A machine learning method for predicting fatigue life of ultra-small sample structures

Abstract

The present invention discloses a method for predicting fatigue life of ultra-small sample structures using machine learning, which belongs to the field of materials science and engineering application technology. This technology develops a high-precision intelligent fatigue life prediction technology based on a very small amount of sample fatigue life test data. First, an equivalent fatigue life model is used to amplify the measured fatigue life test data into a large amount of mixed fatigue life data; then, four commonly used machine learning regression methods, namely random forest regression, gradient boosting regression, distributed gradient boosting regression, and artificial neural network regression, are used to train the mixed data respectively, and the regression method is selected according to the test results; then, the optimal machine learning model for fatigue life prediction is obtained. This technology solves the problem that a multivariate fatigue life prediction model cannot be obtained with a very small amount of fatigue test data. The new technology has the advantages of high precision and simple application, and can be widely used in the prediction of fatigue properties of different metal materials.

Description

Technical Field

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

[0002] Fatigue is the main failure mode of engineering components and has the most serious consequences. Early prediction can effectively avoid fatigue damage of engineering components. Due to the large number of factors affecting the fatigue performance of materials 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 multi-variable 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 fatigue-resistant 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 method for predicting the fatigue life of structures based on a very small amount of test data. This method takes into account multiple factors that affect fatigue performance, can accurately predict the fatigue life of structures, helps to save fatigue performance testing costs, and can guide the safe service of engineering projects.

[0004] To achieve the above object, the technical solutions adopted by the present invention are as follows:

[0005] A machine learning method for predicting fatigue life of ultra-small sample structures includes the following steps:

[0006] (1) Fatigue life test: Fatigue life test is conducted on several fatigue test samples; when testing, three or more stress levels are selected, 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 number of test stress levels, n≥3; after testing the fatigue life of the sample, more than three groups of test fatigue lives with the same fatigue failure mechanism are obtained, which is 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 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 In this way, 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 , thus in the original test data (S i ,a j ,l j ,N i,j ) based on the new data of equivalent life (S k ,a j ,l j ,Nˋ k,j ), thus forming mixed data (S i ,a j ,l j ,N i,j ,S k ,Nˋ 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 l y or lgN y ;μ x is x(x y ) average value; σ x is x(x y ), X y is a random number from standard normal distribution;

[0012] (5) Random data splitting: The mixed data after data normalization 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: The data in the training set and test set of step (5) are processed using a variety of machine learning regression methods; 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 the machine learning library scikit-learn version 1.2.2; gradient boosting regression: function GradientBoostingRegressor in the machine learning library scikit-learn version 1.2.2; distributed gradient boosting regression: function XGBRegressor in the machine learning library xgboost version 1.7.3; artificial neural network regression: function MLPRegressor in the machine learning library scikit-learn version 1.2.2).

[0014] (7) Optimal machine learning model selection: The machine learning model with the largest coefficient of determination and the simplest structure in the test set is selected as the optimal model. The characteristics of the tree ensemble method with a 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 a 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 ) the average value μ x and standard deviation σ x , respectively, use formula (5) to normalize the data (S, a, l) to a value that conforms to the standard normal distribution, and then substitute it into the optimal model obtained in step (7), and then 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 σ 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 The measurements are all made 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 position 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 projected 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 under test stress level i; N` k,j is the equivalent fatigue life of sample j under 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 of the logarithmic fatigue life under stress level k.

[0022] Furthermore, μ in formula (1) i and μ k It is obtained through 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) to obtain 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).

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

[0028] (3.1.1) Calculate any stress level S i All logarithmic fatigue life lgN i,j Average value 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 fit, 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 recorded 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 varies, d = 1 to 100. For artificial neural network regression, the rectified linear unit function is selected as the activation function. The artificial neural network structure is designed from two aspects: the number of layers and the number of neurons in each hidden layer are fixed to a large value, such as u = 100, and only the number of hidden layers varies, v = 1 to 4. The number of hidden layers is fixed, and only the number of neurons in each hidden layer varies.

[0036] (6.2) Learning strategy to prevent overfitting: learn each learning model and obtain the regression model, and record the coefficient of determination R 2 , including the coefficient of determination of the training set and the coefficient of determination 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 for 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 very 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 that affect 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 fatigue life test cycle and high cost, 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 (for example, 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 are unable to 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 In (a2), (b2), (c2), and (d2), the four commonly used machine learning regression methods can all produce reasonable regression models with regression accuracy (the median value of the coefficient of determination of the test data is >95% and the error is <±1%). The method of the present invention solves the problems of insufficient fatigue life test data, multiple factors affecting fatigue life, and the inability to accurately regress the fatigue life model. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 Flowchart 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 The results of the distributed gradient boosting machine learning model in Example 1 are shown in Figure 2, 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 experimental data and the machine learning results based on 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 examples. However, the examples 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 optimization, and fatigue life prediction.

[0049] Example 1:

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

[0051] Conditions: 18 samples. Data from Table 1 in the 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."

[0052] The prediction process is as follows:

[0053] (1) Fatigue life test: To ensure objective results, 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, denoted 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 size a (μm) of the defect at the crack source of the fatigue fracture and the location l of the defect. 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 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] Then, 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, calculate the mean and standard deviation of x according to Table 3. The results are listed in Table 4.

[0078] Table 4 x y The average value μ of (y=1,2,…,z,z=522) x and 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 splitting: 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) Machine Learning Model Structural Design: For tree ensemble methods, the number of trees was set to t = 100, with only the maximum tree depth varying from d = 1 to 100. For artificial neural network regression, the rectified linear unit function was selected as the activation function. The artificial neural network structure was designed from two perspectives: the number of neurons in each hidden layer was fixed at u = 100, with only the number of hidden layers varying from v = 1 to 4; the number of hidden layers was fixed, with only the number of neurons in each hidden layer varying.

[0084] (6.2) Learning strategy to prevent overfitting: learn each learning model and obtain the regression model, and record the coefficient of determination 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 (S i ,a j ,l j , lgN y ), use formula (5) to normalize (S, a, l) to the value that conforms to the standard normal distribution, and then substitute it 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 6, it 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, in order to highlight the advantages of this technology in terms of very small amounts of data, Figure 7 By comparing the differences between the machine learning results based only on test data and the machine learning results 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 from a very small amount 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; when testing, three or more stress levels are selected, 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 number of test stress levels, n≥3; after testing the fatigue life of the sample, more than three groups of test fatigue lives with the same fatigue failure mechanism are obtained, which is 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 number 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 location of the defect j , so that 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 , thus 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 from standard normal distribution; (5) Random data segmentation: The mixed data after data normalization is randomly divided into two parts, including training set and test set; (6) Machine learning regression: The data in the training set and the test set in step (5) are processed using a variety of machine learning models; 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 machine learning model selection: 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 ) the average value μ x and 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 as follows: y ,a y ,l y , lgN y ) are normalized to random numbers from a standard normal distribution according to the following formula: Among them, x y =S y or a y or l y or lgN y ;μ x is x y The average value of σ x is 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 quantitative result of the defect, i.e. the size of the defect a j and the location of the defect j The measurements are all made 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 projected 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 under test stress level i; N` k,j is the equivalent fatigue life of sample j under 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 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, characterized in that: In the equivalent fatigue life model, μ i and μ k It is obtained through 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 into the following formula: lgN=C-mlg(S-S0) Where: S is the stress level; N is the fatigue life; S0, m, and 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 obtain 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, characterized in that: The specific fitting method in step (3.1) includes the following steps (3.1.1)-(3.1.4): (3.1.1) Calculate any stress level S i All logarithmic fatigue life lgN i,j Average value 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 fit, 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 recorded 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 models: 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 layers and the number of neurons in each hidden layer were fixed at u = 100, and only the number of hidden layers was varied, v = 1 to 4; the number of hidden layers was fixed, and only the number of neurons in each hidden layer was varied; (6.2) Learning strategies to prevent overfitting: For each machine learning model, learn 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; for each learning model, record the number of data segmentation 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 σ lgN lgN y The standard deviation of .

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