression; (Random forest regression: function RandomForestRegressor in machine learning library scikit-learn version 1.2.2; gradient boosting regression: function GradientBoostingRegressor in machine learning library scikit-learn version 1.2.2; distributed gradient boosting regression: function XGBRegressor in machine learning library xgboost version 1.7.3; artificial neural network regression: function MLPRegressor in machine learning library scikit-learn version 1.2.2).

[0014] (7) Optimal machine learning model selection: The machine learning model with the largest determination coefficient and simple structure in the test set is selected as the optimal model. The characteristics of the tree ensemble method with simple structure are that the maximum depth d of the tree is small and the number of trees t is small; the characteristics of the artificial neural network with simple structure are that the number of hidden layers v is small and the number of neurons in each hidden layer u is small;

[0015] (8) Fatigue life prediction: For any set of data (S, a, l), based on the mixed data (S y ,a y ,l y ,lgN y ) is the average value μ x With standard deviation σ x , use formula (5) to normalize the data (S, a, l) to values ​​that conform to the standard normal distribution, and then substitute them into the optimal model obtained in step (7) to calculate the result XlgN , and then substitute it into formula (6) to calculate the fatigue life prediction value:

[0016]

[0017] In formula (6): N pre is the fatigue life prediction value; μ lgN lgN y The average value of lgN lgN y The standard deviation of .

[0018] Furthermore, in step (2), the quantitative result of the defect (i.e., the size of the defect a j (μm) and the location of the defect l j They are all measured on a two-dimensional plane image obtained by projecting the fatigue fracture surface along the fatigue load direction, where the defect size a j (μm) refers to the square root of the projected area of ​​the defect at the crack source on a two-dimensional plane. The location of the defect l j =d / (dd min ), where d is half of the nominal diameter of the sample at the fatigue fracture, d min It refers to the minimum distance between the projection boundary of the defect at the crack source on a two-dimensional plane and the fracture boundary of the sample.

[0019] In the above step (3), the equivalent fatigue life model is shown in formula (1);

[0020]

[0021] In formula (1): lgN i,j is the logarithmic value of the fatigue life of sample j at test stress level i; N` k,j is the equivalent fatigue life of sample j at stress level k, k≠i; μ i is the mean value of the logarithmic fatigue life under the test stress level i; μ k is the mean value of the logarithmic fatigue life under stress level k.

[0022] Furthermore, in formula (1), μ i and μ k It is obtained by fitting, and the fitting process includes the following steps (3.1)-(3.2):

[0023] (3.1) The fatigue life test data (S i ,N i,j ) is fitted into formula (2):

[0024] lgN=C-mlg(S-S0)(2);

[0025] In formula (2), S is the stress level; N is the fatigue life; S0, m, and C are all fitting parameters;

[0026] (3.2) Substitute the logarithmic value lgS of any stress level into formula (2) and find the logarithmic value of fatigue life corresponding to S, which is the mean value μ of logarithmic fatigue life under stress level S. When S = S i , then μ=μ i =C-mlg(S i -S0); when S=S k , then μ=μ k =C-mlg(S k -S0).

[0027] Furthermore, the specific fitting method in step (3.1) includes the following steps (3.1.1)-(3.1.4):

[0028] (3.1.1) Find any stress level S i All logarithmic fatigue life lgN i,j The average The test data (S i ,N i,j ) is updated to test data

[0029] (3.1.2) Set different α values, where α∈[0,S min ), and S min is n test stress levels S i The minimum value in the test data Update to data

[0030] (3.1.3) Regarding data Where i = 1, 2, ..., n, according to the least squares linear fitting, the intercept A and slope B of the straight line equation and the goodness of fit ρ are obtained 2 , as shown in formula (3):

[0031]

[0032] (3.1.4) Take ρ 2 The α value corresponding to the maximum value is denoted as α * , then the fitting parameters can be calculated, as shown in formula (4):

[0033]

[0034] Furthermore, step (6) specifically includes steps (6.1)-(6.2):

[0035] (6.1) Structural design of machine learning models: For tree ensemble methods, the number of trees is set to a large value, such as t = 100, and only the maximum depth of the tree changes, d = 1 to 100; for artificial neural network regression, the rectified linear unit function is selected as the activation function, and the artificial neural network structure is designed from two aspects: the number of neurons in each hidden layer is fixed to a large value, such as u = 100, and only the number of hidden layers changes, v = 1 to 4; the number of hidden layers is fixed, and only the number of neurons in each hidden layer changes;

[0036] (6.2) Learning strategy to prevent overfitting: learn each learning model and obtain the regression model, and record the determination coefficient R 2 , including the determination coefficient of the training set and the determination coefficient of the corresponding test set; in order to avoid overfitting, for each learning model, record the number of data segmentation Q, if Q < 100, go to step (5), otherwise go to step (7).

[0037] The advantages and beneficial effects of the present invention are as follows:

[0038] 1. The method of the present invention has the advantage of high precision. Accurate fatigue life prediction is the basis of anti-fatigue design and ensuring the fatigue reliability of structures. Fatigue life prediction error within a 5-fold error band is a potential indicator in the field of fatigue life prediction: -5 times the test result ≤ predicted result ≤5 times the test result. Moreover, there are few methods in the field that can control the fatigue life prediction error within a 3-fold error band: -3 times the test result ≤ predicted result ≤3 times the test result. In particular, the method of the present invention reduces the fatigue life prediction error to within a 1.1-fold error band: -1.1 times the test result ≤ predicted result ≤1.1 times the test result.

[0039] 2. The method of the present invention has the advantage of cost saving. There are many factors affecting the fatigue performance of structures, and usually a large amount of fatigue life test data is required to fit the fatigue life law. Taking the fatigue life law containing only stress as an example, fatigue life tests of at least 4 stress levels × about 15 samples / each level ≈ 60 samples are usually required. In view of the long cycle and high cost of fatigue life tests, there is still a lack of methods to obtain fatigue life laws containing multiple factors from fatigue test data of a small number of samples (such as the case based only on test data in Example 1 - Figure 7Among (a1), (b1), (c1), and (d1), the four commonly used machine learning regression methods cannot obtain a reasonable regression model, and their regression accuracy - the median of the determination coefficient of the test data is <80%, and the error is >±10%). In particular, the method of the present invention starts from a small amount of test data, and through data amplification based on the concept of equivalent fatigue life, the limited test data (such as the test data of 18 samples in Example 1) is amplified to any number of mixed data (such as the mixed data of 522 groups of test data and equivalent fatigue life data in Example 1), and then through data normalization and the use of machine learning methods, a fatigue life law model containing multiple factors (such as the three factors in Example 1, stress, defect size, and defect location) is regressed (such as the case based on mixed data in Example 1 - Figure 7 Among (a2), (b2), (c2), and (d2), the four commonly used machine learning regression methods can all obtain reasonable regression models, and their regression accuracy—the median value of the determination coefficient of the test data is >95%, and the error is <±1%). The method of the present invention solves the problems of little fatigue life test data, many factors affecting fatigue life, and the inability to accurately regress the fatigue life model. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 The figure is a flow chart of the prediction method of the present invention.

[0041] Figure 2 This is the machine learning model result of random forest regression in Example 1, where the number of trees is 100 but the maximum depth of the trees is different.

[0042] Figure 3 This is the result of the gradient enhanced machine learning model in Example 1, where the number of trees is 100 but the maximum depth of the trees is different.

[0043] Figure 4 This is the result of the distributed gradient enhanced machine learning model in Example 1, where the number of trees is 100 but the maximum depth of the trees is different.

[0044] Figure 5 This is the machine learning model result of the artificial neural network in Example 1 with different numbers of hidden layers but 100 neurons in each layer.

[0045] Figure 6 This is the prediction result and verification of this technology in Example 1.

[0046] Figure 7 This is a comparison chart between the machine learning results based only on the experimental data and the machine learning results based on the mixed data in Example 1. DETAILED DESCRIPTION

[0047] In order to further understand the present invention, the present invention is described below in conjunction with embodiments, but the embodiments are only for further elaboration of the features and advantages of the present invention, rather than for limitation of the claims of the present invention.

[0048] The present invention is a machine learning ultra-small sample structure fatigue life prediction method, the prediction process is as follows Figure 1 , specifically including: fatigue life test, fatigue life test data preparation, mixed data generation, data normalization, data random segmentation, machine learning regression, machine learning model selection, and fatigue life prediction.

[0049] Embodiment 1:

[0050] This embodiment is to predict the fatigue life of a kind of steel.

[0051] Conditions: 18 samples. Data are from Table 1 in the literature “W.Wu, MLZhu, X.Liu, FZXuan, Effect oftemperature on high-cycle fatigue and very high cycle fatigue behaviours of alow-strength Cr-Ni-Mo-V steel welded joint. Fatigue Fract. Eng. Mater. Struct., 2016.”

[0052] The prediction process is as follows:

[0053] (1) Fatigue life test: In order to make the results objective, the test results of this embodiment are from the published literature "W. Wu, ML Zhu, X. Liu, F. Z. Xuan, Effect of temperature on high-cycle fatigue and very high cycle fatigue behaviors of a low-strength Cr-Ni-Mo-V steel welded joint. Fatigue Fract. Eng. Mater. Struct., 2016.", with q = 18 fatigue test samples and n = 8 stress levels S i , i is the test stress level, i=1,2,…,n. Test the fatigue life of the sample and obtain the fatigue life of 8 groups of tests with the same fatigue failure mechanism, recorded as N i,j , j is the sample order, j = 1, 2,…, q.

[0054] (2) Fatigue life test data preparation. Check the fracture of the fatigue failure sample and count the defect size a (μm) and defect location l at the fatigue fracture crack source. In this way, for each fatigue life test data, a set of data (S i ,a j ,l j ,N i,j ), and are listed in Table 1.

[0055] Table 1 Fatigue life test data

[0056]

[0057]

[0058] (3) Hybrid data generation. First, the fatigue life test data (S i ,N i,j ), where i = 1, 2, ..., n, j = 1, 2, ..., q; the fitting is: lgN = 23.34-6.78 × lg (S), where: S is the stress level; N is the fatigue life; the fitting parameters are S0 = 0.0, m = 6.78, C = 23.34. And S i After substituting, we can calculate the series μ i With μ k , see Table 2.

[0059] Table 2 Mean values ​​of logarithmic fatigue life

[0060] i k <![CDATA[μ i ]]> <![CDATA[μ k ]]> 1 1 6.0529 6.0529 2 2 6.1912 6.1912 3 3 6.344 6.344 4 4 6.5147 6.5147 5 5 6.7082 6.7082 6 6 6.9314 6.9314 7 7 7.1951 7.1951 8 8 7.5173 7.5173

[0061] Furthermore, according to the equivalent fatigue life model (Formula 1), any fatigue life test data is converted to other stress levels to form mixed data (S i ,a j ,l j ,N i,j ,S k ,N` k,j ), if all mixed data are listed, the data (S y ,a y ,l y ,N y ), y=1,2,…,z=522, see Table 3.

[0062] Table 3 Fatigue life mixed data

[0063]

[0064]

[0065]

[0066]

[0067]

[0068]

[0069]

[0070]

[0071]

[0072]

[0073]

[0074]

[0075]

[0076]

[0077] (4) Data normalization. First, the mean and standard deviation of x are calculated according to Table 3, and the results are listed in Table 4.

[0078] Table 4 x y The average value μ of (y=1,2,…,z,z=522) x With standard deviation σ x

[0079] <![CDATA[x y =S y ]]> <![CDATA[x y =a y ]]> <![CDATA[x y =l y ]]> <![CDATA[x y =lgN y ]]> <![CDATA[μ x ]]> 290 195.29 0.83 6.69 <![CDATA[σ x ]]> 41.83 143.09 0.096 0.47

[0080] Then, according to formula (5), S y 、a y , l y lgN y They were normalized to values ​​that conform to the standard normal distribution.

[0081] (5) Random data segmentation: The normalized mixed data is randomly divided into two parts in a ratio of 7:3, where 70% of the mixed data is set as the training set and the remaining 30% is set as the test set.

[0082] (6) Machine Learning Regression: Choose from a variety of machine learning regression methods: random forest regression, gradient boosting regression, tree ensemble method of distributed gradient boosting regression, and artificial neural network regression.

[0083] (6.1) Structural design of machine learning model: For tree ensemble method, the number of trees is set to t = 100, and only the maximum depth of the tree changes, d = 1 to 100. For artificial neural network regression, the rectified linear unit function is selected as the activation function, and the artificial neural network structure is designed from two aspects: the number of neurons in each hidden layer is fixed to u = 100, and only the number of hidden layers changes v = 1 to 4; the number of hidden layers is fixed, and only the number of neurons in each hidden layer changes.

[0084] (6.2) Learning strategy to prevent overfitting: learn each learning model and obtain the regression model, and record the determination coefficient R 2 , including the coefficient of determination of the training set and the coefficient of determination of the corresponding test set. To avoid overfitting, for each learning model, record the number of data splits Q. If Q < 100, go to step (5), otherwise go to step (7). The machine learning model results of random forest regression with 100 trees but different maximum tree depths are shown in Figure 2 The results of the gradient boosting machine learning model with 100 trees but different maximum tree depths are shown in Figure 3 The results of the distributed gradient boosting machine learning model with 100 trees but different maximum tree depths are shown in Figure 4 The machine learning model results of artificial neural networks with different numbers of hidden layers but 100 neurons in each layer are shown in Figure 5 .

[0085] (7) Optimization of machine learning models. Figure 2-5 , we can know that the machine learning model with the largest coefficient of determination of the test set and a simple structure is Figure 4 A distributed gradient boosting machine learning model with a maximum tree depth of 2 and a number of trees of 100.

[0086] (8) Fatigue life prediction: For any set of test data (S i ,a j ,l j ), based on the mixed data in Table 4 (S i ,a j ,l j ,lgN y ), and use formula (5) to normalize (S, a, l) to values ​​that conform to the standard normal distribution, and then substitute them into the optimal model obtained in step (7), and then calculate the result X lgN , and then substitute it into formula (6) to calculate the fatigue life prediction value. The comparison results between the prediction value and the test value are shown in Figure 6 .

[0087] according to Figure 6It can be seen that the accuracy of the prediction results of this technology is within the error band of 1.1 times the test data. In the field of fatigue life prediction, this accuracy is quite high.

[0088] In addition, to highlight the advantages of this technology for very small amounts of data, Figure 7 By comparing the differences between the machine learning results based only on test data and those based on mixed data, it can be seen that this technology solves the problem that a high-precision fatigue life model with multiple factors cannot be regressed out with very small amounts of data by generating mixed data.

Claims

1. A method for predicting fatigue life of ultra-small sample structures based on machine learning, characterized in that: The method comprises the following steps: (1) Fatigue life test: Fatigue life test is conducted on several fatigue test samples; three or more stress levels are selected during the test, and at least one sample is tested at each stress level; where: S i Refers to the i-th test stress level, i=1,2,…,n, n is the total test stress level, n≥3; after testing the fatigue life of the sample, more than 3 groups of test fatigue lives with the same fatigue failure mechanism are obtained, recorded as N i,j , N i,j is the fatigue life of the jth sample at the i-th stress level, j is the sample order, j = 1, 2, ..., q, q is the total amount of fatigue life test data, i.e. the total amount of samples, and q ≥ 7; (2) Fatigue life test data preparation: Check the fracture of the fatigue failure sample after the test in step (1), and count the size of the defect at the crack source of the fatigue fracture. j and the defect location l j Thus, for each test sample, a set of fatigue life test data (S i ,a j ,l j ,N i,j ); (3) Hybrid data generation: According to the equivalent fatigue life model, each set of fatigue life test data obtained in step (2) is converted to other stress levels, so that the test fatigue life value N of each sample is i,j Multiple equivalent fatigue lives N` can be calculated k,j , so that in the original test data (S i ,a j ,l j ,N i,j ) based on the new equivalent life data (Sk,aj,lj,N`k,j), thus forming a mixed data (S i ,a j ,l j ,N i,j ,S k ,N` k,j ); If all mixed data are listed, the data (S y ,a y ,l y ,N y ), y=1,2,…,z, Sy=Si or Sk, ay=aj, ly=lk, Ny=Ni,j or Ny=N`k,j, z is the total number of mixed fatigue life data, S k The kth stress level is converted from the i-th test stress level; (4) Data normalization: Normalize the data (S y ,a y ,l y ,lgN y ) are normalized to random numbers of standard normal distribution; (5) Random data segmentation: The normalized mixed data is randomly divided into two parts, including a training set and a test set; (6) Machine learning regression: Select multiple machine learning models to process the data in the training set and the test set in step (5); the machine learning models include random forest regression, gradient boosting regression, tree ensemble method of distributed gradient boosting regression, and artificial neural network regression; (7) Optimal selection of machine learning models: The machine learning model with the largest coefficient of determination of the test set and a simple structure is selected as the optimal model; among them, for the tree ensemble method with a simple structure, the maximum depth d of the tree is the smallest within the specified range and the number of trees t is the smallest within the specified range; for the artificial neural network with a simple structure, the number of hidden layers v is the smallest within the specified range and the number of neurons u in each hidden layer is the smallest within the specified range; (8) Fatigue life prediction: For any set of data (S, a, l), based on the mixed data (S y ,a y ,l y ,lgN y ) is the average value μ x With standard deviation σ x , normalize the data (S, a, l) to values ​​that conform to the standard normal distribution, and then substitute them into the optimal model obtained in step (7), and then calculate the result X lgN , and then substitute it into the fatigue life prediction formula to calculate the fatigue life prediction value.

2. The method for predicting fatigue life of ultra-small sample structures using machine learning according to claim 1, characterized in that: The data normalization is specifically: normalizing the data (S y ,a y ,l y ,lgN y ) are normalized to random numbers of standard normal distribution according to the following formula: Among them, x y =S y or a y or y or lgN y ;μ x For x y The average value of x For x y The standard deviation of X y is a random number from a standard normal distribution.

3. The method for predicting fatigue life of ultra-small sample structures using machine learning according to claim 1, characterized in that: In step (2), the quantification result of the defect, i.e., the size of the defect a j and the defect location l j They are all measured on a two-dimensional plane image obtained by projecting the fatigue fracture surface along the fatigue load direction, where the defect size a j It refers to the square root of the projected area of ​​the defect at the crack source on the two-dimensional plane. The location of the defect l j =d / (dd min ), where d is half of the nominal diameter of the sample at the fatigue fracture, d min It refers to the minimum distance between the projection boundary of the defect at the crack source on a two-dimensional plane and the fracture boundary of the sample.

4. The method for predicting fatigue life of ultra-small sample structures using machine learning according to claim 1, characterized in that: In step (3), the equivalent fatigue life model is shown as follows: Where: lgN i,j is the logarithmic value of the fatigue life of sample j at test stress level i; N` k,j is the equivalent fatigue life of sample j at stress level k, k≠i; μ i is the mean value of the logarithmic fatigue life under the test stress level i; μ k is the mean value of the logarithmic fatigue life under stress level k.

5. The method for predicting fatigue life of ultra-small sample structures using machine learning according to claim 3 is characterized by: In the equivalent fatigue life model, μ i and μ k It is obtained by fitting, and the fitting process includes the following steps (3.1)-(3.2): (3.1) The fatigue life test data (S i ,N i,j ) is fitted to the following formula: lgN=C-mlg(S-S0) Where: S is stress level; N is fatigue life; S0, m, C are all fitting parameters; (3.2) Substitute the logarithmic value lgS of any stress level into the fitting formula in step (3.1) to find the logarithmic value of fatigue life corresponding to S, which is the mean value μ of the logarithmic fatigue life under stress level S; when S = S i , then μ=μ i =C-mlg(S i -S0); when S=S k , then μ=μ k =C-mlg(S k -S0).

6. The method for predicting fatigue life of ultra-small sample structures using machine learning according to claim 4 is characterized in that: The specific fitting method in step (3.1) includes the following steps (3.1.1)-(3.1.4): (3.1.1) Find any stress level S i All logarithmic fatigue life lgN i,j The average The test data (S i ,N i,j ) is updated to test data (3.1.2) Set different α values, where α∈[0,S min ), and S min is n test stress levels S i The minimum value in the test data Update to data (3.1.3) Regarding data Where i = 1, 2, ..., n, according to the least squares linear fitting, the intercept A and slope B of the straight line equation and the goodness of fit ρ are obtained 2 , as follows: (3.1.4) Take ρ 2 The α value corresponding to the maximum value is denoted as α * , the fitting parameters can be calculated as follows:

7. The method for predicting fatigue life of ultra-small sample structures using machine learning according to claim 1, characterized in that: Step (6) specifically includes steps (6.1)-(6.2): (6.1) Structural design of machine learning model: For the tree ensemble method, the number of trees is set to t = 100, and only the maximum depth of the tree is changed, d = 1 to 100; For artificial neural network regression, the rectified linear unit function was selected as the activation function, and the artificial neural network structure was constructed from two aspects: the number of neurons in each hidden layer was fixed at u = 100, and only the number of hidden layers was changed, v = 1 to 4; the number of hidden layers was fixed, and only the number of neurons in each hidden layer was changed; (6.2) Learning strategy to prevent overfitting: For each machine learning model, learn and obtain the regression model, and record the determination coefficient R 2 , including the determination coefficient of the training set and the determination coefficient of the corresponding test set; for each learning model, record the number of data segmentation times Q, if Q < 100, go to step (5), otherwise go to step (7).

8. The method for predicting fatigue life of ultra-small sample structures using machine learning according to claim 1, characterized in that: The fatigue life prediction formula is as follows: Where: N pre is the fatigue life prediction value; μ lgN lgN y The average value of lgN lgN y The standard deviation of .

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