Method for predicting probabilistic low-cycle fatigue life of metal material with priori knowledge as guidance

Abstract

The invention discloses a method for predicting probabilistic low-cycle fatigue life of a metal material by taking priori knowledge as guidance. The method is used for predicting the low-cycle fatigue life of an aerospace material under a multi-axis loading condition. The method comprises the following steps: firstly, determining candidate uncertain factors based on preliminary analysis, including model parameters related to material characteristics, multi-axial load conditions and geometric characteristics of parts in a low-cycle fatigue environment bearing multi-axial loads, thereby obtaining priori knowledge including a stress-strain relationship in fatigue behaviors; building a data set based on physical knowledge by utilizing a finite element method based on a data driving mode, building a finite element model based on model parameters, sampling through a Latin hypercube sampling algorithm, and building an independent variable space and a probabilistic prediction training set; and finally, on the basis of combination of a particle swarm algorithm and a LightGBM model, a loss function is defined, prior physical knowledge is introduced, and a model PSO-C-LightGBM with prior knowledge guidance and constraint is obtained.

Description

Technical Field

[0001] The present invention belongs to big data methods and applications, and specifically relates to the field of probabilistic low-cycle fatigue life prediction under specific multi-axial load conditions, in particular to a proxy model prediction method guided by prior knowledge, and in particular to a probabilistic low-cycle fatigue life prediction method for metal materials guided by prior knowledge. Background Art

[0002] Industrial components are subjected to various types of complex loads during use. There are countless structural failures caused by fatigue, so fatigue reliability is a key issue in industrial safety. Fatigue can be divided into low cycle fatigue (LCF), high cycle fatigue (HCF) and combined cycle fatigue (CCF). Low cycle fatigue occurs when the system state changes, such as engine start / stop, aircraft landing gear raising / lowering. Low cycle fatigue caused by a large amount of strain can seriously affect the structural integrity of the component. In addition, due to the influence of multiple uncertain factors, the fatigue life distribution shows a large dispersion. Therefore, a more accurate prediction of (LCF) life plays a vital role in the design of industrial structures with high reliability requirements.

[0003] LCF life is mainly affected by three factors: material properties of components, component structure, and external environmental conditions. Fatigue life prediction under complex environmental loads has always been a challenge. In order to accurately predict fatigue life and successfully estimate the degradation trend of component structure, many studies have focused on evaluating LCF life prediction under multiaxial loading and established physical models, including effective strain-based models, maximum shear strain-based models, and critical surface models. These models are derived from empirical experiments and systematically consider the coupling relationship between stress-strain state and deterministic LCF life. In addition, probabilistic LCF life prediction models have been widely developed to explore the distribution of LCF life under the influence of heterogeneous uncertainty factors. Most of these models consider the influence of multiple sources of uncertainty in a unified space, and some also consider the comprehensive impact of multidimensional influencing factors on uncertainty. Incorporating multi-source randomness considerations into LCF estimation is helpful to establish fatigue reliability and solve the complex challenges encountered in engineering scenarios in the context of reliability-based design optimization (RBDO) and reliability-based robust design optimization (RBRDO).

[0004] In order to explore the physical behavior of structures under fatigue conditions, finite element analysis (FEA) has been proposed to simulate various external environmental scenarios. By incorporating known physical information, such as building a constitutive model and inputting the mechanical properties of materials, the FEA method can simulate the physical state of structures under complex loading conditions. With the increase in engineering requirements and the expansion of the scale of computational tasks, FEA has put forward higher requirements on computing power, resulting in reduced computational efficiency when running on personal computers or low-intensity computing platforms. An effective way to solve the problem of low efficiency is to use surrogate models. Traditional surrogate models such as Kriging, support vector machine (SVM) and polynomial chaos extension (PCE) are helpful to improve the efficiency of structural fatigue reliability analysis with different experimental designs. Machine learning methods are gradually coming into people's field of vision and becoming an appropriate method to replace surrogate models. Compared with traditional surrogate models based on interpolation principles, machine learning methods can identify more complex responses and learn strong nonlinear relationships, showing higher accuracy and efficiency in complex industrial scenarios.

[0005] However, machine learning still has some shortcomings. As a black box model, it inherently lacks interpretability and explainability. In the field of reliability assessment, the ability of the model to provide interpretable insights is particularly important. To address this challenge, physically informed machine learning (PIML) has emerged. PIML combines data-driven techniques with physical knowledge to enhance interpretability while maintaining computational efficiency. PIML includes physically informed neural networks (PINNs), which use partial differential equations and ordinary differential equations (PDEs and ODEs) as guiding principles for the neural network architecture. For example, in fatigue life prediction under multiaxial loading, incorporating the signs of material fatigue parameters in physical equations as constraints into the weights and biases of the neural network can improve the prediction performance and extrapolation capabilities, ensuring that the prediction results maintain strong physical consistency. In addition, another approach in the field of PIML is to combine finite element analysis simulations with machine learning to form a hybrid prediction framework. This framework uses prior physical knowledge to construct finite element analysis models and uses the data generated by these models for data-driven predictions. This method has shown excellent performance in multiple fields, such as creep fatigue reliability prediction of low-pressure turbine disks, fatigue life estimation of turbine blade adhesives, and residual stress prediction of laser shock strengthened samples. This method combines physical mechanism guidance with the ability to supplement insufficient training data in specific cases, which helps to make accurate predictions with higher efficiency and lower cost, and is an ideal alternative modeling method in the field of fatigue assessment. Summary of the invention

[0006] Purpose of the invention: In view of the above-mentioned deficiencies in the prior art, the present invention provides a probabilistic low-cycle fatigue life prediction method for metal materials guided by prior knowledge.

[0007] Technical solution: A probabilistic low-cycle fatigue life prediction method for metal materials guided by prior knowledge, including the following steps:

[0008] S1. Determine candidate uncertainties based on preliminary analysis, including material properties, multiaxial loading conditions, and geometric characteristic parameters of components in a low-cycle fatigue environment subjected to multiaxial loading, thereby obtaining prior knowledge including stress-strain relationships in fatigue behavior, including using the geometric characteristic parameters as parameters of the model;

[0009] S2, based on data-driven approach, using finite element method to construct data set based on physical knowledge, and then building finite element model based on model parameters;

[0010] This step also includes sampling through a Latin hypercube sampling algorithm to construct an independent variable space and a probabilistic prediction training set;

[0011] S3. Based on the particle swarm algorithm and the LightGBM model, with the integrated learning model as the base model, by defining the loss function and introducing prior physical knowledge, a model PSO-C-LightGBM with prior knowledge guidance and constraints is obtained, which is used for probabilistic low-cycle fatigue life prediction of metal materials.

[0012] Further, in step S1, for the stress-strain relationship in fatigue behavior, a Chaboche cyclic hardening model is introduced, wherein the model is calculated by backward identification parameter optimization and is used to describe the physical response of the component subjected to multiaxial loading conditions;

[0013] The Chaboche cyclic hardening model is defined as follows:

[0014]

[0015] Where σ represents the Cauchy stress, α is the back stress, is the equivalent stress correlation coefficient related to isotropic hardening, where is the equivalent plastic strain;

[0016] The back stress of metal materials obeys the following formula from the perspective of differentiation:

[0017]

[0018] Where C and γ represent the dynamic hardening parameters of the material, and the dissociation hardening obeys the Voce hardening criterion, which is expressed as follows:

[0019]

[0020] Where σ0 is the initial yield strength of the material, Q and b chaRepresents the material hardening parameter. Combined with the above back stress formula, the updated formula is:

[0021]

[0022] Further, the stress-strain relationship under standard load conditions can be obtained as follows:

[0023]

[0024] Furthermore, in step S2, the Latin hypercube sampling algorithm constructs the independent variable space specifically including:

[0025] During the training phase, LHS is used for evenly distributed sampling to improve the generalization of data set training;

[0026] During the testing phase, Latin hypercube sampling that obeys a multidimensional normal distribution is used to perform sampling within specified boundaries. The sampling includes circular multiaxial load path parameters and material properties. The material properties include basic properties, Chaboche cyclic hardening parameters, Ramberg-Osgood correction parameters, and cyclic fatigue parameters. The sampling range is determined by the boundaries that obey the normal distribution, and the specific values ​​are determined by the predictor based on actual engineering cases.

[0027] Furthermore, the construction of the model PSO-C-LightGBM in step S3 includes the following steps:

[0028] S31. Use GBDT algorithm to combine multiple decision trees, integrate histogram-based algorithm, mutually exclusive feature bundling, gradient-based one-sided sampling and leaf growth strategy to establish LightGBM base model;

[0029] S32. Use some known relationships to set LightGBM model constraints, where the constraints use custom penalty terms to enhance the loss function, as shown below:

[0030]

[0031] Where E1 represents the baseline loss evaluation metric used by the data-driven method, E2 represents the log-likelihood function, which is used to enforce a log-normal distribution in the predicted LCF lifetime distribution, and t is the number of input data. is the predicted lifespan, y is the target lifespan, is the expected target life span, is the probability density function of predicting life expectancy, is the internal hyperparameter of the model that needs to be optimized.

[0032] Furthermore, for the uncertainty in the LHS candidate data set, each base model is integrated; in the model input, each LightGBM model contains m decision trees in the kth data set. At this time, the input features of the base model are divided into two layers, which are represented as follows:

[0033]

[0034]

[0035] y i is the target life in the ith base model, is the output corresponding to the jth feature in the i-th base model;

[0036] At this time, the prediction value of the independent LightGBM model is:

[0037] When K data sets exist, The results of predictions made using the corresponding number of LightGBM base models are as follows:

[0038]

[0039] Based on the above scheme, in order to achieve the optimal base model described in step S3, the particle swarm algorithm is used to optimize the hyperparameters of each base model, including the following processing:

[0040] S31, initialize the LightGBM base model, and perform independent base model training through randomly selected K LHS candidate data sets;

[0041] S32, for the training set data, optimize K decision trees by particle swarm algorithm, if the loss function meets the convergence threshold, proceed to the next step, if not, repeat the optimization;

[0042] S33, perform five-fold cross validation to find the optimal hyperparameters for the independent model, and repeat the process for all models;

[0043] S34. Test the established model and verify the results.

[0044] Beneficial effects: Compared with the prior art, the present invention is a probabilistic low-cycle fatigue life prediction method for metal materials guided by prior knowledge, which integrates physical knowledge and some known relationships. Inspired by the concept of reliability design optimization, the present invention can predict deterministic and probabilistic low-cycle fatigue life more efficiently and accurately. On the other hand, in order to improve the accuracy and rationality of probabilistic fatigue life prediction, we proposed a prediction model PSO-C-LightGBM guided by prior knowledge. The model is based on an integrated learning method and introduces prior physical knowledge of fatigue life by defining a penalty function, so that the model can efficiently and scientifically predict probabilistic fatigue life. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is a schematic diagram of the framework flow of the method of the present invention;

[0046] Figure 2 It is a sample diagram of an embodiment of the method proposed by the present invention;

[0047] Figure 3 It is a prediction performance diagram of the model proposed in the present invention;

[0048] Figure 4 is a probabilistic fatigue life diagram under different design boundaries and load conditions in the embodiment. DETAILED DESCRIPTION

[0049] In order to explain the technical solution disclosed by the present invention in detail, a specific introduction is given below in conjunction with the accompanying drawings of the specification.

[0050] Considering that metal materials contain complex physical properties, some of which will greatly affect the fatigue behavior of the material. In addition to all the mechanical properties and fatigue properties of the material itself, external load conditions, structural characteristics and geometric responses of the sample are also key factors. Therefore, in order to improve the prediction efficiency and accuracy. The present invention first determines candidate uncertainties based on preliminary analysis, including model parameters related to material properties, multi-axial load conditions and geometric characteristics of components in a low-cycle fatigue environment subjected to multi-axial loads, thereby obtaining prior knowledge including stress-strain relationships in fatigue behavior. In addition to the prior knowledge of material physical information, the present invention also explores the prior distribution of fatigue life under the category of statistical learning, and embeds it into the framework as prior knowledge in subsequent steps. Further, the present invention is based on the data-driven principle and needs to use the finite element method to construct a data set based on physical knowledge. Based on the model parameters, a finite element model is established. Inspired by the idea of ​​reliability design optimization, the present invention introduces the Latin hypercube sampling algorithm for sampling, which can cover the required variable area in a more reasonable sampling manner, thereby constructing an independent variable space to obtain a generalized data set and improve the coverage efficiency of data training relationships. By only considering the physical properties of the research material to predict the fatigue life, the GBDT algorithm with speed and accuracy is considered under the premise of only discrete data input. The present invention proposes a model based on particle swarm algorithm and LightGBM model, which is data-driven and loss function-based, and prior knowledge is placed to obtain a model PSO-C-LightGBM with prior knowledge guidance and constraints, which is used for probabilistic fatigue life prediction of aerospace materials. Considering the very complex fatigue behavior under multi-axial load, the present invention combines the finite element simulation using the critical surface method with the machine learning method enhanced by prior knowledge constraints, thereby establishing a machine learning fatigue life prediction method based on prior knowledge. Generally speaking, by embedding the multi-axial fatigue life prediction method, the distribution constraints based on prior knowledge and the physical response based on finite element analysis, the prediction performance of the model is guided by the laws of physics. Together with the data-physics fusion method, the interpretability and scientific integrity of the black box surrogate model can be significantly enhanced. In addition, the improvement of the speed of fatigue behavior prediction and evaluation of metal materials is also helpful for intelligent life management of components in actual engineering projects.

[0051] Combination Figure 1 As shown in the content, the method provided by the present invention mainly considers the following aspects.

[0052] (1) Determine candidate uncertainty factors through preliminary analysis.

[0053] Uncertainties include key parameters related to material properties, multiaxial loading conditions, and geometric features of components under multiaxial loading low cycle fatigue environments. Based on the research of reliability-based design optimization (RBDO), this paper uses Latin hypercube sampling (LHS) technology to capture the essence of multiple uncertainties, construct a high-reliability independent variable data set for training, and supplement the data source.

[0054] (2) The present invention proposes a machine learning method based on prior knowledge constraints, which can use prior physical knowledge to predict fatigue life with higher accuracy and efficiency. At the same time, compared with traditional black box algorithms, this method has better interpretability and scientificity.

[0055] (3) Multiaxial fatigue behavior is very complex. In order to obtain a result with better generalization, the present invention integrates the model and average pooling based on the previous model. This method can traverse the prediction results of all base models and obtain the best generalization results based on this. In practical applications, it can adapt to fatigue life prediction scenarios under more types of load conditions.

[0056] Specifically, a probabilistic low-cycle fatigue life prediction method for metal materials guided by prior knowledge includes the following steps:

[0057] S1. Based on the preliminary analysis, select candidate uncertainties, including key parameters related to material properties, multiaxial loading conditions, and geometric characteristics of components in low-cycle fatigue environments subjected to multiaxial loading;

[0058] The physical laws guided by prior knowledge included in this step include the following:

[0059] For the stress-strain relationship in fatigue behavior, the Chaboche cyclic hardening model is introduced, which is calculated by backward identification parameter optimization and is used to describe the physical response of components subjected to multiaxial loading conditions. The general definition of the model is as follows:

[0060]

[0061] Where σ represents the Casey stress, α is the back stress, is the isotropic hardening related equivalent stress correlation coefficient, where is the equivalent plastic strain, and the back stress obeys the following formula:

[0062]

[0063] Where C and γ represent the dynamic hardening parameters of the material, assuming that the dissociation hardening obeys the Voce hardening criterion:

[0064]

[0065] Where σ0 is the initial yield strength of the material, Q and b cha Represents the material hardening parameter. Combined with the above back stress formula, the updated formula is:

[0066]

[0067] The stress-strain relationship for the standard load case is then:

[0068]

[0069] S2, establish a high-reliability finite element model based on key parameters and construct the independent variable space using optimization-inspired Latin hypercube sampling to obtain a generalized dataset;

[0070] This step requires the introduction of the Latin hypercube sampling algorithm to construct the independent variable space, which includes the following:

[0071] During the training phase, LHS is used for evenly distributed sampling to improve the generalization of data set training.

[0072] During the testing phase, Latin hypercube sampling that obeys multidimensional normal distribution is used to perform sampling within the specified boundaries. The sampling includes circular multiaxial load path parameters, material properties, and material properties include basic properties, Chaboche cyclic hardening parameters, Ramberg-Osgood correction parameters, and cyclic fatigue parameters. The sampling range is determined by the boundaries that obey the normal distribution, and the specific values ​​can be determined by the forecaster based on actual engineering cases.

[0073] S3. Based on the particle swarm algorithm and LightGBM model, prior knowledge is introduced in the form of data-driven and loss function, and a particle swarm optimization model PSO-C-LightGBM with prior knowledge guidance and constraints is proposed, thereby achieving reliable and efficient probabilistic fatigue life prediction.

[0074] This step establishes the PSO-C-LightGBM model with prior knowledge guidance and constraints, including the following steps:

[0075] S31. First, we consider the LightGBM base model. We use the GBDT algorithm to combine multiple decision trees, integrate the histogram-based algorithm, mutually exclusive feature bundling, gradient-based one-sided sampling and leaf growth strategy to establish the LightGBM base model.

[0076] S32. In order to improve the interpretability of the surrogate model and the interpretability of the prediction results in the reliability analysis, the present invention introduces constraints for the LightGBM base model using some known relationships, where the constraints use custom penalty terms to enhance the loss function, as follows:

[0077]

[0078] Where E1 represents the baseline loss evaluation metric used by the data-driven method, E2 represents the log-likelihood function, which is used to enforce a log-normal distribution in the predicted LCF lifetime distribution, and t is the number of input data. is the predicted lifespan, y is the target lifespan, is the expected target life span, is the probability density function of predicting life expectancy, is the model internal hyperparameter that needs to be optimized.

[0079] In the implementation of the above scheme, in order to consider the uncertainty in the LHS candidate data set in step S3 to obtain better generalization performance, we use the average pooling method to integrate each base model. In the input of the model, each LightGBM model contains m decision trees in the kth data set. At this time, the input features of the base model are:

[0080]

[0081]

[0082] y i is the target life in the ith base model, is the output corresponding to the jth feature in the i-th base model. At this time, the prediction value of the independent LightGBM model is: The final predicted fatigue life is: Where K is the number of data sets sampled by LHS.

[0083] In order to obtain the optimal base model results, the present invention uses a particle swarm algorithm to optimize the hyperparameters of each base model, and has the following steps:

[0084] First, initialize the LightGBM base model, and train the base model independently through K randomly selected LHS candidate data sets; then, for the training set data, optimize the K decision trees through the particle swarm algorithm. If the loss function meets the convergence threshold, proceed to the next step, otherwise, repeat the optimization. Next, perform a five-fold cross validation to find the optimal hyperparameters of the independent model, and repeat the process for all models. Finally, test the established model to verify the results; after execution, the model effect reaches the best state.

[0085] Example

[0086] First, the method described in the present invention was tested on fatigue tests of shaft-shaped samples. The shaft-shaped samples used in the present invention were verified to have three typical structures, namely keyhole, shoulder and bend. Figure 2 The invention is compared with similar ensemble learning methods, and LightGBM, XGBoost and random forest are selected. The evaluation indicators include root mean square error (RMSE), mean absolute error (MAE), regression coefficient (R 2 ) and calculation speed. The experimental results are shown in the attached Figure 3 Displayed in.

[0087] In this example, we will delve into the prediction of low cycle fatigue life under multiaxial loading conditions and then evaluate the performance of the model. Figure 3 A comprehensive overview of the predicted lifetime and FEA simulation results is provided.

[0088] Figure 3 (a) describes the efficacy of the model and various evaluation metrics. In addition to the model PSO-C-LightGBM constructed in the present invention and its corresponding algorithm, we also compare the results of the present invention with those obtained by other popular ensemble learning models, such as Figure 3 (b). It is worth noting that the model PSO-C-LightGBM shows the highest prediction accuracy, which is due to the optimization promoted by the PSO algorithm, coupled with the ability of LLF to impose penalties based on realistic distributions, especially in the case of specific distributions. The computational efficiency of the PSO model is somewhat different from that of the standalone LightGBM model due to the additional constraints imposed. Nevertheless, these computational speeds are still within acceptable ranges, making the proposed model a commendable alternative to surrogate models, effectively replacing time-consuming FEA simulations. Figure 3 (b) depicts the comparison of the FEA simulation results with the surrogate model predictions, showing excellent agreement under various conditions and within the 1.2 scatter band. In addition, the deterministic fatigue life prediction results will be summarized as benchmark results for further studies on probabilistic fatigue life prediction.

[0089] Subsequently, the method described in the present invention is utilized in order to study the fatigue reliability under multiaxial loading conditions, considering the influence of multiple sources of uncertainty. In the probabilistic life prediction, we draw inspiration from the related experimental designs of RBDO and RBRDO, divide the input features into external random perturbation factors (in our case, random multiaxial loading) and objective factors (specifically material properties), define their respective distribution ranges, and assemble a preliminary input data set. The definition of the input data set eigenvalue range is similar to the design boundaries, aiming to study the probabilistic distribution of low-cycle fatigue life under multiaxial loading under different material property distributions. The objective factors considered include the established effects on key material properties such as material density and elastic modulus. For low-cycle fatigue under multiaxial cyclic loading, the influence of related cyclic fatigue properties should be considered.

[0090] During the testing phase, Latin hypercube sampling that follows a multidimensional normal distribution is used to perform sampling within the specified boundaries. The scope and sampling standards are shown in Appendix 1:

[0091] Schedule 1

[0092] Input dataset characteristics

[0093]

[0094] In actual engineering cases, users can customize the standard deviation ratio of the boundaries based on the actual conditions of the parts and materials and prior knowledge such as previous experiments, so as to achieve the best prediction effect.

[0095] Figure 4 Each column is the fatigue life distribution under three design boundaries (determined by the experimenter according to the normal distribution) in the same load spectrum (fatigue life standard number 1677 and fatigue life standard number 2804), and the two columns correspond to the standard life of the parts under the ideal state under the load in the first row. Therefore, using the present invention, the PSO-C-LightGBM model was used in this embodiment to perform 10,000 predictions (for each case). The probabilistic fatigue life prediction results are shown in Figure 2. Figure 4The overall picture shows six experimental results from two random load spectra and three boundaries. Each experiment shows the respective selected boundary and multiaxial loading conditions. In addition, the benchmark for each experiment is shown above the results as a life reference. It is obvious that as the sampling boundary of the input features expands (indicating an increase in the variability of the material properties), the probability distribution of the life also expands. The predicted life is log-normally distributed with the fluctuation of the input parameters, which is consistent with the fatigue life distribution characteristics observed in actual engineering. This shows that the probabilistic low-cycle fatigue life under multiaxial loading can be accurately described by using the multiple material properties adopted, while also capturing obvious distribution characteristics. In addition, compared with other methods using alternative models (such as probabilistic life prediction through Monte Carlo simulation), the proposed physical information hybrid prediction method can provide more reasonable predictions and higher interpretability. From the perspective of different loading paths, the change of multiaxial loading paths has little effect on the probabilistic life distribution, which is mainly consistent with the benchmark life corresponding to the idealized life of each loading path based on standard material properties in this study. This is consistent with the characteristic that the fatigue life distribution follows a log-normal distribution.

Claims

1. A probabilistic low-cycle fatigue life prediction method for metal materials guided by prior knowledge, characterized in that: Includes steps: S1. Determine candidate uncertainties based on preliminary analysis, including material properties, multiaxial loading conditions, and geometric characteristic parameters of components in a low-cycle fatigue environment subjected to multiaxial loading, thereby obtaining prior knowledge including stress-strain relationships in fatigue behavior, including using the geometric characteristic parameters as parameters of the model; S2, based on data-driven approach, using finite element method to construct data set based on physical knowledge, and then building finite element model based on model parameters; This step also includes sampling through a Latin hypercube sampling algorithm to construct an independent variable space and a probabilistic prediction training set; S3. Based on the particle swarm algorithm and the LightGBM model, with the integrated learning model as the base model, by defining the loss function and introducing prior physical knowledge, a model PSO-C-LightGBM with prior knowledge guidance and constraints is obtained, which is used for probabilistic low-cycle fatigue life prediction of metal materials.

2. The method for predicting the probabilistic low-cycle fatigue life of metal materials according to claim 1, characterized in that: Step S1: For the stress-strain relationship in fatigue behavior, the Chaboche cyclic hardening model is introduced, which is calculated by backward identification parameter optimization to describe the physical response of the component subjected to multiaxial loading conditions; The Chaboche cyclic hardening model is defined as follows: Where σ represents the Cauchy stress, α is the back stress, is the equivalent stress correlation coefficient related to isotropic hardening, where is the equivalent plastic strain; The back stress of metal materials obeys the following formula from the perspective of differentiation: Where C and γ represent the dynamic hardening parameters of the material, and the dissociation hardening obeys the Voce hardening criterion, which is expressed as follows: Where σ0 is the initial yield strength of the material, Q and b cha Representing two different material hardening parameters, combined with the back stress formula, the updated formula is: The stress-strain relationship under standard load is further obtained as follows:

3. The method for predicting the probabilistic low-cycle fatigue life of metal materials according to claim 1, characterized in that: In step S2, the Latin hypercube sampling algorithm constructs the independent variable space specifically including: During the training phase, LHS is used for evenly distributed sampling to improve the generalization of data set training; During the testing phase, Latin hypercube sampling that obeys a multidimensional normal distribution is used to perform sampling within specified boundaries. The sampling includes circular multiaxial load path parameters, material properties, and the material properties include basic properties, Chaboche cyclic hardening parameters, Ramberg-Osgood correction parameters, and cyclic fatigue parameters. The sampling range is determined by the boundaries that obey the normal distribution, including the decision of the predictor based on actual engineering cases.

4. The method for predicting the probabilistic low cycle fatigue life of metal materials according to claim 1, characterized in that: The construction of the model PSO-C-LightGBM in step S3 includes the following steps: S31. Use GBDT algorithm to combine multiple decision trees, integrate histogram-based algorithm, mutually exclusive feature bundling, gradient-based one-sided sampling and leaf growth strategy to establish LightGBM base model; S32. Use some known relationships to set constraints on the LightGBM base model, where the constraints use custom penalty terms to enhance the loss function, as shown below: Where E1 represents the baseline loss evaluation metric used by the data-driven method, E2 represents the log-likelihood function, which is used to enforce a log-normal distribution in the predicted LCF lifetime distribution, and t is the number of input data. is the predicted lifespan, y is the target lifespan, is the expected life span of the target, is the probability density function of predicting life expectancy, is the internal hyperparameter of the model that needs to be optimized.

5. The method for predicting the probabilistic low-cycle fatigue life of metal materials according to claim 3, characterized in that: In view of the uncertainty in the LHS candidate data set, each base model is integrated; In the input of the model, each LightGBM model contains m decision trees in the kth data set. At this time, the input features of the base model are divided into two layers, which are represented as follows: y i is the target life in the ith base model, is the output corresponding to the jth feature in the i-th base model; At this time, the prediction value of the independent LightGBM model is: When K data sets exist, The results of predictions made using the corresponding number of LightGBM base models are as follows:

6. The method for predicting the probabilistic low-cycle fatigue life of metal materials according to claim 1 or 3, characterized in that: In order to achieve the optimality of the base model described in step S3, the particle swarm algorithm is used to optimize the hyperparameters of each base model, including the following processing: S31, initialize the LightGBM base model, and perform independent base model training through randomly selected K LHS candidate data sets; S32, for the training set data, optimize K decision trees by particle swarm algorithm, if the loss function meets the convergence threshold, proceed to the next step, if not, repeat the optimization; S33, perform five-fold cross validation to find the optimal hyperparameters for the independent model, and repeat the process for all models; S34. Test the established model and verify the results.

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