A method and computer program for predicting fatigue crack propagation rate

Abstract

This invention relates to the interdisciplinary field of fatigue fracture mechanics and machine learning, and discloses a method and computer program product for predicting fatigue crack propagation rate. The invention first constructs a heterogeneous candidate model pool, and then selects three preferred models from the pool through Bayesian optimization and competitive screening strategies. These three preferred models are then adjusted to achieve unified scheduling, forming an HPD-Stacking ensemble prediction model as the first layer, which, together with the meta-learner in the second layer, performs ensemble learning. Finally, a trained overall model is obtained for prediction. This invention effectively integrates the physical consistency of fracture mechanics laws with the data mining capabilities of ensemble learning. Even when faced with data of varying quality, it can still achieve high-precision prediction of fatigue crack propagation behavior, avoiding overfitting and non-physical fluctuations inherent in traditional single models.

Description

Technical Field

[0001] This invention relates to the field of fatigue fracture mechanics and machine learning, specifically to: 1. a fatigue crack propagation rate prediction method based on hybrid physics-data stacking (HPD-Stacking), which combines physical information neural network (PINN) and integrated machine learning technology; 2. a computer program product. Background Technology

[0002] The fatigue crack initiation and propagation stages account for the vast majority (up to 90%) of the total fatigue life of engineering structures. Accurately predicting the propagation behavior of fatigue cracks is crucial for the safety assessment of high-reliability equipment such as aero-engine blades and marine engineering structures.

[0003] Currently, existing technologies for predicting fatigue crack propagation rates mainly fall into two categories: purely data-driven and purely physical models. For example, Chinese invention patents such as CN202410137939.6, CN202411603051.3, and CN202510509300.0 disclose some specific applications of these two technical solutions. However, relying solely on data-driven or purely physical models requires a large amount of data. The former is prone to overfitting in areas with scarce data and cannot guarantee that the prediction results conform to the monotonicity of fracture mechanics. The latter often lacks generalization ability when facing drastic fluctuations in fatigue cracks and is prone to producing non-physical "step-like" prediction curves, making it difficult to accurately capture the continuous physical process or local fluctuation characteristics of crack propagation. In summary, existing methods struggle to achieve high-precision prediction of fatigue crack propagation rates with data of varying quality. Summary of the Invention

[0004] Therefore, it is necessary to provide a fatigue crack growth rate prediction method and computer program product to address the problems of existing methods for predicting fatigue crack growth rate, which require a large amount of data and have poor prediction performance under data of varying quality.

[0005] This invention is achieved using the following technical solution: In a first aspect, the present invention discloses a method for predicting fatigue crack propagation rate, comprising: A candidate model pool containing several traditional machine learning models and PINN variant models based on different fracture mechanics assumptions was constructed. Based on the fatigue crack sample dataset of the target material, three preferred models were selected from the candidate model pool through Bayesian optimization and competitive screening strategies. The PINN variant model among the three preferred models is adjusted to achieve unified scheduling with the other two traditional machine learning models among the three preferred models; An HPD-Stacking ensemble prediction model is constructed with three optimized models that have achieved unified scheduling in the first layer and a meta-learner in the second layer. The model is then integrated and learned based on the fatigue crack sample dataset of the target material to obtain a trained HPD-Stacking ensemble prediction model. The actual input features of the target material under the predicted working condition are obtained, normalized, and then input into the trained HPD-Stacking ensemble prediction model for processing to obtain the predicted value of the fatigue crack propagation rate under the working condition.

[0006] This fatigue crack propagation rate prediction method implements the method or process according to embodiments of this disclosure.

[0007] In a second aspect, the present invention discloses a computer program product, comprising a computer program. When executed by a processor, the computer program implements the steps of the fatigue crack propagation rate prediction method as disclosed in the first aspect.

[0008] Compared with the prior art, the present invention has the following beneficial effects: This invention first constructs a heterogeneous candidate model pool containing several traditional machine learning models and PINN variant models based on different fracture mechanics assumptions. Based on a fatigue crack sample dataset of the target material, three optimal models are selected from the candidate model pool using Bayesian optimization and competitive screening strategies. These three optimal models are then adjusted to achieve unified scheduling, forming the first layer and working in conjunction with the second layer meta-learner to form the HPD-Stacking ensemble prediction model. This model performs ensemble learning based on the fatigue crack sample dataset of the target material, ultimately obtaining a trained overall model for prediction. This invention effectively integrates the physical consistency of fracture mechanics laws with the data mining capabilities of ensemble learning. Even when faced with data of varying quality, it can still achieve high-precision prediction of fatigue crack propagation behavior, avoiding overfitting and non-physical fluctuations inherent in traditional single models. Attached Figure Description

[0009] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0010] Figure 1A flowchart of the fatigue crack propagation rate prediction method based on hybrid physics-data stacking integration provided in Embodiment 1 of the present invention; Figure 2 for Figure 1 A schematic diagram of the PINN variant model; Figure 3 This is a histogram comparing the performance of models within the candidate model pool provided in Embodiment 2 of the present invention. Figure 4 Box plot showing the distribution of model prediction performance verification provided in Embodiment 2 of the present invention; Figure 5 This is a curve comparison chart of crack propagation rate prediction for CP-Ti provided in Embodiment 2 of the present invention; Figure 6 This is a curve comparison chart of crack propagation rate prediction for TC4-ELI provided in Embodiment 2 of the present invention. Detailed Implementation

[0011] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0012] It should be noted that when a component is said to be "installed on" another component, it can be directly on the other component or it may be in a component that is centered on it. When a component is said to be "set on" another component, it can be directly set on the other component or it may also be in a component that is centered on it. When a component is said to be "fixed to" another component, it can be directly fixed to the other component or it may also be in a component that is centered on it.

[0013] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the specification of this invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "or / and" as used herein includes any and all combinations of one or more of the associated listed items.

[0014] Example 1

[0015] See Figure 1 It illustrates a flowchart of a fatigue crack propagation rate prediction method based on hybrid physics-data stacking integration disclosed in Embodiment 1, which includes: Step 1: Construct a fatigue crack multidimensional dataset of the target material (which can be a single type or multiple types), and preprocess it to remove noise and dimension differences, thereby obtaining a fatigue crack sample dataset of the target material.

[0016] The fatigue crack multidimensional dataset for the target material can use existing publicly available datasets for that material, or it can be constructed independently. In this embodiment 1, it is recommended to use the self-constructed dataset approach: several independent fatigue crack propagation experiments are conducted on the target material, and the experimental results are measured and calculated to obtain experimental data—which includes 6 dimensions: ① crack length c ② Stress ratio R ③ Maximum nominal stress σ max ④ Yield strength σ ys ⑤ Crack tip driving force parameters – including: stress intensity factor range ΔK eff Dimensions of the plastic zone at the crack tip r p Crack tip displacement under monotonic tension Crack tip displacement under cyclic loading ); ⑥, crack propagation rate DC / dN ( N (Indicates the number of stress cycles).

[0017] For the fatigue crack multidimensional dataset, the first 5 dimensions (i.e., parameters ① to ⑤) are assigned to the sample input features containing 5 dimensions, and the 6th dimension (i.e., parameter ⑥) is used as the true label, thus forming the sample feature space.

[0018] The subsequent preprocessing process includes: first smoothing the data, and then normalizing it.

[0019] I. Data smoothing addresses the inherent point-to-point oscillation problem in fatigue crack propagation rate data. A five-point moving average (MAS) method is used for noise reduction—the specific calculation formula is as follows: ; In the formula, Indicates time t The corresponding smoothed crack propagation rate value; x t-i Indicates the time within the sliding window t - i The corresponding original value of the crack propagation rate; M This indicates the size of the sliding window, set to 5.

[0020] II. The following normalization strategy is adopted for the sample feature space to remove dimensional differences, which is more conducive to accelerating the convergence of subsequent models: The sample input features are directly mapped to the [0,1] interval using the Min-Max normalization method; The true labels are first logarithmically transformed, and then mapped to the [0,1] interval using the Min-Max normalization method.

[0021] In other words, the fatigue crack sample dataset contains preprocessed sample input features and true labels.

[0022] Step 2: Construct a candidate model pool containing several traditional machine learning models and PINN variant models based on different fracture mechanics assumptions. Then, select three preferred models from the candidate model pool based on the fatigue crack sample dataset of the target material using Bayesian optimization and competitive screening strategies.

[0023] It should be noted that the three preferred models include: the best-performing PINN variant model among the PINN variant models based on different fracture mechanics assumptions, and the two traditional machine learning models with the top two performance among several traditional machine learning models.

[0024] Step two is actually about finding the optimal composition of the first layer of the subsequent HPD-Stacking ensemble prediction model. The specific process is as follows: S201 is a data-driven model candidate unit that selects several traditional machine learning models (such as Extreme Gradient Boosting (XGBoost), Random Forest, Support Vector Regression (SVR), K-Nearest Neighbors (KNN), Artificial Neural Networks (ANN), etc.) to form a candidate model pool.

[0025] S202, based on the fracture mechanics assumptions, adjust the loss function of the PINN model accordingly to obtain the corresponding PINN variant model, and form the physical driving model candidate part of the candidate model pool.

[0026] It should be noted that, see Figure 2 The PINN variant model is identical to the PINN model in terms of network architecture—both use a fully connected neural network, including an input layer (5 neurons), 3 hidden layers (128, 64, and 32 neurons respectively, with ReLU activation function), and an output layer (1 neuron). The loss function is also identical in structure—both include data-driven loss and physical constraint loss; the difference lies in the specific calculation form of the physical constraint loss.

[0027] In other words, the loss function of the PINN variant model can be expressed as: ; In the formula, Loss total The loss function represents the PINN variant model; Loss data This represents the data-driven loss, which is the mean square error (MSE) between the predicted and actual crack propagation rates. Loss physics Indicates physical constraint loss; ω This represents adaptive physical weights, which can be dynamically adjusted through grid search to balance data fitting accuracy and physical consistency constraints.

[0028] This embodiment 1 provides three PINN variant models based on different fracture mechanics assumptions:

[0029] (1) PINN-Newman model - based on the crack closure effect mechanism, it embeds the Newman crack closure empirical formula as a regularization term into the loss function.

[0030] Specifically, the loss function of the PINN-Newman model Loss PINN-Newman for: ; ; In the formula, Loss phy-Newman This represents the physical constraint loss of the PINN-Newman model; C , m All are empirical parameters; Δ K eff,i The effective stress intensity factor range corresponding to the input feature of the i-th batch; The crack propagation rate prediction value corresponding to the input feature of the i-th batch is given.

[0031] (2) PINN-Ye model - based on the damage accumulation mechanism in the plastic zone, which embeds the damage accumulation model in the plastic zone as a regularization term into the loss function.

[0032] Specifically, the loss function of the PINN-Ye model Loss PINN-Ye for: ; ; In the formula, Loss phy-Ye This represents the physical constraint loss of the PINN-Ye model; r p,i Input the size of the reversible plastic zone at the crack tip corresponding to the feature of the i-th batch.

[0033] (3) PINN-Su model - based on crack tip displacement mechanism, which embeds crack tip displacement model as regularization term into loss function.

[0034] Specifically, the loss function of the PINN-Su model Loss PINN-Su for: ; ; In the formula, Loss phy-Su This represents the physical constraint loss of the PINN-Su model; Input the crack tip displacement parameters under monotonic tension corresponding to the feature of the i-th batch; Input the crack tip displacement parameters under cyclic load corresponding to the feature for the i-th batch.

[0035] For the three PINN variant models mentioned above ω The optimal values ​​are all above 0.8, which means that the model is highly dependent on physical laws to constrain the predicted trend and can effectively prevent overfitting.

[0036] Of course, other PINN variant models can also be designed, which will not be elaborated here.

[0037] S203, divide the fatigue crack sample dataset of the target material into a training set and a test set; The model pool is trained based on the training set, and the hyperparameters of the model are optimized using Bayesian optimization. Performance tests are conducted on each trained model based on the test set (generally using root mean square error RMSE and coefficient of determination R). 2 (Evaluation metrics are used). Referring to the above explanation, the three preferred models should include one PINN variant model and two traditional machine learning models. Therefore, the best-performing PINN variant model is selected from the physics-driven model candidate group—to capture physical monotonicity—and the top two performing traditional machine learning models are selected from the data-driven model candidate group—to capture local nonlinear fluctuations and reduce prediction variance, respectively. This yields the three preferred models.

[0038] Step 3: Adjust the PINN variant model among the three preferred models to achieve unified scheduling with the other two traditional machine learning models.

[0039] Specifically, step three includes: S301 encapsulates the PINN variant model among the three preferred models to eliminate the differences in underlying algorithm architecture between it and traditional machine learning models.

[0040] S301 encapsulates the complex iterative training process of the PINN variant model internally by constructing a standardized interface encapsulation module, enabling the PINN variant model to have fitting and prediction calling instructions consistent with traditional machine learning models at the system level.

[0041] S302 performs tensor dimensionality reduction and format conversion on the output of the class-wrapped PINN variant model to eliminate the differences in data structure with traditional machine learning models.

[0042] The original output of the PINN variant model is typically a high-dimensional tensor with gradient information, while traditional machine learning models output a flattened numerical sequence. Therefore, the original output of the PINN variant model is transformed into a one-dimensional numerical vector with the same specifications as the output of traditional machine learning models to ensure effective concatenation during the subsequent generation of meta-feature matrices.

[0043] Step four: Construct a two-layer HPD-Stacking ensemble prediction model. The first layer consists of three optimized models processed in step three (which have been uniformly scheduled), and the second layer is a meta-learner. The model is then integrated and learned based on the fatigue crack sample dataset of the target material to obtain a trained HPD-Stacking ensemble prediction model.

[0044] Step four is actually about training and predicting the first layer based on the fatigue crack sample dataset and outputting the corresponding first layer prediction results. Based on the first layer prediction results, the second layer is relearned and weighted to improve the generalization ability of the overall model.

[0045] The ensemble learning process in step four is as follows: S401. The fatigue crack sample dataset of the target material is subjected to the Leave-in-Group Cross-Validation (LGO) strategy through the first layer generator feature matrix.

[0046] The fatigue crack sample dataset is divided into: N Groups, each time selected N -1 data set is used as the training set to train the first layer, and the remaining 1 data set is used as the prediction set to obtain the prediction result of the first layer; loop. N This method, which involves predicting all groups and then concatenating all the first-layer predictions to form a meta-feature matrix, effectively prevents data leakage caused by temporal correlation of experimental data within the same group, and also avoids the performance degradation caused by a significant reduction in the training set in traditional K-fold cross-validation.

[0047] S402, based on the meta-feature matrix and the corresponding real labels, performs weight learning and allocation through the second layer to obtain the trained HPD-Stacking ensemble prediction model.

[0048] The second layer is actually learning the optimal weight combination and assigning it to the meta-feature matrix—so that the PINN variant model in the first layer dominates the prediction trend in areas with scarce data, and the traditional machine learning model corrects local biases in areas with fluctuating data, thus making the prediction results of the HPD-Stacking ensemble prediction model closer to the true label.

[0049] The second layer can use a ridge regression model, XGBoost, etc. Lasso Regression, Gaussian process regression, shallow random forest, etc. In this embodiment 1, the second layer is recommended to use the ridge regression model, which uses L2 regularization to handle the high collinearity within the meta-feature matrix in order to automatically learn the optimal weight combination.

[0050] Step 5: Obtain the actual input features of the target material under the predicted working condition, normalize them, and input them into the trained HPD-Stacking ensemble prediction model for processing to obtain the predicted value of the fatigue crack propagation rate under the working condition.

[0051] It is important to emphasize that the five dimensions of the actual input features are consistent with the composition of the sample input features—that is, including the parameter values ​​① to ⑤ under this condition, to ensure the prediction accuracy of the HPD-Stacking integrated prediction model.

[0052] In summary, the above method effectively integrates the physical consistency of fracture mechanics laws with the data mining capabilities of ensemble learning. Even when faced with data of varying quality, it can still achieve high-precision prediction of fatigue crack propagation behavior, avoiding overfitting and non-physical fluctuations of traditional single models.

[0053] Example 2

[0054] This embodiment 2 provides a specific application example and comparison of embodiment 1: Two commonly used titanium alloys were selected as target materials: industrial pure titanium (CP-Ti) and damage-tolerant titanium alloy (TC4-ELI). Twenty sets of independent fatigue crack propagation experimental data were collected and preprocessed to obtain the corresponding fatigue crack sample dataset.

[0055] It should be noted that the experimental data of CP-Ti exhibits typical characteristics of dramatic fluctuations, while the experimental data of TC4-ELI is relatively smooth.

[0056] The candidate model pool in this embodiment 2 includes: PINN-Newman model, PINN-Ye model, PINN-Su model, Extreme Gradient Boosting (XGBoost), Random Forest, Support Vector Regression (SVR), K-Nearest Neighbors (KNN), and Artificial Neural Network (ANN).

[0057] Based on a fatigue crack sample dataset (divided into training and test sets in a 4:1 ratio), three preferred models were selected from the candidate model pool using a Bayesian optimization and competitive selection strategy—based on the RMSE and R-value of each model on the test set. 2 As an evaluation indicator, see the results. Figure 3 .

[0058] It can be seen that among the three PINN variant models, the PINN-Newman model performs best (its RMSE is approximately 0.033, R0.03 is approximately 0.033). 2 The crack closure effect (>0.8) is superior to the PINN-Ye and PINN-Su models. This indicates that the crack closure effect mechanism most accurately describes the physical mechanism for the two titanium alloy materials in Example 2. Therefore, the PINN-Newman model was selected as one of the three preferred models.

[0059] Among several traditional machine learning models, XGBoost and RF show significantly better prediction accuracy than models such as SVR and KNN. Therefore, XGBoost and RF are selected as the other two of the three preferred models.

[0060] Next, the PINN-Newman model was adjusted to achieve unified scheduling with XGBoost and RF. Then, these three were used as the first layer of the HPD-Stacking ensemble prediction model, and the ridge regression model was selected as the second layer of the HPD-Stacking ensemble prediction model.

[0061] The HPD-Stacking ensemble prediction model was ensemble-learned based on a fatigue crack sample dataset to obtain a trained HPD-Stacking ensemble prediction model. The optimal weight combination was obtained as follows: the PINN-Newman model had the highest weight of approximately 0.39, XGBoost had a weight of approximately 0.38, and RF had a weight of approximately 0.23. This indicates that the HPD-Stacking ensemble prediction model relies on the PINN-Newman model to grasp physical trends, on XGBoost to correct local nonlinear biases, and on RF to reduce prediction variance.

[0062] The PINN model, XGBoost, RF, SVR, KNN, and ANN were introduced together with the HPD-Stacking ensemble prediction model to predict the target material. The results were compared with the actual values ​​from the experimental data, and the results are as follows: 1. See Figure 4 Overall, the R-value of the HPD-Stacking ensemble prediction model is... 2 The distribution is most concentrated and the location is highest (average) R 2=0.864), and RMSE is the lowest (only 0.029). In contrast, the individual SVR, KNN, and ANN have extremely large variances, indicating that they are poorly adapted to predicting the fatigue crack propagation rate of the two titanium alloy materials mentioned above.

[0063] Furthermore, the HPD-Stacking ensemble prediction model exhibits the narrowest interquartile range, indicating consistently stable predictive performance. Additionally, the HPD-Stacking ensemble prediction model performs well in R... 2 It maintains the highest lower bound performance, indicating that it can effectively prevent catastrophic prediction failures.

[0064] 2. See Figure 5 For CP-Ti, the XGBoost prediction curve exhibits a distinct step-like characteristic, indicating that the tree model cannot handle continuous regression well, leading to prediction results that violate the physical continuity of crack propagation. In contrast, the HPD-Stacking ensemble prediction model not only eliminates the step effect and maintains good physical monotonicity, but also, compared to the PINN model (whose R1...), shows a significantly higher prediction curve. 2 =0.76) more accurately fits the fluctuation trend of the data, thus improving the final accuracy to R0.76. 2 =0.82.

[0065] 3. See Figure 6 For TC4-ELI, the prediction curve of the HPD-Stacking ensemble prediction model showed extremely high fitting ability, with its predicted values ​​almost perfectly matching the experimental values. R 2 Up to 0.99.

[0066] In summary, this method demonstrates its adaptive adjustment capability—when faced with inconsistent fatigue crack rate data quality, it can fully unleash the fitting potential of the data-driven model and the dominant role of the physics-driven model, achieving accurate prediction of crack propagation rate throughout the entire lifecycle.

[0067] Example 3

[0068] This embodiment 3 discloses a computer device, including a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements the steps of the fatigue crack propagation rate prediction method based on hybrid physical-data stacking integration disclosed in embodiment 1.

[0069] The computer equipment can be either a mobile terminal or a fixed terminal. Examples of the former include mobile phones, laptops, digital radio receivers, PDAs (Personal Digital Assistants), PADs (Portable Application Description), PMPs (Portable Media Players), and in-vehicle terminals (such as in-vehicle navigation terminals); examples of the latter include digital TVs and desktop computers.

[0070] This embodiment 3 also discloses a readable storage medium storing computer program instructions. When the computer program instructions are read and executed by a processor, the steps of the fatigue crack propagation rate prediction method based on hybrid physical-data stacking integration disclosed in embodiment 1 are performed.

[0071] The readable storage medium may include, but is not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination of the above.

[0072] This embodiment 3 also discloses a computer program product, including a computer program. When executed by a processor, the computer program implements the steps of the fatigue crack propagation rate prediction method based on hybrid physical-data stacking integration disclosed in embodiment 1.

[0073] It should be noted that the computer program used to execute the above can be written in one or more programming languages ​​or a combination thereof. These programming languages ​​include object-oriented programming languages—such as Java, Smalltalk, and C++—as well as conventional procedural programming languages—such as C or similar languages. The computer program can be executed entirely on the user's computer, partially on the user's computer, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer through any type of network—including a Local Area Network (LAN) or a Wide Area Network (WAN).

[0074] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0075] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A method for predicting fatigue crack propagation rate, characterized in that, include: A candidate model pool containing several traditional machine learning models and PINN variant models based on different fracture mechanics assumptions was constructed. Based on the fatigue crack sample dataset of the target material, three preferred models were selected from the candidate model pool through Bayesian optimization and competitive screening strategies. The PINN variant model among the three preferred models is adjusted to achieve unified scheduling with the other two traditional machine learning models among the three preferred models; An HPD-Stacking ensemble prediction model is constructed with three optimized models that have achieved unified scheduling in the first layer and a meta-learner in the second layer. The model is then integrated and learned based on the fatigue crack sample dataset of the target material to obtain a trained HPD-Stacking ensemble prediction model. The actual input features of the target material under the predicted working condition are obtained, normalized, and then input into the trained HPD-Stacking ensemble prediction model for processing to obtain the predicted value of the fatigue crack propagation rate under the working condition.

2. The fatigue crack propagation rate prediction method according to claim 1, characterized in that, Methods for constructing fatigue crack sample datasets for target materials include: A multidimensional dataset of fatigue cracks in the target material is constructed and preprocessed to remove noise and dimension differences, resulting in a fatigue crack sample dataset of the target material. The fatigue crack multidimensional dataset forms the sample feature space, and its sample input features include: crack length. c Stress ratio R Maximum nominal stress σ max Yield strength σ ys The driving force parameter at the crack tip is actually labeled as the crack propagation rate. DC / dN ; N Indicates the number of stress cycles; The actual input features are consistent with the sample input features in terms of composition.

3. The fatigue crack propagation rate prediction method according to claim 2, characterized in that, The preprocessing process includes: first smoothing the data, then normalizing it; Among them, the data smoothing process uses a five-point sliding window moving average method for noise reduction. The sample input features are directly mapped to the [0,1] interval using the Min-Max normalization method; The true labels are first logarithmically transformed, and then mapped to the [0,1] interval using the Min-Max normalization method.

4. The fatigue crack propagation rate prediction method according to claim 1, characterized in that, The selection methods for the three preferred models include: S201, Selecting several traditional machine learning models to form a candidate model pool; Data-driven model candidate department. S202, Based on the fracture mechanics assumptions, adjust the loss function of the PINN model accordingly to obtain the corresponding PINN variant model, and form the physical driving model candidate part of the candidate model pool; S203, divides the fatigue crack sample dataset of the target material into a training set and a test set; The model pool is trained based on the training set, and the hyperparameters of the model are optimized using Bayesian optimization. The performance of each trained model was tested based on the test set. The best-performing PINN variant model was selected from the physics-driven model candidate group, and the top two traditional machine learning models were selected from the data-driven model candidate group, thus obtaining three preferred models.

5. The fatigue crack propagation rate prediction method according to claim 1 or 4, characterized in that, PINN variant models include: PINN-Newman model, PINN-Ye model, and PINN-Su model; The loss function of the PINN-Newman model is... Loss PINN-Newman for: ； ； In the formula, Loss data Indicates data-driven loss; ω Indicates adaptive physical weights; Loss phy-Newman This represents the physical constraint loss of the PINN-Newman model; C , m All are empirical parameters; Δ K eff,i The effective stress intensity factor range corresponding to the input feature of the i-th batch; The crack propagation rate prediction value corresponding to the input feature of the i-th batch is used; Loss function of the PINN-Ye model Loss PINN-Ye for: ； ； In the formula, Loss phy-Ye This represents the physical constraint loss of the PINN-Ye model; r p,i Input the size of the reversible plastic zone at the crack tip corresponding to the feature of the i-th batch; Loss function of PINN-Su model Loss PINN-Su for: ； ； In the formula, Loss phy-Su This represents the physical constraint loss of the PINN-Su model; Input the crack tip displacement parameters under monotonic tension corresponding to the feature of the i-th batch; Input the crack tip displacement parameters under cyclic load corresponding to the feature for the i-th batch.

6. The fatigue crack propagation rate prediction method according to claim 5, characterized in that, Loss data The mean square error between the predicted and actual crack propagation rates; ω The values ​​are dynamically adjusted through grid search to balance the data fitting accuracy and physical consistency constraints.

7. The fatigue crack propagation rate prediction method according to claim 1, characterized in that, The methods for adjusting the PINN variant model among the three preferred models include: S301, class-wrapping the PINN variant model among the three preferred models to eliminate the differences in underlying algorithm architecture with traditional machine learning models; S302 performs tensor dimensionality reduction and format conversion on the output of the class-wrapped PINN variant model to eliminate the differences in data structure with traditional machine learning models.

8. The fatigue crack propagation rate prediction method according to claim 1, characterized in that, Ensemble learning methods include: S401. The fatigue crack sample dataset of the target material is subjected to a retain-group cross-validation strategy through the first layer generator feature matrix. S402, based on the meta-feature matrix and the corresponding real labels, performs weight learning and allocation through the second layer to obtain the trained HPD-Stacking ensemble prediction model.

9. The fatigue crack propagation rate prediction method according to claim 1 or 8, characterized in that, The second layer of the HPD-Stacking ensemble prediction model uses a ridge regression model.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the fatigue crack propagation rate prediction method as described in any one of claims 1-9.

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