Turbine blade fatigue life prediction method based on adaptive gene expression programming

Abstract

This application provides a method for predicting the fatigue life of turbine blades based on adaptive gene expression programming. The method includes: establishing a finite element model of the turbine blade and determining key parameters affecting its fatigue life; extracting sample points, calculating fatigue life using the finite element model to form an initial dataset, which is then divided into a training set and a validation set; performing adaptive gene expression initialization programming, mutating and crossovering the population, and selecting and iterating based on fitness to obtain a surrogate model; evaluating the accuracy of the surrogate model; if the accuracy does not meet the requirements, adding the worst-performing points from the validation set to the training set for retraining until the accuracy meets the requirements; and using the obtained surrogate model to predict the expected value and standard deviation of the upper and lower bounds of the fatigue life. This method aims to handle complex, uncertain, coupled problems and improve the efficiency of fatigue life prediction while ensuring computational accuracy.

Description

Technical Field

[0001] This application relates to the field of aerospace computing, and in particular to a method for predicting the fatigue life of turbine blades based on adaptive gene expression programming. Background Technology

[0002] Turbine blades are core components of aero-engines and gas turbines. Under extreme conditions of high temperature, high pressure, and high speed, they endure complex thermodynamic cyclic loads over long periods, making them prone to fatigue cracks that propagate and lead to fracture failure, severely impacting system safety and reliability. Therefore, developing high-precision, high-efficiency life prediction methods is of significant engineering value for ensuring safe system operation and optimizing maintenance strategies.

[0003] In practical engineering applications, the fatigue life of turbine blades is often affected by multiple uncertainties, such as material property dispersion, load fluctuation, and geometric deviation. When using uncertainty models to describe fatigue life, probabilistic models rely on large amounts of data, limiting their applicability when experimental costs are high and data is scarce. Non-probabilistic models, such as interval models and ellipsoidal models, are suitable for small sample situations, with ellipsoidal models being able to handle the correlation between parameters. However, a single uncertainty model is insufficient to describe the characteristics of all uncertainty parameters, necessitating the development of quantitative methods that combine multiple uncertainty models.

[0004] Furthermore, traditional finite element method-based numerical calculations of fatigue life are costly and difficult to apply directly to the large-scale sample analysis required for fatigue life prediction. While traditional surrogate models can improve the computational efficiency of fatigue life, their fixed structure means that their generalization ability and expressive efficiency still face challenges when dealing with highly nonlinear, multi-parameter coupled fatigue life prediction problems. Summary of the Invention

[0005] This application provides a turbine blade fatigue life prediction method based on adaptive gene expression programming, which can handle complex uncertain coupling problems and improve the efficiency of fatigue life prediction while ensuring computational accuracy.

[0006] This application provides a method for predicting the fatigue life of turbine blades based on gene expression programming, including:

[0007] Step 1: Establish the finite element model of the turbine blade, determine the key parameters affecting the fatigue life, and use an interval model to describe the independent key parameters, an ellipsoidal model to describe the related key parameters, and a stochastic model to describe the probability distribution of the key parameters, forming a mixed uncertainty parameter set of interval-ellipsoidal-stochastic.

[0008] Step 2: Extract multiple sample points from the mixed uncertainty parameter set using the Latin hypercube sampling method, and calculate the fatigue life value corresponding to each sample point using the finite element model. The sample points, their corresponding key parameter values, and the fatigue life calculation values ​​form an initial dataset. The dataset is then divided into a training set and a validation set according to a certain ratio.

[0009] Step 3: Perform adaptive gene expression initialization programming on the training set, perform mutation and crossover genetic operations on the parent population to achieve population evolution, generate offspring population, and select the best individuals in the offspring population based on their fitness to obtain a new parent population. Repeat this step until the termination condition is met to obtain the surrogate model.

[0010] Step 4: Use the validation set to evaluate the accuracy of the surrogate model. If the accuracy of the surrogate model is greater than the error threshold, add the sample point with the worst accuracy in the validation set, the corresponding key parameter value, and the fatigue life calculation value to the training set in Step 2 and retrain the surrogate model until the accuracy of the surrogate model is less than or equal to the error threshold.

[0011] Step 5: Perform Monte Carlo sampling on the key parameters described by the stochastic model to obtain multiple new sample points. Based on the final surrogate model, calculate the predicted values ​​of the upper and lower bounds of the fatigue life for each new sample point, and finally predict the uncertainty response of the fatigue life under the mixed uncertainty parameter set.

[0012] In some possible implementations, the interval model describes the independent key parameters through upper and lower bounds of the interval, the ellipsoidal model describes the related key parameters through a shape matrix, and the stochastic model describes the key parameters of the probability distribution through a probability distribution function.

[0013] In some possible implementations, in step three, individual performance is dynamically evaluated through fitness, and the crossover probability is then dynamically adjusted. ;

[0014] The population size is dynamically adjusted based on the degree of stagnation of the optimal fitness within the population. In this process, randomly generated individuals are added to the population for genetic operations, and the crossover probability is... and the population size The adjustment formulas are expressed as follows:

[0015] ;

[0016] ;

[0017] in, and They represent The maximum and minimum values, It is the lower fitness among the individuals participating in the crossover. This indicates the initial population size. This indicates the increase in population size each time the population size is adjusted. This represents the total number of iterations that stagnate to achieve the optimal fitness within the population. For a given positive integer, This is the floor function.

[0018] In some possible implementations, step five, which involves calculating the predicted upper and lower bounds of the fatigue life for each of the new sample points, includes:

[0019] The final proxy model is compiled into executable code, an explicit functional expression between the key parameters and the fatigue life is established, and the predicted fatigue life value is calculated for any given combination of the key parameters.

[0020] The turbine blade fatigue life prediction method based on adaptive gene expression programming provided in this invention has at least the following advantages:

[0021] (1) The fatigue life prediction method in the embodiments of the present invention fully considers the data dispersion caused by multi-source uncertainty in actual engineering, and has more important guiding significance for the fatigue life prediction of turbine blades.

[0022] (2) The fatigue life prediction method in this embodiment of the invention breaks through the limitations of the traditional single uncertainty model and adopts an interval-ellipsoid-stochastic hybrid model to describe the mixed uncertainty parameter set. For the different characteristics of multi-source uncertainties in turbine blade life prediction, key parameters of different characteristics are described by different uncertainty models. This hybrid modeling approach is more in line with engineering practice, can more comprehensively describe the uncertainty factors in complex service environments, and improves the reliability of the prediction results.

[0023] (3) The fatigue life prediction method in this embodiment of the invention adopts adaptive gene expression programming. By dynamically adjusting the genetic operator parameters, the low-fitness offspring population is given priority to participate in genetic operations, and the high-fitness offspring are given priority to be retained, thus automatically mining the nonlinear relationship between key parameters and fatigue life. This method combines the expressive power of symbolic regression with the efficiency of adaptive optimization, breaking through the structural pre-set limitations of traditional surrogate models. When dealing with thermodynamic coupling problems with multiple uncertain parameters, it has better fitting accuracy and generalization ability. Attached Figure Description

[0024] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0025] Figure 1 This is a flowchart of the turbine blade fatigue life prediction method based on adaptive gene expression programming in an embodiment of the present invention.

[0026] Figure 2 This is a simplified flowchart of the turbine blade fatigue life prediction method based on adaptive gene expression programming in an embodiment of the present invention.

[0027] Figure 3 This is a schematic diagram of the geometric model of the turbine blade in an embodiment of the present invention.

[0028] Explanation of reference numerals in the attached figures:

[0029] 1-Edge plate;

[0030] 2-Leaf body.

[0031] The accompanying drawings illustrate specific embodiments of this application, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the concept in any way, but rather to illustrate the concepts of this application to those skilled in the art through reference to particular embodiments. Detailed Implementation

[0032] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0033] The technical solution of this application and how the technical solution of this application solves the above-mentioned technical problems are described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of this application will be described below with reference to the accompanying drawings.

[0034] refer to Figure 1 and Figure 2 This invention provides a method for predicting the fatigue life of turbine blades based on adaptive gene expression programming, comprising the following steps:

[0035] Step 1: Establish a finite element model of the turbine blade, determine the key parameters affecting fatigue life, and use an interval model to describe independent key parameters, an ellipsoidal model to describe related key parameters, and a stochastic model to describe key parameters of probability distribution, forming a mixed uncertainty parameter set of interval-ellipsoidal-stochastic.

[0036] In this embodiment of the invention, to establish a finite element model of a turbine blade, it is necessary to establish a geometric model of the turbine blade structure, discretize the geometric model using a finite element mesh, and set loads and boundary conditions to obtain the finite element model of the turbine blade.

[0037] Key parameters affecting the fatigue life of turbine blades were identified and screened, and the following parameters were selected. Each independent key parameter And described using an interval model; filtered out Key parameters And described using an ellipsoidal model; selected Key parameters of a probability distribution And described using a stochastic model, forming a set of interval-ellipsoid-stochastic mixed uncertainty parameters, denoted as The key parameter vector is expressed as follows:

[0038] ;

[0039] For the key parameters of turbine blade fatigue life selected above, their domains of discourse are determined and expressed as follows:

[0040] ;

[0041] ;

[0042] ;

[0043] in, For the first The universe of discourse for a key parameter described using an interval model. and These are the lower and upper bounds of the interval model, respectively; The universe of discourse for the key parameters described using the ellipsoidal model. , and These are the nominal value vector, weight matrix, and confidence level parameters of the ellipsoidal model, respectively. For the first The universe of discourse for a key parameter described by a stochastic model. Let be the cumulative distribution function of this stochastic model. Let the universe of discourse for all key parameters be denoted as . The expression is as follows:

[0044] ;

[0045] in, For Cartesian product operations, The universe of discourse for all key parameters described by the interval model. Let be the universe of discourse for all key parameters described by stochastic models.

[0046] In one possible implementation, the turbine blade material is GH4169, and the geometric model is as follows: Figure 3 As shown in the figure. In this geometric model, the turbine blade includes a blade body 1 and a rim plate 2. The height of the blade body 1 is 75 mm, and the width of the rim plate 2 is 20 mm. In the global coordinate system, the blade root section is located at... On the plane.

[0047] The geometric model was discretized using a finite element mesh. Specifically, eight-node thermally coupled hexahedral elements were used to mesh the geometric model, resulting in a total of 2979 elements. A fully fixed constraint was applied to the bottom of the geometric model, and surface heat flow was applied to the free boundaries of the side surfaces. At the same time, a rotational speed is applied to the entire geometric model. In the global coordinate system, the blade rotation axis is located at... On the plane of mm, along Arranged along the axial direction.

[0048] Key parameters affecting the fatigue life of turbine blades were identified and screened to obtain the elastic modulus of the turbine blades. A single key parameter described using an interval model; fatigue strength index of turbine blades. Fatigue strength coefficient of turbine blades Two key parameters are related and described using an ellipsoidal model; turbine blade rotation speed. Heat flow on turbine blade surface The key parameters of the two probability distributions are described using a stochastic model. These key parameters form a five-dimensional key parameter vector. The uncertainty models and their characteristics for each key parameter are shown in Table 1.

[0049] Table 1 Uncertainty Models and Characteristics of Key Parameters

[0050] Key parameters Uncertainty Model feature elastic modulus interval [148,162] fatigue strength coefficient Fatigue Strength Index ellipsoid Rotation speed random =2000， =80 Surface heat flow random =2500， =375

[0051] Step 2: Extract multiple sample points from the mixed uncertainty parameter set using the Latin hypercube sampling method. Calculate the corresponding fatigue life value for each sample point using the finite element model. The sample points, their corresponding key parameter values, and the fatigue life calculation values ​​form the initial dataset. Divide the dataset into a training set and a validation set according to a certain ratio.

[0052] In this embodiment of the invention, calculating the fatigue life value corresponding to each sample point using the finite element model means: performing thermo-mechanical coupling simulation using the finite element model to obtain the stress field corresponding to each sample point, then obtaining the fatigue life field through the Basquin equation, and selecting the minimum value in the fatigue life field as the calculated fatigue life value corresponding to that sample point. The Basquin equation is expressed as:

[0053] ;

[0054] in, For fatigue life, For stress amplitude, The fatigue strength coefficient, This is the fatigue strength index.

[0055] The number of sample points drawn within the mixed uncertainty parameter set is Latin hypercube sampling was used to sample all key parameters in the universe of discourse. Stratified sampling is performed within the system, and the extracted values ​​of all key parameters are randomly paired to form... Key parameter vectors As sample points, a sampling matrix is ​​formed. , and what was obtained The corresponding fatigue life calculation values ​​form the output vector. This forms the initial dataset. Set the proportion of the training set to the total dataset as follows: Randomly select from the dataset The training set is formed from 10 sample points. The remaining sample points form the validation set. .

[0056] In one possible implementation, 255 sample points are extracted from the mixed uncertainty parameter set using the Latin hypercube sampling method. The fatigue life of each sample point is calculated using a thermo-mechanical coupling simulation based on the finite element model from step one. The sample points, their corresponding key parameter values, and the calculated fatigue life form the initial dataset. Data for some sample points in the initial dataset are shown in Table 2.

[0057] Table 2 shows the sample point data in the initial dataset.

[0058] Serial Number Rotation speed Surface heat flow elastic modulus fatigue strength coefficient Fatigue Strength Index Fatigue life 1 1932.03 2588.94 161.77 1502.49 -0.1209 11545 2 1980.17 2685.94 150.46 1469.58 -0.1140 23418 3 2036.34 2394.55 151.05 1598.29 -0.1329 19559 4 1980.96 2704.22 159.80 1520.50 -0.1321 5354 … … … … … … … 255 2018.32 2654.50 161.60 1547.16 -0.1377 4376

[0059] The training set was set to a ratio of 250 / 255 to the dataset. 250 sample points were randomly selected from the dataset to form the training set, and the remaining 5 sample points formed the validation set. The data for the sample points in the validation set are shown in Table 3.

[0060] Table 3. Sample point data in the validation set.

[0061] Serial Number Rotation speed Surface heat flow elastic modulus fatigue strength coefficient Fatigue Strength Index Fatigue life 1 2065.44 2441.48 160.51 1631.27 -0.1301 16575 2 1953.22 2601.03 151.93 1260.78 -0.1124 13677 3 2038.77 2322.32 159.70 1322.64 -0.1202 15721 4 2046.25 2833.50 157.65 1255.01 -0.1213 4869 5 1927.48 2535.26 153.07 1522.41 -0.1184 24665

[0062] Step 3: Perform adaptive gene expression initialization programming on the training set, perform mutation and crossover genetic operations on the parent population to achieve population evolution, generate offspring population, and select the best individuals in the offspring population based on their fitness to obtain a new parent population. Repeat this step until the termination condition is met to obtain the surrogate model.

[0063] In this embodiment of the invention, adaptive gene expression initialization programming refers to: based on a set gene head length... Gene tail length function set and parameter set Individuals are randomly generated, represented by linear symbol strings consisting of function symbols and parameter symbols, and are determined according to the set initial population size. Select a corresponding number of individuals to form the initial parent population.

[0064] Fitness refers to the degree to which the surrogate model obtained by decoding the symbol string of an individual conforms to the training set. Fitness is a function of the root mean square error (RMSE). and fitness They are expressed as follows:

[0065] ;

[0066] ;

[0067] in, For calculated values, Indicates the predicted value. This indicates the number of sample points in the training set.

[0068] Mutation refers to the probability of mutation for each individual within the parent population. Mutation occurs. Specifically, a symbol within the corresponding symbol string of an individual is randomly selected and transformed into another random symbol. If the fitness of the newly generated individual is lower than that of the original individual, the original individual is retained and enters the offspring population; if the fitness of the newly generated individual is higher than that of the original individual, the original individual is replaced and enters the offspring population.

[0069] Crossover means that there is a crossover probability for any two individuals in the parent population. Crossover occurs. Specifically, a symbol from the symbol string of one individual is randomly selected to replace a symbol at the same position in the symbol string of another individual. If the fitness of the newly generated individual is lower than that of the replaced individual, the original individual is retained and added to the offspring population; if the fitness of the newly generated individual is higher than that of the replaced individual, the original individual is replaced and added to the offspring population.

[0070] The adaptive method in adaptive gene expression programming includes: dynamically evaluating individual performance based on fitness, and then dynamically adjusting the crossover probability; dynamically adjusting the population size based on the stagnation level of the optimal fitness within the population, specifically by randomly generating individuals and adding them to the population for genetic operations. Crossover probability and population size The adjustment formulas are expressed as follows:

[0071] ;

[0072] ;

[0073] in, and They represent The maximum and minimum values, It is the lower fitness among the individuals participating in the crossover. This indicates the increase in population size each time the population size is adjusted. This indicates the increase in population size each time the population size is adjusted. This represents the total number of iterations that stagnate to achieve the optimal fitness within the population. For a given positive integer, This is the floor function.

[0074] In one possible implementation, the maximum number of generations is 20,000, and the initial population size is [missing information]. The function set is The parameter set is The gene head length is The length of the gene tail is The mutation probability is The maximum crossover probability is The minimum crossover probability is The amount by which the population size increases each time the population size is adjusted. , The selection strategy for individuals to be selected as the next generation population based on fitness is set as a roulette wheel strategy. The termination condition is that the number of iterations reaches the maximum number of generations. The symbol string corresponding to the individual with the highest fitness is decoded to obtain the corresponding fatigue life function expression as the final surrogate model.

[0075] Based on the obtained surrogate model's corresponding fatigue life function expression, the key parameter values ​​for each sample point in the validation set are input, and the predicted fatigue life value for each sample point is calculated. The final comparison between the calculated and predicted fatigue life values ​​in the validation set is shown in Table 4.

[0076] Table 4 Comparison of validation set data

[0077] Serial Number Fatigue life calculation value Fatigue life prediction value relative error 1 16575 14408.64 13.07% 2 13677 19028.18 39.13% 3 15721 20007.64 27.27% 4 4869 6715.76 43.78% 5 24665 19287.71 21.80%

[0078] Step 4: Evaluate the accuracy of the surrogate model using the validation set. If the accuracy of the surrogate model is greater than the error threshold, add the worst-performing sample points in the validation set, along with the corresponding key parameter values ​​and fatigue life calculation values, to the training set in Step 2 and retrain the surrogate model until the accuracy of the surrogate model is less than or equal to the error threshold.

[0079] In this embodiment of the invention, the error threshold for the predicted average relative error is defined as follows: If the average relative error of the validation set If the surrogate model is retained and step five is executed; if the average relative error of the validation set is... Based on the calculation results, the validation point with the largest relative error in the fatigue life prediction value is identified as the validation point with the worst accuracy and added to the training set in step two to form a new expanded training set. Steps three and four are then re-executed using the new expanded training set, and the accuracy of the retrained surrogate model is evaluated on the new validation set until... Mean relative error The expression is as follows:

[0080] ;

[0081] in, The number of validation set sample points, , The first The calculated and predicted fatigue life values ​​for each sample point.

[0082] In one possible implementation, the error threshold for the relative prediction error is set as follows: The average relative error of the fatigue life prediction values ​​in the above validation set If the error exceeds the threshold, iteration is required. After five iterations, the corresponding fatigue life function expression of the surrogate model obtained by programming the final adaptive gene expression is shown in Table 5. The comparison between the calculated and predicted fatigue life values ​​in the validation set after the final iteration is also presented.

[0083] The average relative error of the fatigue life prediction values ​​ultimately calculated from the validation set in this example. If the error is less than the error threshold, the iteration ends and the function expression of the fatigue life of the surrogate model obtained by the final adaptive gene expression programming is recorded.

[0084] Step 5: Perform Monte Carlo sampling on the key parameters described by the stochastic model to obtain multiple new sample points. Based on the final surrogate model, calculate the predicted values ​​of the upper and lower bounds of the fatigue life for each new sample point, and finally predict the uncertainty response of fatigue life under the mixed uncertainty parameter set.

[0085] In this embodiment of the invention, Monte Carlo sampling refers to setting the number of new sample points to be... In the interval Generate the same number of uniformly distributed random numbers, and then convert them into the desired sampling values ​​using an inverse transformation. For random variables that follow a normal distribution, the inverse transformation method is the Box-Muller transform, expressed as:

[0086] ;

[0087] in, For the target sample value, The mean, Standard deviation, and All are intervals Independent uniformly distributed random numbers generated within the system.

[0088] Calculating the predicted upper and lower bounds of fatigue life for each new sample point refers to: (The text abruptly ends here, likely due to an incomplete sentence or missing information.) After each new sample point, at each new sample point Below, the Latin hypercube sampling method is used to extract key parameters within the universe of discourse described by interval and ellipsoidal models. sample points Substituting these values ​​into the proxy model yields each sample point. The maximum and minimum values ​​of the corresponding fatigue life prediction results are used as the upper bounds of the fatigue life at the new sample point. and the lower realm .

[0089] Predicting the uncertainty response of fatigue life under a mixed uncertainty parameter set refers to predicting the expected value and standard deviation of the upper and lower bounds of fatigue life. Specifically, this involves calculating the mean and standard deviation of the upper bound of fatigue life for all new sample points as the expected value and standard deviation of the upper bound of fatigue life under the mixed uncertainty parameter set, and calculating the mean and standard deviation of the lower bound of fatigue life for all new sample points as the expected value and standard deviation of the lower bound of fatigue life under the mixed uncertainty parameter set. and standard deviation They are expressed as follows:

[0090] ;

[0091] ;

[0092] In one possible embodiment, 100 new samples are generated using Monte Carlo sampling based on the features of the key parameters described by the stochastic model in Table 1. The corresponding fatigue life function expression of the surrogate model, obtained by adaptive gene expression programming, is solved using feature sampling based on the key parameters described by the interval model and ellipsoidal model, yielding the upper and lower bounds of the fatigue life at each new sample point. The results, after processing, show the upper and lower bounds of the fatigue life at some of the new sample points in Table 6.

[0093] Table 5 Comparison of validation set data after final iteration

[0094] Serial Number Fatigue life calculation value Fatigue life prediction value relative error 1 16575 1732.85 6.38% 2 13677 13955.42 2.04% 3 15721 15693.79 0.17% 4 4869 4670.88 4.07% 5 24665 25438.36 3.14%

[0095] Ultimately, under the combined influence of all key parameters within the current interval-ellipsoid-random mixed uncertainty parameter set, the expected upper bound of the fatigue life of the turbine blade structure is approximately 12,566 cycles with a standard deviation of approximately 6,386 cycles; the expected lower bound is approximately 7,669 cycles with a standard deviation of approximately 4,803 cycles.

[0096] In summary, the turbine blade fatigue life prediction method based on adaptive gene expression programming provided in this application forms a fusion interval-ellipsoid-random mixed uncertainty parameter set, establishes a surrogate model using the adaptive gene expression programming algorithm, and combines Monte Carlo sampling method to predict the expectation and standard deviation of the upper and lower bounds of fatigue life. This achieves the effect of effectively handling complex uncertainty coupling problems and significantly improving the efficiency of turbine blade fatigue life prediction while ensuring the accuracy of engineering calculations.

[0097] Finally, it should be noted that other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This invention is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein, and is not limited to the precise structures described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of the invention is limited only by the appended claims.

Claims

1. A method for predicting the fatigue life of turbine blades based on adaptive gene expression programming, characterized in that, include: Step 1: Establish the finite element model of the turbine blade, determine the key parameters affecting the fatigue life, and use an interval model to describe the independent key parameters, an ellipsoidal model to describe the related key parameters, and a stochastic model to describe the probability distribution of the key parameters, forming a mixed uncertainty parameter set of interval-ellipsoidal-stochastic. Step 2: Extract multiple sample points from the mixed uncertainty parameter set using the Latin hypercube sampling method, and calculate the fatigue life value corresponding to each sample point using the finite element model. The sample points, their corresponding key parameter values, and the fatigue life calculation values ​​form an initial dataset. The dataset is then divided into a training set and a validation set according to a certain ratio. Step 3: Perform adaptive gene expression initialization programming on the training set, perform mutation and crossover genetic operations on the parent population to achieve population evolution, generate offspring population, and select the best individuals in the offspring population based on their fitness to obtain a new parent population. Repeat this step until the termination condition is met to obtain the surrogate model. Step 4: Use the validation set to evaluate the accuracy of the surrogate model. If the accuracy of the surrogate model is greater than the error threshold, add the sample point with the worst accuracy in the validation set, the corresponding key parameter value, and the fatigue life calculation value to the training set in Step 2 and retrain the surrogate model until the accuracy of the surrogate model is less than or equal to the error threshold. Step 5: Perform Monte Carlo sampling on the key parameters described by the stochastic model to obtain multiple new sample points. Based on the final surrogate model, calculate the predicted values ​​of the upper and lower bounds of the fatigue life for each new sample point, and finally predict the uncertainty response of the fatigue life under the mixed uncertainty parameter set.

2. The method according to claim 1, characterized in that, The interval model describes the independent key parameters through upper and lower bounds of the interval, the ellipsoidal model describes the related key parameters through a shape matrix, and the stochastic model describes the key parameters of the probability distribution through a probability distribution function.

3. The method according to claim 1, characterized in that, In step three, individual performance is dynamically evaluated through fitness, and the crossover probability is then dynamically adjusted. ; The population size is dynamically adjusted based on the degree of stagnation of the optimal fitness within the population. In this process, randomly generated individuals are added to the population for genetic operations, and the crossover probability is... and the population size The adjustment formulas are expressed as follows: ； ； in, and They represent The maximum and minimum values, It is the lower fitness among the individuals participating in the crossover. This indicates the initial population size. This indicates the increase in population size each time the population size is adjusted. This represents the total number of iterations that stagnate to achieve the optimal fitness within the population. For a given positive integer, This is the floor function.

4. The method according to claim 1, characterized in that, Step five, which involves calculating the predicted upper and lower bounds of the fatigue life for each new sample point, includes: The final proxy model is compiled into executable code, an explicit functional expression between the key parameters and the fatigue life is established, and the predicted fatigue life value is calculated for any given combination of the key parameters.

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