A method for predicting fatigue crack propagation of a physical region guided PRG-ABP INN
By using the physical region-guided PRG-ABPINN method, combined with physical stage division and Gaussian weighting function, global and local sub-networks are constructed, solving the problem of nonlinear variation adaptability in crack propagation prediction in existing technologies, and achieving stable and accurate fatigue crack propagation prediction under small sample conditions.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- BEIJING UNIV OF CHEM TECH
- Filing Date
- 2026-02-26
- Publication Date
- 2026-06-19
AI Technical Summary
Existing fatigue crack propagation prediction methods are ill-suited to describing the nonlinear changes in the early, slow stage and the later, accelerated, and unstable stage of crack propagation. Furthermore, they lack physical constraints, resulting in model parameters that rely on experimental calibration and poor prediction stability with small sample sizes.
The Physical Region Guided PRG-ABPINN method is adopted, which constructs global and local subnetworks by dividing the physical stages and using Gaussian weight functions. The model is trained by combining physical residual backpropagation, thereby achieving multi-stage adaptive modeling and local nonlinear expression.
It achieves stable and accurate prediction of crack propagation process under small sample conditions, is applicable to complex working conditions, has physical consistency and high nonlinear fitting capability, and is suitable for fatigue damage monitoring of key components such as aero-engine blades.
Smart Images
Figure CN122241860A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of structural fatigue life prediction and health monitoring technology, and in particular to a fatigue crack propagation prediction method that integrates fracture mechanics and physical information neural networks, applicable to fatigue damage evolution monitoring and life assessment of key components such as aero-engine blades. Background Technology
[0002] Fatigue crack propagation behavior is an important factor affecting the safe service of engineering structures. Especially in high-reliability components such as aero-engine blades, crack propagation failure often has sudden and catastrophic consequences. Therefore, accurate prediction of the crack propagation process is of great engineering significance.
[0003] Existing fatigue crack propagation prediction methods mainly include the following categories:
[0004] 1. Paris's Law Model Based on Fracture Mechanics
[0005] This method has a clear physical meaning, but it is only applicable to the stable propagation stage. It is difficult to describe the nonlinear changes in the early slow stage of crack propagation and the later accelerated instability stage. Furthermore, the model parameters depend on experimental calibration and are difficult to adapt to complex working conditions.
[0006] 2. Pure Data-Driven Neural Network Methods
[0007] This type of method has strong nonlinear fitting ability, but lacks physical constraints, is highly dependent on training data, has poor prediction stability under small sample size or changing operating conditions, and has insufficient extrapolation ability.
[0008] 3. Traditional Physical Information Neural Network (PINN) Method
[0009] Although physical equations are introduced into the loss function to enhance physical consistency, most of them use a single network structure, which is difficult to adapt to the multi-stage strong nonlinear characteristics of crack propagation process, and the subdomain partitioning depends on manual experience setting and lacks a physical guidance mechanism.
[0010] Therefore, there is an urgent need for a crack propagation prediction method that combines physical consistency, multi-stage adaptive modeling capability, and robustness to small samples. Summary of the Invention
[0011] To address the shortcomings of existing technologies, the present invention aims to achieve the above objectives. The technical solution adopted by the present invention is as follows:
[0012] A fatigue crack propagation prediction method guided by physical region PRG-ABPINN includes the following steps:
[0013] S1. Data Acquisition and Preprocessing Module
[0014] The crack length 'a' and the number of cycles 'N' obtained during component fatigue testing or online monitoring are collected and preprocessed, serving as inputs for S2 and S6.
[0015] S2. Physical Stage Division Module – Calculation of Crack Propagation Rate
[0016] The observed rate is calculated using equation (1), and the observed crack propagation rate is calculated based on adjacent data points:
[0017] (1)
[0018] in, and The crack length is between two adjacent measurement points. and The corresponding number of cycles is used to obtain the observed crack propagation rate sequence. Its output is used as the input to S3.
[0019] S3. Adaptive estimation module for physical parameters C and m
[0020] The physical parameters C and m are identified by an adaptive estimation module. First, logarithmic linearization is performed for initial estimation. Then, C and m are set as trainable physical parameters and dynamically updated during model training through the physical residual backpropagation mechanism.
[0021] (2)
[0022] in, This represents the crack propagation rate. The stress intensity factor amplitude is given, and C and m are material constants. The output is the updated physical parameters C and m, which are used as the input to S4.
[0023] S4. Physical Stage Division Module – Calculation of Theoretical Crack Propagation Rate
[0024] The theoretical crack propagation rate is calculated by substituting the updated C and m into equation (2) through the theoretical rate calculation module. The output is a theoretical crack propagation rate sequence, which is used as the input of S5.
[0025] S5. Physical Stage Division Module
[0026] The ratio between the observed crack propagation rate and the theoretical crack propagation rate is constructed by dividing the physical stages into modules and used as a physical deviation index as shown in equation (3):
[0027] (3)
[0028] This ratio characterizes the degree of deviation between actual crack propagation behavior and the theoretical model. Based on the statistical distribution of the ratio, crack propagation is divided into slow propagation, steady propagation, and rapid propagation stages, and the subdomain center parameters are determined. With width parameter The output is the stage division result and subdomain initialization parameters, and its output is used as the input of S6.
[0029] S6. Gaussian Weight Function Module
[0030] Based on the physical stage division results, a Gaussian weight function is constructed for each subdomain as shown in equation (4), which is used to limit the local subnetwork to make significant contributions only within the corresponding crack interval:
[0031] (4)
[0032] in, The center position of the i-th local sub-network. This is the width of the subnetwork. Its output serves as the input to S7.
[0033] S7. Global and local subnetworks based on Gaussian weighted superposition PRG-ABPINN modules
[0034] Building a global neural network module:
[0035] include:
[0036] (1) Input layer (crack length a and number of cycles N output by S1)
[0037] (2) 3 hidden layers
[0038] (3) Output layer (global network prediction loop count) )
[0039] The hidden layer uses a nonlinear activation function to enhance the nonlinear expression capability. A global neural network with Paris formula (2) as the physical constraint is used to learn the overall trend of crack propagation, and its output is a global prediction function.
[0040] Constructing local subnetwork modules:
[0041] Based on the phase division results, multiple lightweight local subnetworks are constructed using local subnetwork modules. Each subnetwork includes:
[0042] (1) Input layer (a and N for each physical stage, subdomain center parameters) With width parameter )
[0043] (2) Hidden layer
[0044] (3) Local output layer (local prediction loop count) )
[0045] Construct a comprehensive prediction model formed by the weighted superposition of a global neural network and multiple local sub-networks, as shown in equation (5):
[0046] (5)
[0047] in, This is the global network prediction result. This is the output of the i-th local subnetwork. This is the Gaussian weighted function of the output of S6. Its output is the complete prediction model, and its output is used as the input of S8.
[0048] S8. Joint Training Optimization Module
[0049] The model is trained by constructing a joint loss function, as shown in equation (6), which includes a data error term and a physical residual term:
[0050] (6)
[0051] in, For data error terms, For physical residuals, For the test set regularization terms, , , is a hyperparameter. The physical residual is used to characterize the degree of deviation of the model prediction results from the physical laws of Paris.
[0052] Simultaneous updates using the backpropagation algorithm:
[0053] (1) Global network parameters
[0054] (2) Local subnetwork parameters
[0055] (3) Physical parameters C and m
[0056] Its output is the trained model parameters and residual distribution, and its output serves as the input to S9.
[0057] S9. Adaptive Subdomain Control Module
[0058] The physical residual distribution is monitored through the adaptive subdomain control module. When the residual in a certain crack interval exceeds a preset threshold:
[0059] (1) Add a local subnetwork
[0060] (2) Update subdomain parameters
[0061] Re-execute S8 for retraining.
[0062] Its output is the optimized model structure and parameters, and its output serves as the input to S10.
[0063] S10. Prediction Output Module
[0064] The prediction output module inputs new crack length data into the trained model to obtain the predicted cycle number and outputs the crack propagation prediction curve. Simultaneously, based on the updated physical parameters C and m, the remaining fatigue life is calculated.
[0065] Based on the above technical solutions, a fatigue crack propagation prediction method based on physical partitioning-guided adaptive basis function physical information neural network is provided to solve the problems of insufficient accuracy, poor stability and strong data dependence in the multi-stage modeling of crack propagation in existing technologies.
[0066] Compared with the prior art mentioned in the background, the advantages of the present invention are as follows:
[0067] 1. Strong physical consistency
[0068] Using Paris' crack propagation law as a global constraint, we ensure that the model prediction results conform to the basic laws of fracture mechanics.
[0069] 2. Strong multi-stage adaptive modeling capability
[0070] By automatically dividing the fracture propagation stage using the physical rate ratio, differentiated modeling of different stages can be achieved;
[0071] 3. Strong ability to express local nonlinearity
[0072] A Gaussian window-weighted local subnetwork structure is used to effectively characterize the local nonlinear behavior during crack propagation.
[0073] 4. Adaptive adjustment of model complexity
[0074] The physical residual-driven subdomain growth mechanism matches the model capability with the physical error region, avoiding unnecessary model redundancy.
[0075] 5. Suitable for small sample engineering scenarios
[0076] Even with limited early monitoring data, it can still achieve stable and accurate crack propagation prediction, and is suitable for complex working conditions such as vibration fatigue of aero-engine blades. Attached Figure Description
[0077] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0078] Figure 1 This is a schematic diagram of the overall framework of the physical information neural network model based on physical partitioning guided by the present invention. It is used to illustrate the overall technical process and module function division of the model from input physical parameters, stage division, subdomain structure construction, physical residual feedback to the final crack propagation prediction output.
[0079] Figure 2 The comparison chart shows the crack propagation prediction results of compact tensile specimens, illustrating the ability of the model of this invention to fit the trend of crack length change with the number of cycles under standard specimen conditions. The comparison shows the prediction results of experimental data, pure physical models, pure data models, traditional physical information neural network models, and the model of this invention.
[0080] Figure 3 The diagram shows a comparison of the error distribution of different prediction methods for compact tensile specimens, illustrating the differences in prediction stability of each method throughout the crack propagation process. The method of this invention exhibits the most concentrated error distribution and the least dispersion.
[0081] Figure 4 This is a schematic diagram of the vibration fatigue test platform for aero-engine blades and the blade installation status, used to illustrate the method of obtaining crack propagation test data and the actual engineering loading environment in the embodiments of the present invention.
[0082] Figure 5 This is a schematic diagram of the crack propagation morphology of the blade after vibration fatigue test, used to illustrate the crack initiation location and propagation path characteristics under vibration fatigue load, and to provide an engineering basis for physical partitioning in this invention.
[0083] Figure 6 The image shows a comparison of the prediction results for crack propagation on multiple aero-engine blades. This is used to illustrate the prediction effect of the model of the present invention on complex engineering components and to compare it with other methods.
[0084] Figure 7 The diagram shows a comparison of the error distribution in predicting crack propagation in aero-engine blades, illustrating the advantages of the method of this invention in terms of prediction accuracy and stability under real engineering vibration fatigue conditions. Detailed Implementation
[0085] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.
[0086] The embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.
[0087] Example 1: Application of crack propagation prediction in compact tensile specimens
[0088] To verify the applicability of the method of the present invention to the standard fatigue crack propagation problem, crack propagation test data of compact tensile specimens were selected for application verification. In this embodiment, the obtained crack length and cycle number data were used as input, and the physical stage division, subdomain initialization, and model training were performed according to the method of the present invention to obtain the prediction curve of the entire crack propagation process. The specific implementation process is as follows:
[0089] S1. Data Acquisition and Preprocessing
[0090] Input: Crack length a and number of cycles N obtained from the crack propagation test of a compact tensile (CT) specimen.
[0091] Processing: Preprocessing the data, such as normalization.
[0092] The preprocessed sample set output is used as input to S2 and S6.
[0093] S2. Physical Stage Division Module – Calculation of Crack Propagation Rate
[0094] The observed rate is calculated using equation (1), and the observed crack propagation rate is calculated based on adjacent data points to obtain the observed crack propagation rate sequence. Its output is used as the input of S3.
[0095] S3. Adaptive estimation of physical parameters C and m
[0096] The physical parameters C and m are identified using an adaptive estimation module. First, logarithmic linearization is performed for initial estimation, and then dynamically updated during model training via backpropagation of physical residuals. The output consists of the updated physical parameters C and m, which are used as input to S4.
[0097] S4. Physical Stage Division Module – Calculation of Theoretical Crack Propagation Rate
[0098] The theoretical crack propagation rate is calculated by substituting the updated C and m into equation (2) through the theoretical rate calculation module. The output is a theoretical crack propagation rate sequence, which is used as the input of S5.
[0099] S5. Physical Stage Division
[0100] Based on equation (3), the ratio between the observed crack propagation rate and the theoretical crack propagation rate is constructed as a physical deviation index through a physical stage division module. According to the distribution of the calculation results, the crack propagation is divided into a slow propagation stage, a stable propagation stage, and a fast propagation stage, and the subdomain center parameters are determined. With width parameter The output is the stage division result and subdomain initialization parameters, and its output is used as the input of S6.
[0101] S6. Subdomain Initialization and Construction of Gaussian Window Weight Function
[0102] Based on the physical stage division results, a Gaussian weighting function is constructed for each subdomain according to equation (4). This is used to limit the local subnetwork to make a significant contribution only within the corresponding crack region. Its output serves as the input to S7.
[0103] S7. Global Neural Network Prediction
[0104] Global neural network module prediction, including:
[0105] (1) Input S1 outputs a and N
[0106] (2) Nonlinear activation of 3 hidden layers
[0107] (3) Output layer
[0108] The hidden layer employs a nonlinear activation function to enhance nonlinear expressive power. A global neural network with Paris formula (2) as the physical constraint is used to learn the overall trend of crack propagation, and its output is... .
[0109] Local subnetwork prediction:
[0110] Based on the stage division results, multiple lightweight local subnetworks are constructed using local subnetwork modules for local prediction, including:
[0111] (1) Input a and N for each physical stage, and subdomain center parameters. With width parameter
[0112] (2) Nonlinear activation of the hidden layer
[0113] (3) Local output of multiple
[0114] The comprehensive prediction formed by the Gaussian weighted superposition of the global neural network and multiple local subnetworks is, according to equation (5):
[0115] (1) Input , and the corresponding
[0116] (2) Output complete predicted value
[0117] Its complete prediction is used as the input to S8.
[0118] S8. Joint Training Optimization
[0119] The model is trained using a joint loss function containing data error terms and physical residual terms constructed according to equation (6). When the loss function value does not meet the requirements, backpropagation is used to update the global network parameters, local network parameters, and C and m simultaneously until the loss function value meets the requirements. The output is the updated model parameters and residual distribution, and its output is used as the input of S9.
[0120] S9. Adaptive Subdomain Growth
[0121] The physical residual distribution is monitored through the adaptive subdomain control module. When the residual in a certain crack interval exceeds a preset threshold:
[0122] (1) Add a local subnetwork
[0123] (2) Update subdomain parameters
[0124] Re-execute S8 for retraining.
[0125] Its output is the optimized model structure and parameters, and its output serves as the input to S10.
[0126] S10. Predicted Output
[0127] The prediction output module takes the crack length data used for testing and inputs it into the trained model to obtain the number of prediction cycles and outputs the crack propagation prediction curve of the CT specimen. Simultaneously, based on the updated physical parameters C and m, it calculates and outputs the remaining fatigue life of the CT specimen.
[0128] like Figure 2 The figure shown is a comparison of the predicted crack length changes of different samples with the number of cycles. Figure 2It is evident that the method of the present invention can maintain a consistent trend with the experimental data in the slow, stable, and accelerated stages of crack propagation. In particular, in the later stage of nonlinear enhancement of crack propagation, the predicted curve did not show significant deviation, indicating that the method of the present invention can effectively characterize the stage-specific nonlinear behavior in the crack propagation process.
[0129] Furthermore, the statistical results of the prediction error are as follows: Figure 3 As shown, the error distribution range of the method of this invention is smaller and the fluctuation is lower than that of the comparative methods, indicating that the prediction stability can be improved while ensuring physical consistency through physical partitioning guidance and adaptive subdomain correction mechanism.
[0130] Therefore, the method of the present invention can achieve stable prediction of the entire crack propagation process under standard sample conditions, and is applicable to common fatigue crack propagation analysis scenarios in engineering.
[0131] Example 2: Application of vibration fatigue crack propagation prediction in aero-engine blades
[0132] Based on the verification using the aforementioned standard samples, the method of this invention was applied to the problem of vibration fatigue crack propagation in actual engineering components, such as aero-engine blades, to verify its engineering applicability. Figure 4 The diagram shows the blade vibration fatigue test platform and the blade's installation state. Loading tests were conducted on the aero-engine blade on the high-frequency vibration fatigue test platform to simulate its high-frequency vibration conditions in actual service. Crack propagation data, including crack length *a* and the number of cycles *N*, were collected. The crack propagation morphology of the blade after the test is shown below. Figure 5 As shown, the cracks gradually extend along the critical section, exhibiting obvious staged characteristics.
[0133] The prediction is performed using the same steps as in Example 1, and the specific implementation process is as follows:
[0134] S1. Data Acquisition and Preprocessing
[0135] Input: Crack length 'a' and number of cycles 'N' obtained from the crack propagation test of aero-engine blades.
[0136] Processing: Preprocessing the data, such as normalization.
[0137] The preprocessed sample set output is used as input to S2 and S6.
[0138] S2. Physical Stage Division Module – Calculation of Crack Propagation Rate
[0139] The observed rate is calculated using equation (1), and the observed crack propagation rate is calculated based on adjacent data points to obtain the observed crack propagation rate sequence. Its output is used as the input of S3.
[0140] S3. Adaptive estimation of physical parameters C and m
[0141] The physical parameters C and m are identified using an adaptive estimation module. First, logarithmic linearization is performed for initial estimation, and then dynamically updated during model training via backpropagation of physical residuals. The output consists of the updated physical parameters C and m, which are used as input to S4.
[0142] S4. Physical Stage Division Module – Calculation of Theoretical Crack Propagation Rate
[0143] The theoretical crack propagation rate is calculated by substituting the updated C and m into equation (2) through the theoretical rate calculation module. The output is a theoretical crack propagation rate sequence, which is used as the input of S5.
[0144] S5. Physical Stage Division
[0145] Based on equation (3), the ratio between the observed crack propagation rate and the theoretical crack propagation rate is constructed as a physical deviation index through a physical stage division module. According to the distribution of the calculation results, the crack propagation is divided into a slow propagation stage, a stable propagation stage, and a fast propagation stage, and the subdomain center parameters are determined. With width parameter The output is the stage division result and subdomain initialization parameters, and its output is used as the input of S6.
[0146] S6. Subdomain Initialization and Construction of Gaussian Window Weight Function
[0147] Based on the physical stage division results, a Gaussian weighting function is constructed for each subdomain according to equation (4). This is used to limit the local subnetwork to make a significant contribution only within the corresponding crack region. Its output serves as the input to S7.
[0148] S7. Global Neural Network Prediction
[0149] Global neural network module prediction, including:
[0150] (1) Input S1 outputs a and N
[0151] (2) Nonlinear activation of 3 hidden layers
[0152] (3) Output layer
[0153] The hidden layer employs a nonlinear activation function to enhance nonlinear expressive power. A global neural network with Paris formula (2) as the physical constraint is used to learn the overall trend of crack propagation, and its output is... .
[0154] Local subnetwork prediction:
[0155] Based on the stage division results, multiple lightweight local subnetworks are constructed using local subnetwork modules for local prediction, including:
[0156] (1) Input a and N for each physical stage, and subdomain center parameters. With width parameter
[0157] (2) Nonlinear activation of the hidden layer
[0158] (3) Local output of multiple
[0159] The comprehensive prediction formed by the Gaussian weighted superposition of the global neural network and multiple local subnetworks is, according to equation (5):
[0160] (1) Input , and the corresponding
[0161] (2) Output complete predicted value
[0162] Its complete prediction is used as the input to S8.
[0163] S8. Joint Training Optimization
[0164] The model is trained using a joint loss function containing data error terms and physical residual terms constructed according to equation (6). When the loss function value does not meet the requirements, backpropagation is used to update the global network parameters, local network parameters, and C and m simultaneously until the loss function value meets the requirements. The output is the updated model parameters and residual distribution, and its output is used as the input of S9.
[0165] S9. Adaptive Subdomain Growth
[0166] The physical residual distribution is monitored through the adaptive subdomain control module. When the residual in a certain crack interval exceeds a preset threshold:
[0167] (1) Add a local subnetwork
[0168] (2) Update subdomain parameters
[0169] Re-execute S8 for retraining.
[0170] Its output is the optimized model structure and parameters, and its output serves as the input to S10.
[0171] S10. Predicted Output
[0172] The prediction output module takes the crack length data used for testing and inputs it into the trained model to obtain the number of prediction cycles and outputs the crack propagation prediction curve for the aero-engine blade. Simultaneously, based on the updated physical parameters C and m, it calculates and outputs the remaining fatigue life of the aero-engine blade.
[0173] The prediction results of crack propagation in multiple blades are as follows: Figure 6 As shown, under the complex condition of vibration fatigue, the method of the present invention can still stably track the crack propagation trend, and no obvious predictive instability phenomenon occurs during the crack propagation acceleration stage.
[0174] Error comparison results of different methods are as follows Figure 7 As shown, the method of this invention has a relatively small overall error value and a concentrated error distribution, indicating that the combination of physical law constraints and local subdomain adaptive correction can effectively improve the prediction accuracy of the model in a strongly nonlinear vibration fatigue environment, which is superior to traditional physical models and conventional neural network methods.
[0175] The proposed method for predicting crack propagation based on physical partitioning-guided adaptive basis function physical information neural network achieves a deep integration of physical laws and neural network structure. It shows significant advantages in multi-stage crack propagation modeling, small sample prediction, and complex engineering applications, and has good prospects for engineering applications.
[0176] Explanation of the overall working mechanism of the model
[0177] like Figure 1 The diagram shown illustrates the overall model framework of the method of this invention. The model first identifies the stages of the crack propagation process using the physical laws of crack propagation, and then constructs a multi-subdomain structure containing a global network and multiple local correction subnetworks. A comprehensive evaluation index is formed by fusing physical residuals and data errors, enabling adaptive adjustment of the number of subdomains and the area of influence. Finally, under the premise of satisfying physical consistency constraints, the model outputs the crack propagation curve and remaining life prediction results.
[0178] As can be seen from the above two embodiments, the method of the present invention is applicable to crack propagation analysis under standard sample conditions, as well as complex engineering scenarios such as vibration fatigue of aero-engine blades. It can achieve stable and accurate crack propagation prediction under small sample conditions and has good engineering application value.
[0179] It should be noted that in this application, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.
[0180] The above description is merely a specific embodiment of this application, enabling those skilled in the art to understand or implement this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features claimed herein.
Claims
1. A fatigue crack propagation prediction method using physically guided PRG-ABPINN, characterized in that, Includes the following steps: S1. Obtain experimental monitoring data of crack length a and cycle number N during component fatigue testing as experimental data input for the model input module; S2. Based on the input crack length a and cycle number N data points, calculate the observed crack propagation rate by dividing the module into physical stages. S3. Based on the input crack length a and the number of cycles N, the material parameters C and m are initially estimated according to the Paris law of fracture mechanics in the physical layer of the model input module. During the model training process, the material parameters are set as updatable physical parameters, and C and m are adaptively adjusted according to the physical residual. S4. Based on the input crack length a and cycle number N data points and the updated material parameters C and m, calculate the theoretical crack propagation rate according to the physical stage division module - theoretical crack propagation rate calculation. S5. Construct the ratio between the observed crack propagation rate and the theoretical crack propagation rate as a physical deviation index, and divide the crack propagation process into stages according to the statistical distribution of the physical deviation index to obtain multiple crack subdomain intervals. S6. Construct a global neural network, using Paris's law as a global physical constraint to learn the overall trend of crack propagation; S7. Construct multiple local sub-networks based on the crack sub-domain interval, and construct a Gaussian weight function for each local sub-network. Weight the output of the global neural network and the output of the local sub-networks and sum them to form a comprehensive prediction model. S8. Construct a joint loss function that includes data error terms and physical residual terms, and update the global neural network parameters, local sub-network parameters, and material parameters C and m simultaneously through the backpropagation algorithm; S9. Identify high-error regions based on the physical residual distribution obtained during training, and add a local subnetwork in the corresponding region and retrain it when the preset conditions are met; S10. Utilize the trained integrated prediction model to output the crack propagation trajectory prediction results, and calculate the remaining fatigue life prediction results based on the updated material parameters.
2. The method as described in claim 1, characterized in that: The material parameters C and m are initially estimated by logarithmically linearizing the Paris crack propagation relation, and are updated as trainable physical parameters through backpropagation of physical residuals during model training.
3. The method as described in claim 1, characterized in that: The physical residual term is constructed based on the difference between the predicted crack propagation rate and the calculation results of the Paris crack propagation model, and is used to constrain the prediction results to meet the physical laws of fracture mechanics.
4. The method as described in claim 1, characterized in that: The crack propagation stage division is based on the ratio of the observed crack propagation rate to the theoretical crack propagation rate, and the stage boundaries are determined according to the ratio.
5. The method as described in claim 1, characterized in that: The stage division divides the crack propagation process into a slow propagation stage, a stable propagation stage, and a rapid propagation stage, and sets corresponding subdomain center and subdomain width parameters for each stage.
6. The method as described in claim 1, characterized in that: The global neural network is a multi-layer fully connected neural network structure used to learn the overall trend of crack propagation, and the local sub-network is a lightweight neural network structure used to correct local stage nonlinear errors.
7. The method as described in claim 1, characterized in that: The local subnetwork is weighted and superimposed with the output of the global neural network using a Gaussian weight function to limit the influence range of the local subnetwork outside the subdomain.
8. The method as described in claim 1, characterized in that: When the physical residual of a certain crack region exceeds a preset threshold during training, a local subnetwork is added to the crack region, and the structure is expanded without exceeding the maximum number of subdomains.
9. The method as described in claim 1, characterized in that: The method is applied to the monitoring of vibration fatigue crack propagation and life prediction of aero-engine blades.