Method for determining parameters of long-life fatigue model of structure containing defects

Abstract

The present application belongs to the field of advanced manufacturing and structure evaluation, in particular to a method for determining parameters of long-life fatigue model of defect-containing structure, comprising the following steps: step one, constructing sample data containing key variables and response relationship by using finite element simulation; step two, parameterizing expression of long-life fatigue model and constructing objective function for parameter identification. The method for determining parameters of long-life fatigue model of defect-containing structure solves the problem that in the field of advanced manufacturing such as welding or additive manufacturing, the parameters of long-life fatigue prediction model of defect-containing structure depend on regression fitting based on experimental test data, the cost is high, and the reliability of model parameter identification result is difficult to guarantee. A new method of comprehensively using finite element analysis, optimization search and Bayesian inference is invented, which reduces the demand for experiments and realizes stable determination of model parameters, thereby improving the reliability and engineering applicability of long-life fatigue life prediction.

Description

Technical Field

[0001] This invention relates to the field of advanced manufacturing and structural evaluation technology, and in particular to a method for determining the parameters of a long-life fatigue model for a defective structure. Background Technology

[0002] Advanced manufacturing technologies such as welding forming and additive manufacturing have been widely applied in aerospace, energy equipment, and engineering machinery. However, due to the characteristics of their manufacturing processes, defects such as porosity, lack of fusion, and inclusions are inevitably introduced during manufacturing. As engineering structural design and service requirements gradually develop towards longer service life, these defects are highly susceptible to evolving into fatigue damage initiation sites under long-term cyclic loading, adversely affecting the service safety and life reliability of the structure. To meet the needs of long-life fatigue assessment of defective structures under different service conditions, engineering practice relies on long-life fatigue models to analyze and predict the fatigue behavior of structures or materials. These models typically contain one or more undetermined model parameters to characterize key factors such as material fatigue performance, damage evolution characteristics, or the degree of defect influence. The accuracy of model predictions depends heavily on the accuracy of the model parameter values. When the parameters change slightly, the predicted fatigue life often deviates significantly, even by several orders of magnitude. Therefore, the reasonable determination of model parameters is the core of ensuring the reliability of fatigue life prediction results and directly relates to the effectiveness of structural safety assessment.

[0003] Traditional long-life fatigue model parameter determination commonly employs regression fitting based on fatigue test data, such as the method disclosed in patent CN119227471A. This type of method obtains life data from fatigue tests, constructs an error evaluation function between the model's prediction results and the sample data, and uses deterministic regression techniques such as least-squares fitting to calibrate the model parameters, thereby obtaining a set of parameter values ​​that minimize the error. While the parameter determination process is intuitive and relatively simple to implement, this type of regression fitting method is essentially a deterministic point estimation strategy. Its results are usually given in the form of single parameter values, which cannot guarantee the unbiasedness of parameter estimation from a statistical inference perspective. When the sample size is limited, the data distribution is uneven, or the data contains certain errors, different sample combinations or fitting methods may lead to significant differences in the point-estimated model parameter values. In such cases, even small parameter deviations can cause significant changes in the predicted life, greatly weakening the stability and reliability of fatigue life prediction results. With the development of high-performance computing technology, finite element analysis has been widely used in the simulation of material and structural behavior, gradually becoming an effective supplement and even replacement for physical testing. Finite element simulation can obtain fatigue response data under different conditions at a lower cost and in a shorter period of time, which alleviates the problems of long cycle and high cost of traditional fatigue testing to some extent. However, finite element simulation is mainly used to expand the data sources required for parameter identification, and the method of determining model parameters is still deterministic point estimation. Its problems in terms of parameter value stability and reliability have not been fundamentally solved.

[0004] Existing research has also attempted to introduce statistical inference methods to analyze the parameters of long-life fatigue models, characterizing their uncertainty by establishing posterior probability distributions of the model parameters. However, these methods mostly focus on describing parameter uncertainty, typically only providing the probability distribution or statistical characteristics of the parameters, lacking a clear decision-making mechanism to transform the statistical inference results into engineering-usable parameter values. This makes it difficult to directly use the obtained parameter results for the actual calculation of fatigue life prediction models, thus limiting their engineering application value.

[0005] Therefore, how to establish clear and stable model parameter selection rules under simulation-substitute experimental conditions while ensuring the statistical rationality of parameters has become an urgent technical problem to be solved in the field of long-life fatigue life prediction of defective structures. Summary of the Invention

[0006] Based on existing technical problems, this invention proposes a method for determining the parameters of a long-life fatigue model for structures with defects. Addressing the need for long-life fatigue prediction of structures with defects in advanced manufacturing fields such as welding and additive manufacturing, this method establishes a comprehensive evaluation of deterministic parameter estimation results and statistical inference results under simulation-substitute experimental conditions, guiding the selection of model parameters accordingly. By introducing a consistency criterion, this method transforms the uncertain description of statistical inference results into a basis for engineering parameter decision-making, solving the problem that statistical parameters are difficult to directly use in fatigue life prediction model calculations. This provides a novel technical path for the rational determination of long-life fatigue model parameters, helping to improve the stability and engineering reliability of the determined model parameters, thereby enhancing the reliability of model predictions in engineering applications.

[0007] The present invention proposes a method for determining the parameters of a long-life fatigue model of a defective structure, including step one: using finite element simulation to construct sample data containing key variables and response relationships.

[0008] Step 2: Parameterize the long-life fatigue model and construct an objective function for parameter identification.

[0009] Step 3: Based on the sample data, establish a global search grid within the preset parameter range, and search the objective function to obtain an initial deterministic estimate.

[0010] Step 4: Based on the global search grid, use Bayesian inference to establish the posterior probability distribution of the model parameters and obtain the statistical inference results of the model parameters.

[0011] Step 5: Based on the statistical consistency between the initial deterministic estimate and the statistical inference results, determine the final model parameter values ​​for fatigue life prediction according to the preset consistency criteria.

[0012] Preferably, in step one, a corresponding finite element analysis model is established based on the geometric characteristics, material properties, and service conditions of the structure or material to be analyzed, combined with the key variables in the target long-life fatigue model.

[0013] Preferably, the finite element analysis model maps key variables in the model to a numerical simulation environment by setting loading conditions, material parameters, geometric features and boundary constraints, so as to construct a high-fidelity finite element model for simulating the target physical process;

[0014] Based on the finite element model, by changing different key variables of the model and setting multiple sets of fatigue load levels or structural characteristic parameters, finite element fatigue simulation calculations are performed to obtain the response behavior of the structure or material under external forces.

[0015] Through the above technical solution and finite element simulation analysis, sample data covering the mapping relationship between key variables and response quantities in the long-life fatigue model is generated. It is used to replace the large amount of physical test data that traditional methods rely on.

[0016] Preferably, in step two, the sample data of the finite element simulation is obtained. Subsequently, the mathematical form of the long-life fatigue model is parameterized or structured to clarify the model parameters to be identified. .

[0017] Preferably, when the Z-parameter model is used as the long-life fatigue model for the defective structure;

[0018] The mathematical expression is ;

[0019] in, Indicates the stress amplitude. Indicates the size of the defect feature. Indicates parameters related to the location of the defect. For model parameters related to material properties, and These are the fitting constants in the model. This refers to fatigue life.

[0020] Preferably, when the model parameters When the target parameter is to be identified, the other parameters are determined by... The linear fit is then obtained. At this point, the logarithm of the mathematical expression of the Z-parameter model is taken to linearize the power-law relationship, resulting in... This enables parameterization of long-life fatigue models.

[0021] Based on the above, the least squares method is then used to fit the relationship between the two sides. and Linear regression was performed to calculate the coefficient of determination. .

[0022] Therefore, the objective function is constructed. This serves as the basis for determining the parameters of the long-life fatigue model.

[0023] Preferably, in step three, a grid search is performed in the candidate parameter space, and the search results are evaluated based on the objective function to obtain initial deterministic estimates of the model parameters.

[0024] First, the candidate parameter space is traversed and calculated globally with a fixed step size, and the corresponding objective function value is calculated respectively. Then, the curve or surface of the candidate parameter and the objective function value is plotted.

[0025] When the curve or surface is unimodal or multimodal, the candidate parameters corresponding to the peak values ​​of the unimodal or multimodal peaks are the initial deterministic estimates of the model parameters. If the curve or surface is monotonic, then the corresponding boundary of the candidate parameter space is considered to be the initial deterministic estimate.

[0026] The above technical solution, through a global search strategy, avoids the influence of local optima on parameter identification results, thereby improving the stability of the identification process.

[0027] Preferably, in step four, based on the initial deterministic estimates of the model parameters obtained in step three, a Bayesian inference method is introduced to obtain the posterior probability distribution of the target model parameters.

[0028] A posterior computation method based on parameter space gridding is employed to numerically approximate the posterior probability distribution of the model parameters. The prior probability distribution can be a normal distribution, log-normal distribution, or uniform distribution, which conforms to the physical meaning of the parameters and the support domain. The statistical features include, but are not limited to, the posterior mean. Posterior variance or posterior standard deviation It is used to characterize the uncertainty and distribution of parameters.

[0029] For each material, based on the mesh search fit in step three Obtain its residual sum of squares and residual standard deviation ,right Introducing a uniform prior distribution, we assume that the model residuals follow a normal distribution. to construct a joint posterior The likelihood function Ultimately marginalized ,get The marginal posterior distribution is calculated, and the posterior mean is calculated accordingly. and posterior standard deviation .

[0030] Preferably, in step five, the initial deterministic estimates of the model parameters obtained in step three are used. Based on the statistical inference results obtained in step four, a criterion is established to measure the consistency between the two, thereby enabling engineering decisions regarding model parameter values. This consistency criterion determines whether the deterministic point estimate falls within a reasonable range supported by statistical inference by comparing the degree of deviation between the deterministic estimation results and the posterior statistical characteristics, thus determining the final model parameter values ​​used for fatigue life prediction.

[0031] Preferably, the consistency criterion is expressed as follows: ;

[0032] in, This represents the initial deterministic estimate of the model parameters. This represents the posterior mean of the model parameters. This represents the posterior standard deviation of the model parameters.

[0033] When the consistency criterion If the result is less than or equal to the preset threshold, it is considered that there is no significant statistical inconsistency between the initial deterministic estimation result and the statistical inference result. In this case, the initial deterministic estimation value is selected as the final model parameter value.

[0034] When the consistency criterion d is greater than the preset threshold, it is considered that there is a significant difference between the initial deterministic estimation result and the statistical inference result. In this case, the posterior mean or other statistics in the statistical inference result are selected as more robust model parameter values.

[0035] The beneficial effects of this invention are as follows:

[0036] By employing finite element simulation to replace numerous physical experiments, this invention provides sufficient data sources without sacrificing accuracy, obtaining sample data covering multiple defect characteristics and load conditions, significantly reducing parameter identification costs and timelines. The invention eliminates the tendency of traditional fitting to get trapped in local optima through a gridded global search method, making the parameter identification process more comprehensive and stable. Consistency evaluation assesses the deviation of deterministic point estimations, and when necessary, uses posterior means to replace point estimations, making parameter identification results more robust and avoiding identification biases caused by data noise, thereby improving the reliability of long-life fatigue models. This invention comprehensively evaluates deterministic estimation results and statistical inference results through consistency criteria, determining the final values ​​of model parameters accordingly. This solves the engineering application problem that statistical parameters are difficult to directly use for fatigue life prediction model calculations, significantly improving the stability and engineering applicability of fatigue life prediction results, and providing reliable assurance for long-life fatigue prediction of welded or additively manufactured structures. Attached Figure Description

[0037] Figure 1 This is a flowchart of a method for determining parameters of a long-life fatigue model for a defective structure proposed in this invention;

[0038] Figure 2 This is a comparison chart of finite element analysis lifetime and experimental lifetime for a method for determining parameters of a long-life fatigue model of a defective structure proposed in this invention.

[0039] Figure 3 This invention provides a typical material for determining the parameters of a long-life fatigue model for a defective structure, as proposed in this invention. Line graph;

[0040] Figure 4 This is a typical posterior distribution diagram of material parameters for a method of determining parameters of a long-life fatigue model for a defective structure proposed in this invention. Detailed Implementation

[0041] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0042] Reference Figures 1-4 A method for determining parameters of a long-life fatigue model of a defective structure includes step one: constructing sample data containing the relationship between key variables and response using finite element simulation; and forming a dataset covering the mapping relationship between key variables and response quantities based on finite element simulation analysis. Specifically, this is achieved as follows:

[0043] Based on the geometric characteristics, material properties, and service conditions of the structure or material to be analyzed, and combined with the key variables in the target long-life fatigue model, a corresponding finite element analysis model is established. Specifically, the finite element analysis model maps the key variables in the model to the numerical simulation environment by setting loading conditions, material parameters, geometric features, and boundary constraints, thereby constructing a high-fidelity finite element model for simulating the target physical process. Based on the finite element model, by changing different key variables and setting multiple sets of fatigue load levels or structural characteristic parameters, finite element fatigue simulation calculations are performed to obtain the response behavior of the structure or material under external forces. The key variables include, but are not limited to, loading conditions, geometric characteristic parameters, material mechanical property parameters, and defect characteristic parameters; the response behavior includes, but is not limited to, stress response, strain response, fatigue damage, or fatigue life. Through the above finite element simulation analysis, sample data covering the mapping relationship between key variables and response quantities in the long-life fatigue model is generated. It is used to replace the large amount of physical test data that traditional methods rely on.

[0044] In one embodiment, such as Figure 2 As shown, a finite element analysis model is established using a defective structure as the research object. Different defect sizes are introduced into the finite element model. and the relative depth of defects and at various load amplitudes Under certain conditions, numerical simulations were performed on six materials to obtain their fatigue life under cyclic loading. The simulation sample data, including defect characteristics, load conditions, and fatigue life response, is constructed for subsequent model parameter identification. To verify the rationality of the simulation data, this embodiment selects simulation results under certain working conditions for comparative analysis with existing fatigue test data. The results show that the two have good consistency within an acceptable error range, thus verifying the feasibility of using finite element simulation data to replace a large number of physical fatigue tests for model parameter identification.

[0045] Step 2: Parametrically represent the long-life fatigue model and construct an objective function for parameter identification. The purpose is to parameterize or structure the mathematical form of the target physical model, clarify the parameters of the model to be identified, and construct a mathematical expression for parameter identification. Specifically:

[0046] Obtain sample data for finite element simulation Subsequently, the mathematical form of the long-life fatigue model is parameterized or structured to clarify the model parameters to be identified. The long-life fatigue model can be an empirical model, a semi-empirical model, or a life prediction model based on physical mechanisms, and should meet the following technical conditions:

[0047] 1. The model contains at least one key parameter that needs to be determined through fitting sample data;

[0048] 2. The key parameters appear in the mathematical expression of the model in an explicit form, enabling the construction of an objective function for parameter identification based on sample data;

[0049] 3. The key parameters mentioned above are significantly sensitive to the results of fatigue life prediction.

[0050] Furthermore, within a predefined candidate parameter space, an objective function is constructed to evaluate the deviation between the model's prediction results and the simulation data. This objective function can be based on the sum of squared errors, goodness of fit, or other evaluation metrics that reflect prediction consistency.

[0051] In one embodiment, the Z-parameter model is used as the long-life fatigue model for structures with defects. The mathematical expression of this model is: ,in, Indicates the stress amplitude. Indicates the size of the defect feature. Indicates parameters related to the location of the defect. For model parameters related to material properties, and These are the fitting constants in the model. This refers to fatigue life. In this embodiment, The target parameters are to be identified; the remaining parameters are determined by... The linear fit was then obtained. The logarithm of the mathematical expression of the Z-parameter model was taken to linearize the power-law relationship, resulting in... This enables parameterization of the long-life fatigue model. Based on this, the least squares method is used to fit the parameters related to... and Linear regression was performed to calculate the coefficient of determination. Therefore, the objective function is constructed. This serves as the basis for determining the parameters of the long-life fatigue model.

[0052] Step 3: Based on the sample data, establish a global search grid within a preset parameter range to search the objective function and obtain an initial deterministic estimate. This is to establish an optimized objective function and perform a grid search within a preset candidate parameter space to obtain deterministic identification results.

[0053] A grid search is performed within the candidate parameter space, and the search results are evaluated based on the objective function to obtain initial deterministic estimates of the model parameters. Specifically, the candidate parameter space is traversed globally with a fixed step size, and the corresponding objective function value is calculated for each set of candidate parameters. A curve or surface is then plotted showing the relationship between the candidate parameters and the objective function value. The fixed step size determines the resolution of the grid search; a larger step size results in lower resolution. The curve or surface should be unimodal or multimodal, and the candidate parameters corresponding to the peak values ​​are the initial deterministic estimates of the model parameters. If the curve or surface is monotonic, the corresponding boundary of the candidate parameter space is considered to be the initial deterministic estimate. A global search strategy is used to avoid the influence of local optima on the parameter identification results, thus improving the stability of the identification process.

[0054] In one embodiment, such as Figure 3 As shown, based on the simulation lifetime sample data of the six materials obtained in step one, the objective function constructed in step two is used to apply the simulation lifetime data of each material in a step size of 0.001. Comprehensive search of material parameters within the scope The initial deterministic estimate, the calculation results are plotted on Curve graphs. All six material curves are unimodal; the material parameters at the peak values ​​are used as initial deterministic estimates of the model parameters. .

[0055] Step 4: Based on the global search grid, use Bayesian inference to establish the posterior probability distribution of the model parameters and obtain the statistical inference results of the model parameters.

[0056] Furthermore, statistical inference methods are introduced to perform inverse analysis on the model parameters, establishing the posterior probability distribution of the target parameters to characterize the statistical properties of the parameters under the sample data conditions. Specifically, it works as follows:

[0057] Based on the initial deterministic estimates of the model parameters obtained in step three, a Bayesian inference method is introduced to obtain the posterior probability distribution of the target model parameters. Specifically, the model parameters to be inferred... Define the prior probability distribution and base it on the model parameters. With sample data The relationship between the prior distribution and the likelihood function is used to construct a likelihood function to characterize the probability of observed data occurring under given parameters. Based on the prior distribution and the likelihood function, the posterior probability distribution of the model parameters is obtained according to Bayes' theorem, and the statistical characteristics of the model parameters are further calculated as the result of statistical inference. In one embodiment, a posterior calculation method based on parameter space gridding can be used to numerically approximate the posterior probability distribution of the model parameters to avoid complex random sampling processes. The prior probability distribution can be a normal distribution, log-normal distribution, or uniform distribution, which conforms to the physical meaning and support domain of the parameters and is used to describe the possible values ​​of the parameters before the sample data is introduced; the statistical characteristics include, but are not limited to, the posterior mean. Posterior variance or posterior standard deviation It is used to characterize the uncertainty and distribution of parameters.

[0058] In one embodiment, a typical posterior distribution of material parameters is shown as follows: Figure 4 As shown, for each material, based on the mesh search fit in step three... Obtain its residual sum of squares and residual standard deviation ,right Introducing a uniform prior distribution, we assume that the model residuals follow a normal distribution. to construct a joint posterior The likelihood function Ultimately marginalized. ,get The marginal posterior distribution is calculated, and the posterior mean is calculated accordingly. and posterior standard deviation .

[0059] Step 5: Based on the statistical consistency between the initial deterministic estimate and the statistical inference results, determine the final model parameter values ​​used for fatigue life prediction according to the preset consistency criterion. This is implemented as follows:

[0060] Based on the initial deterministic estimates of the model parameters obtained in step three Based on the statistical inference results obtained in step four, a criterion is established to measure the consistency between the two, thereby enabling engineering decisions regarding model parameter values. This consistency criterion determines whether the deterministic point estimate falls within a reasonable range supported by statistical inference by comparing the degree of deviation between the deterministic estimation results and the posterior statistical characteristics, thus determining the final model parameter values ​​used for fatigue life prediction. In one embodiment, the consistency criterion can be expressed as... ,in, This represents the initial deterministic estimate of the model parameters. This represents the posterior mean of the model parameters. This represents the posterior standard deviation of the model parameters. When the consistency criterion... When the initial deterministic estimate is less than or equal to a preset threshold, it is considered that there is no significant statistical inconsistency between the initial deterministic estimate and the statistical inference result, and the initial deterministic estimate can be selected as the final model parameter value. When the consistency criterion d is greater than the preset threshold, it is considered that there is a significant difference between the initial deterministic estimate and the statistical inference result, and the posterior mean or other statistics in the statistical inference result can be selected as a more robust model parameter value. The preset threshold can be set according to engineering experience, statistical significance level, or actual application needs. Through the above parameter selection mechanism, the robustness of model parameter estimation can be improved, and the impact of limited sample size or data noise on fatigue life prediction results can be reduced.

[0061] In one embodiment, a consistency criterion is defined. For each material, if the consistency criterion does not exceed a preset threshold, the point estimation is considered to have no significant statistical inconsistency. This is used as the final value; however, when the consistency criterion exceeds a preset threshold, it is considered that there is significant inconsistency in the point estimation, and the value is adopted. This serves as a more robust estimate, and the final value is determined accordingly.

[0062] This invention demonstrates the effectiveness of a Z-parameter model for predicting high-cycle and ultra-high-cycle fatigue life through an embodiment, verifying its potential for wider application in similar problems. In the example, high-fidelity finite element simulation analysis was used to obtain the fatigue life of various materials under different stress amplitudes, defect areas, and defect locations. Comparison with experimental data showed that the deviation between the finite element analysis results and actual values ​​was within an acceptable range. Therefore, simulation data can be used to replace physical fatigue tests to identify material parameters in the Z-parameter model. The value of is determined. In this embodiment, the initial deterministic estimate of the goodness of fit is maximized through grid search, and then the maximum a posteriori and mean a posteriori are obtained based on gridded Bayesian inference. Finally, whether the two are within a certain standard deviation is used as the evaluation criterion for statistical consistency, thereby determining . The value of is determined. This embodiment verifies the feasibility and effectiveness of the method of the present invention, demonstrating its advantages in avoiding a large number of fatigue tests, improving the reliability of parameter identification, and reducing engineering prediction costs.

[0063] Through the above steps, the method of the present invention can achieve stable identification of long-life fatigue model parameters while reducing reliance on physical fatigue tests, and quantitatively characterize the uncertainty of the parameters, thereby improving the reliability and engineering applicability of fatigue life prediction results.

[0064] By employing finite element simulation to replace numerous physical experiments, this invention provides sufficient data sources without sacrificing accuracy, obtaining sample data covering multiple defect characteristics and load conditions, significantly reducing parameter identification costs and timelines. The invention eliminates the tendency of traditional fitting to get trapped in local optima through a gridded global search method, making the parameter identification process more comprehensive and stable. Consistency evaluation assesses the deviation of deterministic point estimations, and when necessary, uses posterior means to replace point estimations, making parameter identification results more robust and avoiding identification biases caused by data noise, thereby improving the reliability of long-life fatigue models. This invention comprehensively evaluates deterministic estimation results and statistical inference results through consistency criteria, determining the final values ​​of model parameters accordingly. This solves the engineering application problem that statistical parameters are difficult to directly use for fatigue life prediction model calculations, significantly improving the stability and engineering applicability of fatigue life prediction results, and providing reliable assurance for long-life fatigue prediction of welded or additively manufactured structures.

[0065] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for determining parameters of a long-life fatigue model of a structure with defects, characterized in that: This includes step one: using finite element simulation to construct sample data containing key variables and response relationships; Step 2: Parameterize the long-life fatigue model and construct an objective function for parameter identification; Step 3: Based on the sample data, establish a global search grid within the preset parameter range, and search the objective function to obtain an initial deterministic estimate; In step three, a grid search is performed in the candidate parameter space, and the search results are evaluated based on the objective function to obtain the initial deterministic estimates of the model parameters. First, the candidate parameter space is traversed and calculated globally with a fixed step size, and the corresponding objective function value is calculated respectively. Then, the curve or surface between the candidate parameter and the objective function value is plotted. When the curve or surface is unimodal or multimodal, the candidate parameters corresponding to the peak values ​​of the unimodal or multimodal peaks are the initial deterministic estimates of the model parameters. If the curve or surface is monotonic, then the corresponding boundary of the candidate parameter space is considered to be the initial deterministic estimate. Step 4: Based on the global search grid, use Bayesian inference to establish the posterior probability distribution of the model parameters and obtain the statistical inference results of the model parameters; In step four, based on the initial deterministic estimates of the model parameters obtained in step three, a Bayesian inference method is introduced to obtain the posterior probability distribution of the target model parameters. Model parameters to be inferred Define the prior probability distribution and base it on the model parameters. With sample data The relationship between the prior probability distribution and the likelihood function is used to construct a likelihood function to characterize the probability of observed data occurring under given parameters. Based on the prior probability distribution and the likelihood function, the posterior probability distribution of the model parameters is obtained according to Bayes' theorem, and the statistical characteristics of the model parameters are further calculated as the result of statistical inference. A posterior calculation method based on parameter space gridding is employed to numerically approximate the posterior probability distribution of the model parameters. The prior probability distribution can be any one of a normal distribution, a log-normal distribution, or a uniform distribution, and the statistical features include the posterior mean. Posterior variance or posterior standard deviation , used to characterize the uncertainty and distribution pattern of parameters; For each material, based on the mesh search fit in step three Obtain its residual sum of squares and residual standard deviation ,right Introducing a uniform prior distribution, we assume that the model residuals follow a normal distribution. to construct a joint posterior The likelihood function Ultimately marginalized ,get The marginal posterior distribution is calculated, and the posterior mean is calculated accordingly. and posterior standard deviation ; Step 5: Based on the statistical consistency between the initial deterministic estimation and the statistical inference results, determine the final model parameter values ​​for fatigue life prediction according to the preset consistency criteria. In step five, the initial deterministic estimates of the model parameters obtained in step three are used. Based on the statistical inference results obtained in step four, establish a criterion to measure the consistency between the two, so as to determine the final model parameter values ​​used for fatigue life prediction. The consistency criterion is expressed as: ; in, This represents the initial deterministic estimate of the model parameters. This represents the posterior mean of the model parameters. Represents the posterior standard deviation of the model parameters; When the consistency criterion If the result is less than or equal to the preset threshold, it is considered that there is no significant statistical inconsistency between the initial deterministic estimation result and the statistical inference result. In this case, the initial deterministic estimation value is selected as the final model parameter value. When the consistency criterion d is greater than the preset threshold, it is considered that there is a significant difference between the initial deterministic estimation result and the statistical inference result. In this case, the posterior mean or other statistics in the statistical inference result are selected as more robust model parameter values.

2. The method for determining parameters of a long-life fatigue model of a defective structure according to claim 1, characterized in that: In step one, a corresponding finite element analysis model is established based on the geometric characteristics, material properties, and service conditions of the structure or material to be analyzed, combined with the key variables in the target long-life fatigue model.

3. The method for determining parameters of a long-life fatigue model of a defective structure according to claim 2, characterized in that: The finite element analysis model maps key variables in the model to a numerical simulation environment by setting loading conditions, material parameters, geometric features and boundary constraints, so as to construct a high-fidelity finite element model for simulating the target physical process. Based on the finite element model, by changing different key variables of the model and setting multiple sets of fatigue load levels or structural characteristic parameters, finite element fatigue simulation calculations are performed to obtain the response behavior of the structure or material under external forces.

4. The method for determining parameters of a long-life fatigue model of a defective structure according to claim 3, characterized in that: In step two, the sample data of the finite element simulation are obtained. Subsequently, the mathematical form of the long-life fatigue model is parameterized or structured to clarify the model parameters to be identified. .

5. The method for determining parameters of a long-life fatigue model of a defective structure according to claim 4, characterized in that: When the Z-parameter model is used as the long-life fatigue model for a structure with defects; The mathematical expression is ; in, Indicates the stress amplitude. Indicates the size of the defect feature. Indicates parameters related to the location of the defect. For model parameters related to material properties, and These are the fitting constants in the model. This refers to fatigue life.

6. The method for determining parameters of a long-life fatigue model of a defective structure according to claim 5, characterized in that: When model parameters When the target parameter is to be identified, the other parameters are determined by... The linear fit is then obtained. At this point, the logarithm of the mathematical expression of the Z-parameter model is taken to linearize the power-law relationship, resulting in... This enables parameterization of long-life fatigue models; Based on the above, the least squares method is then used to fit the relationship between the two sides. and Linear regression was performed to calculate the coefficient of determination. ; Therefore, the objective function is constructed. This serves as the basis for determining the parameters of the long-life fatigue model.

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