A Data- and Physically-Driven Method for Predicting Low-Cycle Fatigue Life of Mechanical Parts

Abstract

This invention relates to a data- and physics-driven method for predicting the low-cycle fatigue life of mechanical parts, comprising: Step S1: conducting finite element analysis of the mechanical parts to determine the maximum stress and strain values ​​at critical locations; Step S2: acquiring experimental data on low-cycle fatigue failure, using stress and strain as inputs, designing and conducting low-cycle fatigue tests on the mechanical part material specimens, and acquiring experimental stress, strain, and low-cycle fatigue cycle test data; Step S3: acquiring physical knowledge of low-cycle fatigue failure, combining existing data to conduct physical knowledge analysis of material low-cycle fatigue, and acquiring physical knowledge of fatigue life and stress; Step S4: establishing a physical information neural network model, with inputs including experimental data and physical knowledge; Step S5: predicting the low-cycle fatigue life of multiple critical locations of the mechanical parts. The lowest lifespan of the critical location is used as the lifespan of the mechanical part. This invention can significantly improve the accuracy of life prediction.

Description

Technical Field

[0001] This invention belongs to the field of aerospace engine technology, specifically relating to a method for predicting the low-cycle fatigue life of mechanical parts driven by both data and physics. Background Technology

[0002] In engineering applications, fatigue failure is a critical issue affecting the long-term reliability of materials and structures. Traditional fatigue life prediction methods rely on empirical models and simplified physical models, which often fail to accurately describe complex failure mechanisms and material behavior under various stress states. With the development of machine learning technology, neural networks have been widely used in fatigue failure analysis. These methods directly predict results by learning from a large number of data samples, and theoretically can handle more complex situations than traditional methods. However, purely data-driven neural networks also have significant shortcomings. First, they are extremely dependent on a large amount of high-quality data. When data is scarce or of low quality, the accuracy and reliability of the model will be greatly reduced. Second, the relationship between input and output is learned solely from data, which may violate some well-known physical laws or knowledge. In addition, for scenarios outside the range of training data, it may overfit existing data and produce unreasonable results. Therefore, it is necessary to combine machine learning technology and physical laws to conduct fatigue failure analysis and establish a data- and physics-driven method for predicting the low-cycle fatigue life of mechanical parts, thereby supporting the prediction of the low-cycle fatigue life of mechanical parts.

[0003] Currently, machine learning-based fatigue life prediction methods have been established: ① The existing literature "A deep learning approach for low-cycle fatigue life prediction under thermal–mechanical loading based on a novel neural network model", *Engineering Fracture Mechanics*, uses low-cycle fatigue data of four different materials to train a neural network and predicts the low-cycle fatigue life of various materials. However, research shows that the prediction accuracy of this method mainly depends on the quality and quantity of training data, relying too heavily on the quality and availability of the data. ② The existing literature "A data-driven fatigue life prediction method based on parameter influence", *Journal of Mechanical Engineering*, establishes a fatigue life prediction method based on a BP neural network, which effectively predicts the fatigue life of single-axis loading, multi-axis loading, high-cycle fatigue, and low-cycle fatigue. However, when the quality of the training data distribution is low, the prediction accuracy also decreases. Regarding inventions, an existing invention, CN115859464A, proposes a method for predicting the low-cycle fatigue life of titanium alloy structural components based on a GA-BP neural network. While this method can predict the low-cycle fatigue life of titanium alloy structural components, it is entirely data-driven and does not consider physical boundary conditions. The data distribution significantly impacts prediction accuracy, and the prediction results sometimes exhibit phenomena that violate physical laws. Therefore, it cannot provide efficient and accurate predictions, making it difficult to implement in engineering applications. In summary, existing methods cannot yet meet the engineering requirements for high-efficiency and high-precision low-cycle fatigue life prediction. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies, this invention proposes a data- and physical-driven method for predicting the low-cycle fatigue life of mechanical parts, supporting the assessment of low-cycle fatigue life of aero-engine mechanical parts. To achieve the above objective, this invention adopts the following technical solution: a data- and physical-driven method for predicting the low-cycle fatigue life of mechanical parts, comprising the following steps:

[0005] Step S1: Determine the stress and strain distribution in the critical area, including: conducting finite element analysis of the mechanical parts to obtain stress and strain distribution, and determining the maximum stress and strain values ​​in the critical area;

[0006] Step S2: Data acquisition, including: using stress and strain as inputs, designing and conducting low-cycle fatigue tests on mechanical part material specimens, and acquiring test stress, strain, and low-cycle fatigue cycle test data;

[0007] Step S3: Obtain physical knowledge of low-cycle fatigue failure, including: conducting physical knowledge analysis of low-cycle fatigue of materials based on existing data, and obtaining physical knowledge of fatigue life and stress;

[0008] Step S4: Establish a physical information neural network model, with inputs including experimental data and physical knowledge;

[0009] Step S5: Conduct low-cycle fatigue life prediction for multiple critical parts of mechanical parts, and use the lowest life of the critical parts as the life of the mechanical parts.

[0010] The advantages of this invention compared to existing technologies are:

[0011] (1) This invention combines the advantages of data-driven and physics-driven approaches, using not only experimental data but also physical knowledge of materials and mechanics. By introducing physical information, this method can capture more details of material behavior and improve the accuracy of fatigue life prediction under different working conditions.

[0012] (2) This invention accurately simulates complex stress and strain distributions through finite element analysis, and, combined with physical knowledge and neural network models, can effectively cope with complex stress states. This method can capture more load condition characteristics and is more adaptable.

[0013] (3) This invention can continuously update experimental data and physical models, and continuously train and optimize neural network models to adapt to new materials and new working conditions, thus maintaining the accuracy and cutting-edge nature of predictions. This allows the model to dynamically adapt to new engineering needs. Attached Figure Description

[0014] Figure 1 is a flowchart of a data- and physical dual-driven method for predicting the low-cycle fatigue life of mechanical parts according to the present invention.

[0015] Figure 2 shows the physical neural network architecture.

[0016] Figure 3 is a flowchart of the training process for the physical neural network model. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other. To achieve the above objectives, this invention adopts the following technical solution.

[0018] This invention provides a data- and physical-driven method for predicting the low-cycle fatigue life of mechanical parts, supporting the assessment of low-cycle fatigue life of aero-engine mechanical parts. To achieve the above objective, this invention adopts the following technical solution:

[0019] First, the stress and strain distribution at critical locations is determined through finite element analysis. Low-cycle fatigue tests are then conducted on mechanical parts to obtain stress, strain, and low-cycle fatigue cycle data. Next, existing data is combined with physical analysis of low-cycle fatigue to obtain physical knowledge of fatigue life and stress. Finally, a physical information neural network model is established to predict the low-cycle fatigue life of mechanical parts, including the following steps:

[0020] Step S1: Determine the stress and strain distribution in the critical area, conduct finite element analysis of the mechanical parts to obtain the stress and strain distribution, and determine the location and value of the maximum stress and strain in the critical area.

[0021] Step S2: Obtain data. Using the stress and strain from step S1 as input, design and conduct low-cycle fatigue tests on mechanical part material specimens to obtain stress, strain, and low-cycle fatigue cycle test data.

[0022] Step S3: Acquire physical knowledge, combine existing data to conduct physical knowledge analysis of low-cycle fatigue of materials, and obtain physical knowledge of fatigue life and stress;

[0023] Step S4: Establish a physical information neural network model, where experimental data and physical knowledge are determined through steps S2 and S3, respectively;

[0024] Step S5: Conduct low-cycle fatigue life prediction for mechanical parts, using the minimum life of the critical part as the life of the mechanical part.

[0025] Furthermore, the specific steps of step S1 are as follows:

[0026] Step S11: First, create a three-dimensional model based on the two-dimensional design drawings of the mechanical parts;

[0027] Step S12: Set the material properties in the finite element analysis software, including elastic modulus, Poisson's ratio, yield strength, etc. If the nonlinear behavior of the material is significant in low-cycle fatigue, a plasticity model, such as a bilinear or multilinear hardening model, should also be considered.

[0028] Step S13: Mesh the part. To ensure calculation accuracy, a denser mesh is used, especially in stress concentration areas (such as holes, grooves, and abruptly changing geometries).

[0029] Step S14: Set boundary conditions based on the actual load conditions of the mechanical parts, establish a finite element model (FEM), and apply static or dynamic loads to the finite element model according to the actual working conditions. This may include axial loads, torsional loads, bending loads, or combined loads. The loading process can simulate a single large load or multiple cyclic loads to observe the stress-strain response of the mechanical parts. If the parts will be subjected to multiaxial loads (such as tension-torsion combinations) in actual use, multiaxial stress analysis is required to more accurately reflect the stress state.

[0030] Step S15: Run a finite element simulation to obtain the stress-strain distribution. The results include key parameters such as von Mises stress, maximum principal stress, shear stress, and plastic strain. Using post-processing tools, visualize the results to generate stress contour maps, deformation contour maps, etc., to identify areas of stress and strain concentration in the part. These areas are potential fatigue-prone locations. Extract the stress and strain values ​​from these critical locations as input data for subsequent experiments and model analyses. If the critical location involves multiple regions, the stress-strain characteristics of each region should be recorded separately.

[0031] Compare the finite element simulation results with actual working conditions or known experimental data. If discrepancies exist, it may be necessary to redefine boundary conditions, optimize mesh generation, or adjust the material model. Ensure that the simulation results are within a reasonable range, especially that the stress and strain distribution in critical areas conforms to physical laws, avoiding oversimplification or model distortion.

[0032] The results of finite element analysis can identify stress concentration areas and critical locations in mechanical parts, providing a basis for the design of subsequent fatigue test programs and the prediction of fatigue life.

[0033] Furthermore, the specific steps of step S2 are as follows:

[0034] Step S21: First, determine the test standards and specifications that the test needs to be based on, and then formulate the test plan accordingly.

[0035] Step S22: Based on the stress and strain values ​​of the critical locations determined in Step S15, determine the test conditions. The test design should simulate the load and environment under actual working conditions as much as possible. Select a suitable material specimen; the specimen shape can be a standard tensile specimen, a plate specimen, or a specially machined characteristic simulation specimen. The specimen dimensions should meet the requirements of the testing machine and ensure uniform stress distribution. Determine the loading method and load level. Low-cycle fatigue tests typically apply cyclic loading, with the number of cycles ranging from tens to thousands, depending on the material properties and design requirements.

[0036] Step S23: Apply cyclic loading to the specimen on the testing machine. The testing machine should be equipped with high-precision strain gauges, strain meters, or displacement sensors to monitor the strain response of the specimen in real time. During the test, record the stress and strain values ​​for each loading cycle, as well as the corresponding number of cycles, until the specimen fractures or shows significant damage. Collect the raw data obtained from the test, including the stress-strain curve for each cycle and the number of cycles. Process and organize the data to generate stress-strain curves, fatigue life curves (such as SN curves), and other key data charts. Perform data smoothing if necessary to eliminate noise and errors in the test. If there are many test samples, statistical analysis can be performed on the data under different conditions to extract the distribution characteristics of fatigue life, such as mean life, standard deviation, and confidence interval.

[0037] Furthermore, the specific steps of step S3 are as follows:

[0038] Step S31: First, conduct an analysis of existing data, collecting historical fatigue data and literature related to the current materials and operating conditions, including published low-cycle fatigue test results, fatigue curves, and material constitutive models. Analyze the existing data to extract fatigue behavior under stress and strain ranges similar to those in the current study. For example, analyze the fatigue limit and fatigue crack propagation laws of similar materials.

[0039] Step S32: Combining experimental and existing data, analyze the fatigue behavior of the material using classical fatigue theories (such as the Coffin-Manson physical model and the Basquin physical model). By fitting the experimental data, determine the material constants and fatigue parameters in these physical models. If the material exhibits significant nonlinear behavior, it may be necessary to use a nonlinear fatigue model or introduce fracture mechanics theory to more accurately describe the fatigue process. Use the physical models to predict fatigue life under different stress levels, generating stress-life (SN) curves, strain-life (ε-N) curves, etc.

[0040] Step S33: Combine the experimental data with the results of the physical model to form a comprehensive low-cycle fatigue life knowledge base. This knowledge base should include fatigue life information under different stress levels, strain amplitudes, loading frequencies, and other conditions, as well as details such as crack propagation rates and fatigue fracture mechanisms. Analyze the relationship between stress, strain, cycle number, and fatigue life to extract key physical laws and empirical formulas, providing physical constraints for subsequent neural network model construction.

[0041] Furthermore, the specific steps of step S4 are as follows:

[0042] Step S41: Based on the data characteristics and prediction task, design a suitable neural network model architecture. Tune the model structure parameters, such as determining the number of network layers, neurons, activation function, and learning rate, to ensure the model has sufficient expressive power to capture complex fatigue behavior.

[0043] Step S42: In the design of the neural network model, introduce physical constraints or prior knowledge. Use physical knowledge as input features of the neural network model, or introduce physical consistency constraints through regularization terms to ensure that the output of the neural network model conforms to physical laws.

[0044] Step S43: In order to incorporate physical knowledge, the training of the neural network is formulated as a constrained optimization problem.

[0045] Step S44: Define a custom loss function to transform the constrained optimization problem into an unconstrained optimization problem.

[0046] Step S45: Preprocess the experimental data obtained in Step S2. This includes data cleaning (removing outliers and noise) and normalization (scaling the data to the same range) to ensure the data is easier for the neural network model to learn. Based on physical laws and fatigue theory, extract characteristic parameters that affect fatigue life prediction from data such as stress, strain, and cycle count, such as maximum stress, strain amplitude, and plastic strain range. Train the model using the preprocessed experimental data. During training, the model continuously adjusts its internal parameters (such as weights and biases) through the backpropagation algorithm to minimize prediction error. Cross-validation is used to ensure the neural network model performs well on both the training and validation sets, avoiding overfitting. During training, monitor metrics such as loss function and accuracy in real time to determine the model's convergence. If the model performance is poor, it can be improved by increasing training data, introducing data augmentation techniques (such as adding noise or smoothing), or modifying the network architecture.

[0047] Analyze the model's prediction results, calculate evaluation metrics such as prediction error, correlation coefficient, and mean squared error (MSE), and assess the model's generalization ability. If the model has a large error under certain specific conditions, it may be necessary to further optimize the model or adjust the dataset.

[0048] Furthermore, the specific steps of step S5 are as follows:

[0049] Step S51: Input the test data of the critical parts identified in Step S1 into the neural network model trained in Step S4 to predict the lifespan. For different stress levels and strain amplitudes, the model will output the corresponding fatigue life prediction value. Generally, the overall lifespan of a part is considered to be the minimum lifespan of its most critical part (the part with the greatest stress and strain).

[0050] Step S52: Compare the prediction results of the neural network model with the actual lifespan of mechanical parts in use to analyze the prediction accuracy and reliability of the neural network model. If there is a significant deviation between the actual lifespan and the predicted lifespan, it may be necessary to retrain the model or adjust the parameters. Through multiple applications and feedback, gradually optimize the model to make its prediction results more accurate and stable.

[0051] Ultimately, a systematic fatigue life prediction process was developed, combining data and physical dual-drive models to provide reliable technical support for the design and maintenance of mechanical parts.

[0052] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0053] like Figure 1 As shown, the present invention provides a data- and physical-driven method for predicting the low-cycle fatigue life of mechanical parts, comprising the following steps:

[0054] Step S1: Conduct finite element analysis of the mechanical parts to obtain stress and strain distribution, and determine the location and value of the maximum stress and strain.

[0055] Step S11: Taking a turbine disk as an example, perform finite element analysis based on UG and ABAQUS software. Model the turbine disk in 3D according to the 2D drawings, and then import the 3D model into ABAQUS for the next step of finite element analysis.

[0056] Step S12: Set the turbine disk material to GH720Li, set the material properties to multi-segment linear kinematic hardening in ABAQUS, and set other material properties, including elastic modulus, Poisson's ratio, yield strength, etc.

[0057] Step S13: Mesh the turbine disk. To ensure calculation accuracy, a denser mesh is used, especially in stress concentration areas (such as holes, tenons, and abruptly changing geometries).

[0058] Step S14: During finite element analysis, the boundary conditions of the turbine disk should be as close as possible to the load conditions under service environment. The boundary conditions are set as follows:

[0059] 1) The temperature field distribution of the turbine disk is applied based on the function obtained by fitting the heat transfer calculation results;

[0060] 2) Apply the corresponding rotational angular velocity according to the turbine disk rotation speed;

[0061] 3) The centrifugal force generated by the turbine disk blades is applied as pressure to the upper half of the tenon unit;

[0062] 4) The axial and circumferential displacements of the turbine disk are constrained by applying UZ and UY=0 at the mounting edge.

[0063] Step S15: Calculate the stress distribution using ABAQUS for finite element analysis. When performing stress analysis on the turbine disk, it is necessary to pay attention not only to the stress and strain conditions of critical parts, but also to extract stress and strain for analysis in stress concentration areas (such as holes, tenons, and abruptly changing geometries).

[0064] Step S2: Data Acquisition. Conduct low-cycle fatigue tests on the mechanical parts material specimens to acquire stress, strain, and low-cycle fatigue cycle data. Specific steps are as follows:

[0065] The purpose of conducting low-cycle fatigue tests is to obtain stress-strain data and low-cycle fatigue life of mechanical parts materials, so as to provide data support for the prediction of low-cycle fatigue life of mechanical parts.

[0066] Step S21: The test references GB / T 15248-2008 "Metallic Materials - Axial Constant Amplitude Low Cyclic Fatigue Test Method", GB / T 26077-2010 "Metallic Materials - Fatigue Test Method - Axial Strain Control Method", HB 5195-1996 "Metallic Materials - High Temperature Tensile Test Method", and adjusts the clamping method, loading method, etc. according to the actual situation of the test piece.

[0067] Step S22: The specimens were taken from the same batch of GH720Li blank discs. The specimens were designed according to GJB standards and were forged using isothermal forging. The heat treatment process was (1080~1110)℃×(2~4)h / oil quenching + 650℃×24h / air cooling + 760℃×16h / air cooling. Based on the results of the finite element analysis in step S1, the test conditions were determined as follows:

[0068] Turbine disk samples from the same batch were taken at a temperature of 650℃, a stress ratio of 0.05, and loads of 800MPa, 900MPa, 1000MPa, 1100MPa, and 1200MPa, with 5 test pieces for each load condition.

[0069] Step S23: All specimens were tested on the same MTS 370.10 hydraulic servo fatigue testing machine under stress control conditions, with a triangular wave load and a loading frequency of 5 Hz. Extensometers were used to measure strain data throughout the test. The number of cycles and test time were recorded after the test.

[0070] The experimental data obtained in step S2 can be used to train a physical information neural network to predict the low-cycle fatigue life of mechanical parts.

[0071] Step S3: Acquire Physical Knowledge. Combine existing data to conduct a physical analysis of low-cycle fatigue in materials, acquiring physical knowledge related to fatigue life and stress. Specific steps are as follows:

[0072] Step S31: First, conduct an analysis of existing data, collecting historical fatigue data and literature related to the current materials and operating conditions, including published low-cycle fatigue test results, fatigue curves, material constitutive models, etc. Analyze the existing data to extract fatigue behavior under stress and strain ranges similar to those of the mechanical parts in this invention.

[0073] Step S32: Combine experimental data and existing data to analyze the fatigue behavior of the material. By fitting the experimental data, determine the material constants and fatigue parameters in these models. Use the physical models to predict the fatigue life under different stress levels, generating stress-life (SN) curves, strain-life (ε-N) curves, etc.

[0074] Step S33: Combine the experimental data with the results of the physical model to form a comprehensive low-cycle fatigue life knowledge base. Analyze the relationship between stress, strain, cycle number, and fatigue life, and extract key physical laws and empirical formulas. These mainly include: as the stress amplitude decreases, the variance of fatigue life increases; fatigue life shows a monotonically decreasing trend with increasing stress amplitude; when the stress amplitude decreases to the fatigue limit, the curvature of the SN curve decreases with decreasing stress.

[0075] Step S4: Establish a physical information neural network model, where experimental data and physical knowledge are determined through steps S2 and S3, respectively. The specific steps are as follows:

[0076] Step S41: The physical neural network model architecture used in this invention is as follows: Figure 2 As shown, the network consists of three layers: an input layer, hidden layers, and an output layer. The number of hidden layers is determined by the complexity of the problem; this invention uses a network structure with one hidden layer. Unlike conventional neural networks that learn only the average of the output from collected distributed data, the output layer has two output neurons: the mean and the standard deviation. The loss function uses the negative log-likelihood function, i.e.:

[0077] (1)

[0078] In the formula, n is the number of training data, x and y are the input and output variables respectively, and θ is the set of neural network parameters. , represents the conditional probability density function of the output variable y given the input variable x and the neural network parameters θ. Let represent the cumulative distribution function of the output variable y given the input variable x and the neural network parameters θ. It is a failure indicator, expressed as:

[0079] (2)

[0080] For the input layer, the neural network definition does not use an activation function. The hyperbolic tangent activation function (tanh) is used for the neurons in the hidden layers. The expression for the tanh activation function is:

[0081] (3)

[0082] In the formula, z is the output of the corresponding neuron.

[0083] The mean of the output layer uses a linear (i.e., identity) activation function, the expression of which is:

[0084] (4)

[0085] Since the standard deviation is non-negative, the exponential linear unit (ELU) activation function is chosen. The expression for the ELU activation function is:

[0086] (5)

[0087] Step S42: The network input is the stress amplitude x, and the output is the mean μ and standard deviation σ of the predicted fatigue life y. To ensure that the physical indicators are consistent with basic physical knowledge, the derivatives of the physical indicators with respect to the stress amplitude are calculated, and conditions that need to be met, i.e., physical constraints, are imposed. The physical knowledge determined in step S3 is expressed as the physical constraints as follows:

[0088] (1) As the stress amplitude decreases, the variance of fatigue life increases: the first derivative of the standard deviation is negative.

[0089] (6)

[0090] (2) Fatigue life decreases monotonically with increasing stress amplitude: the first derivative of the mean is negative.

[0091] (7)

[0092] (3) The curvature of the stress-life curve decreases as the stress amplitude decreases: the mean second derivative is positive.

[0093] (8)

[0094] Step S43: In order to incorporate physical knowledge, the training of the neural network is formulated as a constrained optimization problem.

[0095] (9)

[0096] Note that all three constraints must be met simultaneously.

[0097] Step S44: Solve the optimization problem in equation (9) using the penalty function method, transforming the constrained optimization problem into an unconstrained optimization problem. Therefore, the composite loss function is defined as:

[0098] (10)

[0099] In the formula, L0(θ) is the negative log-likelihood function in equation (1), and L1(θ) is the loss function corresponding to the first physical constraint, expressed as:

[0100] (11)

[0101] L2(θ) is the loss function corresponding to the second physical constraint, and its expression is:

[0102] (12)

[0103] L3(θ) is the loss function corresponding to the third physical constraint, and its expression is:

[0104] (13)

[0105] Punishment factor , , This is to maintain a balance between data fitting and physical constraints, which are enforced and can only be as close to zero as possible. Typically, a penalty factor... , , A value that is too small cannot guarantee physical constraints, resulting in a penalty factor. , , An excessively large value may lead to overfitting. Therefore, choosing an appropriate penalty factor is crucial. , , A higher value can achieve better fitting results.

[0106] Step S45: In summary, the training flowchart of the physical neural network is as follows: Figure 3 As shown, the specific steps for predicting fatigue life using a physical neural network are as follows:

[0107] Step S451: Divide the original data into training, testing, and validation sets, and begin training the neural network. (Penalty factor) , , The initial value is 1. The neural network training stops when the data fitting loss converges. The physical constraint loss at the end of step S451 may not be zero.

[0108] Step S452: Determine if the physical constraints are met. If they are, the entire process terminates. If not, increase the penalty factor to gradually adjust the neural network to meet the physical constraints while keeping the data fitting loss from changing significantly. Reduce the learning rate to prevent the updated neural network weights and biases from differing too much from the previously trained results. Reassign the initial weights and biases to values.

[0109] Step S453: After parameter updates, the neural network restarts training, monitoring the physical constraint loss. When the physical constraint loss converges, neural network training stops. Then, proceed to step S452 to continue computation.

[0110] Step S5: Conduct low-cycle fatigue life prediction for mechanical parts. The minimum lifespan of the critical component is used as the lifespan of the mechanical part. The specific steps are as follows:

[0111] Step S51: Using the experimental data obtained in step S2 as input, import it into the physical neural network model trained in step S4 to predict low-cycle fatigue life, and use the minimum life of all critical parts as the life of mechanical parts.

[0112] Step S52: Compare the model's prediction results with the actual lifespan of mechanical parts in use to analyze the prediction accuracy and reliability of the neural network model. If there is a significant deviation between the actual lifespan and the predicted lifespan, it may be necessary to retrain the neural network model or adjust its parameters. Through multiple applications and feedback, gradually optimize the model to make its prediction results more accurate and stable.

[0113] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for predicting the low-cycle fatigue life of mechanical parts driven by both data and physical factors, characterized in that, The steps include the following: Step S1: Determine the stress and strain distribution in the critical area, including: conducting finite element analysis of the mechanical parts to obtain the stress and strain distribution, and determining the stress and strain values ​​in the critical area; Step S2: Data acquisition, including: using stress and strain as inputs, designing and conducting low-cycle fatigue tests on mechanical part material specimens, and acquiring test stress, strain, and low-cycle fatigue cycle test data; The specific steps of step S2 are as follows: Step S21: First, determine the test standards and specifications that the test needs to be based on, and then formulate the test plan accordingly; Step S22: Based on the stress and strain values ​​of the identified critical parts, determine the test conditions, simulate the load and environment under actual working conditions, select appropriate material specimens, the specimen shape is a standard tensile specimen, a plate specimen or a specially processed characteristic simulation specimen, the size of the specimen meets the requirements of the testing machine, and ensures uniform stress distribution, determine the loading method and load level, and apply cyclic load for low cycle fatigue test. Step S23: Apply cyclic loading to the specimen on the testing machine. The testing machine is equipped with strain gauges, strain meters, or displacement sensors to monitor the strain response of the specimen in real time. During the test, record the stress and strain values ​​of each loading cycle, as well as the corresponding number of cycles, until the specimen fractures or suffers significant damage. Collect the raw data obtained from the test, including the stress-strain curve for each cycle and the number of cycles. Process and organize the data to generate stress-strain curves and fatigue life curves. Perform statistical analysis on the data under different conditions to extract the distribution characteristics of fatigue life, including mean life, standard deviation, and confidence interval. Step S3: Obtain physical knowledge of low-cycle fatigue failure, including: conducting physical knowledge analysis of low-cycle fatigue of materials based on existing data, and obtaining physical knowledge of fatigue life and stress; The specific steps of step S3 are as follows: Step S31: First, conduct an analysis of existing data, collect historical fatigue data and literature related to the current materials and working conditions, including low-cycle fatigue test results, fatigue curves, and material constitutive models, analyze the data, and extract the fatigue behavior of mechanical parts under stress and strain ranges. Step S32: Combine experimental data and existing data to analyze the fatigue behavior of materials; by fitting experimental data, determine the material constants and fatigue parameters in the physical model, use the physical model to predict the fatigue life under different stress levels, and form the stress-life curve (SN curve) and strain-life curve (ε-N curve). Step S33: Combine the experimental data with the results of the physical model to form a low-cycle fatigue life knowledge base, analyze the relationship between stress, strain, number of cycles and fatigue life, and extract key physical laws, including: as the stress amplitude decreases, the variance of fatigue life increases; fatigue life shows a monotonically decreasing trend with the increase of stress amplitude; when the stress amplitude decreases to the fatigue limit, the curvature of the SN curve decreases with the decrease of stress. Step S4: Establish a physical information neural network model, with inputs including experimental data and physical knowledge; Step S5: Conduct low-cycle fatigue life prediction for multiple critical parts of mechanical parts, and use the minimum life of the critical parts as the life of the mechanical parts. The specific steps of step S4 are as follows: Step S41: Set the network architecture to include three layers: an input layer, a hidden layer, and an output layer. Set the number of hidden layers to 1, and the output layer to have two output neurons: the mean and the standard deviation. Use the negative log-likelihood function as the loss function, i.e.: (1) In the formula, n is the number of training data, x and y are the input and output variables respectively, and θ is the set of neural network parameters. , represents the conditional probability density function of the output variable y given the input variable x and the neural network parameters θ. Let represent the cumulative distribution function of the output variable y given the input variable x and the neural network parameters θ. It is a failure indicator, expressed as: (2) For the input layer, the definition of the neural network does not use an activation function. Instead, the hyperbolic tangent activation function tanh is used for the neurons in the hidden layer. The expression for the tanh activation function is: (3) In the formula, z is the output of the corresponding neuron; The mean of the output layer uses a linear activation function, the expression of which is: (4) We choose the exponential linear unit ELU activation function. The expression for the ELU activation function is: (5) Step S42: The network input variable x is the stress amplitude, and the output variable y is the mean μ and standard deviation σ of the predicted fatigue life; By calculating the derivative of the physical index with respect to the stress amplitude and imposing the conditions that need to be met, i.e., physical constraints, the physical knowledge determined in step S3 is expressed as physical constraints, as follows: 1) As stress amplitude decreases, the variance of fatigue life increases: the first derivative of the standard deviation becomes negative. (6) 2) Fatigue life decreases monotonically with increasing stress amplitude: the first derivative of the mean is negative. (7) 3) The curvature of the stress-life curve decreases as the stress amplitude decreases: the mean second derivative is positive. (8) Step S43: In order to incorporate physical knowledge, the training of the neural network is formulated as a constrained optimization problem: (9) All three constraints must be met simultaneously. Step S44: Solve the optimization problem in equation (9) using the penalty function method, transforming the constrained optimization problem into an unconstrained optimization problem. Therefore, the composite loss function is defined as: (10) In the formula, L0(θ) is the negative log-likelihood function in equation (1), and L1(θ) is the loss function corresponding to the first physical constraint, expressed as: (11) L2(θ) is the loss function corresponding to the second physical constraint, and its expression is: (12) L3(θ) is the loss function corresponding to the third physical constraint, and its expression is: (13) in, , , It is a punishment factor; Step S45: Train the physical information neural network according to the above network settings for subsequent prediction of low-cycle fatigue life of mechanical parts.

2. The method for predicting the low-cycle fatigue life of mechanical parts driven by both data and physical processes according to claim 1, characterized in that, The specific steps of step S1 are as follows: Step S11: Based on the two-dimensional design drawings of the mechanical parts, establish a three-dimensional model of the mechanical parts; Step S12: Set the material properties of the mechanical parts in the finite element analysis software, including elastic modulus, Poisson's ratio, and yield strength; Step S13: Mesh the part; use a denser mesh in stress concentration areas, including holes, grooves, and abruptly changing geometries; Step S14: Set boundary conditions based on the actual load conditions of the mechanical parts, establish a finite element model, and apply static or dynamic loads to the finite element model according to the actual working conditions. Step S15: Run finite element simulation to obtain stress and strain distribution; the results include key parameters such as von Mises stress, maximum principal stress, shear stress, and plastic strain; use post-processing tools to visualize and analyze the results, generate stress cloud maps and deformation cloud maps, identify the areas of stress and strain concentration in the mechanical parts, these areas are potential fatigue hazard areas, extract the stress and strain values ​​of the hazard areas as input data, if the hazard area involves multiple areas, record the stress and strain characteristics of each area separately; 。 3. The method for predicting the low-cycle fatigue life of mechanical parts driven by both data and physical processes according to claim 2, characterized in that, The specific steps of step S45 are as follows: Step S451: Divide the original data into training set, test set, and validation set, and begin training the neural network; penalty factor , , The initial value is 1. The neural network training stops when the data fitting loss converges. Step S452: Determine whether the physical constraints are met. If the physical constraints are met, the entire process terminates. If not, increase the penalty factor to gradually adjust the neural network to meet the physical constraints, while keeping the data fitting loss from changing significantly, reducing the learning rate, and preventing the updated neural network weights and biases from differing too much from the previous training results. The initial weights and biases are then redistributed to the values. Step S453: After the parameters are updated, the neural network restarts training, monitors the physical constraint loss, and when the physical constraint loss converges, the neural network training stops, and then proceeds to step S452 to continue calculation.

4. The method for predicting the low-cycle fatigue life of mechanical parts driven by both data and physical processes according to claim 3, characterized in that, The specific steps of step S5 are as follows: Step S51: Using the experimental data obtained in step S2 as input, import it into the physical neural network trained in step S4 to predict low-cycle fatigue life, and use the minimum life of all dangerous parts as the life of mechanical parts. Step S52: Compare the prediction results of the neural network model with the actual lifespan of mechanical parts in use, and analyze the prediction accuracy and reliability of the neural network model; if there is a significant deviation between the actual lifespan and the predicted lifespan, retrain the neural network model or adjust the parameters, and gradually optimize the neural network model through multiple applications and feedback.

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