CN115344960A - Bayesian information fusion-based turbine disk reliability evaluation method - Google Patents
Bayesian information fusion-based turbine disk reliability evaluation method Download PDFInfo
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Abstract
The invention relates to a Bayesian information fusion-based turbine disk reliability evaluation method, which comprises the following steps of: (1) Selecting a material probability model, and calculating the simulation probability life of the turbine disc by adopting a partitioning method; (2) Determining the service life overall distribution type of the turbine disc as lognormal distribution, and obtaining prior distribution of service life overall distribution parameters according to the simulation probability service life of the turbine disc; (3) Developing a turbine disk whole disk test, acquiring whole disk low-cycle fatigue life data, and obtaining a likelihood function of a life overall distribution parameter; (4) Obtaining a posterior distribution density function by combining a Bayes formula with a prior distribution density function and a likelihood function of the service life overall distribution parameters; (5) And analyzing the overall service life distribution of the turbine disk according to the posterior distribution function of the parameters, and carrying out reliability evaluation on the turbine disk. The method provided by the invention can further improve the low cycle fatigue reliability evaluation precision of the turbine disc under the condition that the whole disc test sample size is small.
Description
Technical Field
The invention belongs to the technical field of aerospace engines, and particularly relates to an evaluation method for low cycle fatigue reliability of a turbine disk of an aerospace engine, which is an evaluation method for low cycle fatigue reliability of a turbine disk under a small sample condition based on finite element simulation technology and Bayesian statistical inference.
Background
The turbine disk is a key weight and life-limiting part of an aircraft engine, and the reliability of the turbine disk is directly related to the flight safety of the engine. The improvement of the engine performance needs to continuously improve the front temperature of the turbine, increase the rotating speed of the turbine and reduce the weight of the turbine disc, and the turbine disc bears the increasingly large cyclic stress, so that the low cycle gradually becomes the most main failure mode of the turbine disc, and the accurate low cycle fatigue reliability evaluation is carried out on the turbine disc, so that the method has important significance for improving the engine performance and ensuring the flight safety.
In engineering practice, the fatigue life prediction of a turbine disk is subject to more uncertainties due to materials, processes and operating conditions, and a large number of test samples are required for supporting the uncertainties in quantification. Under the condition that the test sample is lack, the Bayesian reliability method is applied to the reliability evaluation process of the turbine disk, and the prior information can be used as the supplement of the test sample, so that a more credible reliability evaluation result of the turbine disk is obtained. Document "quantitative reliability analysis of fatigue life uncertainty of regional-based GH720Li turbine disk [ J ]. Wanglong bridge et al, aerospace technology, 2017, 70:300-309, inferring material model parameters by adopting a Bayesian method, and applying the obtained material model to a turbine disk reliability evaluation process, but the whole disk test sample cannot be processed. The method comprises the following steps of document' fatigue life reliability research of an aeroengine turbine disk based on Bayesian assessment [ J ]. Wanhongqiang, high rigidity, butyl peak, mechanical manufacturing and automation 2016, (5): 13-15. The method directly takes the existing experience and data as prior information, and does not consider how to obtain objective and effective prior information; in addition, the method only infers the position parameters of the service life distribution, and simply adopts the mean value of the posterior distribution of the position parameters to replace the posterior distribution in the reliability evaluation process, so that the dispersion characteristic of the service life of the turbine disk cannot be reasonably considered.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a turbine disk fatigue reliability assessment method based on Bayesian information fusion, which can further improve the turbine disk low-cycle fatigue reliability assessment accuracy under the condition that the whole disk test sample size is small.
The solution of the invention is as follows:
a turbine disk fatigue reliability assessment method based on Bayesian information fusion comprises the following steps:
(1) Selecting a proper material model according to the material and the working environment of the turbine disc, calculating the stress of the turbine disc by adopting a finite element method, partitioning the turbine disc, and determining a failure key area; in each failure key area, sampling and calculating a plurality of groups of life values, fitting a response surface model to obtain the life distribution of each failure key area, and then performing combined risk analysis to obtain the simulation probability life of the whole turbine disc;
(2) Fitting the simulated probability life of the whole turbine disk by using a lognormal distribution, determining a prior distribution type of a total distribution parameter by using the normal distribution obeyed by the lognormal distribution as the total distribution, and calculating the value of each parameter in the prior distribution according to the simulated probability life of the whole turbine disk;
(3) Developing a low-cycle fatigue test of the whole turbine disc, obtaining a test sample of the service life of the whole turbine disc, and obtaining a likelihood function of overall distribution parameters according to the overall distribution type of the service life of the turbine disc;
(4) Substituting the probability density function and the likelihood function of the prior distribution into a Bayes formula, calculating to obtain a posterior distribution density function, further defining posterior distribution types, and determining posterior distribution parameters;
(5) And sampling the overall distribution according to the posterior distribution of the overall distribution parameters to obtain the service life prediction result of the whole turbine disk, calculating the service life under each reliability degree, and carrying out reliability evaluation on the turbine disk.
Further, the step (2) is specifically realized as follows:
a. taking the lognormal distribution as the overall distribution type of the service life of the turbine disk, wherein the lognormal distribution type of the overall service life of the turbine disk is subject to the normal distribution lgN-N (mu, sigma) 2 ) (ii) a N is the cycle life of the turbine disc, mu is the logarithmic mean value of the life of the turbine disc, and sigma is the logarithmic standard deviation of the life of the turbine disc.
b. Definition of accuracy of Normal distribution
The unknown parameters of the total distribution of the logarithmic life are mean value mu and precision lambda, and the prior distribution type is set as normal-gamma distribution (mu, lambda) -NG (mu, lambda | mu) 0 ,κ 0 ,α 0 ,β 0 )，μ 0 Is the mean of the prior distribution, κ 0 A degree of freedom being a priori distributed 0 And beta 0 Respectively a shape parameter and an inverse scale parameter of prior distribution;
c. sampling k groups of the simulation probability life of the whole turbine disk obtained in the step (1), wherein k is more than or equal to 10 5 Each group kappa 0 Sample, κ 0 N-1, n is the number of test samples in the step (3), and the mean value of each group is set as mu i (ii) a Accuracy of lambda i Mean value μ 0 By passing
Obtaining; precision value lambda i (i =1, \8230;, k) is fitted to the gamma distribution G (α) 0 ,β 0 ) To find the shape parameter alpha 0 And inverse scale parameter beta 0 。
Further, the step (3) is specifically realized as follows:
obtaining a whole disc life test sample set D = (x) 1 ，x 2 ，…，x n ) The overall distribution likelihood function is expressed as:
wherein n is the number of samples,
is the mean value of the samples, s 2 Is the sample variance.
Further, the step (4) is specifically realized as follows:
substituting the likelihood function and the probability density function of the prior distribution into a Bayes formula,
order to
Then, the posterior distribution density function is expressed as:
the posterior distribution density function is used for obtaining the posterior distribution, and the posterior distribution is also normal-gamma distribution, namely: p (μ, λ | D) · N (μ | μ - n ,(κ n λ) -1 )×Ga(λ|α n ,β n )，
Wherein mu is the logarithmic mean value of the service life of the turbine disk, sigma is the logarithmic standard deviation of the service life of the turbine disk, and mu n Mean of posterior distribution; kappa n Is the degree of freedom of the posterior distribution; alpha is alpha 0 Is a shape parameter; beta is a n Is an inverse scale parameter.
Further, the step (5) is specifically realized as follows:
a. the posterior distribution types of mean and precision of the overall parameters of the logarithmic life of the turbine disk are determined in the step (4) as normal-gamma distribution (mu, lambda) to NG (mu, lambda | mu) n ,κ n ,α n ,β n ) In which μ n Mean of posterior distribution; kappa n Is the degree of freedom of the posterior distribution; alpha is alpha 0 Is a shape parameter; beta is a beta n Is an inverse scale parameter;
b. from the gamma distribution Ga (lambda | alpha) n ,β n ) A precision value lambda is obtained by sampling once i Then from the normal distribution N (μ |) n ,(κ n λ i ) -1 ) A first sampling is performed to obtain a precision value mu i LN (μ) distributed from the lognormal i ,λ i ) A life value N is obtained by sampling once i ；
c. Sampling in step b is carried out 10 5 Then, 10 is obtained 5 And (4) grouping the service life value of the turbine disk, carrying out reliability evaluation on the turbine disk, drawing a service life distribution diagram and a reliability curve, and giving the service life value under specific reliability.
Compared with the prior art, the invention has the advantages that:
(1) According to the method, the finite element method is used for obtaining the reliability prior information of the turbine disk, so that the reliability evaluation process is prevented from being influenced by subjective factors.
(2) According to the invention, each parameter of the overall distribution of the service life of the turbine disk is deduced, the posterior distribution is solved, the overall service life of the turbine disk is solved by combining a Gibbs sampling method, the uncertainty in the reliability evaluation process of the turbine disk is fully considered, and the evaluation result better reflects the dispersion characteristic of the service life of the turbine disk.
Drawings
FIG. 1 is a flow chart of a turbine disk reliability evaluation method based on Bayesian information fusion according to the present invention;
FIG. 2 is a flow chart of an automation of reliability calculation for the ISIGHT platform;
FIG. 3 is an equivalent stress distribution diagram of a turbine disk, (1) stress distribution at the center of the turbine disk, and (2) stress distribution at the mortise of the turbine disk;
FIG. 4 is a turbine disk simulated probabilistic life distribution plot;
FIG. 5 is a turbine disk life overall map.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not limit the invention. In addition, the technical features involved in the respective embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
As shown in FIG. 1, the method for evaluating the fatigue reliability of the turbine disk based on Bayesian information fusion comprises the following steps:
(1) And selecting a probabilistic Ramberg-Osgood equation as a stress-strain model according to the material and the working temperature of the turbine disk, and selecting a probabilistic Manson-coffee equation as a strain-life model. And (3) stress calculation is carried out on the turbine disk by adopting finite element analysis software, the turbine disk is partitioned according to the temperature and the stress level, and a region with higher temperature and higher stress is selected as a failure key region. In each failure key area, an ISIGHT platform is used for sampling and calculating a plurality of groups of service life values by taking the stress, the rotating speed and the key size of the turbine disc as variables, a response surface model between the service life and the variables is fitted, then the response surface model is sampled and calculated to obtain the service life distribution of each failure key area, and then combined risk analysis is carried out to obtain the simulation probability service life of the whole turbine disc.
(2) Fitting the simulation probability life of the whole turbine disk to be lognormal distribution, wherein the lognormal distribution lgN-N (mu, sigma) is obeyed to the lognormal life 2 ) (ii) a Where N is the cycle life of the turbine disk and μ is the logarithm of the life of the turbine diskThe mean, σ, is the logarithmic standard deviation of the turbine disk life. And taking the normal distribution as the overall distribution of the logarithmic service life of the turbine disk, wherein the logarithmic mean value mu of the service life of the turbine disk and the logarithmic standard deviation sigma of the service life of the turbine disk are unknown parameters. Definition of the accuracy of the normal distribution as
The prior distribution of the unknown parameter mean μ and precision λ is a normal-gamma distribution, which can be expressed as:
NG(μ,λ|μ 0 ,κ 0 ,α 0 ,β 0 )＝N(μ|μ 0 ,(κ 0 λ) -1 )Ga(λ|α 0 ,β 0 )
wherein, mu 0 Taking the mean value of the logarithmic life of the simulation probability of the turbine disk as the mean value of the prior distribution; kappa 0 Being a degree of freedom, κ, of a priori distribution 0 = n-1, wherein n is the number of samples in the whole disc test; with κ 0 After the logarithmic life of the simulation probability of the turbine disk is sampled for the sample size, the sample precision lambda is calculated, the gamma distribution is used for fitting the lambda to obtain the shape parameter alpha of the prior distribution 0 And inverse scale parameter beta 0 The prior distribution density function is:
(3) And carrying out a low-cycle fatigue test of the whole turbine disc, wherein the maximum rotating speed is the cruising rotating speed. Obtaining a whole disc life test sample set D = (x) 1 ，x 2 ，…，x n ) The overall distribution likelihood function may be expressed as:
wherein mu is the logarithmic mean of the life of the turbine disk, and sigma is the vortexLogarithmic standard deviation of the service life of the wheel disc, n is the number of samples,
is the sample mean, s 2 Is the sample variance.
(4) Substituting the likelihood function and the probability density function of the prior distribution into a Bayesian formula,
order to
The posterior distribution density function can be expressed as
It can be observed from the posterior distribution density function, and the posterior distribution is also normal-gamma distribution, namely: p (μ, λ | D) oc ^ N (μ | D) n ,(κ n λ) -1 )×Ga(λ|α n ,β n )。
Wherein, mu n Is the mean of the posterior distribution; kappa n Is the degree of freedom of the posterior distribution; alpha is alpha 0 Is a shape parameter; beta is a n Is an inverse scale parameter.
(5) Gibbs sampling was performed on the posterior distribution: from the gamma distribution Ga (lambda | alpha) n ,β n ) A precision value lambda can be obtained by sampling once i And then from normal distribution N (μ |) n ,(κ n λ i ) -1 ) The first sampling is carried out to obtain an accuracy value mu i From lognormal distribution LN (. Mu.) i ,λ i ) A life value N is obtained by sampling once i . In total run 10 5 Sub-sampling to obtain 10 5 The service life value of the turbine disk is combined, and accordingly, the reliability evaluation and the service life drawing of the turbine disk are carried outThe lifetime distribution graph and the reliability curve give the lifetime value under a specific reliability.
The technical scheme of the turbine disk fatigue reliability evaluation method based on Bayesian information fusion is further explained below with reference to the accompanying drawings.
As shown in fig. 1, the method for evaluating fatigue reliability of a turbine disk based on bayesian information fusion mainly comprises: the method comprises the following steps of turbine disk simulation probability life calculation, prior distribution construction, whole disk low-cycle fatigue test, posterior distribution function solution and turbine disk reliability evaluation, and is realized by the following steps:
(1) The probability stress-strain model of FGH95 at 550 ℃ can be obtained by consulting the literature:
probabilistic strain-life model of FGH95 at 550 ℃:
static strength analysis is carried out on the XX type turbine disc by using finite element analysis software ANSYS, and an obtained equivalent stress field cloud chart is shown in fig. 3, wherein the stress at the bottom of a mortise of the turbine disc is maximum, and the disc center is second. Taking the bottom of the mortise and the disc center as examination areas, calculating the service life by adopting the ISIGHT automatic simulation cycle shown in figure 2 at the temperature of 550 ℃ and the rotating speed of 46750r/min, and then carrying out combined risk analysis to obtain the simulated probability service life of the whole turbine disc, wherein the service life distribution is shown in figure 4.
(2) According to Jarqe-Bera test, the simulation probability life of the XX type turbine disk is distributed according to the log normal distribution under the confidence level of 99%, and accordingly, the life of the turbine disk is assumed to be distributed according to the log normal distribution. The log mean value mu of the life of the turbine disk of the log-normal population and the log standard deviation sigma of the life of the turbine disk are unknown parameters. Definition of the accuracy of the normal distribution as
The prior distribution of the mean μ and precision λ is a normal-gamma distribution, which can be expressed as:
NG(μ,λ|μ 0 ,κ 0 ,α 0 ,β 0 )＝N(μ|μ 0 ,(κ 0 λ) -1 )Ga(λ|α 0 ,β 0 )
wherein, mu 0 Taking the mean value of the logarithmic life of the simulation probability of the turbine disk as the mean value of the prior distribution; kappa 0 Being a degree of freedom of a prior distribution, κ 0 = n-1, where n is the number of samples in the entire disc test; with κ 0 After the logarithmic life of the simulation probability of the turbine disk is sampled for the sample size, the sample precision lambda is calculated, the gamma distribution is used for fitting the lambda to obtain the shape parameter alpha of the prior distribution 0 And inverse scale parameter beta 0 The prior distribution density function is:
(3) And carrying out a low-cycle fatigue test of the whole turbine disc, wherein the maximum rotating speed is the cruising rotating speed. Obtaining a whole disc life test sample set D = (x) 1 ，x 2 ，…，x n ) The overall distribution likelihood function may be expressed as:
wherein n is the number of samples,
is the mean value of the samples, s 2 Is the sample variance.
(4) The likelihood function and the prior density function are substituted into a Bayes formula,
order to
The posterior distribution density function can be expressed as:
it can be observed from the posterior distribution function that the posterior distribution is also normal-gamma distribution, i.e. p (μ, λ | D). Varies.. Alpha.N (μ |) n ,(κ n λ) -1 )×Ga(λ|α n ,β n ). Wherein, mu n Is the mean of the posterior distribution; kappa n Is the degree of freedom of the posterior distribution; alpha is alpha 0 Is a shape parameter; beta is a beta n Is an inverse scale parameter.
(5) Gibbs sampling was performed on the posterior distribution: from the gamma distribution Ga (lambda | alpha) n ,β n ) A precision value lambda can be obtained by sampling once i Then from the normal distribution N (μ |) n ,(κ n λ i ) -1 ) The first sampling is carried out to obtain an accuracy value mu i From lognormal distribution LN (. Mu.) i ,λ i ) A life value N is obtained by sampling once i . In total run 10 5 Subsampling to obtain 10 5 The group turbine disk life value and the overall distribution of the turbine disk life are shown in fig. 5.
The above examples are provided only for the purpose of describing the present invention, and are not intended to limit the scope of the present invention. The scope of the invention is defined by the appended claims. Various equivalent substitutions and modifications can be made without departing from the spirit and principles of the invention, and are intended to be within the scope of the invention.
Claims (5)
1. A turbine disk reliability assessment method based on Bayesian information fusion is characterized by comprising the following steps:
(1) Selecting a proper material model according to the material and the working environment of the turbine disc, calculating the stress of the turbine disc by adopting a finite element method, partitioning the turbine disc, and determining a failure key area; in each failure key area, sampling and calculating a plurality of groups of life values, fitting a response surface model to obtain the life distribution of each failure key area, and then performing combined risk analysis to obtain the simulation probability life of the whole turbine disc;
(2) Fitting the simulated probability life of the whole turbine disk by using a lognormal distribution, determining a prior distribution type of a total distribution parameter by using the normal distribution obeyed by the lognormal distribution as the total distribution, and calculating the value of each parameter in the prior distribution according to the simulated probability life of the whole turbine disk;
(3) Developing a low-cycle fatigue test of the whole turbine disc, obtaining a test sample of the service life of the whole turbine disc, and obtaining a likelihood function of overall distribution parameters according to the overall distribution type of the service life of the turbine disc;
(4) Substituting the probability density function and the likelihood function of the prior distribution into a Bayes formula, calculating to obtain a posterior distribution density function, further determining the posterior distribution type, and determining posterior distribution parameters;
(5) And sampling the overall distribution according to the posterior distribution of the overall distribution parameters to obtain the service life prediction result of the whole turbine disk, calculating the service life under each reliability degree, and carrying out reliability evaluation on the turbine disk.
2. The Bayesian information fusion-based turbine disk fatigue reliability assessment method according to claim 1, characterized in that: the step (2) is specifically realized as follows:
a. taking the lognormal distribution as the overall distribution type of the service life of the turbine disk, wherein the lognormal distribution type of the overall service life of the turbine disk is subject to the normal distribution lgN-N (mu, sigma) 2 ) (ii) a Wherein N is the cycle life of the turbine disc, mu is the logarithmic mean value of the life of the turbine disc, and sigma is the logarithmic standard deviation of the life of the turbine disc;
b. definition of accuracy of Normal distribution
The unknown parameters of the total distribution of the logarithmic life are mean value mu and precision lambda, and the prior distribution type is set as normal-gamma distribution (mu, lambda) -NG (mu, lambda | mu) 0 ,κ 0 ,α 0 ,β 0 )，μ 0 Is the mean of the prior distribution, κ 0 Being a degree of freedom of a prior distribution, alpha 0 And beta 0 Respectively a shape parameter and an inverse scale parameter of prior distribution;
c. sampling k groups of the simulation probability life of the whole turbine disk obtained in the step (1), wherein k is more than or equal to 10 5 Each group kappa 0 Sample, κ 0 N-1, n is the number of test samples in the step (3), and the mean value of each group is set as mu i (ii) a Accuracy of lambda i Average value of 0 By passing
Obtaining; precision value lambda i (i =1, \8230;, k) is fitted to the gamma distribution G (α) 0 ,β 0 ) To find the shape parameter alpha 0 And inverse scale parameter beta 0 。
3. The Bayesian information fusion-based turbine disk fatigue reliability assessment method according to claim 2, characterized in that: the step (3) is specifically realized as follows:
obtaining a whole disc life test sample set D = (x) 1 ，x 2 ，…，x n ) The overall distribution likelihood function is expressed as:
where μ is the logarithmic mean of the turbine disk life and σ is the pair of turbine disk lifeThe number standard deviation, n is the number of samples,
is the mean value of the samples, s 2 Is the sample variance.
4. The Bayesian information fusion-based turbine disk fatigue reliability assessment method according to claim 3, wherein: the step (4) is specifically realized as follows:
substituting the likelihood function and the probability density function of the prior distribution into a Bayesian formula,
order to
Then, the posterior distribution density function is expressed as:
the posterior distribution density function is used for obtaining the posterior distribution, and the posterior distribution is also normal-gamma distribution, namely: p (μ, λ | D) oc ^ N (μ | D) n ,(κ n λ) -1 )×Ga(λ|α n ,β n )，
Wherein mu is the logarithmic mean value of the service life of the turbine disk, lambda is the precision of the logarithmic normal distribution of the service life of the turbine disk, and mu n Is the mean of the posterior distribution; kappa n A degree of freedom that is a posterior distribution; alpha is alpha 0 Is a shape parameter; beta is a n Is an inverse scale parameter.
5. The Bayesian information fusion-based turbine disk fatigue reliability assessment method according to claim 4, wherein: the step (5) is specifically realized as follows:
a. the posterior distribution types of mean and precision of the overall parameters of the logarithmic life of the turbine disk are determined in the step (4) as normal-gamma distribution (mu, lambda) to NG (mu, lambda | mu) n ,κ n ,α n ,β n ) In which μ n Is the mean of the posterior distribution; kappa n Is the degree of freedom of the posterior distribution; alpha is alpha 0 Is a shape parameter; beta is a n Is an inverse scale parameter;
b. from gamma distribution Ga (lambda | alpha) n ,β n ) A precision value lambda is obtained by sampling once i Then from the normal distribution N (μ |) n ,(κ n λ i ) -1 ) The first sampling is carried out to obtain an accuracy value mu i From lognormal distribution LN (. Mu.) i ,λ i ) A life value N is obtained by sampling once i ；
c. Sampling in step b is performed 10 5 Then, 10 is obtained 5 And (4) grouping the service life value of the turbine disk, carrying out reliability evaluation on the turbine disk, drawing a service life distribution diagram and a reliability curve, and giving the service life value under specific reliability.
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| CN117574554B (en) * | 2024-01-19 | 2024-04-16 | 中国航发四川燃气涡轮研究院 | Turbine disc low cycle fatigue reliability assessment method based on ambient air inlet temperature |
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