Fatigue crack propagation prediction method and system based on incremental information machine learning modeling

Abstract

The invention provides a fatigue crack propagation prediction method and system based on incremental information machine learning modeling, and relates to the technical field of fatigue crack propagation prediction. The method comprises the following steps: firstly, acquiring an early-stage data sample of a sample fatigue crack propagation test as an original data set, and carrying out iterative expansion on the data sample through machine learning modeling interpolation prediction to obtain an expanded data set; and constructing an incremental information sample data set based on the expanded data set. And carrying out secondary machine learning modeling to obtain a fatigue crack growth rate prediction model. And finally, obtaining a crack length value and a confidence interval thereof in the later stage of the fatigue crack propagation test of the sample by utilizing the fatigue crack propagation rate prediction model through multi-path prediction weighted average, and finally obtaining a complete fatigue crack propagation curve of the sample. According to the method, through data expansion of interpolation prediction and machine learning modeling based on incremental information, efficient and accurate prediction of the fatigue crack propagation curve is realized through fusion of the incremental information.

Description

Technical Field

[0001] This invention belongs to the technical field of fatigue crack propagation prediction, and more specifically relates to a fatigue crack propagation prediction method and system based on incremental information machine learning modeling. Background Technology

[0002] Fatigue in metallic materials and the resulting sudden fracture of components are typical failure modes in engineering, easily causing serious economic losses and personal injury. Therefore, the fatigue properties of materials, such as fatigue strength and fatigue life, have always been important bases for the reliable design and life assessment of mechanical components in major engineering projects and key equipment.

[0003] Traditional methods for obtaining fatigue performance data typically require a large number of experimental samples and lengthy testing cycles. The advantages of data technologies, such as machine learning, in fitting complex nonlinear relationships offer new ideas and methods for optimizing fatigue testing experiments and accelerating fatigue performance evaluation, thereby significantly improving the efficiency of obtaining material fatigue performance data and effectively reducing fatigue testing costs. For example, Chinese patent CN117421982A discloses a machine learning-based method for predicting the fatigue life of single-crystal metallic materials, used to predict fatigue life, reduce experimental costs, and improve material utilization efficiency; Chinese patent CN119580902A discloses a material fatigue prediction method and system based on a physics-guided neural network, thereby improving the accuracy of material fatigue prediction; and Chinese patent CN120449668A discloses a metal fatigue life prediction method and system based on deep learning with small-sample incremental iterative training using a self-attention mechanism, used to quickly obtain the fatigue limit of materials. Chinese patent CN120524164A discloses a data-coupled fatigue life assessment method and system for actuating mechanisms, which can realize multi-dimensional data coupling analysis, accurately assess fatigue life, and improve assessment accuracy and maintenance efficiency; Chinese patent CN120429744A discloses a multi-scale fatigue crack propagation prediction method and system based on physical information neural networks, which solves the problem of accurate prediction of multi-scale fatigue crack propagation behavior in metallic materials; Chinese patent CN120509183A discloses a data processing method for piecewise fitting of fatigue crack propagation rate curves, which obtains accurate fatigue crack propagation rates and provides a reliable basis for materials engineering applications.

[0004] However, existing methods lack attention to the crack propagation process in fatigue tests, and there is still no effective method for predicting fatigue crack propagation length, which limits the acceleration effect of fatigue tests and results in insufficient accuracy in predicting fatigue crack propagation laws, making it difficult to adapt to complex working conditions and data characteristics. Summary of the Invention

[0005] To address the issues of large prediction bias and low testing efficiency caused by small sample modeling in existing fatigue crack propagation prediction methods, this invention provides a fatigue crack propagation prediction method and system based on incremental information machine learning modeling. By using data augmentation through interpolation prediction iterations and data enhancement and machine learning modeling based on incremental information, efficient and accurate prediction of fatigue crack propagation curves can be achieved.

[0006] To achieve the above-mentioned technical effects, the technical solution of the present invention is as follows: This invention provides a fatigue crack propagation prediction method and system based on incremental information machine learning modeling, comprising the following steps: S1: Collect early data samples of fatigue crack propagation test of the specimen as the original dataset; S2: Based on the original dataset, machine learning modeling and interpolation prediction are used to iteratively expand the data samples to obtain an expanded dataset; S3: Based on the expanded dataset, construct an incremental information sample dataset containing the cycle increment and crack length increment; S4: Based on the incremental information sample dataset, perform secondary machine learning modeling to obtain a fatigue crack propagation rate prediction model; S5: Using the fatigue crack propagation rate prediction model, the crack length value and its confidence interval in the later stage of the fatigue crack propagation test of the sample are obtained by multi-path prediction weighted average, and the complete fatigue crack propagation curve of the sample is obtained.

[0007] Furthermore, the steps for collecting early-stage fatigue crack propagation test data samples from the specimens as the raw dataset are as follows: Early-stage data of the fatigue crack propagation curve of the specimen were collected through fatigue crack propagation testing to obtain the original dataset; the expression of the original dataset is: D n ={(a 1 ,N 1 ), (a 2 ,N 2 ), ..., (a n ,N n )} In the formula, n This indicates the number of data samples in the original dataset. N n Indicates the number of cycles in the fatigue test. a n express N n Crack length corresponding to each cycle number; The original dataset was collected from an Reaching the fatigue crack propagation length before specimen fracture a We obtain the original dataset by dividing it by half. D n .

[0008] Furthermore, the process of step S2 is as follows: Step 1: Construct a neural network model, wherein the neural network model is defined by the number of iterations. N For input, crack length a For output; Step 2: Train the neural network model based on the original dataset of fatigue crack propagation test of the specimen to obtain the trained neural network model; Step 3: Reduce the cycle number range of the original dataset to [N1, N]. n Divide the interval into p equally spaced intervals to obtain P. n There are 1 cycle number of nodes; where the initial p=2; Step 4: Using the trained neural network model, predict the crack length corresponding to each cycle node to obtain the expanded dataset. D 2n Meanwhile, the crack length prediction error E of the neural network model on the original dataset is obtained; Step 5: Let Using augmented datasets D 2n Retrain to update the neural network model, repeat steps three and four, and iteratively update the expanded dataset based on interpolation predictions. D 3n , D 4n ...until the fluctuation of the crack length prediction error E of the neural network model on the original dataset is less than the preset error value, thus obtaining the expanded dataset. D pn Its expression is: D pn ={(a 1 ,N 1 ), (a 2 ,N 2 ), ... ,(a i ,N i ),..., (a j ,N j ),..., (a pn ,N pn )} In the formula, D pnThis indicates an expanded dataset.

[0009] Further, step S3 specifically includes: Based on the expanded dataset D pn Calculate the cycle increment between each sample point in the augmented dataset. ΔN ij = N j - N i and crack length increment Δa ij = a j - a i Where j>i, the crack propagation rate between each sample point is obtained. Δa ij / ΔN ij Incremental information sample dataset is constructed. S Its expression is S = { (N 1 , ΔN 12 , Δa 12 / ΔN 12 ), (N 1 , ΔN 13 , Δa 13 / ΔN 13 ), ... ,(N i , ΔN ij , Δ a ij / ΔN ij ),..., (N (pn-1) , ΔN (pn-1)pn , Δa (pn-1)pn / ΔN (pn-1)pn )} The incremental information sample dataset S Includes: input features and output target; the input features include: cycle number. N i and cycle interval ΔN ij The output target is the crack propagation rate. Δaij / ΔN ij .

[0010] Further, step S4 involves: constructing a single-hidden-layer feedforward neural network model based on an incremental information sample dataset. S A single-hidden-layer feedforward neural network model is trained, and the mean squared error is used as the loss function during the training process until the loss function converges, thus obtaining a fatigue crack propagation rate prediction model.

[0011] Further, step S5 includes: obtaining the average crack propagation rate using a fatigue crack propagation rate prediction model; including: Step 1: With D pn The cycle interval between adjacent sample points in the expanded dataset is the step size. Δn Construct the set of cycles corresponding to the later stage of fatigue crack propagation testing of the specimen: [ N n＋1 , N n＋2 ,..., N n＋i ,..., N 2pn ], in, N n＋2 -N n＋1 =Δn ; Step 2: Calculate the sum of each cycle number in the cycle set. D n The cycle interval for each sample point in the dataset, for N n＋i， The general formula for calculation is: ΔN 1(n＋i) , ΔN 2(n＋i) , ... , ΔN i(n＋i) , ..., ΔN j(n＋i) , ..., Δ N n(n＋i) ; Step 3: Construct a dataset for predicting crack length in the later stages of fatigue crack propagation testing of specimens, targeting... N n＋i， The general formula for calculation is: (N 1 , ΔN 1(n＋i) ) , (N 2 , ΔN2(n＋i) ) , ... , (N i , ΔN i(n＋i) ) ,... , (N j , ΔN j(n＋i) ) , ... , (N n , ΔN n(n＋i) ) ; Step 4: Input the dataset from Step 3 into the trained fatigue crack propagation rate prediction model to obtain the fatigue crack propagation rate at the corresponding cycle number in the later stage of the fatigue crack propagation test of the specimen. against N n＋i， The general formula for calculation is: Δa 1(n＋i) / ΔN 1(n＋i) , Δa 2(n＋i) / ΔN 2(n＋i) , ... , Δa i(n＋i) / Δ N i(n＋i) , ... , Δa j(n＋i) / ΔN j(n＋i) , ... , Δa n(n＋i) / ΔN n(n＋i) .

[0012] Furthermore, by using a multi-path prediction weighted average, the crack length value and its confidence interval in the later stage of the fatigue crack propagation test of the specimen are obtained, thus obtaining the complete fatigue crack propagation curve of the specimen. The specific process is as follows: Based on the n predicted fatigue crack propagation rates at the corresponding cycle number in the later stage of the fatigue crack propagation test, the n fatigue crack lengths at the corresponding cycle number in the later stage of the fatigue crack propagation test are calculated: against N n＋i， The general formula for calculation is:

[0013] By integrating n fatigue crack lengths and using a multi-path prediction weighted average, the crack length value and its confidence interval in the later stage of fatigue crack propagation testing of the specimen are obtained: For cycle number N n＋i The lengths of n fatigue cracks: {a 1(n＋i) ,a 2(n＋i) ,...,a n(n＋i) Based on the set of predicted crack lengths at the target prediction points, the weighted average of the predicted crack lengths is calculated to obtain the complete fatigue crack propagation curve of the sample, specifically: Based on the increment Δa for each predicted crack length i,n＋i The path length weight is calculated using the following expression:

[0014] In the formula, ω i Let Δa represent the weight of the i-th path. k,n+i This represents the crack length increment of the k-th path, where n represents the number of fixed reference starting points; The final predicted crack length is calculated using the following expression:

[0015] In the formula, a n+i,final Represents the target prediction point N n+i The corresponding final predicted crack length; The confidence interval is calculated using the following expression:

[0016] In the formula, sd(a n+i ) represents the target prediction point N n+i The corresponding standard deviation of the predicted crack length, i.e. the confidence interval.

[0017] Furthermore, it also includes: sequentially connecting the fatigue cracks in the early and late stages of the fatigue crack propagation test of the sample to obtain a complete fatigue crack propagation curve of the sample.

[0018] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and running on the processor, wherein when the fatigue crack propagation prediction program based on incremental information machine learning modeling is executed by the processor, the steps of the fatigue crack propagation prediction method based on incremental information machine learning modeling are implemented.

[0019] This invention also provides a fatigue crack propagation prediction system based on incremental information machine learning modeling, comprising: The data acquisition module is used to collect early data samples from the fatigue crack propagation test of the specimen as the raw dataset; The data augmentation module is used to iteratively augment the data samples based on the original dataset through machine learning modeling and interpolation prediction to obtain an augmented dataset. The data augmentation module is used to construct an incremental information sample dataset containing cycle increments and crack length increments based on the expanded dataset. The training and modeling module is used to perform secondary machine learning modeling based on the incremental information sample dataset to obtain a fatigue crack propagation rate prediction model. The prediction module is used to obtain the crack length value and its confidence interval in the later stage of the fatigue crack propagation test of the sample by using a fatigue crack propagation rate prediction model and weighted averaging through multi-path prediction, thus obtaining the complete fatigue crack propagation curve of the sample.

[0020] Compared with existing technologies, the beneficial effects of this method are: This invention provides a fatigue crack propagation prediction method and system based on incremental information machine learning modeling, belonging to the technical field of fatigue crack propagation prediction. First, early-stage data samples from fatigue crack propagation tests of specimens are collected as the original dataset. The data samples are iteratively expanded using machine learning modeling and interpolation prediction to obtain an expanded dataset. Based on the expanded dataset, an incremental information sample dataset is constructed. Secondary machine learning modeling is performed to obtain a fatigue crack propagation rate prediction model. Finally, using the fatigue crack propagation rate prediction model, a multi-path prediction weighted average is used to obtain the crack length value and its confidence interval in the later stages of the fatigue crack propagation test of the specimen, ultimately obtaining the complete fatigue crack propagation curve of the specimen. This invention achieves efficient and accurate prediction of fatigue crack propagation curves by integrating incremental information through data expansion via interpolation prediction and machine learning modeling based on incremental information. Attached Figure Description

[0021] Figure 1 A flowchart illustrating the fatigue crack propagation prediction method based on incremental information machine learning modeling proposed in this embodiment of the invention; Figure 2 This diagram shows a comparison of the prediction results of the fatigue crack propagation prediction method based on incremental information machine learning modeling proposed in this invention and the existing method in 7B04 T6 aluminum alloy. Figure 3 The graph shows a comparison of the prediction performance of the fatigue crack propagation prediction method based on incremental information machine learning modeling proposed in this embodiment of the invention and existing methods in 7B04 T6 aluminum alloy using the first training set. Figure 4 The graph shows a comparison of the prediction performance of the fatigue crack propagation prediction method based on incremental information machine learning modeling proposed in this embodiment of the invention and existing methods in 7B04 T6 aluminum alloy using the second training set. Figure 5This diagram shows a comparison of the prediction performance of the fatigue crack propagation prediction method based on incremental information machine learning modeling proposed in this invention and existing methods in TA15 titanium alloy. Figure 6 A schematic diagram illustrating the electronic device proposed in an embodiment of the present invention; Figure 7 This diagram illustrates the structure of the fatigue crack propagation prediction system based on incremental information machine learning modeling proposed in this embodiment of the invention. Detailed Implementation

[0022] The accompanying drawings are for illustrative purposes only and should not be construed as limiting the scope of this patent. To better illustrate this embodiment, some parts of the accompanying drawings may be omitted, enlarged, or reduced, and do not represent the actual dimensions; It is understandable to those skilled in the art that some well-known details may be omitted from the accompanying drawings.

[0023] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0024] The positional relationships depicted in the accompanying drawings are for illustrative purposes only and should not be construed as limiting this patent. Example 1 This embodiment proposes a method for predicting fatigue crack propagation patterns based on machine learning, such as... Figure 1 The flowchart shown illustrates the method, and the method proposed in this embodiment generally includes the following steps: S1: Collect early data samples of fatigue crack propagation test of the specimen as the original dataset; S2: Based on the original dataset, machine learning modeling and interpolation prediction are used to iteratively expand the data samples to obtain an expanded dataset; S3: Based on the expanded dataset, construct an incremental information sample dataset containing the cycle increment and crack length increment; S4: Based on the incremental information sample dataset, perform secondary machine learning modeling to obtain a fatigue crack propagation rate prediction model; S5: Using the fatigue crack propagation rate prediction model, the crack length value and its confidence interval in the later stage of the fatigue crack propagation test of the sample are obtained by multi-path prediction weighted average, and the complete fatigue crack propagation curve of the sample is obtained.

[0025] This invention proposes a fatigue crack length prediction method and system that combines data information enhancement and knowledge information fusion. Based on early measured data of fatigue crack propagation, it can accurately predict the crack propagation length in the later stages of fatigue testing, thereby accelerating fatigue testing, shortening the fatigue test cycle, reducing fatigue test costs, further promoting the efficiency of fatigue-resistant material research and development, and providing an efficient solution for exploring the fatigue performance of materials. It has important engineering application and research significance.

[0026] This invention is applicable to predicting the remaining crack propagation in the early stages of fatigue testing or during component service, using only a limited number of initial data points (i.e., the first segment of the aN curve). It transforms sparse experimental data into rich training samples and reconstructs the complete aN curve through accurate prediction of crack propagation rate, achieving accurate prediction with a small sample size.

[0027] In this embodiment, the step of collecting early-stage fatigue crack propagation test data samples from the specimen as the original dataset is as follows: Early-stage data of the fatigue crack propagation curve of the specimen were collected through fatigue crack propagation testing to obtain the original dataset; the expression of the original dataset is: D n ={(a 1 ,N 1 ), (a 2 ,N 2 ), ..., (a n ,N n )} In the formula, n This indicates the number of data samples in the original dataset. N n Indicates the number of cycles in the fatigue test. a n express N n Crack length corresponding to each cycle number; The original dataset was collected from a n Reaching the fatigue crack propagation length before specimen fracture a We obtain the original dataset by dividing it by half. D n .

[0028] The process of step S2 is as follows: Step 1: Construct a single hidden layer feedforward neural network model, wherein the neural network model takes the number of iterations N as input and the crack length a as output; Step 2: Train the neural network model based on the original dataset of fatigue crack propagation test of the specimen to obtain the trained neural network model; Step 3: Reduce the cycle number range of the original dataset to [N1, N]. n Divide the interval into p equally spaced intervals to obtain P. n There are 1 cycle number of nodes; where the initial p=2; Step 4: Using the trained neural network model, predict the crack length corresponding to each cycle node to obtain the expanded dataset. D 2n Meanwhile, the crack length prediction error E of the neural network model on the original dataset is obtained; Step 5: Let (P=2,3,4,...), using augmented datasets D 2n Retrain to update the neural network model, repeat steps three and four, and iteratively update the expanded dataset based on interpolation predictions. D 3n , D 4n ...until the fluctuation of the crack length prediction error E of the neural network model on the original dataset is less than the preset error value, then the expanded dataset is determined. D pn Its expression is: D pn ={(a 1 ,N 1 ), (a 2 ,N 2 ), ... ,(a i ,N i ),..., (a j ,N j ),..., (a pn ,N pn )} For example, the neural network model is a single-layer neural network model with ≤15 hidden layer neurons. The preset error value is set to 5%.

[0029] In this embodiment, step S3 specifically includes: Based on the expanded dataset D pn Calculate the cycle increment between each sample point in the augmented dataset. ΔN ij = N j - N iand crack length increment Δa ij = a j - a i Where j>i, the crack propagation rate between each sample point is obtained. Δa ij / ΔN ij Incremental information sample dataset is constructed. S Its expression is S = { (N 1 , ΔN 12 , Δa 12 / ΔN 12 ), (N 1 , ΔN 13 , Δa 13 / ΔN 13 ), ... ,(N i , ΔN ij , Δ a ij / ΔN ij ),..., (N (pn-1) , ΔN (pn-1)pn , Δa (pn-1)pn / ΔN (pn-1)pn )} The incremental information sample dataset S includes: input features and output target; the input features include: cycle number N. i and the cycle interval ΔN ij The output target is the crack propagation rate Δa. ij / ΔN ij ; The expression for calculating the crack propagation rate is:

[0030] The input features of the sample dataset are standardized to obtain the standardized sample dataset; that is, the initial loop count N in the input features is standardized. i and the interval ΔN of the number of cycles ij Perform Z-score normalization separately, the expression is:

[0031]

[0032] In the formula, This represents the mean of all initial loop counts in the sample dataset. This represents the standard deviation of all initial loop counts in the sample dataset. This represents the mean of the intervals between all iterations. This represents the standard deviation of the intervals between all iterations.

[0033] Step S4 is: Construct a single-hidden-layer feedforward neural network model based on the incremental information sample dataset. S A single-hidden-layer feedforward neural network model is trained, and the mean squared error is used as the loss function during the training process until the loss function converges, thus obtaining a fatigue crack propagation rate prediction model.

[0034] A single-hidden-layer feedforward neural network model is used as the crack propagation rate prediction model; (the number of hidden layer neurons is ≤15), and the input layer contains 2 neurons (corresponding to N). i and ΔN ij The output layer contains one neuron (corresponding to Δa). ij / ΔN ij ).

[0035] Using a standardized incremental information sample dataset, a pre-defined crack propagation rate prediction model is trained. During the training process, the mean squared error is used as the loss function until the loss function converges, thus obtaining the fatigue crack propagation rate prediction model.

[0036] During training, mean squared error (MSE) is used as the loss function to focus on the deviation between the predicted value and the true value.

[0037] The total number of samples in dataset S can be calculated by summing an arithmetic sequence, as shown in the following expression: S = (m - 1) + (m - 2) +... + 1 = m (m - 1) / 2 In the formula, m This indicates the number of data points in the expanded dataset.

[0038] For example, m When the value is 491, the sample dataset contains approximately 120,000 valid samples, achieving an exponential increase in the utilization rate of the original data.

[0039] Step S5 includes: obtaining the average crack propagation rate using a fatigue crack propagation rate prediction model. A complete set of prediction data points is generated using a multi-point backtracking weighted averaging strategy, and a quantitative assessment of the inherent uncertainty of the prediction results is achieved. Using the trained fatigue crack propagation rate prediction model, the fatigue crack propagation rate at the corresponding cycle number in the later stage of the fatigue crack propagation test of the specimen is obtained. The specific process is as follows: Step 1: With D pn The cycle interval between adjacent sample points in the expanded dataset is the step size. Δn Construct the set of cycles corresponding to the later stage of fatigue crack propagation testing of the specimen: [ N n＋1 , N n＋2 ,..., N n＋i ,..., N 2pn ], in, N n＋2 -N n＋1 =Δn .

[0040] Step 2: Calculate the sum of each cycle number in the above cycle set. D n Cycle interval for each sample point in the dataset: against N n＋i， The general formula for calculation is: ΔN 1(n＋i) , ΔN 2(n＋i) , ... , ΔN i(n＋i) , ..., ΔN j(n＋i) , ..., ΔN n(n＋i) ; but, for N n＋1 The calculation result is: ΔN 1(n＋1) , ΔN 2(n＋1) , ... , ΔN i(n＋1) , ..., ΔN j(n＋1) , ..., ΔN n(n＋1) ; for N n＋2 The calculation result is: ΔN1(n＋2) , ΔN 2(n＋2) , ... , ΔN i(n＋2) , ..., ΔN j(n＋2) , ..., ΔN n(n＋2) ; ... ... for N 2pn The calculation result is: ΔN 1(2pn) , ΔN 2(2pn) , ... , ΔN i(2pn) , ..., ΔN j(2pn) , ..., Δ N n(2pn) .

[0041] Step 3: Construct a dataset for predicting crack length in the later stages of fatigue crack propagation testing of specimens. This dataset includes: against N n＋i， The general formula for calculation is: (N 1 , ΔN 1(n＋i) ) , (N 2 , ΔN 2(n＋i) ) , ... , (N i , ΔN i(n＋i) ) ,... , (N j , ΔN j(n＋i) ) , ... , (N n , ΔN n(n＋i) ) ; but, for N n＋1 ,have: (N 1 , ΔN 1(n＋1) ) , (N 2 , ΔN 2(n＋1) ) , ... , (Ni , ΔN i(n＋1) ) , ... , (N j , ΔN j(n＋1) ) , ... , (N n , ΔN n(n＋1) ) ; for N n＋2 ,have: (N 1 , ΔN 1(n＋2) ) , (N 2 , ΔN 2(n＋2) ) , ... , (N i , ΔN i(n＋2) ) , ... , (N j , ΔN j(n＋2) ) , ... , (N n , ΔN n(n＋2) ) ; ... ... for N 2pn ,have: (N 1 , ΔN 1(2pn) ) , (N 2 , ΔN 2(2pn) ) , ... , (N i , ΔN i(2pn) ) , ... , (N j , ΔN j(2pn) ) , ... , (N n , ΔN n(2pn) ) .

[0042] Step 4: Input the dataset corresponding to Step 3 into the trained fatigue crack propagation rate prediction model to obtain the fatigue crack propagation rate at the corresponding cycle number in the later stage of the fatigue crack propagation test of the specimen. against N n＋i， The general formula for calculation is: Δa 1(n＋i) / ΔN 1(n＋i) , Δa 2(n＋i) / ΔN 2(n＋i) , ... , Δa i(n＋i) / Δ N i(n＋i) , ... , Δa j(n＋i) / ΔN j(n＋i) , ... , Δa n(n＋i) / ΔN n(n＋i) ; but, for N n＋1 The corresponding n fatigue crack propagation rates are predicted as follows: Δa 1(n＋1) / ΔN 1(n＋1) , Δa 2(n＋1) / Δ N 2(n＋1) , ... , ​ i(n＋1) / ​ i(n＋1) , ... , ​ j(n＋1) / ​ j(n＋1) , ... , ​ n(n＋1) / ​ n(n＋1) ; for N n＋2 The corresponding n fatigue crack propagation rates are predicted as follows: ​ 1(n＋2) / ​ 1(n＋2) , ​ 2(n＋2) / ​ N 2(n＋2) , ... , ​i(n＋2) / ​ i(n＋2) , ... , ​ j(n＋2) / ​ j(n＋2) , ... , ​ n(n＋2) / ​ n(n＋2) ; ... ... for N 2pn The corresponding n fatigue crack propagation rates are predicted as follows: ​ 1(2pn) / ​ 1(2pn) , ​ 2(2pn) / ​ N 2(2pn) , ... , ​ i(2pn) / ​ i(2pn) , ... , ​ j(2pn) / ​ j(2pn) , ... , ​ n(2pn) / ​ n(2pn) .

[0043] Based on the average crack propagation rate, the crack length and its confidence interval in the later stage of the fatigue crack propagation test are obtained by multi-path prediction weighted averaging, and finally the complete fatigue crack propagation curve of the sample is obtained. The specific process is as follows: Step 1: Based on the n predicted fatigue crack propagation rates for the corresponding number of cycles in the later stage of the fatigue crack propagation test of the above specimen, calculate the n fatigue crack lengths for the corresponding number of cycles in the later stage of the fatigue crack propagation test of the specimen: against N n＋i， The general formula for calculation is:

[0044] but, for N n＋1 The lengths of the n fatigue cracks calculated based on the prediction results are:

[0045] for N n＋2The lengths of the n fatigue cracks calculated based on the prediction results are: ... ... for N 2pn The lengths of the n fatigue cracks calculated based on the prediction results are:

[0047] Step 2: Integrate n fatigue crack lengths, and obtain the crack length value and its confidence interval in the later stage of the fatigue crack propagation test by multi-path prediction weighted averaging: against N n＋i， The general formula for calculation is:

[0048]

[0049]

[0050] but, For cycle number N n＋i The lengths of n fatigue cracks: {a 1(n＋i) ,a 2(n＋i) ,...,a n(n＋i) Based on the set of predicted crack lengths for the target prediction points, a weighted average of the predicted crack lengths is calculated to obtain the final predicted crack length value, specifically: Based on the increment Δa for each predicted crack length i,n＋i The path length weight is calculated using the following expression:

[0051] In the formula, ω i Let Δa represent the weight of the i-th path. k,n+i Let represent the crack length increment along the k-th path, and n represent the number of fixed reference starting points, satisfying . ; The final predicted crack length is calculated using the following expression:

[0052] In the formula, a n+i,final Represents the target prediction point N n+i The corresponding final predicted crack length.

[0053] The confidence interval is calculated using the following expression:

[0054] In the formula, sd(a n+i) represents the target prediction point N n+i The corresponding standard deviation of the predicted crack length, i.e. the confidence interval.

[0055] but, for N n＋1 The lengths of n fatigue cracks: {a 1(n＋1) ,a 2(n＋1) ,...,a n(n＋1) Based on the set of predicted crack lengths for the target prediction points, a weighted average of the predicted crack lengths is calculated to obtain the final predicted crack length value, specifically:

[0056]

[0057]

[0058] for N n＋2 The lengths of n fatigue cracks: {a 1(n＋2) ,a 2(n＋2) ,...,a n(n＋2) Based on the set of predicted crack lengths for the target prediction points, a weighted average of the predicted crack lengths is calculated to obtain the final predicted crack length value, specifically:

[0059]

[0060] ... ... for N 2pn The lengths of n fatigue cracks: {a 1(2pn) ,a 2(2pn) ,...,a n(2pn) Based on the set of predicted crack lengths for the target prediction points, a weighted average of the predicted crack lengths is calculated to obtain the final predicted crack length value, specifically:

[0062]

[0063]

[0064] By sequentially connecting the fatigue cracks in the early and late stages of the fatigue crack propagation test of the specimen, a complete fatigue crack propagation curve of the specimen is obtained. This achieves the goal of predicting the fatigue crack propagation in the later stages based on small sample data from the early test, thereby accelerating the fatigue crack propagation test experiment.

[0065] Observe and analyze the distribution of the prediction standard deviation at each point on the entire prediction curve. If the prediction standard deviation remains low at a certain stage of crack propagation, it indicates that the multi-path prediction results from different starting points are highly consistent at this stage, and the model has high prediction confidence in this interval. If the prediction standard deviation increases significantly, it indicates that there is a large divergence in the prediction results from different paths, and the model's prediction uncertainty increases in this interval.

[0066] This invention enables the prediction of the complete aN curve of a fatigue crack based on a small amount of initial data. This method effectively overcomes the limitations of traditional data-driven methods under small sample conditions and ensures that the prediction results strictly follow the physical laws of fatigue crack propagation.

[0067] Example 2 This embodiment illustrates a fatigue crack propagation prediction method based on incremental information machine learning modeling mentioned in Embodiment 1.

[0068] This embodiment takes 7B04 T6 aluminum alloy as the research object, with a stress ratio R=0.5 and a maximum stress σ. max Under fatigue load conditions of 54.9 MPa and initial crack length a0 = 6.35 mm, the prediction results of the method of the present invention on the fatigue crack propagation law, that is, the prediction effect of the fatigue crack aN curve, are verified.

[0069] Fatigue crack propagation tests were conducted to collect complete aN curves of the aluminum alloy specimen under specific test conditions, yielding a total of 79 valid data points. The first 50% of these data points (i.e., the first 40 data points) were selected to construct the original dataset D. n ={(a1,N1), (a2,N2), ..., (a 40 N 40 This dataset simulates scenarios where only early data is available in real-world applications. The number of iterations covered ranges from approximately 0 to 2.4 × 10⁻⁶. 5 The crack length increased from approximately 6.35 mm to 18.35 mm.

[0070] The original dataset is preprocessed to ensure that the data meets the physical law of monotonically increasing crack length a and cycle number N, outliers are removed, and the data is standardized.

[0071] The neural network model is trained based on the original dataset to obtain a trained neural network model; The original dataset's cycle number range [N1, N] 40 Divide the interval into p equally spaced intervals to obtain P. n There are 1 cycle number of nodes; where the initial p=2; Using a trained neural network model, the crack length corresponding to each cycle node is predicted, resulting in the expanded dataset D. 2n Meanwhile, the crack length prediction error E of the neural network model on the original dataset is obtained; make Using augmented datasets D 2n Retrain to update the neural network model, repeat the data augmentation process, and iteratively update the augmented dataset based on interpolation predictions. D 3n , D 4n ...until the fluctuation of the crack length prediction error E of the neural network model on the original dataset is less than 5%, then the expanded dataset is determined. D pn ； In this embodiment, when P=4, the fluctuation of the prediction error E is less than 5%, at which point the augmented dataset D is obtained. 4n It contains a total of 160 data points, and its expression is: D 4n ={(a 1 ,N 1 ), (a 2 ,N 2 ), ... ,(a i ,N i ),..., (a j ,N j ),..., (a 4n ,N 4n )} Based on the expanded dataset D 4n Calculate the cycle increment between each sample point in the dataset. ​ ij = N j - N i and crack length increment ​ ij = a j - a i Where j>i, the crack propagation rate between each sample point is obtained. ​ ij / ​ ij Incremental information sample dataset is constructed. S Its expression is ​ 1 ​ 12 ​ 12 / ​ 12 ), (N 1 ​ 13 ​ 13 / ​ 13 ), ... ,(N i ​ ij ​ a ij / ​ ij ),..., (N (4n-1) ​ (4n-1)4n ​ (4n-1)4n / ​ (4n-1)4n )} Incremental Information Sample Dataset S Includes: input features and output target; the input features include: cycle number. N i and cycle interval ​ ij The output target is the crack propagation rate. ​ ij / ​ ij ; A total of approximately 12,700 valid training samples were generated, achieving a utilization rate improvement of nearly 80 times over the original 160 data points.

[0072] Input features of the sample (N) i ,ΔN ij Z-score standardization is performed to improve the stability and convergence speed of subsequent model training.

[0073] A single-hidden-layer feedforward neural network model was used for training. The input layer contains two neurons, corresponding to the initial loop count N. i and the interval ΔN of the number of cycles ij The number of neurons, number of layers, activation function, etc. in the hidden layer are the same as before; the output layer contains 1 neuron, corresponding to the crack propagation rate Δa / ΔN.

[0074] A single-hidden-layer feedforward neural network model was constructed and trained on the incremental information sample dataset S. During the training process, the mean squared error was used as the loss function until the loss function converged, thus obtaining a fatigue crack propagation rate prediction model.

[0075] by D 4n The cycle interval between adjacent sample points in the dataset is the step size. ​ Construct the set of cycles corresponding to the later stage of fatigue crack propagation testing of the specimen: [ N n＋1 , N n＋2 ,..., N n＋i ,..., N 8n ], in, N n＋2 -N n＋1 ​ .

[0076] Calculate the sum of each cycle number in the above cycle number set. D n Cycle interval for each sample point in the dataset: against N n＋i， The general formula for calculation is: ​ 1(n＋i) , ​ 2(n＋i) , ..., ​ 40(n＋i) ; but, for N n＋1 The calculation result is: ​ 1(n＋1) , ​ 2(n＋1) , ..., ​ 40(n＋1) ; for N n＋2 The calculation result is: ​ 1(n＋2) , ​ 2(n＋2) , ..., ​ 40(n＋2) ; ... ... for N 8n The calculation result is: ​ 1(8n) ,​ 2(8n) , ..., ​ 40(8n) .

[0077] A dataset was constructed for predicting crack length in the later stages of fatigue crack propagation testing of specimens. This dataset is as follows: against N n＋i， The general formula for calculation is: (N 1 ​ 1(n＋i) ) , (N 2 ​ 2(n＋i) ) , ... , (N 40 ​ 40(n＋i) ) ; but, for N n＋1 ,have: (N 1 ​ 1(n＋1) ) , (N 2 ​ 2(n＋1) ) , ... , (N 40 ​ 40(n＋1) ) ; for N n＋2 ,have: (N 1 ​ 1(n＋2) ) , (N 2 ​ 2(n＋2) ) ,... , (N 40 ​ 40(n＋2) ) ; ... ... for N 8n ,have: (N 1 ​ 1(8n) ) , (N 2 ​ 2(8n) ) , ... , (N40 ​ 40(8n) ) .

[0078] The dataset of predicted crack lengths for the later stages of fatigue crack propagation testing is input into the trained fatigue crack propagation rate prediction model to obtain the fatigue crack propagation rate for the later stages of fatigue crack propagation testing. against N n＋i， The general formula for calculation is: ​ 1(n＋i) / ​ 1(n＋i) , ​ 2(n＋i) / ​ 2(n＋i) , ... , ​ 40(n＋i) / ​ N 40(n＋i) ; but, for N n＋1 The predicted fatigue crack propagation rates were as follows: ​ 1(n＋1) / ​ 1(n＋1) , ​ 2(n＋1) / ​ 2(n＋1) , ... , ​ 40(n＋1) / ​ 40(n＋1) ; for N n＋2 The predicted fatigue crack propagation rates were as follows: ​ 1(n＋2) / ​ 1(n＋2) , ​ 2(n＋2) / ​ 2(n＋2) , ... , ​ 40(n＋2) / ​ 40(n＋2) ; ... ... for N 8n The predicted fatigue crack propagation rates were as follows: ​ 1(8n) / ​ 1(8n) ,​ 2(8n) / ​ N 2(8n) , ... , ​ 40(8n) / ​ 40(8n) .

[0079] By using a multi-path prediction weighted average, the crack length value and its confidence interval in the later stage of the fatigue crack propagation test of the sample are obtained, and finally the complete fatigue crack propagation curve of the sample is obtained. The specific process is as follows: Based on the 40 predicted fatigue crack propagation rates at the corresponding cycle counts during the later stages of the fatigue crack propagation test of the above-mentioned specimens, the 40 fatigue crack lengths at the corresponding cycle counts during the later stages of the fatigue crack propagation test of the specimens were calculated: against N n＋i， The general formula for calculation is:

[0080] but, for N n＋1 The lengths of the 40 fatigue cracks calculated based on the prediction results are as follows: for N n＋2 The lengths of the 40 fatigue cracks calculated based on the prediction results are as follows: ... ... for N 8n The lengths of the 40 fatigue cracks calculated based on the prediction results are as follows: .

[0082] By integrating 40 fatigue crack lengths and using a multi-path prediction weighted average, the crack length value and its confidence interval in the later stage of fatigue crack propagation testing of the specimen were obtained. against N n＋i， The general formula for calculation is:

[0083]

[0084]

[0085] but, for N n＋1 The lengths of the 40 fatigue cracks: {a 1(n＋1) ,a2(n＋1) ,...,a 40(n＋1) Based on the set of predicted crack lengths for the target prediction points, a weighted average of the predicted crack lengths is calculated to obtain the final predicted crack length value, specifically:

[0086]

[0087]

[0088] for N n＋2 The lengths of the 40 fatigue cracks: {a 1(n＋2) ,a 2(n＋2) ,...,a 40(n＋2) Based on the set of predicted crack lengths for the target prediction points, a weighted average of the predicted crack lengths is calculated to obtain the final predicted crack length value, specifically:

[0089]

[0090] ... ... for N 8n The lengths of the 40 fatigue cracks: {a 1(8n) ,a 2(8n) ,...,a 40(8n) Based on the set of predicted crack lengths for the target prediction points, a weighted average of the predicted crack lengths is calculated to obtain the final predicted crack length value, specifically:

[0092]

[0093]

[0094] The fatigue cracks in the early and late stages of the fatigue crack propagation test of the specimen were connected sequentially to obtain the complete fatigue crack propagation curve of the specimen.

[0095] The prediction curve (solid green line) and its confidence interval (light green area) obtained by the method of this invention are compared with the complete experimental data and the prediction results (solid red line) of the traditional direct modeling method. ​ The comparison chart of prediction results is shown. Specifically, it illustrates the results when the stress ratio R = 0.5 and the maximum stress σ... maxUnder fatigue loading conditions of 54.9 MPa and an initial crack length of a0 = 6.35 mm, with the training set comprising 50% of the data, the aN curves predicted by the method of this invention and existing direct modeling methods are compared with the complete experimental data. Existing methods show a gradual increase in prediction deviation beyond the training data range, while the prediction curve generated by the method of this invention shows a high degree of agreement with the experimental data. Furthermore, the confidence interval of this method begins at 2.4 × 10⁻⁶. 5 The narrowing of the path during the second cycle indicates a high degree of consistency in the multipath prediction results, suggesting the model is in a stable prediction state with high confidence. The reasonable widening near failure indicates a divergence in the multipath prediction results, spontaneously signaling an increase in uncertainty. This demonstrates that the prediction results of this invention are not only accurate, but the uncertainty quantification it provides is reliable and physically meaningful, significantly outperforming traditional methods.

[0096] To fully verify the robustness and superiority of the method of this invention under small sample conditions, a comparative experiment was conducted in this embodiment. Under exactly the same initial conditions (R=0.5, σ... max At a pressure of 54.9 MPa and a0 = 6.35 mm, the training set percentages were set to 40% (first 32 data points) and 60% (first 48 data points) for comparison. ​ The comparison charts shown below illustrate the prediction performance using the first training set and, as shown below... ​ The chart shown compares the prediction performance using the second training set. ​ The first training set accounts for 60%. ​ The second training set comprised 40% of the total training data. When the proportion of the training set decreased from 60% to 40%, the deviation between the prediction curve of the existing method and the experimental data increased significantly. Even in the latter half of the training set, a significant deviation began to appear, indicating that the existing method has an inherent defect: when the training samples are reduced, the model has difficulty learning the crack propagation law, leading to a sharp decline in prediction stability and reliability.

[0097] When the proportion of the training set was reduced from 60% to 40%, the prediction curve of the method of the present invention did not change significantly compared with the experimental data. Although the confidence interval was reasonably widened, the vast majority of experimental data still fell within the interval. This shows that the method of the present invention can still provide high-precision predictions under such small sample conditions.

[0098] The comparative experiments described above fully demonstrate the significant advantages of the method of this invention. Compared with the high sensitivity of traditional methods to the amount of training data, this invention significantly reduces the dependence on the number of samples by introducing crack propagation rate, data augmentation, and multi-path backtracking prediction mechanisms. This characteristic makes this invention highly valuable for practical engineering scenarios where obtaining experimental data is difficult or expensive.

[0099] Example 3 To verify the universality and robustness of the machine learning-based fatigue crack propagation prediction method mentioned in Example 1 under different materials and load conditions, this example uses TA15 titanium alloy as the research object, with a stress ratio R=0.5 and a maximum stress σ. max Under fatigue load conditions of 115.9 MPa and initial crack length a0 = 7.15 mm, the prediction results of the method of the present invention on the fatigue crack propagation law, that is, the prediction effect of the fatigue crack aN curve, are verified.

[0100] Fatigue crack propagation tests were conducted to collect complete aN curves of the titanium alloy specimen under specific test conditions, yielding a total of 34 valid data points. The first 50% of these data points (i.e., the first 17 data points) were selected to construct the original dataset D. n ={(a1,N1), (a2,N2), ..., (a 17 N 17 This dataset simulates scenarios where only early data is available in real-world applications. The number of loops covered ranges from approximately 0 to 2 × 10⁻⁶. 5 The crack length increased from approximately 7.15 mm to 14.41 mm.

[0101] The original dataset is preprocessed to ensure that the data meets the physical law of monotonically increasing crack length a and cycle number N, outliers are removed, and the data is standardized.

[0102] The neural network model is trained based on the original dataset to obtain a trained neural network model; The original dataset's cycle number range [N1, N] 17 Divide the interval into p equally spaced intervals to obtain P. n There are 1 cycle number of nodes; where the initial p=2; Using a trained neural network model, the crack length corresponding to each cycle node is predicted, resulting in the expanded dataset D. 2n Meanwhile, the crack length prediction error E of the neural network model on the original dataset is obtained; make Using augmented datasets D 2n Retrain to update the neural network model, repeat the data augmentation process, and iteratively update the augmented dataset based on interpolation predictions. D 3n , D 4n ...until the fluctuation of the crack length prediction error E of the neural network model on the original dataset is less than 5%, then the expanded dataset is determined. D pn ； In this embodiment, when P=5, the fluctuation of the prediction error E is less than 5%, at which point the augmented dataset D is obtained. 5n It contains a total of 85 data points, and its expression is: D 4n ={(a 1 ,N 1 ), (a 2 ,N 2 ), ... ,(a i ,N i ),..., (a j ,N j ),..., (a 5n ,N 5n )} Based on the expanded dataset D 5n Calculate the cycle increment between each sample point in the dataset. ​ ij = N j - N i and crack length increment ​ ij = a j - a i Where j>i, the crack propagation rate between each sample point is obtained. ​ ij / ​ ij Incremental information sample dataset is constructed. S Its expression is ​ 1 ​ 12 ​ 12 / ​ 12 ), (N 1 ​ 13 ​ 13 / ​ 13 ), ... ,(N i ​ ij ​ a ij / ​ ij ),..., (N (5n-1) ​ (5n-1)5n ​ (5n-1)5n / ​ (5n-1)5n )} Incremental Information Sample Dataset S Includes: input features and output target; the input features include: cycle number. N i and cycle interval ​ ij The output target is the crack propagation rate. ​ ij / ​ ij ; Approximately 3,600 valid training samples were generated, achieving a 40-fold increase in utilization of the original 85 data points.

[0103] Input features of the sample (N) i ,ΔN ij Z-score standardization is performed to improve the stability and convergence speed of subsequent model training.

[0104] A single-hidden-layer feedforward neural network model was used for training. The input layer contains two neurons, corresponding to the initial loop count N. i and the interval ΔN of the number of cycles ij The number of neurons, number of layers, activation function, etc. in the hidden layer are the same as before; the output layer contains 1 neuron, corresponding to the crack propagation rate Δa / ΔN.

[0105] A single-hidden-layer feedforward neural network model was constructed and trained on the incremental information sample dataset S. During the training process, the mean squared error was used as the loss function until the loss function converged, thus obtaining a fatigue crack propagation rate prediction model.

[0106] The expression for the loss function is:

[0107] In the formula, Represents the total number of samples. and These represent the predicted crack length and the actual crack length, respectively, under the same number of cycles.

[0108] The formula for calculating the total number of samples is:

[0109] In the formula, m represents the number of data points in the expanded dataset.

[0110] by D 5n The cycle interval between adjacent sample points in the dataset is the step size. ​ Construct the set of cycles corresponding to the later stage of fatigue crack propagation testing of the specimen: [ N n＋1 , N n＋2 ,..., N n＋i ,..., N 10n ], in, N n＋2 -N n＋1 ​ .

[0111] Calculate the sum of each cycle number in the above cycle number set. D n Cycle interval for each sample point in the dataset: against N n＋i， The general formula for calculation is: ​ 1(n＋i) , ​ 2(n＋i) , ..., ​ 17(n＋i) ; but, for N n＋1 The calculation result is: ​ 1(n＋1) , ​ 2(n＋1) , ..., ​ 17(n＋1) ; for N n＋2 The calculation result is: ​ 1(n＋2) , ​ 2(n＋2) , ..., ​ 17(n＋2) ; ... ... for N 10n The calculation result is: ​ 1(10n) , ​ 2(10n) , ..., ​ 17(10n) .

[0112] A dataset was constructed for predicting crack length in the later stages of fatigue crack propagation testing of specimens. This dataset is as follows: against N n＋i， The general formula for calculation is: (N 1 ​ 1(n＋i) ) , (N 2 ​ 2(n＋i) ) , ... , (N 17 ​ 17(n＋i) ) ; but, for N n＋1 ,have: (N 1 ​ 1(n＋1) ) , (N 2 ​ 2(n＋1) ) , ... , (N 17 ​ 17(n＋1) ) ; for N n＋2 ,have: (N 1 ​ 1(n＋2) ) , (N 2 ​ 2(n＋2) ) ,... , (N 17 ​ 17(n＋2) ) ; ... ... for N 10n ,have: (N 1 ​ 1(10n) ) , (N 2 ​ 2(10n) ) , ... , (N 17 ​ 17(10n) ) .

[0113] The dataset of predicted crack length for the later stages of fatigue crack propagation testing is input into the trained fatigue crack propagation rate prediction model to obtain the fatigue crack propagation rate for the later stages of fatigue crack propagation testing. against N n＋i， The general formula for calculation is: ​ 1(n＋i) / ​ 1(n＋i) , ​ 2(n＋i) / ​ 2(n＋i) , ... , ​ 17(n＋i) / ​ N 17(n＋i) ; but, for N n＋1 The predicted fatigue crack propagation rates are as follows: ​ 1(n＋1) / ​ 1(n＋1) , ​ 2(n＋1) / ​ 2(n＋1) , ... , ​ 17(n＋1) / ​ 17(n＋1) ; for N n＋2 The predicted fatigue crack propagation rates are as follows: ​ 1(n＋2) / ​ 1(n＋2) , ​ 2(n＋2) / ​ 2(n＋2) , ... , ​ 17(n＋2) / ​ 17(n＋2) ; ... ... for N 10n The predicted fatigue crack propagation rates are as follows: ​ 1(10n) / ​ 1(10n) , ​ 2(10n) / ​ N 2(10n) , ... , ​17(10n) / ​ 17(10n) .

[0114] By using a multi-path prediction weighted average, the crack length value and its confidence interval in the later stage of the fatigue crack propagation test of the sample are obtained, and finally the complete fatigue crack propagation curve of the sample is obtained. The specific process is as follows: Based on the 17 predicted fatigue crack propagation rates at the corresponding cycle counts during the later stages of the fatigue crack propagation test of the above-mentioned specimens, the 17 fatigue crack lengths at the corresponding cycle counts during the later stages of the fatigue crack propagation test of the specimens were calculated: against N n＋i， The general formula for calculation is:

[0115] but, for N n＋1 The lengths of the 17 fatigue cracks calculated based on the prediction results are as follows:

[0116] for N n＋2 The lengths of the 17 fatigue cracks calculated based on the prediction results are as follows: ... ... for N 10n The lengths of the 17 fatigue cracks calculated based on the prediction results are as follows:

[0118] By integrating 17 fatigue crack lengths and using a multi-path prediction weighted average, the crack length value and its confidence interval in the later stage of fatigue crack propagation testing of the specimen were obtained. against N n＋i， The general formula for calculation is:

[0119]

[0120]

[0121] but, for N n＋1 The 17 fatigue crack lengths: {a 1(n＋1) ,a 2(n＋1) ,...,a 17(n＋1)Based on the set of predicted crack lengths for the target prediction points, a weighted average of the predicted crack lengths is calculated to obtain the final predicted crack length value, specifically:

[0122]

[0123]

[0124] for N n＋2 The 17 fatigue crack lengths: {a 1(n＋2) ,a 2(n＋2) ,...,a 17(n＋2) Based on the set of predicted crack lengths for the target prediction points, a weighted average of the predicted crack lengths is calculated to obtain the final predicted crack length value, specifically:

[0125]

[0126] ... ... for N 10n The 17 fatigue crack lengths: {a 1(10n) ,a 2(10n) ,...,a 17(10n) Based on the set of predicted crack lengths for the target prediction points, a weighted average of the predicted crack lengths is calculated to obtain the final predicted crack length value, specifically:

[0128]

[0129]

[0130] The fatigue cracks in the early and late stages of the fatigue crack propagation test of the specimen were connected sequentially to obtain the complete fatigue crack propagation curve of the specimen.

[0131] The prediction curve (solid green line) and its confidence interval (light green area) obtained by the method of this invention are compared with the prediction results of complete experimental data and existing direct modeling methods, such as... ​ The comparison chart of predicted results shown (taking TA15 titanium alloy as the research object) illustrates the results under stress ratio R=0.5 and maximum stress σ. maxUnder fatigue loading conditions of 115.9 MPa and an initial crack length of a0 = 7.15 mm, with the training set accounting for 50%, the aN curves predicted by the method of this invention and existing direct modeling methods are compared with the complete experimental data. When extrapolating predictions to the test set, the existing method exhibits a significant systematic deviation between its predicted curve (solid red line) and the actual experimental data points. This deviation increases continuously with the number of iterations, and the predicted curve fails to capture the crack propagation pattern, indicating that the existing method has insufficient generalization ability and is difficult to predict accurately.

[0132] The prediction curve generated by the method of this invention shows a high degree of agreement with the experimental data throughout the entire cycle number range. Furthermore, the confidence interval of this invention begins at 2.1 × 10⁻⁶. 5 The narrower path during the second cycle indicates that the multipath prediction results are concentrated and the model prediction confidence is high; the reasonable widening when approaching failure spontaneously reflects the signal of increased uncertainty.

[0133] The results show that, despite significant differences in materials, load conditions, and data scale compared to Example 2, the predicted aN curve generated by the method of the present invention is also in high agreement with the complete experimental data, and the provided prediction confidence interval can effectively cover the vast majority of experimental data points. The joint verification of this embodiment and Embodiment 2 shows that the prediction method provided by the present invention is insensitive to changes in key factors such as material type, load conditions, initial crack size and data scale, and has wide applicability and good robustness, and can provide reliable data support for fatigue life assessment of various metallic materials.

[0134] Example 4 like ​ As shown, this embodiment of the invention also proposes an electronic device, including a memory 101, a processor 102, and a computer program stored in the memory 101 and running on the processor 102, wherein when the processor 102 executes the computer program, it implements the steps of the prediction method for fatigue crack propagation law based on machine learning proposed in this embodiment.

[0135] Specifically, in this embodiment, the processor 102 may include a central processing unit (CPU) or a specific integrated circuit, or one or more integrated circuits configured to implement this embodiment. The memory 101 may include a mass storage device for data or instructions. It may include a hard disk drive (HDD), floppy disk drive, flash memory, optical disk, magneto-optical disk, magnetic tape, or Universal Serial Bus (USB) drive, or a combination of two or more of these. Where appropriate, the memory 101 may include removable or non-removable (or fixed) media. Where appropriate, the memory 101 may be internal or external to the integrated gateway disaster recovery device.

[0136] Memory 101 may include read-only memory (ROM), random access memory (RAM), disk storage media device, optical storage media device, flash memory device, electrical, optical, or other physical / tangible memory storage device. Therefore, typically, memory includes one or more tangible (non-transitory) computer-readable storage media (e.g., memory devices) encoded with software including computer-executable instructions, and when the software is executed (e.g., by one or more processors), it is operable to perform steps implementing the machine learning-based fatigue crack propagation prediction method proposed in this embodiment.

[0137] Example 5 A fatigue crack propagation prediction system based on incremental information machine learning modeling is shown in the system structure diagram below. ​ As shown, it includes: The data acquisition module is used to collect early data samples from the fatigue crack propagation test of the specimen as the raw dataset; The data augmentation module is used to iteratively augment the data samples based on the original dataset through machine learning modeling and interpolation prediction to obtain an augmented dataset. The data augmentation module is used to construct an incremental information sample dataset containing cycle increments and crack length increments based on the expanded dataset. The training and modeling module is used to perform secondary machine learning modeling based on the incremental information sample dataset to obtain a fatigue crack propagation rate prediction model. The prediction module is used to obtain the crack length value and its confidence interval in the later stage of the fatigue crack propagation test of the sample by using a fatigue crack propagation rate prediction model and weighted averaging through multi-path prediction, thus obtaining the complete fatigue crack propagation curve of the sample.

[0138] The embodiments described are merely examples to clearly illustrate the present invention and are not intended to limit the implementation of the invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively describe all possible implementations. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A fatigue crack propagation prediction method based on incremental information machine learning modeling, characterized in that, Includes the following steps: S1: Collect early data samples of fatigue crack propagation test of the specimen as the original dataset; S2: Based on the original dataset, machine learning modeling and interpolation prediction are used to iteratively expand the data samples to obtain an expanded dataset; S3: Based on the expanded dataset, construct an incremental information sample dataset containing the cycle increment and crack length increment; S4: Based on the incremental information sample dataset, perform secondary machine learning modeling to obtain a fatigue crack propagation rate prediction model; S5: Using the fatigue crack propagation rate prediction model, the crack length value and its confidence interval in the later stage of the fatigue crack propagation test of the sample are obtained by multi-path prediction weighted average, and the complete fatigue crack propagation curve of the sample is obtained.

2. The fatigue crack propagation prediction method based on incremental information machine learning modeling according to claim 1, characterized in that, The steps for collecting early-stage fatigue crack propagation test data samples from specimens as the raw dataset are as follows: Early-stage data of the fatigue crack propagation curve of the specimen were collected through fatigue crack propagation testing to obtain the original dataset; the expression of the original dataset is: D n ={(a 1 ,N 1 ), (a 2 ,N 2 ), ..., (a n ,N n )} In the formula, n This indicates the number of data samples in the original dataset. N n Indicates the number of cycles in the fatigue test. a n express N n Crack length corresponding to each cycle number; The original dataset was collected from a n Reaching the fatigue crack propagation length before specimen fracture a We obtain the original dataset by dividing it by half. D n .

3. The fatigue crack propagation prediction method based on incremental information machine learning modeling according to claim 1, characterized in that, The process of step S2 is as follows: Step 1: Construct a neural network model, wherein the neural network model is based on the number of iterations. N For input, crack length a For output; Step 2: Train the neural network model based on the original dataset of fatigue crack propagation test of the specimen to obtain the trained neural network model; Step 3: Reduce the cycle number range of the original dataset to [N1, N]. n Divide the interval into p equally spaced intervals to obtain P. n Each cycle node; Where the initial p=2; Step 4: Using the trained neural network model, predict the crack length corresponding to each cycle node to obtain the expanded dataset. D 2n Meanwhile, the crack length prediction error E of the neural network model on the original dataset is obtained; Step 5: Let Using augmented datasets D 2n Retrain to update the neural network model, repeat steps three and four, and iteratively update the expanded dataset based on interpolation predictions. D 3n , D 4n ...until the fluctuation of the crack length prediction error E of the neural network model on the original dataset is less than the preset error value, thus obtaining the expanded dataset. D pn Its expression is: D pn ={(a 1 ,N 1 ), (a 2 ,N 2 ), ... ,(a i ,N i ),..., (a j ,N j ),..., (a pn ,N pn )} In the formula, D pn This indicates an expansion of the dataset.

4. The fatigue crack propagation prediction method based on incremental information machine learning modeling according to claim 1, characterized in that, Step S3 specifically involves: Based on the expanded dataset D pn Calculate the cycle increment between each sample point in the augmented dataset. ΔN ij = N j - N i and crack length increment Δa ij = a j - a i Where j>i, the crack propagation rate between each sample point is obtained. Δa ij / ΔN ij Incremental information sample dataset is constructed. S Its expression is S={ (N 1 , ΔN 12 , Δa 12 / ΔN 12 ), (N 1 , ΔN 13 , Δa 13 / ΔN 13 ), ... ,(N i , ΔN ij , Δa ij / ΔN ij ),..., (N (pn-1) , ΔN (pn-1)pn , Δa (pn-1)pn / ΔN (pn-1)pn )} The incremental information sample dataset S Includes: input features and output target; the input features include: cycle number. N i and cycle interval ΔN ij The output target is the crack propagation rate. Δa ij / ΔN ij .

5. The fatigue crack propagation prediction method based on incremental information machine learning modeling according to claim 1, characterized in that, Step S4 is as follows: Construct a single-hidden-layer feedforward neural network model based on the incremental information sample dataset. S A single-hidden-layer feedforward neural network model is trained, and the mean squared error is used as the loss function during the training process until the loss function converges, thus obtaining a fatigue crack propagation rate prediction model.

6. The fatigue crack propagation prediction method based on incremental information machine learning modeling according to claim 5, characterized in that, Step S5 includes: obtaining the average crack propagation rate using a fatigue crack propagation rate prediction model; including: Step 1: With D pn The cycle interval between adjacent sample points in the expanded dataset is the step size. Δn Construct the set of cycles corresponding to the later stage of fatigue crack propagation testing of the specimen: [ N n＋1 , N n＋2 ,..., N n＋i ,..., N 2pn ], in, N n＋2 -N n＋1 =Δn ; Step 2: Calculate the sum of each cycle number in the cycle set. D n The cycle interval for each sample point in the dataset, for N n＋i， The general formula for calculation is: ΔN 1(n＋i) , ΔN 2(n＋i) , ... , ΔN i(n＋i) , ..., ΔN j(n＋i) , ..., Δ N n(n＋i) ; Step 3: Construct a dataset for predicting crack length in the later stages of fatigue crack propagation testing of specimens, targeting... N n＋i， The general formula for calculation is: (N 1 , ΔN 1(n＋i) ) , (N 2 , ΔN 2(n＋i) ) , ... , (N i , ΔN i(n＋i) ) , ..., (N j , ΔN j(n＋i) ) , ... , (N n , ΔN n(n＋i) ) ; Step 4: Input the dataset from Step 3 into the trained fatigue crack propagation rate prediction model to obtain the fatigue crack propagation rate at the corresponding cycle number in the later stage of the fatigue crack propagation test of the specimen. against N n＋i， The general formula for calculation is: Δa 1(n＋i) / ΔN 1(n＋i) , Δa 2(n＋i) / ΔN 2(n＋i) , ... , Δa i(n＋i) / Δ N i(n＋i) , ... , Δa j(n＋i) / ΔN j(n＋i) , ... , Δa n(n＋i) / ΔN n(n＋i) .

7. The fatigue crack propagation prediction method based on incremental information machine learning modeling according to claim 1, characterized in that, By using multi-path prediction weighted averaging, the crack length value and its confidence interval in the later stage of the fatigue crack propagation test of the specimen are obtained, thus obtaining the complete fatigue crack propagation curve of the specimen. The specific process is as follows: Based on the n predicted fatigue crack propagation rates at the corresponding cycle number in the later stage of the fatigue crack propagation test, the n fatigue crack lengths at the corresponding cycle number in the later stage of the fatigue crack propagation test are calculated: against N n＋i， The general formula for calculation is: By integrating n fatigue crack lengths and using a multi-path prediction weighted average, the crack length value and its confidence interval in the later stage of fatigue crack propagation testing of the specimen are obtained: For cycle number N n＋i The lengths of n fatigue cracks: {a 1(n＋i) ,a 2(n＋i) ,...,a n(n＋i) Based on the set of predicted crack lengths at the target prediction points, the weighted average of the predicted crack lengths is calculated to obtain the complete fatigue crack propagation curve of the sample, specifically: Based on the increment Δa for each predicted crack length i,n＋i The path length weight is calculated using the following expression: In the formula, ω i Let Δa represent the weight of the i-th path. k,n+i This represents the crack length increment of the k-th path, where n represents the number of fixed reference starting points; The final predicted crack length is calculated using the following expression: In the formula, a n+i,final Represents the target prediction point N n+i The corresponding final predicted crack length; The confidence interval is calculated using the following expression: In the formula, sd(a n+i ) represents the target prediction point N n+i The corresponding standard deviation of the predicted crack length, i.e. the confidence interval.

8. The fatigue crack propagation prediction method based on incremental information machine learning modeling according to claim 7, characterized in that, Also includes: The fatigue cracks in the early and late stages of the fatigue crack propagation test of the specimen were connected sequentially to obtain the complete fatigue crack propagation curve of the specimen.

9. An electronic device, characterized in that, The system includes a memory, a processor, and a computer program stored in the memory and running on the processor. When the fatigue crack propagation prediction program based on incremental information machine learning modeling is executed by the processor, it implements the steps of the fatigue crack propagation prediction method based on incremental information machine learning modeling as described in any one of claims 1-8.

10. A fatigue crack propagation prediction system based on incremental information machine learning modeling, used to implement the fatigue crack propagation prediction method based on incremental information machine learning modeling as described in any one of claims 1-8, characterized in that, include: The data acquisition module is used to collect early data samples from the fatigue crack propagation test of the specimen as the raw dataset; The data augmentation module is used to iteratively augment the data samples based on the original dataset through machine learning modeling and interpolation prediction to obtain an augmented dataset. The data augmentation module is used to construct an incremental information sample dataset containing cycle increments and crack length increments based on the expanded dataset. The training and modeling module is used to perform secondary machine learning modeling based on the incremental information sample dataset to obtain a fatigue crack propagation rate prediction model. The prediction module is used to obtain the crack length value and its confidence interval in the later stage of the fatigue crack propagation test of the sample by using a fatigue crack propagation rate prediction model and weighted averaging through multi-path prediction, thus obtaining the complete fatigue crack propagation curve of the sample.

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