1. A method for analyzing the creep-fatigue composite probability life of a blade based on heteroscedastic regression is characterized by comprising the following steps:

acquiring fatigue test data of a target turbine blade material, and determining the low-cycle fatigue probability life according to the test data, wherein the determination of the low-cycle fatigue probability life comprises determining preset parameters in a probability life equation and correcting the probability life equation under a standard strain ratio to the probability life equation under an arbitrary strain ratio;

determining the creep probability life according to the test data, wherein independent variables in a creep life equation comprise temperature and load-holding stress, and a creep probability life model is obtained through binary variance regression analysis;

establishing a finite element analysis model of the turbine blade, wherein the finite element analysis model comprises establishing a geometric model, setting material properties, applying boundary conditions and external loads and extracting a finite element analysis result;

extracting random samples of the probability life auxiliary variable, and obtaining random samples of the low-cycle fatigue life and random samples of the creep life through the analysis of a life equation by combining with a finite element output result; obtaining a random sample of creep-fatigue composite life through a linear accumulated damage theory;

determining a probability density function of the creep-fatigue composite life according to a nuclear density method;

and obtaining the composite life confidence interval corresponding to the given confidence level under different survival probabilities by a self-service sampling method.

2. The analysis method according to claim 1, wherein the obtaining of fatigue test data of the target turbine blade material, and the determining of the low cycle fatigue probability life according to the test data comprises determining preset parameters in a probability life equation and performing a modification of the probability life equation at a standard strain ratio to the probability life equation at an arbitrary strain ratio, and comprises:

acquiring fatigue life data of the material under a strain cycle ratio;

establishing a probability-strain-life model of the fatigue life according to the fatigue life data;

and (4) determining a corrected fatigue life probability model by correcting the average stress and replacing the fatigue life standard deviation of the asymmetric cycle with the fatigue life standard deviation of the symmetric cycle.

3. The analytical method of claim 2, wherein the probability-strain-lifetime model is:

wherein, Delta epsilon_tAs total strain amplitude, Δ ε_eAmplitude of elastic strain, Δ ε_pFor plastic strain amplitude, u is a standard normal random variable, E is Young's modulus, u is an auxiliary variable and follows a standard normal distribution, N_fIn order to determine the number of fatigue cycles,are the mean values, σ, of the four parameters, respectively_e0、σ_p0Respectively representing logarithmic lifetimes y_e、y_pIn logarithmic strain component x_e0、x_p0Standard deviation of (a), theta_e、θ_pRespectively represent sigma_e、σ_pThe slope of the linear change.

4. The analysis method according to claim 2, wherein the modified fatigue life probability model is:

wherein, Delta epsilon_tTo total strain amplitude, σ_mIs the mean stress.

5. The analysis method according to claim 1, wherein the random samples of the probability life auxiliary variables are extracted, and the random samples of the low cycle fatigue life and the random samples of the creep life are obtained through the analysis of a life equation by combining the finite element output results; obtaining a random sample of creep-fatigue composite life by a linear accumulated damage theory, comprising:

obtaining the creep life of the material at different temperatures and under different holding stresses;

and obtaining a probability creep life equation by using binary variance regression analysis.

6. The analytical method of claim 5, wherein the probabilistic creep life equation is:

lg N_c＝b₀+b₁T+b₂lg S+b₃(lg S)²+b₄(lg S)³+σ₀|1+θ_T(T-x_T0)+θ_S(S-x_S0)|μ

wherein N is_cDenotes creep life, T is temperature, S is holding stress, b_i(i ═ 0, 1.., 4) is the model parameter, σ₀Logarithmic life lg N_cAt a temperature component x_T0And a holding stress component x_S0Standard deviation of (a), theta_T、θ_SThe slope of the log life standard deviation with temperature and holding stress, u is an auxiliary variable and follows a standard normal distribution.

7. The analytical method of claim 6, wherein the random error term is related to temperature and stress by:

σ(S,T)＝σ₀|1+θ_T(T-T₀)+θ_S(S-S₀)|

wherein T is₀Is a standard temperature, S₀The standard holding stress.

8. The analytical method of claim 6, wherein the creep probability lifetime heterovariance regression analysis model is:

Y＝2.2252×10⁴-2.8117×10⁴X+1.1845×10⁴X²-1.6637×10³X³+ε

ε～(0，0.0132×(1-0.1295×(X-2.3754))

wherein Y represents a logarithmic lifetime and X represents a logarithmic holding stress.

9. The analytical method of claim 5, wherein the creep-fatigue composite life samples are:

wherein N is_C-FTo compound life, N₁Fatigue life of the main cycle, N₂Fatigue life for the sub-cycle, N₃Creep life is considered.

10. The analysis method of claim 1, wherein the probability density function is:

where K (u) is the kernel function, n is the number of kernel functions, h_i>0 is window width, α_iIs the weight of each kernel function, and 0<α_i<1，

Background

Aircraft engines and gas turbines are sources of aircraft and marine power, turbine components are the core, and the life of turbine components largely determines the life of the engine. The turbine component has a complex structure and a severe working environment, is subjected to complex working conditions such as high temperature, high pressure, centrifugal load and vibration load, and is very easy to lose effectiveness such as creep deformation and fatigue.

Therefore, providing a complete set of creep-fatigue life estimation methods is of great importance for analyzing and improving the life performance of turbine components.

It is to be noted that the information disclosed in the above background section is only for enhancement of understanding of the background of the present invention and therefore may include information that does not constitute prior art known to a person of ordinary skill in the art.

Disclosure of Invention

The invention aims to provide a blade creep-fatigue composite probability life analysis method based on heteroscedastic regression, which can obtain 95% confidence intervals of life estimation values of turbine blades under different survival probabilities.

According to an aspect of the embodiment of the invention, a method for analyzing the creep-fatigue composite probability life of a blade based on heteroscedastic regression is provided, and the method comprises the following steps:

acquiring fatigue test data of a target turbine blade material, and determining the low-cycle fatigue probability life according to the test data, wherein the determination of the low-cycle fatigue probability life comprises determining preset parameters in a probability life equation and correcting the probability life equation under a standard strain ratio to the probability life equation under an arbitrary strain ratio;

determining the creep probability life according to the test data, wherein independent variables in a creep life equation comprise temperature and load-holding stress, and a creep probability life model is obtained through binary variance regression analysis;

establishing a finite element analysis model of the turbine blade, wherein the finite element analysis model comprises establishing a geometric model, setting material properties, applying boundary conditions and external loads and extracting a finite element analysis result;

extracting random samples of the probability life auxiliary variable, and obtaining random samples of the low-cycle fatigue life and random samples of the creep life through the analysis of a life equation by combining with a finite element output result; obtaining a random sample of creep-fatigue composite life through a linear accumulated damage theory;

determining a probability density function of creep-fatigue composite life according to the nuclear density;

and obtaining the composite life confidence interval corresponding to the given confidence level under different survival probabilities by a self-service sampling method.

In an exemplary embodiment of the disclosure, the obtaining fatigue test data of a target turbine blade material, and determining a low-cycle fatigue probability life according to the test data, where the determining of the low-cycle fatigue probability life includes determining preset parameters in a probability life equation and performing a modification of the probability life equation under a standard strain ratio to the probability life equation under an arbitrary strain ratio, includes:

acquiring fatigue life data of the material under a strain cycle ratio;

establishing a probability-strain-life model of the fatigue life according to the fatigue life data;

and (4) determining a corrected fatigue life probability model by correcting the average stress and replacing the fatigue life standard deviation of the asymmetric cycle with the fatigue life standard deviation of the symmetric cycle.

In an exemplary embodiment of the present disclosure, the probability-strain-life model is:

wherein, Delta epsilon_tAs total strain amplitude, Δ ε_eAmplitude of elastic strain, Δ ε_pFor plastic strain amplitude, u is a standard normal random variable, E is Young's modulus, u is an auxiliary variable and follows a standard normal distribution, N_fIn order to determine the number of fatigue cycles,are the mean values, σ, of the four parameters, respectively_e0、σ_p0Respectively representing logarithmic lifetimes y_e、y_pIn logarithmic strain component x_e0、x_p0Standard deviation of (a), theta_e、θ_pRespectively represent sigma_e、σ_pThe slope of the linear change.

In an exemplary embodiment of the present disclosure, the modified fatigue life probability model is:

wherein, Delta epsilon_tTo total strain amplitude, σ_mIs the mean stress.

In an exemplary embodiment of the disclosure, the random samples of the probabilistic life auxiliary variables are extracted, and the random samples of the low cycle fatigue life and the random samples of the creep life are obtained through the analysis of a life equation by combining with the finite element output results; obtaining a random sample of creep-fatigue composite life by a linear accumulated damage theory, comprising:

obtaining the creep life of the material at different temperatures and under different holding stresses;

and obtaining a probability creep life equation by using binary variance regression analysis.

In an exemplary embodiment of the present disclosure, the probabilistic creep life equation is:

lg N_c＝b₀+b₁T+b₂ lg S+b₃(lg S)²+b₄(lg S)³+σ₀|1+θ_T(T-x_T0)+θ_s(S-x_s0)|μ

wherein N is_cDenotes creep life, T is temperature, S is holding stress, b_i(i ═ 0, 1.., 4) is the model parameter, σ₀Logarithmic life lg N_cAt a temperature component x_T0And a holding stress component x_S0Standard deviation of (a), theta_T、θ_SThe slope of the log life standard deviation with temperature and holding stress, u is an auxiliary variable and follows a standard normal distribution.

In one exemplary embodiment of the present disclosure, the random error term is related to temperature and stress by:

σ(S，T)＝σ₀|1+θ_T(T-T₀)+θ_S(S-S₀)|

wherein T is₀Is a standard temperature, S₀The standard holding stress.

In an exemplary embodiment of the present disclosure, the creep probability lifetime heteroscedastic regression analysis model is:

Y＝2.2252×10⁴-2.8117×10⁴X+1.1845×10⁴X²-1.6637×10³X³+εE～(0，0.0132×(1-0.1295×(X-2.3754))

wherein Y represents a logarithmic lifetime and X represents a logarithmic holding stress.

In an exemplary embodiment of the present disclosure, the creep-fatigue composite life sample is:

wherein N is_C-FTo compound life, N₁Fatigue life of the main cycle, N₂Fatigue life for the sub-cycle, N₃Creep life is considered.

In an exemplary embodiment of the present disclosure, the probability density function is:

where K (u) is the kernel function, n is the number of kernel functions, h_iGreater than 0 is window width, alpha_iIs the weight of each kernel function, and 0 < alpha_i＜1，

According to the method for analyzing the creep-fatigue composite probability life of the blade based on the different variance regression, firstly, fatigue life test data of the blade material DZ125 at 800 ℃ can be obtained through tests, and a probability life equation of the DZ125 material at 800 ℃ is obtained through a univariate different variance regression analysis; creep life test data of the turbine blade material DZ125 under three different temperature and load-holding stresses are obtained through tests, a binary variance regression analysis model is deduced and established, and a creep probability life model of the creep life variance along with the change of creep temperature and load-holding stress is established. Secondly, extracting fatigue life dispersity characterization auxiliary variables and creep life dispersity characterization auxiliary variable samples, obtaining corresponding fatigue life and creep life samples through probability life model analysis, and obtaining creep-fatigue life samples through a linear damage accumulation theory. And finally, obtaining creep-fatigue composite life probability distribution through nuclear density estimation based on a creep-fatigue life sample, and obtaining a 95% confidence interval of the life estimation value of the turbine blade under different survival probabilities through resampling and repeated analysis of the test data by a Bootstrap (self-help sampling method).

It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention, as claimed.

Drawings

The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and together with the description, serve to explain the principles of the invention. It is obvious that the drawings in the following description are only some embodiments of the invention, and that for a person skilled in the art, other drawings can be derived from them without inventive effort. In the drawings:

FIG. 1 is a flow chart of a method for analyzing a creep-fatigue composite probability life of a blade based on heteroscedastic regression according to an embodiment of the disclosure;

FIG. 2 provides a P- ε -N curve of DZ125 at 800 ℃ for one embodiment of the present disclosure;

FIG. 3 is a graph illustrating creep life at various survival rates at 980 ℃ according to an embodiment of the present disclosure;

FIG. 4 is a flow chart of a creep-fatigue probability life analysis for a turbine blade provided in accordance with an embodiment of the present disclosure;

FIG. 5 is a geometric model of a turbine blade provided by an embodiment of the present disclosure;

FIG. 6 illustrates turbine blade finite element analysis results provided by an embodiment of the present disclosure;

FIG. 7 is a probability density function plot of turbine blade creep-fatigue composite life provided by one embodiment of the present disclosure.

Detailed Description

Example embodiments will now be described more fully with reference to the accompanying drawings. Example embodiments may, however, be embodied in many different forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the concept of example embodiments to those skilled in the art.

The flow charts shown in the drawings are merely illustrative and do not necessarily include all of the contents and operations/steps, nor do they necessarily have to be performed in the order described. For example, some operations/steps may be decomposed, and some operations/steps may be combined or partially combined, so that the actual execution sequence may be changed according to the actual situation.

Embodiments of the present disclosure provide a method for analyzing a creep-fatigue composite probability life of a blade based on heteroscedastic regression, as shown in fig. 1 and 4, the method including:

s100, obtaining fatigue test data of a target turbine blade material, and determining the low-cycle fatigue probability life according to the test data, wherein the determination of the low-cycle fatigue probability life comprises the steps of determining preset parameters in a probability life equation and correcting the probability life equation under a standard strain ratio to the probability life equation under an arbitrary strain ratio;

s200, determining the creep probability life according to the test data, wherein independent variables in a creep life equation comprise temperature and load-holding stress, and a creep probability life model is obtained through binary different variance regression analysis;

step S300, establishing a turbine blade finite element analysis model, including establishing a geometric model, setting material properties, applying boundary conditions and external loads, and extracting a finite element analysis result;

s400, extracting random samples of the probability life auxiliary variable, and obtaining random samples of the low cycle fatigue life and random samples of the creep life through the analysis of a life equation by combining with a finite element output result; obtaining a random sample of creep-fatigue composite life through a linear accumulated damage theory;

s500, determining a probability density function of the creep-fatigue composite life according to a nuclear density method;

and S600, obtaining a composite life confidence interval corresponding to a given confidence level under different survival probabilities by a self-service sampling method.

According to the method for analyzing the creep-fatigue composite probability life of the blade based on the different variance regression, firstly, fatigue life test data of the blade material DZ125 at 800 ℃ can be obtained through tests, and a probability life equation of the DZ125 material at 800 ℃ is obtained through a univariate different variance regression analysis; creep life test data of the turbine blade material DZ125 under three different temperature and load-holding stresses are obtained through tests, a binary variance regression analysis model is deduced and established, and a creep probability life model of the creep life variance along with the change of creep temperature and load-holding stress is established. Secondly, extracting fatigue life dispersity characterization auxiliary variables and creep life dispersity characterization auxiliary variable samples, obtaining corresponding fatigue life and creep life samples through probability life model analysis, and obtaining creep-fatigue life samples through a linear damage accumulation theory. And finally, obtaining creep-fatigue composite life probability distribution through nuclear density estimation based on a creep-fatigue life sample, and obtaining a 95% confidence interval of the life estimation value of the turbine blade under different survival probabilities through resampling and repeated analysis of the test data by a Bootstrap (self-help sampling method).

In the following, each step in the method for analyzing the creep-fatigue composite probability life of the blade based on the variance regression provided by the present disclosure will be described in detail.

In step S100, fatigue test data of a target turbine blade material is obtained, and a low-cycle fatigue probability life is determined according to the test data, where the determination of the low-cycle fatigue probability life includes determining preset parameters in a probability life equation and performing correction of the probability life equation under a standard strain ratio to the probability life equation under an arbitrary strain ratio.

Specifically, the fatigue probability life model in step S100 is obtained by a unitary anisotropic regression method, and the probability life of the structural assessment site under the current stress cycle level is obtained by extracting a random sample of the auxiliary variable in combination with the cyclic stress of the structural assessment site. The specific substeps in S100 are as follows:

step S101: fatigue life data for the investigated materials at strain cycle ratios were collected. Taking the turbine blade material DZ125 targeted as an example, table 1 is the DZ125 alloy casting low cycle fatigue life data.

Table 1: low cycle fatigue performance of DZ125 alloy casting

Step S102: and establishing a probability-strain-life model of fatigue life estimation.

The basic theory of heterovariance regression is as follows:

the strain-life curve is more suitable for plastic deformation of a material under large load, and is more suitable for calculating the low cycle fatigue life, the most common model is a Manson-coffee model, and the specific expression is as follows:

wherein, Delta epsilon_t＝ε_max-ε_min，

Wherein, Delta epsilon_tIs the total strain amplitude, Delta epsilon_eIs the elastic strain amplitude, Delta epsilon_pIs plastic strain amplitude, sigma'_fIs fatigue strength coefficient, E is elastic modulus, N_fIs fatigue cycle number, b is fatigue strength index, epsilon'_fThe fatigue plasticity coefficient and the fatigue plasticity index are c.

The P-epsilon-N curve is a set of epsilon-N curves at different survival rates P. This set of curves gives the following information: distribution data of fatigue life N at a given strain cycle.

The core of the Manson-coffee formula is that in a log-log coordinate, the fatigue life is respectively in a linear relation with an elastic strain amplitude and a plastic strain amplitude, and is expressed as follows:

let y_e＝log(2N)，The standard linear equation for the available elastic threads is:

y_e＝a_e+b_ex_e (4)

in the same way, let y_p＝log(2N)，The standard linear equation for the available plasticity line is:

y_p＝a_p+b_px_p (5)

a large number of fatigue test data show that the log life dispersion is a function of Δ ε_e、Δε_pThe standard deviation of logarithmic life is in linear relation with logarithmic elastic strain component and logarithmic plastic strain component, namely:

y＝a+bx+ε (6)

wherein, epsilon to N (0, sigma)²(x) σ (x) is expressed as:

σ(x)＝σ₀[1+θ(x-x₀)] (7)

in the formula, σ₀Is logarithmic life at x₀Standard deviation at the strain component.

Suppose that the sample obtained from n independent experiments is (x)₁，y₁)、(x₂，y₂)、...、(x_n，y_n) Then, the estimated quantities of the parameters in equations (6) and (7) are calculated as:

wherein ν is the degree of freedom of variance, and when θ is 0, ν is n-2, i.e. degenerates to the case of homovariance; when θ ≠ 0, ν ═ n-3. Other process parameters are as follows:

I(x_i，θ)＝1+θ(x_i-x₀) (13)

substituting equations (16) to (21) into equation (11) to solve theta, and solving theta to obtain subsequent equations (8) to (10) solving parameters a, b and sigma₀。

A in Manson-coffee formula under different survival rates_e、a_p、b_e、b_pIn contrast, and therefore considering the P-epsilon-N function fitting, these four parameters are random variables, the mean of these four parameters, respectively, the linear standard deviation of the elastic and plastic lines can be expressed by equation (7):

σ_e(x_e)＝σ_e0[1+θ_e(x_e-x_e0)] (22)

σ_p(x_p)＝σ_p0[1+θ_p(x_p-x_p0)] (23)

in the formula, σ_e0、σ_p0Respectively representing logarithmic lifetimes y_e、y_pIn logarithmic strain component x_e0、x_p0Standard deviation of (a), theta_e、θ_pRespectively represent sigma_e、σ_pThe slope of the linear change.

Since the log-life follows a normal distribution, the mean value is(plastic segment)) Standard deviation of σ_e(x_e) (plastic segment σ)_p(x_p) Therefore, convert it to standard normal variables:

therefore, the following steps are obtained:

the corresponding plastic line is expressed as:

in the formula, u is a standard normal random variable.

The relationship between the four parameters and the auxiliary variable u in the Manson-coffee formula is as follows:

the DZ 125P-epsilon-N curve is obtained by using the different variance regression analysis theory and combining the fatigue life data of the DZ125 material at 800 ℃ in the step S101, and is shown as follows:

obtaining related estimation parameters of the elastic line according to heteroscedastic regression analysis:

in a similar way, the related estimation parameters of the plastic line are obtained according to the heteroscedastic regression analysis:

therefore, the probability strain-life curve (strain ratio R) based on the univariate variance regression analysis_εIs-1) is:

the fatigue life of the material can be estimated from equation (37) for different survival probabilities and different cyclic stress levels, and fig. 2 gives the strain life curves for 0.01, 0.5 and 0.99 survival probabilities P. Fig. 2 shows that the smaller the strain amplitude, the longer the fatigue life, and the greater the dispersion of the fatigue life.

Step S103: by Morrow mean stress modification, replacing the fatigue life standard deviation of asymmetric cycles with the fatigue life standard deviation of symmetric cycles, a modified fatigue life probability model can be obtained, namely:

wherein σ_mIs the average stress, E is the Young's modulus, uAre auxiliary variables and follow a standard normal distribution.

In step S200, determining a creep probability life according to the test data, where independent variables in a creep life equation include temperature and holding stress, and the creep probability life model is obtained through a binary variance regression analysis.

Specifically, the creep probability life model in step S200 is obtained by a binary heteroscedastic regression method, and the creep probability life of the structure assessment site under the current holding stress is obtained by extracting random samples of auxiliary variables and combining the cyclic stress of the structure assessment site. The specific substeps in step S200 are as follows:

step S201: the creep life of the material under investigation at different temperatures and different holding stresses was collected, taking the turbine blade material DZ125 as an example, and table 2 shows the creep life data of the DZ125 alloy castings at 760 ℃, 980 ℃ and 1040 ℃.

Table 2: creep life test data of DZ125 under different temperatures and different stresses

Step S202: the following probability creep life equation is obtained by using the binary variance regression analysis, namely:

lg N_c＝b₀+b₁T+b₂ lg S+b₃(lg S)²+b₄(lg S)³+σ₀|1+θ_T(T-x_T0)+θ_S(S-x_S0)|μ (39)

wherein N is_cDenotes creep life, T is temperature, S is holding stress, b_i(i ═ 0, 1.., 4) is the model parameter, σ₀Logarithmic life lg N_cAt a temperature component x_T0And a holding stress component x_S0Standard deviation of (a), theta_T、θ_SThe slope of the log life standard deviation with temperature and holding stress, u is an auxiliary variable and follows a standard normal distribution.

The basic theory of the proposed binary heteroscedastic regression is as follows:

in the endurance test and the creep test, as the stress or temperature is increased, the life dispersion is necessarily decreased, i.e., the logarithmic life variance at each stress or temperature is unequal. Therefore, it is necessary to establish a binary different variance regression model to solve the problem of establishing the probabilistic creep life model.

First, assume that the relationship between the random error term and temperature and stress is:

σ(S，T)＝σ₀|1+θ_T(T-T₀)+θ_S(S-S₀)| (40)

wherein, temperature and stress are represented by T and S. The variance term of random error under different temperature and stress is different, generally, the higher the temperature is, the larger the stress is, the smaller the service life is, the smaller the dispersion of the service life is, the smaller the standard deviation of the service life is, therefore, the theta_TAnd theta_SAnd should generally be negative. Using the M-S equation in the analysis of the binary variance creep life, i.e.

lg t_c＝b₀+b₁T+b₂X+b₃X²+b₄X³ (41)

The creep life equation can be written as:

Y＝b₀+b₁T+b₂X+b₃X²+b₄X³ (42)

wherein Y ═ lg t_cX is lg sigma, let X₁＝T，X₂＝X，X₃＝X²，X₄＝X³Then equation (41) can be expressed as:

Y＝b₀+b₁X₁+b₂X₂+b₃X₃+b₄X₄ (43)

consideration of creep life dispersancy with respect to stress X₁And X₂The variance of (2) can be considered as followsHeteroscedastic models of terms, i.e.

Y＝b₀+b₁X₁+b₂X₂+b₃X₃+b₄X₄+ε (44)

Wherein epsilon-N0, sigma (x)₁，x₂)]，σ(x₁，x₂)＝σ₀|1+θ₁(x₁-x₁₀)+θ₂(x₂-x₂₀)|。

Order to

Equation (43) can be expressed as:

N_c＝b₀Z₀+b₁Z₁+b₂Z₂+b₃Z₃+b₄Z₄+u (45)

wherein the content of the first and second substances,then

The heteroscedastic equivalence can be converted into homoscedastic linear regression by means of weighting through the formula (45).

θ₁、θ₂The solution of (2) uses maximum likelihood estimation:

the likelihood function L is maximum, then only need The minimum, i.e. the sum of the squared residuals of the least squares, is minimized.

Thus, an optimization concept can be employed to solve for θ₁、θ₂And coefficient matrix b ═ b₀，b₁，b₂，b₃，b₄]。

Solving for theta₁、θ₂And coefficient matrix b ═ b₀，b₁，b₂，b₃，b₄]The optimization model is as follows:

the calculation of σ 0 is:

obtaining the DZ 125P-T-S-N by combining the heterovariance regression analysis theory with the creep life data of the DZ125 material in the step S201_cThe curves, as follows:

Y＝2.2252×10⁴-2.8117×10⁴X+1.1845×10⁴X²-1.6637×10³X³+ε

ε～(0，0.0132×(1-0.1295×(X-2.3754)) (53)

wherein Y represents a logarithmic lifetime and X represents a logarithmic holding stress.

The probability creep life of the researched material under different temperatures and different holding stresses can be estimated by combining test data with a binary heteroscedastic regression model in the patent.

The fatigue life of the material can be estimated according to the formula (54) under different survival probabilities and different holding stresses, and fig. 3 shows holding stress-life curves under the conditions that the survival probabilities P are 0.01, 0.5 and 0.99. The results of FIG. 3 show that the smaller the holding stress, the longer the lifetime, and the greater the dispersibility of the lifetime.

In step S300, a finite element analysis model of the turbine blade is established, including establishing a geometric model, setting material properties, applying boundary conditions and external loads, and extracting a finite element analysis result.

Specifically, a geometric model of the turbine blade is shown in FIG. 5. The material is DZ125, the working temperature is 800 ℃, and the material attribute and working condition information are shown in tables 3 and 4. Table 5 shows the cyclic stress and cyclic strain information obtained from the finite element analysis results under different conditions. The results of finite element analysis at 13880rpm are shown in FIG. 6.

Table 3: material Properties of DZ125 Material at 800 deg.C

Material properties	Young's modulus	Modulus of shear	Poisson ratio	Yield strength	Coefficient of linear expansion
						Unit of	GPa	GPa	-	MPa	10-6·℃-1
Longitudinal direction	102	90.5	0.43	933	14.55
						Transverse direction	139.5	52.5	0.29	783	14.43

Table 4: main cycle and damaged secondary cycle (average rise and fall)

Table 5: stress-strain analysis result for examining air film hole under two working conditions

In step S400, random samples of the probability life auxiliary variables are extracted, and the random samples of the low-cycle fatigue life and the random samples of the creep life are obtained through the analysis of a life equation by combining the finite element output results; and obtaining a random sample of the creep-fatigue composite life through a linear accumulated damage theory.

Specifically, in step S400, a corresponding life random sample is obtained through the transmission of the auxiliary variable randomness to the fatigue life and the creep life, and a corresponding composite life random sample is obtained through the linear damage accumulation. The method comprises the following specific steps:

step S401: let P_LiSurvival indicating fatigue Life of class iProbability, P_CIndicating the probability of survival for creep life. Since the survival probability is between 0 and 1, it is [0,1 ]]Respectively randomly extracting n numbers of the samples in the intervalAnd P_COf (2) a sample, i.e.Obtaining corresponding auxiliary variable samplesWherein the content of the first and second substances,the kth sample representing the auxiliary variable in the ith-stage fatigue life analysis equation,the kth sample of the auxiliary variables in the i-th order creep life analysis equation is represented.

Step S402: setting k to 1;

step S403: according to the P-epsilon-N curve and P-T-S-N_CThe curve calculates the survival rate asFatigue life ofCreep life under

Step S404: according to the linear damage accumulation theory, the composite life of the blade is calculated

Step S405: judging whether k is larger than n, and continuing to execute when k is larger than n; otherwise, let k be k +1, and return to step S403;

step S406: to composite lifeAre ordered, i.e. Calculating the composite life of the blade under different survival probabilities according to the sorted data, wherein when the survival probability is p, the corresponding composite life isWherein [. ]]Representing a rounding operation.

In step S400, a random sample of the probabilistic life auxiliary variable is extracted, and a random sample of the low cycle fatigue life and a random sample of the creep life are obtained through analysis of a life equation by combining with a finite element output result; obtaining a random sample of the creep-fatigue composite life by a linear accumulated damage theory, wherein the method comprises the following specific steps:

step S410: by using N₁Representing the fatigue life of the main cycle, N₂Denotes the fatigue life of the sub-cycle, N₃Represents creep life;

step S420: mean stress for the first main cycle regimeTotal strain amplitudeThe sample of the auxiliary normal variable u is extracted as { u₍₁₎，u₍₂₎,...,u_(n)N, the corresponding n sets of lifetimes are calculated according to equation (37), i.e.:

step S430: mean stress for the second sub-cycle regimeTotal strain amplitudeThe sample of the auxiliary normal variable u is extracted as { u₍₁₎,u₍₂₎,...,u_(n)N, the corresponding n sets of lifetimes are calculated according to equation (37), i.e.:

step S440: for the creep case, the holding stress is 415.2125MPa, and the sample of the extracted variable ε is { ε₍₁₎,ε₍₂₎,...,ε_(n)N, the corresponding n sets of lifetimes are calculated according to equation (37), i.e.:

step S450: from the life samples in the three modes, creep-fatigue composite life samples were calculated as follows:

wherein 100min represents the load-holding time of the average stress of the one-time take-off and landing working condition 1.

In step S500, a probability density function of creep-fatigue life is estimated according to a kernel density method.

Specifically, according to the composite life sample obtained in step S400A probability density function of the composite life is estimated in conjunction with the kernel density estimate. The probability density function of the creep-fatigue composite life distribution is shown in fig. 7. The principle of the nuclear density estimation method is as follows:

let K (u) be a given probability density function over R, then:

referred to as overall probability density f_n(x) K (u) is a kernel function (also called a window function), n is the number of kernel functions, h_i>0 is window width, α_iIs the weight of each kernel function, and 0<α_i<1，

In step S600, a Bootstrap sampling method is used to obtain a composite lifetime confidence interval corresponding to a given confidence level under different survival probabilities.

Specifically, step S600 includes: step S601: and obtaining fatigue life test data and creep life test data. Let { (x)⁽ⁱ⁾,y⁽ⁱ⁾)；i＝1,...,S₁Denotes the amplitude of the strain cycle at the temperature studied as x⁽ⁱ⁾(i＝1,...,S₁) Fatigue test data y⁽ⁱ⁾(i＝1,...,S₁)，{(T⁽ⁱ⁾,s⁽ⁱ⁾,n_c ⁽ⁱ⁾)；i＝1,...,S₂Denotes the temperature T⁽ⁱ⁾Holding stress of s⁽ⁱ⁾Creep life test data n_c ⁽ⁱ⁾；

Step S602: let k equal to 1;

step S603: and acquiring a kth set of Bootstrap samples. Sample data of fatigue test { (x)⁽ⁱ⁾,y⁽ⁱ⁾)；i＝1,...,S₁Withdraw S with a return₁A sample, is marked Sample data for creep test { (T)⁽ⁱ⁾,s⁽ⁱ⁾,n_c ⁽ⁱ⁾)；i＝1,...,S₂Withdraw S with a return₂A sample, is marked

Step S604: using samplesAnd combining with univariate variance regression analysis to obtain model parameters in the probability-strain-fatigue life model under the group of samples and a corresponding probability-strain-fatigue life model; using samplesAnd obtaining model parameters in the probability-temperature-stress-creep life model and a corresponding probability-temperature-stress-creep life model under the group of samples by combining with the binary different variance regression analysis.

Step S605: let k be k +1, and return to step S603. When k is larger than M (M represents the preset number of Bootstrap sample groups), the following steps are continuously executed.

Step S606: for strain cycles of x^*Holding stress of s^*At a temperature of T^*And estimating by using the life equation under the M groups of resampling samples to obtain M groups of fatigue lives and M groups of creep lives under different survival probabilities P, and performing statistical inference, such as a confidence interval, on the M groups of creep-fatigue composite lives corresponding to the linear damage accumulation theory through the M groups of creep-fatigue composite lives.

In Table 6 are the composite life samples obtained in step S500Calculating creep-fatigue recovery under different survival probabilitiesThe resultant life and the corresponding equivalent flight time (the time of one flight is 100 min). In table 7 is the 95% confidence interval for the creep-fatigue composite life estimation for different survival probabilities of turbine blades by the Bootstrap method.

Table 6: creep-fatigue composite life at different survival probabilities

Table 7: 95% confidence intervals for creep-fatigue composite life estimation for turbine blades at different probabilities of survival

Other embodiments of the invention will be apparent to those skilled in the art from consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the invention following, in general, the principles of the invention and including such departures from the present disclosure as come within known or customary practice within the art to which the invention pertains. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the invention being indicated by the following claims.

It will be understood that the invention is not limited to the precise arrangements described above and shown in the drawings and that various modifications and changes may be made without departing from the scope thereof. The scope of the invention is limited only by the appended claims.