CN113626942B - Double-amplitude turbine disk fatigue creep life reliability optimization method based on proxy model - Google Patents
Double-amplitude turbine disk fatigue creep life reliability optimization method based on proxy model Download PDFInfo
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Abstract
The invention provides a proxy model-based double-amplitude turbine disk fatigue creep life reliability optimization method, which comprises the following steps: establishing a geometric simulation model of the double-amplitude plate turbine disc; determining the relation between the random variable and the fatigue creep life of the double-amplitude plate turbine disk; establishing a fatigue creep life reliability optimization design model of the double-amplitude plate turbine disc; adopting a self-adaptive Kriging approximate model to construct a Kriging approximate agent model with reliability constraint and target function convergence in an expansion space; determining an inverse design point under given design parameters and reliability indexes, performing local sampling at the inverse design point, and updating the reliability constraint of convergence and a Krigin approximate proxy model of a target function; based on the obtained kriging approximate agent model and the inverse design point of the constraint function and the target function, converting the reliability optimization problem into a deterministic optimization problem for optimization solution by using a sequence optimization and reliability evaluation method; and if the optimization solution is judged to be converged, outputting an optimization result.
Description
Technical Field
The invention relates to the technical field of aircraft engines, in particular to a method for optimizing fatigue creep life reliability of a double-amplitude turbine disk based on a proxy model.
Background
The turbine disk is one of the main parts of an aircraft engine, works at high temperature and high speed, bears complex load, is in a harsh environment, and can cause serious consequences once a destructive fault occurs. The life of a turbine disk determines to a large extent the life of an aircraft engine. Therefore, the reliability optimization design of the turbine disk can help engineering designers to reasonably establish safety tolerance and control the influence of random parameters on the safety of the turbine disk, so that the service life prediction work and reliability analysis of the turbine disk are more consistent with the actual working performance, and the design parameters of the turbine disk with enough safety reliability and optimal performance can be obtained.
The service life reliability structural design of the existing double-spoke turbine disk is very few, and the analysis process of the existing structural design method of the turbine disk needs a large amount of calculation and consumes a long time. Therefore, an efficient method for designing the fatigue creep life reliability optimization of the double-amplitude plate turbine disk with less calculation amount and short time consumption needs to be researched.
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 aim of the embodiment of the disclosure is to provide a method for optimizing fatigue creep life reliability of a double-amplitude turbine disk based on a proxy model, wherein the updating of a kriging approximate proxy model is embedded into the whole process of design parameter optimization searching, and the updating is carried out in real time along with the searching change of the design parameters, so that the proxy precision of the kriging approximate proxy model in the whole optimization process is strictly ensured.
According to one aspect of the disclosure, a method for optimizing fatigue creep life reliability of a double-amplitude turbine disk based on a proxy model is provided, and the method comprises the following steps:
establishing a geometric simulation model of the double-amplitude plate turbine disc;
analyzing the geometric simulation model according to a finite element method, and determining a random variable influencing the fatigue creep life of the double-amplitude plate turbine disk and a relation between the random variable and the fatigue creep life of the double-amplitude plate turbine disk;
establishing a fatigue creep life reliability optimization design model of the double-amplitude plate turbine disc by taking the maximum mean value of the fatigue creep life as a design target and the fatigue creep life reliability as a constraint according to the relation between the determined random variable and the fatigue creep life of the double-amplitude plate turbine disc;
adopting a self-adaptive Kriging approximate model to construct a Kriging approximate agent model with reliability constraint and target function convergence in an expansion space;
determining an inverse design point under given design parameters and reliability indexes, performing local sampling at the inverse design point, adopting a self-adaptive learning function to identify a target mode, updating the converged reliability constraint, and adopting a learning function based on a coefficient of variation to update a Kriging approximate proxy model of the target function;
converting the reliability optimization problem into a deterministic optimization problem to be solved by using a sequence optimization and reliability evaluation method based on the obtained kriging approximate agent model and the inverse design point of the constraint function and the target function, and obtaining an optimized solution;
and judging whether the optimization solution is converged, and if so, outputting an optimization result.
In an exemplary embodiment provided by the present disclosure, the optimization method further includes:
if the optimization solution does not converge, the current optimization solution is used as the initial value of the design parameter in the next iteration.
In an exemplary embodiment provided by the present disclosure, constructing a kriging approximation proxy model with reliability constraint and objective function convergence in an extended space using an adaptive kriging approximation model includes:
adopting Latin hypercube sampling in the expanded reliability space to obtain a sample pool of input variables;
selecting part of initial training sample points from a sample pool, and selecting a basic function and a co-correlation function of the Kriging approximate agent model according to input-output information of a real reliability constraint function;
adopting a multi-mode learning function to carry out self-adaptation on the kriging approximate proxy model and update until all the kriging approximate proxy models of the reliability constraint function are converged;
according to the relation between the constraint function and the target function, an initial Krigin approximate agent model of the current target function can be obtained at the same time;
and adopting a learning function based on the coefficient of variation to carry out self-adaptive updating on the kriging approximate proxy model of the target function until the kriging approximate proxy model of the target function converges.
In one exemplary embodiment provided by the present disclosure, the kriging approximate proxy model is:
wherein f (x) is ═ f 1 (x)，...，f p (x)] T Expressed as a basis function, β ═ β 1 ，...，β p } T Z (x) is expressed as a zero-mean Gaussian for the corresponding regression coefficients.
In one exemplary embodiment provided by the present disclosure, the identifying important failure modes using an adaptive learning function includes:
determining a learning function u (x) at a sample point in a sample pool of local samples at the current inverse design point:
wherein the content of the first and second substances,
and
respectively representing the predicted mean value and standard deviation of the jth reliability constraint function at the random input parameter realization value x;
i.e. w is a set consisting of the numbers of failure modes;
identifying a failure mode corresponding to the IM reliability constraint function as an important failure mode, wherein the specific expression of a failure mode index IM is as follows:
in an exemplary embodiment provided by the present disclosure, updating an objective function with a learning function based on a coefficient of variation includes:
determining a learning function cov (x) at a sample point in the sample pool of local samples at the current inverse design point:
wherein N is fj A lifetime value representing the jth mode;
and
respectively representing life functions N fj The kriging approximate agent model realizes the prediction mean value and standard deviation of the value x at random input parameters;
if it is
The proxy model of the objective function is converged, otherwise a new sample point is selected
And updating the proxy model of the current objective function.
In an exemplary embodiment provided by the present disclosure, a sequence optimization and reliability evaluation method is adopted to convert a reliability optimization problem into a deterministic optimization problem, which is specifically represented as follows:
wherein the content of the first and second substances,
for the offset vector of the jth reliability constraint function at the kth cycle,
the expression is as follows:
wherein the content of the first and second substances,
to input parameter mean at random
The inverse design point of (c).
In an exemplary embodiment provided by the present disclosure, determining an inverse design point under given design parameters and reliability indexes, performing local sampling at the inverse design point, identifying a target pattern using an adaptive learning function, updating the converged reliability constraint, and updating a target function using a learning function based on a coefficient of variation, includes:
initializing optimal design parameter values
And the cycle number k of the sequence optimization design;
using current design variable parameters
And
solving each at a given reliability
Lower corresponding inverse design point
Defining an inverse design point with a current iteration
A central local sampling region with a radius R ═ 1.2+0.3nc β t Wherein nc is a nonlinear correction system; generating a local area sample pool in the local sampling area
In that
Updating the proxy model by using the U learning function under multiple modes as a point selection criterion, updating the important failure mode IM only, and repeating the process until all the proxy models
All converge;
in that
The method utilizes a learning function cov (x) based on a coefficient of variation to approximate a proxy model of adaptive Krigin, and updates the proxy model of an objective function according to the relation between the fatigue creep life and a reliability constraint function
Until convergence.
In an exemplary embodiment provided by the present disclosure, based on the obtained kriging approximate agent model and inverse design point of the constraint function and the objective function, a sequence optimization and reliability evaluation method is used to convert a reliability optimization problem into a deterministic optimization problem solution, and an optimal solution is obtained, including:
establishing an equivalent deterministic optimization mathematical model by using a sequence optimization and reliability evaluation method, and obtaining an optimization result of the kth iteration
In an exemplary embodiment provided by the present disclosure, determining whether an optimization solution converges, and if so, outputting an optimization result, including:
judging whether the feasibility of the optimization solution and the whole reliability optimization process are converged, and if so, finishing the calculation; if not, let k equal to k +1, return to step: initializing optimized design values
And the cycle number k of the sequence optimization design.
The purpose of the disclosure is to provide a method for efficiently solving design parameters aiming at the reliability optimization design of the fatigue life of a double-amplitude plate turbine disk. The method aims to solve the problems of large sample size and long time consumption in the existing method, improves the efficiency of optimization solution, and has strong engineering significance on the reliability optimization design method of the finite element simulation model of the double-amplitude plate turbine disk. By combining the self-adaptive Kriging agent model with local sampling at an inverse design point, the self-adaptive agent model of the reliability constraint function and the target function can accurately and efficiently act on a key area. And the training sample points are purposefully selected by a self-adaptive method to construct the Kriging proxy model, so that the Kriging proxy model for construction can identify the important mode which has the maximum contribution to the alternative sample pool generated at the reverse design point, and the problem of introducing extra calculated amount due to updating of the proxy model of the unimportant mode is avoided, thereby further improving the efficiency of proxy model convergence and effectively shortening the calculation time required by optimization. And the self-adaptive agent model is embedded into the whole process of optimization search of the design parameters and is updated in real time along with the search change of the design parameters, so that the agent precision of the Kriging agent model in the whole optimization process is strictly ensured theoretically.
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 schematic flow chart of a method for optimizing fatigue creep life reliability of a double-amplitude turbine disk based on a proxy model according to an embodiment of the present disclosure.
Fig. 2 is a detailed flowchart of a reliability analysis method based on a mixture of an adaptive kriging approximate proxy model and local sampling according to an embodiment of the present disclosure.
Fig. 3 is an integrated model of a double-web turbine disk and cooling airflow holes according to an embodiment of the disclosure.
Fig. 4 is a meridian plane parametric model of a turbine disk provided in an embodiment of the present disclosure.
FIG. 5 is a cloud graph of a temperature field distribution of a turbine disk provided in accordance with an embodiment of the present disclosure.
FIG. 6 is a finite element schematic diagram of a turbine disk provided in an 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.
Furthermore, the described features or characteristics may be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided to give a thorough understanding of embodiments of the invention. One skilled in the relevant art will recognize, however, that the inventive aspects may be practiced without one or more of the specific details, or with other methods, steps, and so forth. In other instances, well-known methods have not been shown or described in detail to avoid obscuring aspects of the invention.
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.
The embodiment of the disclosure provides a proxy model-based method for optimizing fatigue creep life reliability of a double-amplitude turbine disk, as shown in fig. 1, the method includes:
s100, establishing a geometric simulation model of the double-amplitude plate turbine disc;
s200, analyzing the geometric simulation model according to a finite element method, and determining a random variable influencing the fatigue creep life of the double-amplitude plate turbine disk and a relation between the random variable and the fatigue creep life of the double-amplitude plate turbine disk;
s300, establishing a fatigue creep life reliability optimization design model of the double-amplitude plate turbine disc by taking the mean value of the fatigue creep life as a maximum design target and the fatigue creep life reliability as a constraint according to the relation between the determined random variable and the fatigue creep life of the double-amplitude plate turbine disc;
s400, adopting an adaptive Kriging (Kriging) approximation model to construct a Kriging approximation (Kriging) agent model with reliability constraint and objective function convergence in an expansion space;
s500, determining an inverse design point under given design parameters and reliability indexes, performing local sampling at the inverse design point, adopting a self-adaptive learning function to identify a target mode, updating the converged reliability constraint, and adopting a learning function based on a coefficient of variation to update a Krigin approximate proxy model of the target function;
s600, converting a reliability optimization problem into a deterministic optimization problem to be solved by using a sequence optimization and reliability evaluation method based on the obtained kriging approximate agent model and the inverse design point of the constraint function and the target function, and obtaining an optimized solution;
and S700, judging whether the optimization solution is converged, and if so, outputting an optimization result.
As shown in fig. 1, the optimization method provided by the present disclosure further includes:
step S800, if the optimization solution does not converge, the current optimization solution is used as the initial value of the design parameter in the next iteration.
The purpose of the disclosure is to provide a method for efficiently solving design parameters aiming at the reliability optimization design of the fatigue life of a double-amplitude plate turbine disk. The method aims to solve the problems of large sample size and long time consumption in the existing method, improves the efficiency of optimization solution, and has strong engineering significance on the reliability optimization design method of the finite element simulation model of the double-amplitude plate turbine disk. By combining the self-adaptive Kriging agent model with local sampling at an inverse design point, the self-adaptive agent model of the reliability constraint function and the target function can accurately and efficiently act on a key area. And the training sample points are purposefully selected by a self-adaptive method to construct the Kriging proxy model, so that the Kriging proxy model for construction can identify the important mode which has the maximum contribution to the alternative sample pool generated at the reverse design point, and the problem of introducing extra calculated amount due to updating of the proxy model of the unimportant mode is avoided, thereby further improving the efficiency of proxy model convergence and effectively shortening the calculation time required by optimization. And the self-adaptive agent model is embedded into the whole process of optimization search of the design parameters and is updated in real time along with the search change of the design parameters, so that the agent precision of the Kriging agent model in the whole optimization process is strictly ensured theoretically.
In the following, each step in the proxy model-based dual-amplitude turbine disk fatigue creep life reliability optimization method provided by the present disclosure will be described in detail.
In step S100, a geometric simulation model of the double-deck turbine disk is created.
Specifically, a finite element simulation model of the turbine disk is established by using ANSYS Mechanical APDL software, and the uncertainty variable of the double-plate turbine disk is parameterized.
In step S200, the geometric simulation model is analyzed according to a finite element method, and a random variable affecting the fatigue creep life of the double-amplitude plate turbine disk and a relationship between the random variable and the fatigue creep life of the double-amplitude plate turbine disk are determined.
Specifically, a finite element analysis method is used, namely ANSYS finite element software is adopted to analyze the geometric simulation model of the double-width plate turbine disk, and a random vector x which influences the fatigue creep life of the double-width plate turbine disk is determined to be { x ═ x { 1 ，x 2 ，...，x n } T And x is a random variable { x ═ x 1 ，x 2 ，...，x n } T Relationship to fatigue creep life of a double-amplitude plate turbine disk.
In step S300, according to the relation between the determined random variable and the fatigue creep life of the double-amplitude plate turbine disk, establishing a fatigue creep life reliability optimization design model of the double-amplitude plate turbine disk by taking the mean value of the fatigue creep life as the maximum design target and the fatigue creep life reliability as the constraint;
specifically, as shown in FIG. 2, a reliability constraint function g of a double-plate turbine disk is determined j (x) (j ═ 1, 2.. multidot.m) and an objective function N fj (x) And establishing a reliability optimization design model of the fatigue creep life of the double-amplitude plate turbine disk.
The mean value of fatigue-creep life under the 'start-max-start' cyclic load state is selected as an optimization target, and the reliability design optimization problem model is described as follows:
wherein N is f1 (X) expressed as fatigue life per cycle of double-amplitude plate turbine disk, N f2 (X) is expressed as creep life of the double-radial-plate turbine disk under maximum equivalent stress in a loaded state. The two failure probability constraints are: the probability that the service life of the double-amplitude plate turbine disc per cycle is less than 800 is equal to
The probability that the creep life of the double-amplitude plate turbine disk under the maximum equivalent stress in a load state is less than or equal to 600 is less than or equal to
In step S400, a kriging approximation proxy model with reliability constraints and objective function convergence is constructed in the extended space using the adaptive kriging approximation model.
Specifically, an initial Kriging agent model of each failure mode is established in an extended reliability space
And a Kriging proxy model of the objective function.
Illustratively, step S411: and adopting Latin hypercube sampling in an extended reliability space to obtain a sample pool X of the input variable.
Step S412: selecting part of initial training sample points from a sample pool, selecting a basic function and a co-correlation function of Kriging according to input-output information of a real reliability constraint function, wherein a Kriging agent model at an input realization value x is as follows:
wherein f (x) is ═ f 1 (x)，...，f p (x)] T Expressed as a basis function, β ═ β 1 ，...，β p } T Z (x) is represented as a zero-mean Gaussian process for the corresponding regression coefficients, and its covariance model is represented as σ 2 R(x i ，x j ). Therefore, an initial Kriging agent model of the reliability constraint function is established
And is
And
are respectively as
The predicted mean and the predicted variance.
Step S413: and adopting a multi-mode learning function U (x) to carry out self-adaption on the Kriging agent model and update until all the Kriging agent models of the reliability constraint function converge.
Specifically, step S4131: calculating a learning function u (x) at a sample point in the sample pool of local samples at the current inverse design point:
wherein the content of the first and second substances,
and
respectively representing the predicted mean value and standard deviation of the jth reliability constraint function at the random input parameter realization value x;
i.e., w is a set consisting of the numbers of failure modes.
Step S4132: identifying a failure mode corresponding to the IM reliability constraint function as an important failure mode, wherein the specific expression of a failure mode index IM is as follows:
step S414: according to the relation between the constraint function and the objective function, the initial Kriging agent model of the current objective function can be obtained at the same time.
Step S415: and adopting a learning function cov (x) based on the coefficient of variation to carry out self-adaptive updating on the Kriging agent model of the objective function until the Kriging agent model of the objective function converges.
Specifically, step S4151: calculating a learning function cov (x) at a sample point in the sample pool of local samples at the current inverse design point:
wherein N is fj Indicating the lifetime value for the jth mode.
And
respectively representing life functions N fj The Kriging agent model realizes the prediction mean value and standard deviation of the value x at random input parameters;
step S4152: if it is
The proxy model of the objective function is converged, otherwise a new sample point is selected
And updating the proxy model of the current objective function.
By way of example, an initial Kriging proxy model for each constraint function is built in an extended reliability space
And an objective function
Step S421: scale of formation N E Extended spatial sample pool of (2)
Step S422: from the sample cell
Extracting N from T0 An initial training sample point x ET Then, calling the real output value g of the function of the double-amplitude plate turbine disk j (x ET ) Based on x ET And corresponding function output value g j (x ET ) Constructing an initial training sample set T j ＝{x ET ，g j (x ET )}。
Step S423: according to training sample set T j Constructing an initial Kriging agent model
And is
And
are respectively as
The predicted mean and the predicted variance of (c).
Step S424: calculate the pool according to the following equation
At each sample point x E The corresponding multi-mode U learning function:
step S425: judging the current Kriging model
The convergence of (2). When in use
In time, the current Kriging model can judge the sample cell with 97.7% of accuracy
The adaptive learning process can be stopped by the sign of the output response value corresponding to each sample point, and step S427 is executed; if it is
Step S426 is performed.
Step S426: adaptively selecting the important failure mode IM to be updated:
and selects and updates training sample points
And calculating the output value of the corresponding function of the important failure mode based on the finite element
Added to the training sample set corresponding to the important failure mode, i.e.
Return is made to step S423.
Step S427: obtaining extended space based sample pools
Kriging model of lower convergence
And an initial Kriging proxy model of the objective function
Step S428: the calculation is at the current calculation
Corresponding to the middle sample point, based on a coefficient of variation cov (x) learning function, judging the current Kriging model
Convergence of (A) if
Step S429 is performed; otherwise, step S500 is executed.
Step S429: selecting and updating training sample points
And calculating the output value g of the function based on the finite element j (x new ) Adding corresponding training sample set and updating Kriging agent model
I.e. update
Returning to step S428.
In step S500, an inverse design point is determined under given design parameters and reliability indexes, local sampling is performed at the inverse design point, a target pattern is identified using an adaptive learning function, the converged reliability constraint is updated, and a kriging approximation proxy model of the target function is updated using a learning function based on a coefficient of variation.
Specifically, step S511: inputting initial value u of each random variable k And target reliability index beta t And k is 0.
Step S512: calculating the function value g (u) k ) And gradient
Calculating
A finite difference method may be used.
Step S513: u is calculated using the formula k+1 ：
Step S514: if g (u) k+1 )＜g(u k ) Step S515 is performed; otherwise, the process proceeds to step S516.
Step S515: if u is k+1 -u k Less than or equal to epsilon, output u k+1 And g (u) k )，u k+1 Finally, the obtained inverse design point is obtained, and the algorithm is ended; otherwise, let k be k +1, go to step S512.
Step S516: calculating initial step length h ═ u k+1 -u k λ, λ is the step scaling factor, and can be 0.5-0.9.
Step S517: u 'was calculated from the following formula' k+1
Step S518: if g (u' k+1 )＜g(u k ) Then let u k+1 ＝u′ k+1 Step S515 is performed; otherwise, go to step S517.
For example, step S500 may include: step S521: initializing optimized design values
And the cycle number k of the sequence optimization design.
Step S522: using current design variable parameters
And
solving each at a given reliability
Lower corresponding inverse design point
Defining an inverse design point with a current iteration
A central local sampling region with a radius R ═ 1.2+0.3nc β t And nc is a nonlinear correction system. Generating a local area sample pool in the local sampling area
Step S523: in that
Updating the proxy model by using the U learning function under multiple modes as a point selection criterion, updating the important failure mode IM only, and repeating the process until all the proxy models
Are all converged.
Step S524: in that
In the method, a learning function Coy (x) self-adaptive Kriging surrogate model based on a coefficient of variation is utilized, and the surrogate model of an objective function is updated according to the relation between the fatigue creep life and a reliability constraint function
Until convergence.
For example, step S500 may include: step S531: using current design variable parameters
And
solving each at a given reliability
Lower corresponding inverse design point
Defining an inverse design point with a current iteration
A central local sampling region with a radius R ═ 1.2+0.3nc β t And nc is a nonlinear correction system. Generating a local area sample pool in the local sampling area
Step S532: sample pool in local area
Kriging model of medium-update constraint function
And Kriging agent model of objective function
Step S533: calculating the current
Judging the current Kriging model by the multi-mode U learning function corresponding to the middle sample point
Convergence of (A) if
Step S534 is executed; otherwise, step S535 is performed.
Step S534: selecting an important failure mode IM to be updated according to the multi-mode U learning function,
and selects and updates training sample points
And calculating the output value of the corresponding function of the important failure mode based on the finite element
Adding the training sample set corresponding to the important failure mode and updating the Kriging agent model
Return to step S533.
Step S535: the converged Kriging agent model corresponding to lifespan obtained from step S533
To be provided with
As an initial proxy model of the objective function.
Step S536: the calculation is at the current calculation
Judging the current Kriging model based on the coefficient of variation cov (x) learning function corresponding to the middle sample point
Convergence of (A) if
Step S537 is executed; otherwise, step S600 is performed.
Step S537: selecting and updating training sample points
And calculating the output value g of the function based on the finite element j (x new ) Adding corresponding training sample set and updating Kriging agent model
I.e. update
Returning to step S536. In step S600, based on the obtained kriging approximate proxy model and the inverse design point of the constraint function and the objective function, a reliability optimization problem is converted into a deterministic optimization problem by using a sequence optimization and reliability evaluation method to solve, and an optimization solution is obtained.
Specifically, the method for converting the reliability optimization problem into the deterministic optimization problem by using the sequence optimization and reliability evaluation method is specifically represented as follows:
wherein the content of the first and second substances,
the offset vector of the jth reliability constraint function at the kth cycle is expressed as:
wherein the content of the first and second substances,
to input parameter mean at random
The inverse design point of (c).
The step S600 may include: establishing an equivalent deterministic optimization mathematical model by using a sequence optimization and reliability evaluation method, and obtaining an optimization result of the kth iteration
Based on the convergent constraint function and objective function proxy model in step S500, a mathematical model of equivalent deterministic optimization is established by using a sequence optimization and reliability evaluation method, and the optimization result of the kth iteration is obtained
In step S700, it is determined whether the optimization solution converges, and if so, the optimization result is output.
Specifically, the feasibility of the optimization solution and whether the whole reliability optimization process is converged are judged, and if yes, the calculation is finished.
In step S800, if the optimization solution does not converge, the current optimization solution is used as the initial value of the design parameter in the next iteration.
Specifically, if not converging, let k be k +1, return to step: initializing optimized design values
And the cycle number k of the sequence optimization design.
In the following, a specific optimization procedure of the present disclosure will be exemplified:
in step S100: and establishing a geometric simulation model of the double-amplitude plate turbine disc. According to the method, the disk center cooling hole is considered as a part of the double-spoke plate disk body, structures such as bosses and mortises on the outer side of a wheel rim are omitted to simplify the model, and an integrated model of the double-spoke plate turbine disk and the cooling airflow hole is established, as shown in fig. 3. The method is characterized in that a meridian plane parameterized model of the double-spoke-plate turbine disk is shown in FIG. 4, and symbols and geometric meanings of main geometric parameters are shown in Table 1.
TABLE 1 Main characteristic parameters of double-spoke-plate turbine disk body
In step S200: the method is characterized in that a finite element analysis method is used, namely ANSYS finite element software is used for analyzing the geometric simulation model of the double-width plate turbine disc, and the method is realized by the following steps:
step S2100: definition of Material genusAnd (4) sex. The double-spoke turbine disk is made of a nickel-based superalloy GH 4169. The density of the material is rho 8240kg/m 3 The poisson ratio is γ equal to 0.31. The data of the linear expansion coefficient, the elastic modulus, the yield strength, the tensile strength, the thermal conductivity and the like of the material at the same temperature are respectively shown in tables 2 to 6.
TABLE 2 linear expansion coefficient of GH4169 material
| Temperature T (. degree. C.) | 20～100 | 20～200 | 20～300 | 20～400 | 20～500 |
| Coefficient of linear expansion alpha (10) -6 ·℃ -1 ) | 11.8 | 13.0 | 13.5 | 14.1 | 14.4 |
| Temperature T (. degree. C.) | 200～600 | 20～700 | 20～800 | 200～900 | 20～1000 |
| Coefficient of linear expansion alpha (10) -6 ·℃ -1 ) | 14.8 | 15.7 | 17.0 | 18.1 | 18.7 |
TABLE 3 modulus of elasticity of GH4169 material
| Temperature T (. degree. C.) | 20 | 300 | 400 | 500 | 600 | 650 | 700 |
| Modulus of elasticity E (GPa) | 204 | 181 | 176 | 160 | 150 | 146 | 141 |
TABLE 4 ultimate Strength of GH4169 material
TABLE 5 yield strength at different temperatures of GH4169
TABLE 6 thermal conductivity of GH4169 materials
Step S2200: and (5) grid division. In the overall structure of the double-radial-plate turbine disk, a sweeping method is adopted, and hexahedral leading grids are used for division. Because the research of the invention focuses on the disk body of the double-spoke-plate turbine disk, the grid of the disk body is thinned, the unit size is 1.0mm, the grid division result of the three-dimensional sector model of the disk is shown in FIG. 6, and 520753 nodes and 492688 units are divided in total.
Step S2300: load and restraint are applied. In order to simplify the finite element calculation model, the above parts are cut by taking the bottom of the wheel rim mortise as a radius, and a circular disc with the outer surface of the wheel rim as a free surface is generated. The centrifugal force evenly distributed with tenon piece, blade isotructure above the tongue-and-groove bottom is in rim plate outer fringe free surface department, and this equipartition load can be simplified and is derived by the following formula:
in the formula, N blade The number of the blades is m, the mass of structures such as a tenon block and a blade on the outer side of a wheel rim is m, omega is the working rotating speed of the double-radial-plate turbine disk, and r is blade The center of mass radius of structures such as the tenon block and the blade on the outer side of the wheel rim. And applying cyclic symmetry constraint to the sector model, and applying rigid body displacement constraint in the axial direction and the circumferential direction to one point outside the hub so as to ensure that the model does not generate rigid body displacement in the finite element calculation process.
Under the stable working state of the engine, the temperature distribution from the outer edge of the nickel-based alloy wheel disc to the center of the disc can be estimated according to the following formula:
wherein T is the temperature at the sought R; t is 0 And T k Is the temperature at the center and outer edge of the wheel disc; r 0 And R k The radius at the center and outer edge of the disc. As shown in FIG. 5, the temperature of the disk center of the double-radial-plate turbine disk is T 0 480, rim temperature T k 570, so that the temperature field distribution of the double disk can be simplified by:
step S2400: and (5) analyzing a calculation result. And carrying out local thermal elastoplasticity analysis on the double-amplitude plate to obtain the corresponding stress strain at the rotating speed omega of 18750r/min, so as to obtain the maximum strain at the top of the inner cavity of the radial plate of the turbine disk, and thus, taking the part as the dangerous part of the turbine disk to carry out subsequent analysis.
Step S2500: a turbine disk creep-fatigue model is determined. After the check points are determined, the fatigue life of the turbine disk is predicted by adopting the SWT modified Manson-coffee model. The fatigue life models at different temperatures determined using the least squares method from the experimental data are:
under the condition of 360 ℃:
at 550 ℃, the temperature of the mixture is as follows:
at 650 ℃ conditions:
wherein, Delta epsilon is the strain amplitude; sigma m Is the maximum stress; e is the modulus of elasticity; n is a radical of f Fatigue life is considered; u. of 1 And u 2 As an auxiliary variable subject to a standard normal distribution, i.e. u 1 ～N(0，1 2 )，u 2 ～N(0，1 2 ). Considering that the fatigue life model is temperature dependent, the fatigue life at other temperatures can be obtained by interpolating the equations at the three temperatures.
The invention adopts Larson-Miller (L-M) parameter method and Bayesian model average method to carry out statistical analysis on relevant test data, and the creep life model obtained by fitting is as follows:
in the formula, N c Denotes creep life, σ denotes stress at the reference point, u 3 And u 4 As an auxiliary variable subject to a standard normal distribution, i.e. u 3 ～N(0，1 2 )，u 4 ～N(0，1 2 )。
Step S2600: and optimizing a design model of creep-fatigue life reliability of the turbine disk. Although the double-radial-plate turbine disk has a complicated structure and numerous geometric parameters, the geometric parameters can be known from past engineering experienceThe impact on the probability lifetime is small. Therefore, it is not necessary to consider the influence of all the geometric dimensions, and only the parameters having a large influence on the fatigue life of each examined portion of the wheel disc are selected and designed. Considering the effect of geometric uncertainty on fatigue, creep life and structural weight, 6 critical geometric dimensions were selected
Mean value of (a) D As design variables, the design parameters of the double-disc turbine disc and the upper and lower limits thereof are shown in table 7. Furthermore, consider 3 random input parameters
As a random environment variable, wherein
Is the fatigue plasticity coefficient/elastic modulus, b is the fatigue strength index, C 0 Are creep life model parameters and are assumed to all follow a standard normal distribution. Let the random input variable composed of these 9 random input variables be X, i.e.
Since the creep-fatigue life of a turbine disk is affected by X, the creep-fatigue life of a turbine disk can be expressed as a function N of an input variable X fj (X)。
TABLE 7 design parameters of double-radial-plate turbine disk and its upper and lower limits
In step S400, the number of sample points used to construct the initial Kriging model is N-100.
In step S500, the initial design point value is
In steps S500-S800, the proxy model is updated 5 times in total, and the convergence condition is satisfied.
TABLE 8 reliability optimization design results for double-spoke plate turbine disk
The invention aims at the reliability optimization design of the fatigue creep life of the double-spoke plate turbine disk, and firstly establishes a finite element model of the double-spoke plate turbine disk by means of finite element analysis software. Then, aiming at the defects of the existing reliability optimization design method, the reliability constraint function of the double-spoke-plate turbine disk is fitted by using a Kriging surrogate model method, and the reliability constraint function and the objective function are updated and proxied according to the characteristic that the constraint function and the objective function are connected with the safe service life. In order to fit a reliability constraint function with the least amount of calculation, the important failure mode in each iteration is adaptively identified in a local sampling region at an inverse point, and a training sample point which has a large influence on the model prediction precision is selected to establish the Kriging model. And finally, converting the complex reliability optimization design problem into a deterministic optimization problem by combining a sequence optimization and reliability evaluation method, and performing reliability optimization design on the parameterized double-spoke plate turbine disk structure by combining finite element analysis software ANSYSMECHANICALAPDL and mathematical software MATLAB.
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.
Claims (10)
1. A double-amplitude turbine disk fatigue creep life reliability optimization method based on a proxy model is characterized by comprising the following steps:
establishing a geometric simulation model of the double-amplitude plate turbine disc;
analyzing the geometric simulation model according to a finite element method, and determining a random variable influencing the fatigue creep life of the double-amplitude plate turbine disk and a relation between the random variable and the fatigue creep life of the double-amplitude plate turbine disk;
establishing a fatigue creep life reliability optimization design model of the double-amplitude plate turbine disc by taking the maximum mean value of the fatigue creep life as a design target and the fatigue creep life reliability as a constraint according to the relation between the determined random variable and the fatigue creep life of the double-amplitude plate turbine disc;
adopting a self-adaptive Kriging approximate model to construct a Kriging approximate agent model with reliability constraint and target function convergence in an expansion space;
determining an inverse design point under given design parameters and reliability indexes, performing local sampling at the inverse design point, adopting a self-adaptive learning function to identify a target mode, updating the converged reliability constraint, and adopting a learning function based on a coefficient of variation to update a Kriging approximate proxy model of the target function;
converting the reliability optimization problem into a deterministic optimization problem to be solved by using a sequence optimization and reliability evaluation method based on the obtained kriging approximate agent model and the inverse design point of the constraint function and the target function, and obtaining an optimized solution;
and judging whether the optimization solution is converged, and if so, outputting an optimization result.
2. The optimization method according to claim 1, further comprising:
if the optimization solution does not converge, the current optimization solution is used as the initial value of the design parameter in the next iteration.
3. The reliability optimization method of claim 1, wherein constructing a kriging approximation proxy model with reliability constraints and objective function convergence in an extended space using an adaptive kriging approximation model comprises:
adopting Latin hypercube sampling in the expanded reliability space to obtain a sample pool of input variables;
selecting part of initial training sample points from a sample pool, and selecting a basis function and a co-correlation function of the Kriging approximate agent model according to input-output information of a real reliability constraint function;
adopting a multi-mode learning function to carry out self-adaptation on the kriging approximate agent model and update until all the kriging approximate agent models of the reliability constraint function are converged;
according to the relation between the constraint function and the target function, an initial Krigin approximate agent model of the current target function can be obtained at the same time;
and adopting a learning function based on the coefficient of variation to carry out self-adaptive updating on the kriging approximate proxy model of the target function until the kriging approximate proxy model of the target function converges.
4. The reliability optimization method of claim 3, wherein the kriging approximation proxy model is:
wherein f (x) is ═ f 1 (x),...,f p (x)] T Expressed as a basis function, β ═ β 1 ,...,β p } T Z (x) is expressed as a zero-mean Gaussian for the corresponding regression coefficients.
5. The reliability optimization method of claim 3, wherein identifying important failure modes using an adaptive learning function comprises:
determining a learning function u (x) at a sample point in the sample pool of local samples at the current inverse design point:
wherein the content of the first and second substances,
and
respectively representing the predicted mean value and standard deviation of the jth reliability constraint function at the random input parameter realization value x;
i.e. w is a set consisting of the numbers of failure modes;
identifying a failure mode corresponding to the IM reliability constraint function as an important failure mode, wherein the specific expression of a failure mode index IM is as follows:
6. the reliability optimization method of claim 3, wherein updating the objective function with a learning function based on the coefficient of variation comprises:
determining a learning function cov (x) at a sample point in the sample pool of local samples at the current inverse design point:
wherein, N fj A lifetime value representing the jth mode;
and
respectively representing life functions N fj The kriging approximate agent model predicts the mean value and the standard deviation of the value x at the random input parameter realization;
if it is
The proxy model of the objective function is converged, otherwise a new sample point is selected
And updating the proxy model of the current objective function.
7. The reliability optimization method according to claim 1, wherein the reliability optimization problem is converted into a deterministic optimization problem by using a sequence optimization and reliability evaluation method, specifically represented as:
Findμ X
min N fj (μ X )
wherein the content of the first and second substances,
for the offset vector of the jth reliability constraint function at the kth cycle,
the expression is as follows:
wherein the content of the first and second substances,
to input parameter mean at random
The inverse design point of (c).
8. The reliability optimization method of claim 1, wherein determining an inverse design point, performing local sampling at the inverse design point, identifying a target pattern using an adaptive learning function, updating the converged reliability constraint, and updating the target function using a coefficient of variation-based learning function, given design parameters and reliability metrics, comprises:
initializing optimal design parameter values
And cycle number k of sequence optimization design;
using current design variable parameters
And
solving for each given reliability
Lower corresponding inverse design point
Defining an inverse design point with a current iteration
A central local sampling region with a radius R ═ 1.2+0.3nc β t Where nc is a non-linear correctionA system; generating a local area sample pool in the local sampling area
In that
Updating the proxy model by using the U learning function under multiple modes as a point selection criterion, updating the important failure mode IM only, and repeating the process until all the proxy models
All converge;
in that
The method utilizes a learning function cov (x) based on a coefficient of variation to approximate a proxy model of adaptive Krigin, and updates the proxy model of an objective function according to the relation between the fatigue creep life and a reliability constraint function
Until convergence.
9. The reliability optimization method according to claim 8, wherein the reliability optimization problem is converted into a deterministic optimization problem solution by using a sequence optimization and reliability evaluation method based on the obtained kriging approximate agent model and inverse design points of the constraint function and the objective function, and an optimized solution is obtained, comprising:
establishing an equivalent deterministic optimization mathematical model by using a sequence optimization and reliability evaluation method, and obtaining the optimization result of the kth iteration
10. The reliability optimization method according to claim 9, wherein determining whether the optimization solution converges, and if so, outputting the optimization result comprises:
judging whether the feasibility of the optimization solution and the whole reliability optimization process are converged, and if so, finishing the calculation; if not, let k equal to k +1, return to step: initializing optimized design values
And the cycle number k of the sequence optimization design.
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