Defective material service life prediction method based on M integral physical information neural network

Abstract

The invention discloses a defect-containing material life prediction method based on an M integral physical information neural network, and the method comprises the steps: constructing a damage parameter, namely an equivalent damage area, of a defect-containing metal material according to an energy equivalent method based on a classical fracture mechanical parameter M integral; establishing an M integral fatigue model according to a power-law relationship between the equivalent damage area and the M integral, and constructing a physical loss function; constructing a mixed loss function by adopting the physical loss function and the data related loss function, and constructing a physical information neural network based on the mixed loss function; optimizing hyper-parameters of the physical information neural network to obtain an optimal life prediction model; and evaluating the fatigue life of the defect-containing metal material by using the prediction model. According to the method, the influence of multi-defect features on fatigue failure is considered, the life prediction result meets the correlation between the fatigue data and conforms to the physical law, the dependence on the fatigue data is reduced, and the prediction precision and the analysis efficiency are remarkably improved.

Description

Technical Field

[0001] This invention belongs to the field of advanced manufacturing materials fatigue life prediction and artificial intelligence interdisciplinary technology, and relates to a method for predicting the fatigue life of defective metallic materials based on M-integral and physical information neural network. Background Technology

[0002] Many fatigue failures in engineering structures are caused by process defects during manufacturing. Advanced manufacturing processes (such as additive manufacturing, integrated casting, laser welding, etc.) inevitably result in a large number of defects of various shapes in metal materials, which directly affect their fatigue fracture performance and restrict the service performance and service life of key structural components.

[0003] Currently, methods for predicting fatigue performance fall into two categories: those based on critical distance or stress and those based on fracture mechanics. The former correlates applied stress or strain with the number of cycles leading to failure (e.g., SN curves, ε-N curves), and is typically used to analyze the fatigue life of defect-free materials under cyclic uniaxial stress conditions, but is not applicable to materials with multiple defects. On the other hand, for fracture mechanics-based methods like Paris's law, the fatigue crack propagation rate is linked to the stress intensity factor amplitude through a simple power-law relationship; however, Paris's law no longer applies to multi-defect materials without macroscopic cracks or with multiple fatigue cracks. While machine learning techniques, which have developed rapidly in recent years, are widely used for predicting fatigue performance due to their powerful nonlinear processing and generalization capabilities for complex physical phenomena, the robustness and accuracy of purely data-driven methods are significantly limited by the number of training samples.

[0004] In summary, existing fatigue life analysis methods (such as SN curves, ε-N curves, Paris's law, and purely data-driven methods) cannot quantify the characteristics of multiple defects (defect number, morphology, spatial distribution, etc.) when evaluating the fatigue life of defective metallic materials. They are also unable to assess the synergistic effect of defects and fatigue crack evolution, and it is difficult to accurately predict the fatigue life of defective metallic materials. Furthermore, fatigue performance evaluation is significantly dependent on fatigue test data. Summary of the Invention

[0005] The purpose of this invention is to provide a method for predicting the life of defective materials based on an M-integral physical information neural network. This method considers the influence of multiple defect characteristics on fatigue failure, and the life prediction results satisfy both the correlation between fatigue data and follow physical laws, reducing the dependence on fatigue data and significantly improving prediction accuracy and analysis efficiency.

[0006] The technical solution adopted in this invention is a method for predicting the lifetime of defective materials based on an M-integral physical information neural network, the steps of which are as follows: Step 1: Based on the classical fracture mechanics parameter M-integral, construct the damage parameter of the defective metallic material—equivalent damage area—according to the energy equivalence method; Step 2: Based on the power-law relationship between the equivalent damage area and the M-integral, establish the M-integral fatigue model and construct the physical loss function; Step 3: Construct a hybrid loss function using the physical loss function and the data correlation loss function, and build a physical information neural network based on the hybrid loss function; Step 4: Optimize the hyperparameters of the physical information neural network using a grid search method to obtain the optimal lifetime prediction model; Step 5: Use a prediction model to assess the fatigue life of the defective metallic material.

[0007] The invention is further characterized by: In step 1, the integral value of M and the change in the total potential energy of the system are used. CTPE Based on the relationships between them, we obtain the global M-integral that includes all defective systems, i.e.:

[0008] In the formula: σ is the cyclic stress load value, For sample size, u and u 0 represents the displacement value before and after fatigue damage; Furthermore, based on the energy equivalence method, the equivalent damage area of ​​all defective systems can be obtained. A D The calculation formula is as follows:

[0009] In the formula: E It is the elastic modulus.

[0010] According to the change in the total potential energy of the system CTPE The process of calculating the integral value of M is as follows: First, a monotonically increasing uniaxial load is applied to a defect-free specimen with the same material properties and dimensions as the multi-defect specimen. p The load-displacement curve Curve-0 was obtained; secondly, fatigue loading was applied to the multi-defect specimen, with the number of fatigue cycles being [number missing]. N The maximum fatigue load is p max The minimum fatigue load is p min Finally, the defective specimens were recorded through uniaxial tensile calculations. N Load-displacement curve after fatigue cycles (Curve-1); Based on the physical meaning of the change in the system's total potential energy, curves Curve-0, Curve-1, p = pmax The area enclosed is CTPE Value, taking into account p max and p min The effect on fatigue driving force, curves Curve-0, Curve-1, p = p max , p = p min The enclosed area is named Δ CTPE Repeat this measurement process until the sample fails and breaks, and calculate the integral value of M.

[0011] Step 2 is as follows: Based on the equivalent damage area A D Based on the power-law relationship with the M-integral, an M-integral fatigue model is established, namely:

[0012] In the formula: λ and w Δ is the empirical parameter of the model. M Defined as the M-integral magnitude for each load cycle, that is, the difference between the M-integral values ​​corresponding to the maximum and minimum loads for each load cycle. N This represents the number of loop iterations. When all defects are calculated from the initial equivalent damage area before cyclic loading A Equivalent damage area when evolving from 0 to final failure A C Then, by performing integral calculations on the M-integral fatigue model, the fatigue life of the defective metallic material is derived. N f for:

[0013] To ensure the prediction of fatigue life The correlation between the equivalent damage area of ​​defects and material properties conforms to the physical relationship in the above formula, improving prediction efficiency, preventing lifetime prediction results that contradict physical laws, and reducing prediction errors. The physical loss function is constructed as follows:

[0014] In the formula: n For the sample size, For the first i Predicted fatigue life for each sample, Δ M 0 represents the initial equivalent damage area. A The M integral amplitude of 0, For the first iThe initial equivalent damage area of ​​each sample.

[0015] In step 3, the hybrid loss function is used in the training process of the neural network. The fatigue life prediction error is calculated by backpropagating the hybrid loss function to achieve error gradient descent.

[0016] In step 3, the data-related loss function To reduce the error in predicting fatigue data, the mean squared error is used as the data correlation loss function, i.e.:

[0017] Then the mixed loss function L for:

[0018] In the formula: L FP For physical loss function, p A penalty factor to adjust the proportion of the influence of the physical loss function. n For the sample size, and The first i Predicted fatigue life and actual fatigue life for each sample λ and w Δ is the empirical parameter of the model. M 0 represents the initial equivalent damage area. A The M-integral amplitude of 0; For the first i The initial equivalent damage area of ​​each sample.

[0019] Step 4 is as follows: The input data features of the physical information neural network are cyclic stress load and equivalent damage area. The dataset is preprocessed and divided into training and test sets in an 8:2 ratio. First, a traditional neural network is used to train the input dataset to fit the empirical parameters in the M-integral fatigue model. Through regression analysis, the relevant results are used to calculate the physical loss function. Then, the input dataset is trained according to the physical information neural network with a hybrid loss function to predict fatigue life. Adopting based on k The grid search method of cross-validation is used to obtain the number of hidden layers, the number of neurons in each hidden layer, the epoch, the batch size, the learning rate, the optimization algorithm, the penalty factor of the physical loss function, and the empirical parameters of the physical loss function.

[0020] The steps for preprocessing the input data are as follows: Columns are normalized to normalize the entire database to the (0, 1) range to eliminate size differences and reduce the impact of extreme values ​​and outliers, thus maintaining model stability; for the range ( x min , x max Variables within ) x Normalization operator H (x) is: .

[0021] The beneficial effects of this invention are: (1) The method of the present invention predicts the fatigue life of defective metal materials based on M-integral and physical information neural network. The fracture mechanics parameter M-integral is integrated into the machine learning process to construct the physical information neural network framework. It can efficiently predict the fatigue life of defective metal materials based on fatigue load conditions and multiple defect characteristics, which significantly improves the prediction accuracy and analysis efficiency. It solves the shortcomings of existing models that cannot consider the influence of multiple defect characteristics. It is applicable to the assessment of the remaining life of metal structural parts with defects such as cracks and pores in aerospace, energy equipment, rail transportation and other fields. (2) The life prediction model of the method of the present invention is simple and easy to implement. Only the cyclic stress load and the equivalent damage area of ​​multiple defects need to be input to obtain the fatigue life of the defective metal material. (3) The method of the present invention uses the M-integral fatigue model as a constraint and integrates the fatigue model into the neural network gradient descent algorithm. Compared with the pure data-driven method, it improves the generalization performance of the neural network, reduces the dependence on fatigue data, takes into account both physical laws and data correlation, and requires less fatigue data compared with the pure data-driven fatigue performance evaluation method. Attached Figure Description

[0022] Figure 1 This is a schematic diagram illustrating the calculation of the integral value of M based on the change in the total potential energy of the system in the method of the present invention; Figure 2 This is a schematic diagram of the multi-defect equivalent quantization in the method of the present invention; Figure 3 A schematic diagram of the M-integral fatigue model analysis for fatigue failure of defective No. 45 steel; Figure 4 This is a schematic diagram illustrating the effect of the penalty factor variation on error gradient descent in the method of this invention; Figure 5 This is a schematic diagram illustrating the prediction of fatigue life of defective metallic materials using a physical information neural network in the method of this invention. Figure 6 A schematic diagram illustrating the effect of integrating neural networks into the M-integral fatigue model on improving prediction accuracy; Figure 7A schematic diagram illustrating the impact of incorporating a neural network into the M-integral fatigue model on the gradient descent of prediction error. Detailed Implementation

[0023] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0024] This invention relates to a method for predicting the lifetime of defective materials based on an M-integral physical information neural network, which is implemented according to the following steps: Step 1: Based on the classical fracture mechanics parameter M-integral, construct the damage parameter—equivalent damage area—for defective metallic materials using the energy equivalence method, and quantitatively characterize the influence of different defect features on overall fatigue damage failure. This step mainly includes two aspects: (1) Calculate the global M-integral that includes all defective systems. The physical interpretation of the global M-integral within a domain encompassing all defects is the sum of local energy releases resulting from the random expansion of each specific defect. Essentially, regardless of the specific damage form, the M-integral represents the total potential energy change of the defective material. This can be achieved by utilizing the M-integral value and the change in the system's total potential energy (…). CTPE The relationship between ) is used to obtain the global M-integral that includes all defective systems, i.e.: (1) In the formula: σ is the cyclic stress load value; The sample size; u and u 0 represents the displacement value before and after fatigue damage.

[0025] According to the change in the total potential energy of the system ( CTPE The process of calculating the integral value of M is as follows: Figure 1 As shown. First, a monotonically increasing uniaxial load is applied to a defect-free specimen with the same material properties and dimensions as the multi-defect specimen. p The load-displacement curve Curve-0 was obtained. Next, fatigue loading was applied to the multi-defect specimen, with the number of fatigue cycles being [number missing]. N The maximum fatigue load is p max The minimum fatigue load is p min Finally, the defective specimens were recorded through uniaxial tensile calculations. N The load-displacement curve Curve-1 after one fatigue cycle. Based on the physical meaning of the change in the system's total potential energy, curves Curve-0, Curve-1, and... p = p max The area enclosed is CTPE Value. Considering p max and pmin The effect on fatigue driving force, curves Curve-0, Curve-1, p = p max , p = p min The enclosed area is named Δ CTPE (i.e., the CTPE amplitude caused by each fatigue cycle). Repeat this measurement process until the specimen fails and fractures. This calculation process is applicable to both experimental measurements and numerical calculations of the M integral value.

[0026] (2) Calculate the equivalent damage area of ​​all defective systems ( A D ) like Figure 2 As shown, according to the energy equivalence method, when the damage caused by multiple potential defects in a material is equivalent to the overall damage to the system caused by an equivalent damage area, the M integral values ​​of a material system containing multiple defects and a material system containing an equivalent damage area are equal.

[0027] Two-dimensional M-integral of an elastic material with a central circular notch M Notch The value can be determined according to the formula The result was obtained through analysis.

[0028] The equivalent damage area can be derived from this. A D ,Right now: (2) In the formula: E It is the elastic modulus.

[0029] Step 2: Based on the power-law relationship between the equivalent damage area and the M-integral obtained in Step 1, establish the M-integral fatigue model, derive the explicit expression for the fatigue life of the defective metallic material, and construct the physical loss function (…). L FP ).

[0030] Based on the power-law relationship between the equivalent damage area and the M-integral, an M-integral fatigue model is established, namely: (3) In the formula: λ and w Empirical parameters for the model; Δ M Defined as the M integral magnitude for each load cycle, that is, the difference between the M integral values ​​corresponding to the maximum and minimum loads for each load cycle; N This represents the number of iterations.

[0031] The M-integral fatigue model is a nonlinear damage model that considers the energy accumulation process, where the equivalent damage area is used to determine the energy level. A D The influence of different defect characteristics on the overall fatigue damage evolution was considered, and the M integral amplitude Δ M Characterizing the driving force of fatigue damage evolution. A D / d N This represents the fatigue damage evolution process. Taking defective 45 steel as an example, its d A D / d N- Δ M It is a good logarithmic linear relationship, such as Figure 3 As shown. This fatigue model can also be used to analyze other metallic materials.

[0032] When all defects are calculated from the initial equivalent damage area before cyclic loading A Equivalent damage area when evolving from 0 to final failure A C At that time, the fatigue life of the defective metallic material was derived by performing integral calculations on the M-integral fatigue model. N f )for: (4) Substituting formulas (2) and (3) into formula (4), fatigue life can be characterized as: (5) when The fatigue model based on M-integral can be simplified to: (6) To ensure the prediction of fatigue life The correlation between the equivalent damage area of ​​defects and material properties conforms to the physical relationship in the above formula, improving prediction efficiency, preventing lifetime prediction results that contradict physical laws, and reducing prediction errors. The physical loss function is constructed as follows: (7) In the formula: n The number of samples; For the first i Predicted fatigue life for each sample; Δ M 0 represents the initial equivalent damage area. A The M-integral amplitude of 0; For the first i The initial equivalent damage area of ​​each sample. The physical loss function defined in formula (7). L FPThis ensures that the values ​​on both sides of the equation (6) are equal, meaning that the fatigue life changes with the internal defects of the material according to the empirical relationship defined by the fatigue driving force.

[0033] Step 3, use the physical loss function ( L FP ) and data-related loss function ( L data Construct a hybrid loss function ( L It is then integrated into the neural network algorithm framework for the training process of the neural network. The fatigue life prediction error is calculated through backpropagation of the hybrid loss function to achieve error gradient descent.

[0034] The data correlation loss function is used to reduce the error in predicting fatigue data. The mean squared error is used as the data correlation loss function, i.e.: (8) In the formula: n The number of samples; and The first i The predicted fatigue life and actual fatigue life of each sample.

[0035] Mean squared error defines the data correlation loss function L data This represents the error in how machine learning algorithms explore the mapping relationships between data. L data =0 means that the predicted fatigue life is equal to the actual fatigue life.

[0036] A hybrid loss function is constructed using the physical loss function and the data correlation loss function, namely: (9) In the formula: p The penalty factor is used to adjust the proportion of influence of the physical loss function. The diagram illustrating the impact of changes in the penalty factor on the overall neural network error gradient descent is shown below. Figure 4 As shown. Compared to traditional artificial neural networks, the physical information neural network proposed in this invention adds λ, w , p Three hyperparameters.

[0037] Using a hybrid loss function L The neural network algorithm is executed, and the training process of the neural network achieves gradient descent of the prediction error by backpropagating the fatigue life prediction error using a hybrid loss function. This is based on the hybrid loss function. L The neural network is called a physical information neural network, such as Figure 5 As shown.

[0038] The backpropagation process in a neural network achieves a non-linear mapping from the input layer to the output layer through linear weighting and activation functions. For neural networks with multiple hidden layers, its... The output of the layer can be represented as: (10) In the formula: w l+1 and b l+1 These are the weight and bias vectors; It is an activation function; yes The output of the layer. Due to the simplicity and flexibility of the nonlinear input-output relationship, the sigmoid function is used as the activation function for the hidden neurons. Linear functions are typically used for the output neurons. Here, stochastic gradient descent is used for training by minimizing the loss function. For the ... Neurons in the layer j , No. i The adaptive representation of each connection weight and bias is as follows: (11) (12) In the formula: t It is the time step. η It is the learning rate that controls the training speed. θ It is a momentum factor that prevents the solution from getting trapped in a local optimum. δ This represents the error between the target value and the predicted value. The training process of a neural network includes finding the optimal weight matrix and bias vector.

[0039] Step 4: Optimize the hyperparameters of the physical information neural network in Step 3 using a grid search method, including: number of hidden layers, number of neurons in each hidden layer, epoch, batch size, learning rate, optimization processing algorithm, penalty factor of physical loss function, empirical parameters of physical loss function, etc., to obtain the optimal lifetime prediction model.

[0040] like Figure 5 As shown, the input data features are cyclic stress load and equivalent damage area. The dataset is preprocessed and divided into training and test sets in an 8:2 ratio. First, a traditional neural network is used to train the input dataset to fit the empirical parameters in the M-integral fatigue model (i.e., w And λ), through regression analysis, the relevant results are used to calculate the physical loss function. Then, according to the process in step 3, the input dataset is trained with a physical information neural network using a hybrid loss function to predict fatigue life.

[0041] Adopting based on kThe grid search method of cross-validation is used to obtain the number of hidden layers, the number of neurons in each hidden layer, the epoch, the batch size, the learning rate, the optimization algorithm, the penalty factor of the physical loss function, and the empirical parameters of the physical loss function.

[0042] The number of cross-validation folds is selected based on the data size, computational resources, and model stability requirements. When the data volume is greater than 1000 but less than 10000... k =10; when the data volume is greater than 10000. k =5.

[0043] Simultaneously, to ensure predictive performance, the input data is preprocessed. Columns (features) are normalized, normalizing the entire database to the (0, 1) range to eliminate size differences and reduce the impact of extreme and outlier values, thus maintaining model stability. For the range ( x min , x max Variables within ) x Normalization operator H (x) is: (13) Step 5: Call the fatigue life prediction model for defective metallic materials trained in Step 4 to evaluate its prediction performance, accuracy, and robustness. Finally, evaluate the fatigue life of the defective metallic materials by inputting the cyclic stress load value and the equivalent damage area.

[0044] Example 1: Following the above method, the fatigue life of defective metallic materials is predicted using both the physical information neural network of this invention and a traditional artificial neural network, with prediction accuracy comparable to, for example... Figure 6 As shown, the method of the present invention integrates the M-integral fatigue model into the neural network, demonstrating superior fatigue life prediction performance for defective metallic materials.

[0045] Example 2: Figure 7 This invention demonstrates traditional artificial neural networks and the physical information neural network of this invention. p The effects of taking values ​​of 0.1 and 0.3 on the gradient descent of prediction error show that the M-integral fatigue model of this invention can well reflect the relationship between different defect characteristics and fatigue life, and the physical loss function derived from it can well guide the gradient descent of the neural network training process.

[0046] Example 3: This embodiment uses an M-integral physical information neural network to predict the lifetime of defective materials. The steps are as follows: Step 1: Based on the classical fracture mechanics parameter M-integral, construct the damage parameter of the defective metallic material—equivalent damage area—according to the energy equivalence method; Step 2: Based on the power-law relationship between the equivalent damage area and the M-integral, establish the M-integral fatigue model and construct the physical loss function; Step 3: Construct a hybrid loss function using the physical loss function and the data correlation loss function, and build a physical information neural network based on the hybrid loss function; Step 4: Optimize the hyperparameters of the physical information neural network using a grid search method to obtain the optimal lifetime prediction model; Step 5: Use a prediction model to assess the fatigue life of the defective metallic material.

[0047] Example 4: Based on Example 3, in step 1, the integral value of M and the total potential energy of the system are changed. CTPE Based on the relationships between them, we obtain the global M-integral that includes all defective systems, i.e.:

[0048] In the formula: σ is the cyclic stress load value, For sample size, u and u 0 represents the displacement value before and after fatigue damage; Furthermore, based on the energy equivalence method, the equivalent damage area of ​​all defective systems can be obtained. A D The calculation formula is as follows:

[0049] In the formula: E It is the elastic modulus.

[0050] Example 5: Based on Example 4, according to the change in the total potential energy of the system CTPE The process of calculating the integral value of M is as follows: First, a monotonically increasing uniaxial load is applied to a defect-free specimen with the same material properties and dimensions as the multi-defect specimen. p The load-displacement curve Curve-0 was obtained; secondly, fatigue loading was applied to the multi-defect specimen, with the number of fatigue cycles being [number missing]. N The maximum fatigue load is p max The minimum fatigue load is p min Finally, the defective specimens were recorded through uniaxial tensile calculations. N Load-displacement curve after fatigue cycles (Curve-1); Based on the physical meaning of the change in the system's total potential energy, curves Curve-0, Curve-1, p = p max The area enclosed is CTPE Value, taking into account p max and p min The effect on fatigue driving force, curves Curve-0, Curve-1, p = p max , p = p min The enclosed area is named Δ CTPE Repeat this measurement process until the sample fails and breaks, and calculate the integral value of M.

[0051] Example 6: Based on Example 5, step 2 specifically includes: Based on the equivalent damage area A D Based on the power-law relationship with the M-integral, an M-integral fatigue model is established, namely:

[0052] In the formula: λ and w Δ is the empirical parameter of the model. M Defined as the M-integral magnitude for each load cycle, that is, the difference between the M-integral values ​​corresponding to the maximum and minimum loads for each load cycle. N This represents the number of loop iterations. When all defects are calculated from the initial equivalent damage area before cyclic loading A Equivalent damage area when evolving from 0 to final failure A C Then, by performing integral calculations on the M-integral fatigue model, the fatigue life of the defective metallic material is derived. N f for:

[0053] To ensure the prediction of fatigue life The correlation between the equivalent damage area of ​​defects and material properties conforms to the physical relationship in the above formula, improving prediction efficiency, preventing lifetime prediction results that contradict physical laws, and reducing prediction errors. The physical loss function is constructed as follows:

[0054] In the formula: n For the sample size, For the first iPredicted fatigue life for each sample, Δ M 0 represents the initial equivalent damage area. A The M integral amplitude of 0, For the first i The initial equivalent damage area of ​​each sample.

Claims

1. A method for predicting the lifetime of defective materials based on an M-integral physical information neural network, characterized in that, The steps are as follows: Step 1: Based on the classical fracture mechanics parameter M-integral, construct the damage parameter of the defective metallic material—equivalent damage area—according to the energy equivalence method; Step 2: Based on the power-law relationship between the equivalent damage area and the M-integral, establish the M-integral fatigue model and construct the physical loss function; Step 3: Construct a hybrid loss function using the physical loss function and the data correlation loss function, and build a physical information neural network based on the hybrid loss function; Step 4: Optimize the hyperparameters of the physical information neural network using a grid search method to obtain the optimal lifetime prediction model; Step 5: Use a prediction model to assess the fatigue life of the defective metallic material.

2. The method for predicting the lifetime of defective materials based on an M-integral physical information neural network according to claim 1, characterized in that, In step 1, the integral value of M and the change in the total potential energy of the system are used. CTPE Based on the relationships between them, we obtain the global M-integral that includes all defective systems, i.e.: In the formula: σ is the cyclic stress load value, For sample size, u and u 0 represents the displacement value before and after fatigue damage; Furthermore, based on the energy equivalence method, the equivalent damage area of ​​all defective systems can be obtained. A D The calculation formula is as follows: In the formula: E It is the elastic modulus.

3. The method for predicting the lifetime of defective materials based on an M-integral physical information neural network according to claim 2, characterized in that, According to the change in the total potential energy of the system CTPE The process of calculating the integral value of M is as follows: First, a monotonically increasing uniaxial load is applied to a defect-free specimen with the same material properties and dimensions as the multi-defect specimen. p The load-displacement curve Curve-0 was obtained; secondly, fatigue loading was applied to the multi-defect specimen, with the number of fatigue cycles being [number missing]. N The maximum fatigue load is p max The minimum fatigue load is p min Finally, the defective specimens were recorded through uniaxial tensile calculations. N Load-displacement curve after fatigue cycles (Curve-1); Based on the physical meaning of the change in the system's total potential energy, curves Curve-0, Curve-1, p = p max The area enclosed is CTPE Value, taking into account p max and p min The effect on fatigue driving force, curves Curve-0, Curve-1, p = p max , p = p min The enclosed area is named Δ CTPE Repeat this measurement process until the sample fails and breaks, and calculate the integral value of M.

4. The method for predicting the lifetime of defective materials based on an M-integral physical information neural network according to claim 1, characterized in that, Step 2 is as follows: Based on the equivalent damage area A D Based on the power-law relationship with the M-integral, an M-integral fatigue model is established, namely: In the formula: λ and w Δ is the empirical parameter of the model. M Defined as the M-integral magnitude for each load cycle, that is, the difference between the M-integral values ​​corresponding to the maximum and minimum loads for each load cycle. N This represents the number of loop iterations. When all defects are calculated from the initial equivalent damage area before cyclic loading A Equivalent damage area when evolving from 0 to final failure A C Then, by performing integral calculations on the M-integral fatigue model, the fatigue life of the defective metallic material is derived. N f for: To ensure the prediction of fatigue life The correlation between the equivalent damage area of ​​defects and material properties conforms to the physical relationship in the above formula, improving prediction efficiency, preventing lifetime prediction results that contradict physical laws, and reducing prediction errors. The physical loss function is constructed as follows: In the formula: n For the sample size, For the first i Predicted fatigue life for each sample, Δ M 0 represents the initial equivalent damage area. A The M integral amplitude of 0, For the first i The initial equivalent damage area of ​​each sample.

5. The method for predicting the lifetime of defective materials based on an M-integral physical information neural network according to claim 1, characterized in that, In step 3, the hybrid loss function is used in the training process of the neural network. The fatigue life prediction error is calculated by backpropagating the hybrid loss function to achieve error gradient descent.

6. The method for predicting the lifetime of defective materials based on an M-integral physical information neural network according to claim 1, characterized in that, In step 3, the data-related loss function To reduce the error in predicting fatigue data, the mean squared error is used as the data correlation loss function, i.e.: Then the mixed loss function L for: In the formula: L FP For physical loss function, p A penalty factor to adjust the proportion of the influence of the physical loss function. n For the sample size, and The first i Predicted fatigue life and actual fatigue life for each sample λ and w Δ is the empirical parameter of the model. M 0 represents the initial equivalent damage area. A The M-integral amplitude of 0; For the first i The initial equivalent damage area of ​​each sample.

7. The method for predicting the lifetime of defective materials based on an M-integral physical information neural network according to claim 1, characterized in that, Step 4 is as follows: The input data features of the physical information neural network are cyclic stress load and equivalent damage area. The dataset is preprocessed and divided into training and test sets in an 8:2 ratio. First, a traditional neural network is used to train the input dataset to fit the empirical parameters in the M-integral fatigue model. Through regression analysis, the relevant results are used to calculate the physical loss function. Then, the input dataset is trained according to the physical information neural network with a hybrid loss function to predict fatigue life. Adopting based on k The grid search method of cross-validation is used to obtain the number of hidden layers, the number of neurons in each hidden layer, the epoch, the batch size, the learning rate, the optimization algorithm, the penalty factor of the physical loss function, and the empirical parameters of the physical loss function.

8. The method for predicting the lifetime of defective materials based on an M-integral physical information neural network according to claim 7, characterized in that, The steps for preprocessing the input data are as follows: Column normalization is performed to normalize the entire database to the (0, 1) range, eliminating size differences and reducing the impact of extreme and outlier values ​​to maintain model stability; for the range ( x min , x max Variables within ) x Normalization operator H (x) is: 。

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